EXPERIMENTAL SET UP FOR CHARACTERIZATION OF ACOUSTO-OPTIC MODULATOR SYSTEM
NORSHAHIDA BINTI ISMAIL
A thesis submitted in fulfilment of the requirements for the award of the degree of Master of Science (Physics)
Faculty of Science Universiti Teknologi Malaysia
JAN 2010
A thesis submitted in fulfilment of the requirements for the award of the degree of Master of Science (Physics)
iii
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iv
ACKNOWLEDGEMENT
In the name of Allah, Most Gracious, Most Merciful. Praise is to Allah, the Cherisher and Sustainer of the worlds. For His Mercy has given me the strength and time to complete this project. I would like to express my sincere gratitude and appreciation to my supervisor, Profesor Dr. Rosly Abd Rahman for his support, supervision and mentoring. Profesor Rosly is always available to provide support and suggestions and answer questions. Without his patience and consideration I certainly would not have finished this work. I would like to acknowledgement the help and kindly assistance of the following persons; Mr. Ahmad Bin Imbar, Mr. Nasir, Mr. Salehudin, Mr. Abd. Rasid Isnin, Mrs. Ruzilah and Mr. Sakifli for assisting in carrying out experimental works and colleagues from Optoelectronics, Laser and Advanced Optical Materials Research Group (AOMRG) Lab for their continuing corporation, encouragement and useful comment to complete the work My thanks are also due to Government of Malaysia through IRPA grant vote 74534 for giving us financial support. Without this financial support, this project would not be possible. Thanks also to all my friends and course mates for their views, concerns and encouragement. Last but not least, my appreciations go to my family for continuing support, patience throughout the present work and who have favored me with correspondence, I have much pleasure in expressing my obligation. May Allah bless those who have involved in this project.
v
ABSTRACT
Acousto-optic effect can be used in many useful devices such as modulators, switches, filters, frequency shifters and spectrum analyzers. In this study, the modulating effect was generated by low cost SF6 glass with a lithium niobate transducer. Tunable Helium Neon Laser was used
as the main light source. The function generator was used to generate external input signal and to vary the amplitude of acoustic wave. The modulated output signal was measured and analyzed using laser beam profiler, spectrometer, Si photo detector and power meter. The investigation shows that there was a shift of the horizontal main beam spot position when the driving frequency of the modulator is changed. A shift of beam spot between 4.0 mm to 5.5 mm was observed for a frequency range between 70 MHz to 90MHz. This is accordance with the expected theoretical model of the modulator. Results also show that a modulator can produce output signals, which are of the same type as the input signal. Increasing the amplitude of modulating signal in the range of 119 mV to 196 mV decreases the amplitude of modulated square wave signal from 2.6 V to 0.4 V. There was a decrease in the output power of the zero order diffraction but an increase in the
first order diffraction with respect to the increase of the RF driving power.
vi
ABSTRAK
Kesan akusto-optik banyak digunakan dalam pelbagai peranti seperti pemodulasi, pensuisan, penapisan, penganjak frekuensi, dan penganalisa spektrum. Dalam kajian ini, kesan modulasi dijanakan oleh bahan kaca SF6 dengan pemindah aruh Lithium Niobate. Laser Helium Neon boleh laras digunakan sebagai sumber cahaya utama. Penjana denyut digunakan untuk menjana isyarat masukan luaran dan mengubah amplitud kuasa akustik. Isyarat keluaran termodulasi diukur dan dianalisis menggunakan penganalisa alur laser, pengesan spectrum, pengesan-foto dan meter kuasa. Kajian ini menunjukkan bahawa berlaku anjakan melintang pada titik cahaya apabila pembawa frekuensi pemodulasi diubah. Anjakan titik sinaran antara 4.0 mm hingga 5.5 mm dapat dilihat untuk jarak frekuensi antara 70 MHz hingga 90 MHz. Ianya mematuhi jangkaan model teori pemodulasi. Keputusan juga menunjukkan bahawa pemodulasi boleh menghasilkan isyarat keluaran yang mana sama dengan bentuk isyarat masukan. Pertambahan amplitud isyarat modulasi antara 119 mV hingga 196 mV akan mengurangkan amplitud isyarat termodulasi daripada 2.6 V hingga 0.4 V. Didapati bahawa kuasa keluaran bagi pembelauan tertib sifar menyusut tetapi ianya meningkat bagi pembelauan tertib pertama bilamana kuasa pemacu RF bertambah.
vii
TABLE OF CONTENTS
CHAPTER
TITLE
DECLARATION
ii
DEDICATION
iii
ACKNOWLEDGEMENT
iv
ABSTRACT
v
ABSTRAK
vi
TABLE OF CONTENTS
vii
LIST OF TABLES
xi
LIST OF FIGURES
xiii
LIST OF ABBREVIATIONS
xvi
LIST OF SYMBOLS
xvii
LIST OF APPENDICES
1
PAGE
xx
INTRODUCTION 1.1
Introduction
1
1.2
Background of study
2
1.3
Objective of Research
3
1.4
Problem Statement
3
1.5
Scope of Research
4
1.6
Thesis Outline
4
viii 2
THEORY 2.1
Introduction
6
2.2
Acousto-Optic Interaction
7
2.2.1
9
2.3
2.4
3
Isotropic Acousto-Optic Interaction
2.2.2 Anisotropic Acousto-Optic Interaction
14
Acousto-Optic Modulator
15
2.3.1
Deflection
17
2.3.2
Intensity
17
2.3.3
Frequency
18
2.3.4
Phase
18
Acousto-Optic Material selection
18
EXPERIMENTAL WORKS 3.1
Introduction
20
3.2
Instrumentations
20
3.2.1
Equipment used in preliminary study
20
3.2.1.1 Acousto-Optic Modulator M040-8J-FxS
21
3.2.1.2 AOM Driver
22
3.2.1.3 Newport
24
3.2.1.4 Fiber Optic Light Source
25
3.2.1.5 Power Meter
25
3.2.1.6 NIR Diode Array Spectrometer
26
Equipments used in Acousto- optic Modulator system
26
3.2.2.1 Tuneable HeNe Laser
27
3.2.2.2 AO Modulator
27
3.2.2.3 AO Modulator Driver
28
3.2.2.4 Laser Beam Profiler (LBP)
29
3.2.2
ix
3.3
3.2.2.5 Amplified Silicon Detector
30
3.2.2.6 Fiber Optic Spectrometer
31
3.2.2.7 Polarizer and analyzer
31
Experimental works
32
3.3.1
32
Preliminary Experiments on the AOM 3.3.1.1 Investigating the effect of driving signal on AOM output power
3.3.2
3.3.3
32
3.3.1.2 Investigating the spectral output of the AOM
33
3.3.1.3 Investigating the Light Source Sensitivity
34
3.3.1.4 Programming
35
Calibration of instruments
35
3.3.2.1 Calibration of the Tunable He-Ne Laser
35
3.3.2.2 Calibration of Function Generator
36
Experimental works on the AOM constructed
37
3.3.3.1 Set -up for calibration of function generator
38
3.3.3.2 Investigating the internal RF frequency Range
38
3.3.3.3 AOM System
39
3.3.3.4 Geometry Characteristics of AOM
40
3.3.3.5 Characteristics of Modulated Optical Signal
41
3.3.3.6 Temporal characteristics of Acousto-Optic Modulator (AOM)(External Modulated)
4
42
3.3.3.7 Determining the Types of Output Signals
42
3.3.3.8 Effects of modulating signal amplitude
43
3.3.3.9 Effects of RF power
43
EXPERIMENTAL RESULTS AND ANALYSIS 4.1
Introduction
44
4.2
Preliminary experimental results
44
4.2.1 Observation of Driving Signal
44
4.2.2
Investigating the Characteristics of AOM
46
4.2.2.1 Spectrums
47
4.2.2.2 Graphs
48
x 4.2.3
4.2.4 4.3
Light Source Sensitivity
49
4.2.3.1 Spectrums
49
Programming
50
Experimental result and discussion of an AOM
52
4.3.1
Calibration Instruments
52
4.3.1.1 Tunable He-Ne Laser
53
4.3.1.2 Determination the Polarization of the Laser Light
56
4.3.2 Determination of Shifting of First Order Beam
56
4.3.3
Effects of input frequency on output frequency
58
4.3.4
Effects of Driving Power on Output Optical Power
59
of First Order Beam 4.3.5
5
Varied the RF power to determine first order power
CONCLUSIONS AND SUGGESTIONS 5.1
Conclusions
71
5.2
Suggestions
73
REFERENCES
75
Appendices
A
The spectrums from the spectrometer
Appendices
B
Three types of output signal at input
Appendices
64
C
85
frequency 100 Hz to 1.8 kHz
93
Least Square Method- Equations
96
xi
LIST OF TABLES
TABLE NO.
TITLE
PAGE
2.1
Acousto optic materials selection
19
4.1
Driving signal
45
4.2
The Characteristic of AOM
46
4.3
Light source sensitivity
49
4.4
Data Calibration for Tunable HeNe Laser
55
4.5
Data from experiments and references value
55
4.6
Determination the polarization of the laser light
56
4.7
Effect of driving frequency on horizontal shifting, d
57
4.8
Values of output frequency for square wave, triangle
61
wave and sine wave signals 4.9
Value of input amplitude for 119 mV to 870mV
62
4.10
Value of input amplitude and output amplitude
64
4.11
Ratio of output amplitude to input amplitude
65
4.12
The first order power for minimum RF power to maximum RF power (position 1 to position 3)
67
4.13
The first order power for minimum RF power to
68
maximum RF power (position 4 to position 14)
xii
4.14
The average power for RF power position, z
70
xiii
LIST OF FIGURES
FIGURE NO.
TITLE
PAGE
2.1
The sinusoidal variation of index of refraction
7
2.2
Raman-Nath acousto-optic diffraction geometry
11
2.3
Bragg acousto-optic diffraction geometry
12
2.4
Interaction of photon and phonon
13
2.5
Wave vector diagram for isotropic Bragg diffraction
13
2.6
Wave vector diagram for general case anisotropic
15
diffraction 2.7
Mechanisms in piezoelectric transducer for AOM
16
3.1
AOM M040-8J-F2S
21
3.2
AOM M040-8J-F2S diagramatic
22
3.3(a)
AOM Driver and the diagram of the driver
23
3.3(b)
Output Level section of AOM
23
3.4
Newport
24
3.5
Kingfisher Fiber Optic Light Source KI 7822
25
3.6
Kingfisher Power Meter KI7600
25
3.7
NIR Diode Array Spectrometer
26
3.8
Tunable Laser
27
xiv 3.9
AO Modulator
28
3.10
AO Modulator Driver
29
3.11
Laser Beam Profiler ( LBP )
30
3.12
Amplified Silicon Detector
30
3.13
Fiber Optic Spectrometer
31
3.14
Experimental setup of an acousto optic modulator
33
(AOM) 3.15
Experimental setup to investigate the sensitivity of
34
two types of light source; E- LED 1330nm and the laser light source 1553nm 3.16
Observation on the wavelengths of Tunable He-Ne
36
Laser experimental setup 3.17
Observation on the optical power of Tunable He-Ne
36
Laser 3.18
Set up for calibration of function generator
36
3.19
Experimental setup
37
3.20
Determining the polarization of the laser light
38
3.21
Investigating the Internal RF frequency range
39
3.22
Set up experiment for an acousto-optic modulator
40
3.23
Enlarged view of an Acousto-Optic Modulator
40
3.24
Geometry characteristics of AOM
41
3.25
Characteristic of modulated optical signal
41
experimental setup 3.26
Temporal characteristics of acousto-optic modulator
47
set up 4.7
Screenshot of the Visual Basic Programming
52
xv 4.8
Spectrum of Tunable HeNe Laser
54
4.9
Position of polarizer
56
4.10
Effect of driving frequency on first order shift angle,
57
z 4.11
58
4.12
Three types of output signal at input frequency 100 Hz to 1800Hz Relation between input signal and output signal
4.13
Graph of output amplitude at various input amplitude
66
4.14
Graph of first order power from minimum RF power to maximum RF power
71
61
xvi
LIST OF ABBREVIATIONS
AO
Acousto-optic
AOM
Acousto-optic modulator
CW
Continuous wave
DC
Direct current
FWHM
Full wave half maximum
OSC
Oscillator
RF
Radio frequency
LBP
Laser Beam Profiler
xvii
LIST OF SYMBOLS
c
Light velocity
z
Distance between zero order beam and first order beam
Frequency of acoustic waves
H
Height of transducer
K
Wave vector of photon
L
AO interaction length along the direction of propagation of light
M
Figure of merit
m
Diffraction order
n
Refractive index of material
Q
Quality factor
V
Velocity of sound in material
Planck constant
K
Wave vector of new photon
ka
Wave number of acoustic wave (Wave vector of phonon)
ki
Wave number of incident light (Wave vector of incident photon)
xviii Kd
Wave number of scattered light (Wave vector of scattered photon)
Pa
Acoustic power
Speed of sound
d
Frequency of Scattered light (Angular frequency of photon)
i
Frequency of incident light (Angular frequency of photon
o
Angular frequency of new phonon
B
Bragg angle
shift
Shift angle
Io
Incident optical beam density
m
Separation angle between mth diffracted order beam and undiffracted order beam
i
Incident angle
d
Diffracted angle
0
Angle
tr
Rise time
Density of material
Diffraction efficiency
Wavelength of the acoustic waves
Optical beam wavelength
xix a
Frequency of the acoustic wave
t
Oscillation time,
n
Amplitude of the refractive index change due to the acoustic strain
ni
Refractive index of incident beam
nd
Refractive index of diffracted beam
xx
LIST OF APPENDICES
APPENDIX
TITLE
PAGE
A
The spectrums from the spectrometer
85
B
Three types of output signal at input frequency 100 Hz to
93
1.8 kHz C
Least Square Method- Equations
96
CHAPTER I
INTRODUCTION
1.1
Introduction
Applications of laser light often require a means for modulating some properties of the laser light wave, such as intensity (amplitude), phase wavelength (frequency) or polarization (direction of propagation) (Schawlow, 1969; Hammer, 1975). A modulator is a device that alters a detectable property of a light wave corresponding to an applied electric signal (Hammer, 1975).
There are number of methods that can be used to modulate laser light such as mechanical, electro-optic, acousto-optic and magneto-optic. Most mechanical methods such as rotating mirror and mechanical shutter or chopper used for laser beam modulation are slow, unreliable and have much inertia to allow for faster light modulation (Kaminow and Turner, 1996; Schawlow, 1969). Thus the mechanical methods are seldom used in modern modulation equipment. Hence, the interaction between laser wave and electric, magnetic or acoustic fields acting through the electro-optic, magneto-optic and acousto-optic effect are used to modulate laser-beam (Kaminow and Turner, 1996; Chen 1970). Modulation of laser-beam by using these effects is faster and more reliable than the mechanical methods.
2 Optical modulators, using acousto-optic, magneto-optic or electro-optic effects, as the principal components for external modulation of light wave have presently played the important role in modern long-haul ultra-high speed optical communications and photonic signal processing systems. Other common uses of acousto-optic media include devices for modulating light for communication, detecting light, convolving or correlating signals, optical matrix processing, analyzing the spectrum of signals, optical sources, laser mode lockers, Q-switchers, delay lines, image processing, general and adaptive signal processing, tomography transformations, optical switches, neural networks, optical computing, and much more.
1.2
Background of Study
Brilliouin predicted light diffraction by an acoustic wave propagating in a medium of interaction in 1922. In 1932, Debye and Sears, Lucas and Biquard carried out the first experimentation to check the phenomena. The particular case of diffraction on the first order, under a certain angle of incidence, (also predicted by Brillouin), has been observed by Rytow in 1935. Raman and Nath (1937) have design a general ideal model of interaction taking into account several orders. This model was developed by Phariseau (1956) for diffraction including one diffraction order. Then, with development of the laser in 1960s, acousto-optics became an engineering pursuit as devices to control photons became necessary (Parygin, Balakshy, Voloshinov, 2001). Research and development over the last decades has produced many types of acousto-optic devices including optical modulators (Robert J.F., 2003).
One of the earliest uses of an AOM in electro-optics system is for large screen television images projection in theaters (Goutzoulis, Pape, 1994). Today it is not only being used in scanning and imaging but also apply in telecommunication (Parygin, Balakshy, Voloshinov, 2001). An effective and efficient communication system is now used in the paperless world. The study of acousto-optic modulator design and fabrication is increasingly important due to its high gain in modulation (Goutzoulis, Pape, 1994).
3 There are three main types of acousto-optic devices, namely, bulk acousto-optic devices, integrated optic devices and all-fibre acousto-optic devices (Goutzoulis, Pape, 1994). Since this technology is considered new in our country, the study will start from the most basic level of the AOM design which is bulk acousto-optic devices. In bulk devices an optical beam which propagates through an optical medium in the presence of an acoustic wave, can generate a diffracted beam, producing a frequency shift in the diffracted ray. These devices are called Bragg cell and have many advantages. The main problem in applying Bragg cells to optical fibre is that they contribute to insertion loss interface reflection and diffraction loss in the bulk medium.
1.3
Objective of Research
The objective of this research are:
1.4
i.
Investigate the principles of an AOM
ii.
Identify critical parameters in the design of AOM
iii.
Construction of AOM system
iv.
Evaluation of the performance of the AOM setup
Problem Statement
Acousto-optic Modulator is the most important device used to modulate signal in optical telecommunication technology. This is an initial study in the design and construction of an acousto-optic modulator. The success of designing and constructing AOM will bring about new applications for use in research at UTM. Even though this type of modulator is available in the market, but there is a need to produce or manufacture this kind of modulator for local use. This research will be a good start for Malaysia to get involve in AOM manufacturing.
4 1.5
Scope of Research
In this research, a equipments use in the experiments was studied. The equipments include Tunable HeNe Laser, NEOS Technology AO Modulator ( 24080 ), AO Modulator Driver, Laser Beam Profiler ( LBP ), PDA 55 Amplified Silicon Detector, Fiber Optic Spectrometer, Polarizer and analyzer and Power And Energy Meter System.
A preliminaries experiment is carried out using a fibre coupled AOM using chalcogenide glass with refractive index 2.6. This study focus on investigating the characteristic of AOM, studying the theory and working principle of AOM and other equipment in experimental set up, to get the relationship between driving voltage from RF driver and output power from modulator causes by the changes in output level from radio frequency (RF) driver, to observe several light source sensitivity.
The AOM was precisely aligned with rotating stage in order to diffract the light at Bragg angle. The characterization of AOM was carried out in term of laser beam profile, power and signal configuration.
1.6
Thesis Outline
This thesis composes of six chapters. The first chapter of this thesis presents an introduction and overview of the previous research works regarding the AOM. The objective and scope for this research is briefly address and clarify the aim of this research. Chapter 2 presents the theoretical background related to this research. It explains the principle of acousto-optic interaction.
5 Chapter 3 explains the equipments and how the methodology of the research is conducted. In this chapter, the method for the characterization of the modulation output is outline. This includes the experimental setup and procedures for Bragg angle alignment, laser beam profiling and the measurement of output power. The characterization of AOM output is detail out in Chapter 4. The characterization parameters observed includes the beam profile, power and signal. In laser beam profile characterization the RF signal is varied and details analysis that covers diffraction angle, diffraction efficiency and optimum frequency is carried out. The optimum frequency is important to drive the AOM for the next characterization methods. The laser beam power is characterized by varying the RF drive power. The modulation signal is characterized based on pulse width. This is conducted by varying the RF drive power and RF input pulses. Finally the conclusion of the project is described in Chapter 5. This includes the summarization of the whole project. Some works to be carried out in the future are suggested.
CHAPTER II
THEORY
2.1
Introduction
The objective of this chapter is to review the theory of acousto-optic (AO). In general there are three types of AO devices (deflectors, modulators, and tunable filters or AOTFs), each of which can used different type of light and sound interactions. The type of the AO interaction is determined by the light- sound geometry and the optical and acoustic properties of the material. All AO interactions are based on the photoelastic effect, and they can be either isotropic or anisotropic, depending on the optical properties of the AO crystal. Isotropic AO interactions do not changed the polarization of the optical beam, and they can be result in either multiple or single diffracted optical beams (or order).the multiple-order isotropic diffraction is called Raman-Nath (Young et al, 1981; Noriah, 2002; Goutzoulis and Kludzin, 1994), and because of its low diffraction efficiency it is not frequently used in practical devices. The single-order isotropic diffraction is called Bragg; it is much more efficient and therefore it is widely used in practical devices. Anisotropic AO interactions change the polarization of the optical beam and they result in a single diffracted order. They offer higher efficiencies and larger acoustic and optical bandwidths than the isotropic AO interactions. The principles of acousto- optics is discuss in section 2.2. Section 2.3 is briefly discuss the Acousto-optic modulator concept. The section 2.4 describes the AO material properties.
7 2.2
Acousto-optic Interaction
Acousto-optic devices are based on the photoelastic or elesto-optic effect (Raman and Nath, 1935; Klein, 1967). AO interaction occurs in all optical mediums when an acoustic signal and optical beam are present in the mediums. When an acoustic signal is injected by piezoelectric mean into an AO crystal, a strain which changes the optical properties of crystal will be produced. The region of compression and rarefraction generates a refractive index wave that behaves like a sinusoidal grating. When an optical beam passes through the crystal, it may be deflected or modulated, and frequency shifted.
Figure 2.1: The sinusoidal variation of index of refraction (Yariv and Yeh, 1984)
8 Figure 2.1 shows the travelling acoustic wave. Its consist of alternating region of compression (dark) and rare fraction (white), which travel at the sound velocity, V. Also shown is the instantaneous variation of the index of refraction that accompanies acousticwave. In practice, the term incident optical wave, because in most cases the presence of the optical wave does not change the acoustic properties of the medium. Thus, OA interaction can be treated as a parametric process which the acoustic field changes the refractive index of the medium. By using the classical method, AO interaction can be described as diffraction of the optical wave by a periodical phase grating induced by an acoustic wave. The phase grating generated by the acoustic wave is not stationary and travels with the speed of sound in AO medium and its parameters can vary with time. This is the fundamental difference between phase grating and an ordinary grating.
An RF signal applied to a piezoelectric transducer, bonded to a suitable crystal, will generate an acoutic wave. This acts like a phase grating, traveling through the crystal at the acoustic velocity of the material and with an acoustic wavelength dependent on the frequency of the RF signal. An incident laser beam will diffracted by this grating, generally giving a number of diffracted beams. When piezoelectric transducer is placed in contact with AO material and high frequency oscillating voltage is applied, it will expand as the voltage varies. This will give pressure on AO material and cause the launch of an acoustic wave that travels through the material. The frequency of an acoustic wave, f is equal to the frequency of the applied voltage. The acoustic wave will have a wavelength, given by Saleh and Teich (1991) as V f
(2.1)
9 where V is velocity of sound in material is the wavelength of the acoustic waves and f is frequency of acoustic wave. For a material with a fixed acoustic velocity, the acoustic wavelength or grating spacing is a function of the frequency of the RF driver signal. The acoustic wavelength controls the angle of deflection. Intensity of deflected light is a function of RF power. Modulation of the light beam is achieved by maintaining a constant RF which allows the deflected beam to emerge from the modulator and modulate the power of transducer. Thus, modulator will be in its off state when no acoustic wave is applied and vice versa.
2.2.1
Isotropic Acousto- optic Interactions
An isotropic interaction is also referred as a longitudinal mode interaction. In such a situation, the acoustic wave travels longitudinally in the crystal and the incident and diffracted laser beam see the same refractive index. This is a situation of great symmetry and the angle of incidence is found to match the angle of diffraction. There is no change in polarization associated with the interaction (Goutzoulis, A.P., and Kludzin, V.V., 1994). These interactions usually occur in homogenous crystals, or in birefringent crystals cut appropriately. In the isotropic situation, the angle of incidence of the light must be equal to the Bragg angle, B
B
f 2
(2.2)
The separation angle, shift between the first order and the zero order beams is twice the angle of incidence and, therefore, twice the Bragg angle
shift
f
(2.3)
10 A parameter, Q had been introduced by Klein and Cook which is defined as Q
2o L n2 cos o
(2.4)
where 0 is the optical beam wavelength, n is the refractive index of the material, L is the AO interaction length along the direction of propagation of light , is the wavelength of the acoustic waves and 0 is angle. Parameter Q can be used for examining AO interaction geometries in which an appreciable amount of light can be transferred out of the zero order into the diffracted orders.
This parameter is only considered as appropriate because it measures the
differences in phase of the various partial waves due to the different directions of propagation. When Q is small, Q 0.3, the AO interaction is called Raman-Nath (Goutzoulis and Kludzin, 1994) and results in multiple diffraction orders similar to those produced by a thin diffraction grating as shown in Figure 2.2. From the figure, the light is transferred from the zeroth order to the first order and from the first order to the second order and so on. The mth diffracted order is separated from the undiffracted order by an angle m which can be approximated by
m
mo n
(2.5)
As Raman and Nath noted, an examination of the output light intensity shows that phase rather than amplitude modulation is possible. This acoustically induced phase modulation can be transformed into amplitude modulation via well-known Schlieren imaging techniques.
11
Diffracted orders m = +2
m = +1
Incident Optical Beam
m=0 m = -1
m = +2
L a
Figure 2.2: Raman-Nath acousto-optic diffraction geometry
For Q > 0.7, the acoustic grating is no longer thin. The AO interaction becomes sensitive to the angles of incident optical beam. This diffraction regime is called Bragg and is the most widely used in practical applications. Because the energy transfer is most effective between optical waves with the same phase term, the diffracted light will appear predominantly in a single order. The basic geometry for Bragg diffraction and the resulting single diffraction order is shown in Figure 2.3. The Bragg angle, B can be expressed by
sin B
o 2 n
The Bragg condition can be derived by considering the Bragg interaction as a collision between photons and phonons.
(2.6)
12
Diffracted orders
Incident Optical Beam
m = +1 B
B B
m=0 m = -1
L a Figure 2.3: Bragg acousto-optic diffraction geometry
The interaction of light and sound can be described in term of wave interaction or particle collisions (Chang, 1976; Korpel, 1981; Goutzoulis and Kludzin, 1994; Banerjee and Poon1991; Torrieri, 1996). In particle picture, light consist of photons with energy i and momentum ki interacts with sound consists of phonons of frequency a and momentum Ka, where is Planck k is wave vector. When a photon and a phonon collide, one of two results is possible: the phonon is annihilated (Figure 2.4(a), new phonon is created as illustrated in (Figure 2.4(b)). The interaction produces new photon at frequency d and momentum Kd and a phonon at frequency a with momentum Ka. Thus, according to energy and momentum conversation laws, the following relationships produced: d = i a
(2.7)
kd = ki Ka
(2.8)
13
Incident photon ki
Scattered photon kd
Ka
Ka
ki Incident photon
Ka
(a) Annihilation
kd Scattered photon
Ka
(b) Creation
Figure2.4: Interaction of photon and phonon The + and sign applies when the optical wave move against or with the acoustic wave respectively. When the Bragg condition is satisfied, the angle between the incident optical beam and the diffracted beam is 2B as shown in Figure 2.5. It is noted that the wave vectors lie on one circle because for the isotropic AO interaction, the refractive indices of the incident and diffracted light beams are equal (Goutzoulis and Kludzin, 1994).
ni= nd kd
Ka
B B ki
x
z
B
Figure2.5: Wave vector diagram for isotropic Bragg diffraction
14 2.2.2
Anisotropic Acousto-optic Interactions
In an anisotropic interaction, the refractive indexes of the incident and diffraction beam will be different due to a change in polarization associated with the interaction. The same asymmetry which causes the difference in refractive indexes also causes the acoustic wave to travel in a mode Anisotropic interaction generally offer an increase in efficiency and in both acoustic and optical bandwidth. They are used almost universally in large aperture devices. Anisotropic AO interaction take place in optically anisotropic crystal and involve diffraction between ordinary and extraordinary optical beams. The anisotropic AO interaction is often called birefringent because of these optical beams face different refractive indices ( no-ne = n). It also involves the rotation of the polarization of the diffracted beam by 90o with respect to that of the incident beam. This is an important feature of the anisotropic diffraction because polarization filtering can be used to reduce optical noise and to separate the diffracted and undiffracted beams.
The favorable anisotropic interaction takes place for a slow optical wave interacting with the acoustic wave and then is diffracted into a fast optical wave. In the birefringent crystal, the diffracted light wave vector kd can differ in magnitude from the incident light wave vector ki if the polarization is changed in the diffraction process. The wave vector diagram for birefringent diffraction in a negative unixial crystal is shown in Figure 2.6.
15
d
i
x
Ka
ki kd
z Ka
kd nd= ne
ni= nd
Figure2.6: Wave vector diagram for general case anisotropic diffraction
From this figure, it is noted that a change in the direction of the diffracted wave vector kd to kd can be obtained by a change in the magnitude of the acoustic wave vector Ka to Ka. This means that when the acoustic frequency is changed, the mismatch in angular direction is at minimum because of the tangential property and allowing longer interaction length. Thus, an optical beam can be deflected simply by varying the frequency of a wellcollimated acoustic beam which remains fixed in direction.
2.3
Acousto optic Modulator (AOM)
An AOM is a device which allows control of the power, frequency or spatial direction of a laser beam with an electrical drive signal. It is based on the acousto optic effect; the modification of the refractive index by the oscillating mechanical pressure of a sound wave. The key element of an AOM is a transparent crystal (or a piece of glass) through which the light propagates (Figure 2.7). A piezoelectric transducer attached to the crystal is used to excite a high frequency sound wave (with a frequency in order of 100 MHz). An
16 acousto optic device is constructed by bonding an acousto electric transducer onto photo elastic medium, enabling the acoustic wave to be launched into the medium. That transducer (piezoelectric) is metalized on both faces so that an electric field can be applied, which induces a strain throughout the piezoelectric crystal. Light can be diffracted then at the periodic refractive index grating generated by the sound wave. The scattered beam has a slightly modified optical frequency and a slightly different direction. The frequency and direction of the scattered beam can be controlled via the frequency of the sound wave, while the acoustic power allows the control of the optical powers. For sufficiently high acoustic power, more than 50% of the optical power can be diffracted.
Figure 2.7: Mechanisms in piezoelectric transducer for AOM An acousto-optic modulator (AOM) consists of a piezoelectric transducer which creates sound waves in a material like glass or quartz. A light beam is diffracted into several orders. By vibrating the material with a pure sinusoid and tilting the AOM so the light is reflected from the flat sound waves into the first diffraction order. Up to 90% deflection efficiency can be achieved. The diffracted efficiency, is given by equation 2.9.
2 I1 L 2 M 2 Pa I in 2 H
(2.9)
17 where I1 and Iin represent the diffracted and incident light intensity, wavelength. M2 is figure of merit of the materials. L is the interaction width and H represents height of transducer. Pa is acoustic power. This configuration offers less than 100% diffraction efficiency and 70% are common (Johnson, 1994). The properties of the light exiting the AOM can be controlled in four ways; by deflection, intensity, frequency or phase.
2.3.1
Deflection
A diffracted beam emerges at an angle h of the light, and the wavelength of the sound, : sin
m 2
(2.10)
where m = ...-2,-1,0,1,2,... is the order of diffraction. The angular deflection can range from 50 to 5000 beam widths (the number of resolvable spots). Consequently, the deflection is typically limited to tens of miliradians.
2.3.2
Intensity
The amount of light diffracted depends on the intensity of the sound wave. Hence, the intensity of the sound can be used to modulate the intensity of the light in the diffracted beam.
18 2.3.3
Frequency
One difference from Bragg diffraction is that the light is scattered from moving planes. A consequence of this is the frequency of the diffracted beam f in order m will be Doppler-shifted by an amount equal to the frequency of the sound wave F.
This frequency shift is also required by the fact that energy and momentum (of the photons and phonons) are conserved in the process. The maximum possible frequency shift is typically limited to tens of megahertz.
2.3.3
Phase
In addition, the phase of the diffracted beam will also be shifted by the phase of the sound wave. The phase can be changed by an arbitrary amount.
2.4
Acousto-Optic Material Selection
A variety of different acousto-optic materials are used depending on the laser parameters such as laser wavelength (optical transmission range), polarization, and power density. Table 2.1 is a summary of the most common materials used for acoustooptic modulators. For the visible region and near infrared region the modulators are commonly made from gallium phosphide, tellurium dioxide, indium phosphide (Brimrose Pioneered), of fused quartz. At the infrared region, germanium is the only commercially available modulator material with relatively high figure of merit. Lithium n iobate, indium phospide, and gallium phosphide are used for high frequency (GHz) signal processing devices.
19 Table 2.1 : Acousto optic materials Selection
MATERIAL
OPTICAL RANGE (micron)
FIGURE OPTICAL MAX CW REFRACTIVE ACOUSTIC ACOUSTIC POLARIZATION LASER POWER INDEX MODE VELOCITY O F MERIT 2 (watt/mm ) (k m/sec) x10 -15 m 2 /w
Chalcogen ide Glass
1.0 - 2.2
Random
0.5
2.6
L
2.52
164
Flint Glass SF6
0.45 - 2.0
Random
0.7
1.8
L
3.51
8
Fused Quartz
0.2 - 4.5
Linear
> 100
1.46
L
5.96
1.56
Gallium Phosphide
0.59 - 10.0
Linear
5
3.3
L
6.3
44
Germaniu m
2.0 - 12.0
Linear
2.5
4.0
L
5.5
180
Indium Phosphide
1.0 - 1.6
Linear
5
3.3
L
5.1
80
Lithium Niobate
0.6 - 4.5
Linear
0.5
2.2
L
6.6
7
Lithium Niobate
0.6 - 4.5
Linear
0.5
2.2
S
3.6
15
Tellurium Oxide
0.4 - 5.0
Random
5
2.25
L
0.62
34
Tellurium Oxide
0.4 - 5.0
Circular
5
2.25
S
5.5
1000
CHAPTER III
EXPERIMENTAL WORKS
3.1
Introduction
In this chapter, all the elements used in the experimental works and signal detection will be discussed. The discussion will start from the development of the acousto- optic modulator system and other equipments required for the preliminary works and the setup of an acousto-optic modulator system.
3.2
Instrumentations
All equipment required in this research will be discussed in detail in the following section.
3.2.1
Equipment used in preliminary study
In this section the equipment used in priliminary study will be described. These included Acousto-Optic Modulator M040-8J-F2S, a AOM Driver, Newport
21 Fiber Optic Light Source, Kingfisher Power Meter, Analog Oscilloscope, Function Generator 0.2Hz-2MHz, DC Power Supply and NIR Diode Array Spectrometer.
3.2.1.1 Acousto-Optic Modulator
The modulator is used in the preliminary study is a fiber-coupled AO modulator with a driving frequency of 40MHz (Figure 3.1), optimized for low insertion loss at 1550 nm. A 2 meter single mode fiber is attach to the modulator with FC/ PC connector or SeikoGeiken at the two end. The use of chalcogenide glass as interaction material provides essentially no polarization sensitive loss or polarization mode dispersion (Gooch & Housego PLC, 2002). Very high extinction ratio and rise-time make this device suitable for all optical switching and re-routing application.
Fiber Connector
AOM
Figure 3.1: AOM M040-8J-F2S
22
Figure 3.2: AOM M040-8J-F2S diagramatic
3.2.1.2 AOM Driver
The AOM Driver A 118 is a quartz stabilized oscillator driver for acousto-optic modulator (AOM) applications. The A 118 is a special type of low power driver that is designed for analogue modulation. It has the characteristics of high technical performance and guarantees wide modulation bandwidth and excellent switching. In these study it is used to drive the modulator.
23
BNC input
BNC output Output Signal
Input Signal RF Driver
Light source
Oscilloscope
Figure 3.3(a): AOM Driver and the diagram of the driver
Output Level
Figure 3.3(b): Output Level section of AOM
3.2.1.3 Newport The Newport !!" light source (Figure 3.4) in order to investigate the driving signal. The instrument mainframe contains the power supply, central processor and communication functions.
24
LCD display
Figure 3.4: Newport
3.2.1.4 Fiber Optic Light Source
Fiber Optic Light Source (Figure 3.5) is used to test the fiber optic system at the wavelength of 850 nm, 1310 nm and 1550 nm. It has the general application of 3 assorted LED or laser sources, for general multimode or single mode testing and switched dual wavelength source through one interchangeable connector and also to test tone generation, detection and fiber identification. In this project, the light source with 1310 nm and 1550 nm is used in investigating the characterisic of the AOM and the light source sensitivity.
25
Power Light
display
Figure 3.5: Kingfisher Fiber Optic Light Source KI 7822
3.2.1.5 Power Meter
The Power Meter (Figure3.6) is used for field or lab testing of fiber optic system at varies wavelength of 850 nm, 1300 nm, 1310 nm and 1550 nm for single mode application and also to test tone measurement and fiber communication. It is used in this project to measure the AOM output power
Light Power display
Figure 3.6: Kingfisher Power Meter KI7600
26 3.2.1.6 NIR Diode Array Spectrometer
The NIR Diode Array Spectrometer(Figure 3.7) is a fixed diffraction grating and post disperses devise with a 128-element InGaAs photodiode array. A polychromatic tungsten halogen light source is positioned over the sample and the dispersed light from the sample is collected by a collimating lens and fed back to the spectrometer via fiber optic cable. The measurement range of the spectrometer is 900 nm to 1700 nm.
Figure 3.7: NIR Diode Array Spectrometer
3.2.2 Equipments used in Acousto- optic Modulator system
In this section the equipment used in acousto optic modulator system will be described. These included Tuneable HeNe Laser, NEOS Technology AO Modulator, AO Modulator Driver, Laser Beam Profiler ( LBP ) and Amplified Silicon Detector.
27 3.2.2.1 Tuneable HeNe Laser
In this project, the tunable HeNe laser (Figure 3.8) is used as a source. It is chosen because it can operates on all of the main visible neon laser transitions (543 nm, 594 nm, 604 nm, 612 nm, and 633 nm) by adjusting the angle of the Littrow with micrometer adjustments on the rear panel. The system uses a low loss plasma tube with one sealed Brewster window and an external Littrow prism to select among the five wavelengths. A power supply is housed internally in the laser, making the unit completely self-contained.
Figure 3.8: The Tunable Laser
3.2.2.2 NEOS Technology AO Modulator
There are variety of AOM found in today # $ % study (Figure 3.9) is a low cost SF6 (Sulfur hexafluoride) glass material with a lithium niobate transducer. SF6 glass was used as the AO interaction medium as this is acoustically and optically isotropic, thus simplifing the design process. Once the acousto-optic material is selected, it is optically polished and a lithium niobate transducer is metal-pressure bonded to the modulator medium using an advanced technique. The metal bonding provides a far superior acoustic coupling than epoxy bonding.
28 The modulator assembly was mounted on a fixture to provide sufficient adjusment to maximize the modulator effciency. The range of operating wavelength for the modulator is between 440 nm to 850 nm. The modulator can be driven with any good driver with a nominal 50 ohm output of 80 MHz. The acoustic mode of this modulator is longitudinal and it & $ '! ( ')) $ rise time of the modulator is 185 ns/mm beam diameter.
Input Signal Laser HeNe (Source Signal)
AOM
Figure 3.9: Acousto-Optic Modulator
3.2.2.3 AO Modulator Driver
The AO driver shown in Figure 3.10 is a RF frequency generator that used to supply a signal of variable frequency 70 MHz to 90 MHz and amplitude of up to 1 watts maximum output, centered at 80 MHz normally. It is used to drive the AOM. It can drive internally or externally.
29
Output Signal Power (ON / OFF)
RF Power (Level Adjust)
RF Frequency ( frequency Adjust)
Figure 3.10: The AO Modulator Driver
3.2.2.4 Laser Beam Profiler ( LBP )
The laser beam profiler (LBP) shown in Figure 3.11 is used in this research as a detector to study the beam characteristics. LBP is the central component at the heart of the optical beam measurement system. It is a complete beam diagnostic measurement system. For continuous or pulsed laser beams, it provides an extensive range of graphical presentations and analysis capabilities of laser beam parameters, such as: beam width, shape, position, power and intensity profiles.
The CCD camera is equipped with a built-in filter wheel, enabling the use of up to four, 0.5 in. diameter, attenuators. Three attenuators are included with the system: LBPNG4, LBP-NG9 and LBP-NG10, while additional ones may be purchased separately. The camera can be post-mounted via a single 8/32 threaded hole, centered directly below the sensor surface.
30 CCD Camera (Filter)
Cable to PC
Figure 3.11: The Laser Beam Profiler
3.2.2.5 Amplified Silicon Detector
Figure 3.12 shows Amplified Silicon Detector. The detector is used to detect the light signal in order to study the optical signal of diffracted light including the temporal response characteristics. This detector have 5- position rotary switch to vary the gain in 10 dB steps. The active area of the detector is (3.6 mm x 3.6 mm) and response to 320 nm to 1100 nm of wavelength. The detector was connected to oscilloscope which performs as analyzer.
Figure 3.12: Amplified Silicon Detector
31 3.2.2.6 Fiber Optic Spectrometer
Figure 3.13 shows an fiber optic spectrometer systems consist of low-cost, modular data acquisition components. OOIBase32 is the operating software for Ocean Optics spectrometers It has the possibility to perform spectroscopic measurements such as absorbance, reflection and emission. The program allows data collecting from up to 8 spectrometer channels simultaneously and to display the results in a single spectral window. The software can be used under Windows 95/98, Windows NT and later version. OOIBase32 is a 32-bit, user-friendly, advanced acquisition program that provides a real time interface to a multitude of signal processing functions, such as electrical dark-signal correction, stray light correction, signal averaging and boxcar pixel smoothing.
Figure 3.13: Fiber Optic Spectrometer
3.2.2.6 Polarizer and analyzer
Two Melles Griot polarizer were used to ensure that the incident laser light was linearly polarized. The analyzer, oriented at 90* & being transmitted when no voltage is applied. When the correct voltage is applied to the device, the direction of the polarization is rotated by 90+$ the analyzer.
32
3.3
Experimental works
Section 3.3.1 presents the preliminary experiments on the AOM while the main experimental works for this study was presented in section 3.3.2.
3.3.1
Preliminary Experiments on the AOM
A study on fibre coupled AOM using chalcogenide glass with refractive index of 2.6 has been carried out. This study focused on investigating the characteristics of AOM: studying the theory and working principle of AOM and other equipment in the experimental set up, to get the relationship between driving voltage from RF driver and output power from modulator by changing the output level from on the radio frequency (RF) driver and to observe the effect of several light sources on the characteristics.
3.3.1.1 Investigating the effect of driving signal on AOM output power
Figure 3.14 shows the experimental setup for investigating the effect of the RF driving signal on the characteristics of the AOM. The 1550 nm light source was connected to the AOM and a fixed voltage of 13 V from the dc power supply was applied to the RF driver. A pulse generator was used to generate the desired pulse with different pulse width at different pulse rate. The digital oscilloscope was connected to the RF driver to observe the driving voltage. The AOM output power is observed when the light source was switched on.
33
Light source Power meter AOM Spectrometer
Computer
Vpeak to peak
DC Power Supply
RF D i
Pulse generator
Oscilloscope (OSC) Optical fibre Electrical circuit
Figure 3.14: Experimental setup of an acousto optic modulator (AOM)
3.3.1.2 Investigating the spectral output of the AOM
For the second setup, the power meter was replaced with the spectrometer as shown in Figure 3.15. A 1553 nm light source was used with analog oscilloscope and a function generator. The input voltage to the RF driver was varied to observe the relationships between the output powers with the driving voltage. A infrared fiber optic spectrometer was used to display the spectrum.
34
3.3.1.3 Investigating the Light Source Sensitivity
Figure 3.15 shows the experimental setup to investigate the sensitivity of two types of light source; E- LED 1330 nm and the laser light source 1553 nm. The E-LED light source was connected to the AOM and a fixed voltage of 13 V from the dc power voltage was applied to the RF driver. The analog oscilloscope was connected to the RF driver to observe the driving voltage. The AOM output was observed using the spectrometer setup. The procedures were repeated for the 1553 nm laser light source.
Light source
AOM
Spectrometer
Computer
Vpeak to peak
DC Power Supply
RF Driver
Function generator
Oscilloscope (OSK)
Optical fiber Electrical circuit
Figure 3.15: Experimental setup to investigate the sensitivity of two types of light source; E- LED 1330 nm and the laser light source 1553 nm
35
3.3.1.4 Programming
A simple program has been designed using Mathlab software to determine the Bragg angle B, for different AO parameters namely the driving frequency for the modulator (f), the acoustic wavelength () and the refractive index of the AO material (n) as given by Equation (2.6). A program using Visual basic is also designed to calculate the shift angle, shift and the Bragg angle, B for different wavelengths, driving frequencies, f and speed of sound, .
3.3.2
Calibration of instruments
The calibrations were done to the instruments before all the experiments were carried out. Calibration is one of the methods to ensure all the instruments used during the experiments were functioned correctly.
3.3.2.1 Calibration of the Tunable He-Ne Laser
Figure 3.16 shows the experimental set up to verify the wavelengths of the tunable He-Ne laser. The laser was connected to the Ocean Optics Spectrometer. The OOIBase32 Spectrometer Operating Software was utilized to obtain the spectrum of the laser beam with different wavelength. The laser beam with different wavelength is selected by adjusting the angle of the Littrow with micrometer adjustments on the rear panel. For every wavelength the spectrometer is replaced with an optical power meter to measure the optical power (Figure 3.17). All the data were compared with those given by the manufacture
36
Computer
Tunable HeNe laser spectrometer
Figure 3.16:.Observation on the wavelengths of Tunable He-Ne Laser experimental setup
Tunable HeNe laser
Power meter
Figure 3.17: Observation on the optical power of Tunable He-Ne Laser
3.3.2.2 Calibration of Function Generator
Figure 3.18 shows the set up for calibrating the function generator. The function generator can produces three types of signals which are square wave, sinusoidal wave and triangular wave. The calibration was done by connecting the function generator to the oscilloscope in order to determine the output signals.
Function Generator
oscilloscope
Figure 3.18: Set up for calibration of function generator
37
3.3.3
Experimental works on the constructed AOM
Experiments were done in order to determine the polarization of the laser beam, to investigate the relation between the type of input signals and output signals, to determine the change of output amplitude on varying the amplitude of input signals and also to measure the change of the first order power when the RF power were increased. Experiments were done using all the instruments above. Figure 3.19 shows the set up for this study. The tunable HeNe laser with 632.8nm wavelength was used as the main light source. Light from the laser at certain wavelength was sent through the AOM with refractive index of 2.6. The AOM will deflect the light at the Bragg angle, B. The angle deflection of light will depend on the frequency of the sound wave generated by the AOM Driver. The output signal will be detected by using different detector system, namely a CCD Laser Beam Profiler, a photodetector (PDA 55) and a power meter.
Tunable He-Ne Laser
AOM
Detector system
AOM driver
Figure 3.19: Experimental setup
38
3.3.3.1 Determining the polarization of the laser beam
The modulator is polarization sensitive and requires linear polarization. So the first experiment is to check the specified optical polarization is correct for optimum AO efficiency. Figure 3.20 shows the experimental setup to determine the polarization of the laser beam. In this experiment, a beam of plane polarized light is needed from the tunable He-Ne laser. Determination of the polarization of the laser light is done by placing a piece of sheet polarizer throughout the beam, mounted on the angular rotation mount.
The beam emerged directly from the polarizer into the power meter as shown in Figure 3.10. The polarizer is rotated through 360+ variation of the power meter is observed. If the beam is plane polarized, the reading of the power meter should decrease to zero at two positions 180+ ,"+ intensity is zero, the intensity will rise to a maximum. In this case, the laser output is plane polarized and it may be used with the modulator.
Tunable He-Ne Laser (633nm)
4cm
6cm
Power meter
polarizer Figure 3.20: Determining the polarization of the laser light
3.3.3.2 Investigating the Internal RF Frequency Range
Figure 3.21 showed the experimental setup to verify the range of RF frequency driver. The RF driver is set to (internal) and the RF frequency is set to (minimum). The RF power is set to center. The minimum frequency of the driver is measured using the
39 oscilloscope. The center and maximum frequency is measured by adjusting the frequency adjustable knob to center and maximum.
Oscilloscope
RF driver Driving frequency adjustable
Driving power adjustable
center
minimum
center
maximum
minimum
maximum
Figure 3.21: Investigating the Internal RF frequency range
3.3.3.3 AOM System
A Tunable He-Ne Laser (wavelength 633nm) and AO modulator was mounted on a breadboard as shown in Figure 3.22 so that the beam passed through the AO modulator and fell on a target at least 1m away. The RF driver was connected to the modulator using a 50Ohm coaxial cable connector. To energize the modulator, the RF driver is set to internal and the drive control was set to full power (maximum on the control which represents 100% drive power). The angle of incidence was varied using the mount until diffraction was seen. By changing the drive control from zero to full power (this is easily done by switching the INT/EXT switch to EXT with no external signal applied), the capability of the modulator to function can be varied.
40
Surface target Tunable He-Ne Laser
AOM
RF driver Figure 3.22: Set up experiment for an acousto-optic modulator
Acousto-optic modulator SF6
Rotation stage
Transducer
Figure 3.23: Enlarged view of an Acousto-Optic Modulator
3.3.3.4 Geometry Characteristics of AOM
Figure 3.24 shows the experimental setup for investigating the geometry characteristics of AOM. When the source, HeNe laser is on, it will go through the acousto optic modulator. The laser output was examing using the LBP. The pattern of laser beam with various characteristics was examined. The characteristics of the sample were analised. Variations of distance between LBP and AOM, distance of HeNe laser beam from the AOM. The aim of this study is to investigate the effect of radio frequency (RF) signal on diffraction angle and output intensity. Diffracted beam was detected using Laser beam profiler (LBP) and analized using a software.
41
Tunable He-Ne Laser
AOM
LBP Computer
AOM driver
Figure 3.24: Geometry characteristics of AOM
3.3.3.5 Characteristics of Modulated Optical Signal
Figure 3.25 shows the modulator mounted in the optical path with the laser beam passing through the device window on the window vertically and close to the transducer (in the modulator). With the laser beam going through the optical cystal (in the modulator) and close to the transducer that is driven by AOM driver at 80 MHz operating frequency, the Bragg angle can be adjusted by rotating the modulator, to allow the diffracted first order beam away from the AOM. The diffracted first order beam is detected using Si photodetector and observed using the oscilloscope. The beam block was used to block the zero order beam in order to get a good result. The output from the modulator with various characteristics was examined. The effects on the variations of RF frequency and RF power were also studied.
Tunable He-Ne Laser
AOM
Beam block Oscilloscope
AOM driver
Detector
Figure 3.25: Characterictic of modulated optical signal experimental setup
42 3.3.3.6 Temporal Characteristics of Acousto-Optic Modulator (AOM) (External Modulated)
Experiments were done in order to investigate the relation between the type of input signals and output signals, to determine the change in output amplitude when the amplitude of input signals was varied and also to measure the change of first order power when the Radio Frequency power was increased. Figure 3.25 shows the set up for this study. Input frequency from the function generator then mixed with the signal from RF Driver. The diffracted signal will be detected by using Amplified Silicon Detector. The output signal was displayed on the oscilloscope.
Tunable He-Ne Laser
Beam block
AOM
Oscilloscope AOM driver
Function generator
Detector
Figure 3.26: Temporal characteristics of acousto-optic modulator set up
3.3.3.7 Determining the Types of Output Signals
The objectives of this experiment are to determine the output signals when varying the type of input signals. A function generator was used to produced the type of input signals. Three types of input signals; square wave, sine wave and triangle wave were used. The frequency of input signals was varied from 100 Hz to 2000Hz.
43 3.3.3.8 Effects of modulating signal amplitude
The amplitude of input signals was varied from a minimum value to a certain value. Some parameters are constant, which are the frequency of input signal (800 Hz), RF power (set to maximum) and central frequency, CF (set to maximum). Output signals from the oscilloscope were analyzed.
3.3.3.9 Effects of RF power
The RF power at RF Driver panel was tuned in order to measure the output power of the first order. The frequency of the input signals is constant at 800 Hz. A power meter was used to measure the optical power.
CHAPTER IV
EXPERIMENTAL RESULTS AND ANALYSIS
4.1
Introduction
This chapter presents the experimental data and its analysis. Section 4.2 presents data of the preliminary experiment, while the section 4.3 presents the results from the constructed experimental setup using a tunable laser source.
4.2
Preliminary experimental results
The all preliminary experiments data and analysis are presented in this section.
4.2.1
Observation of Driving Signal
An observation has been done to see the input signal and the output signal for the driving signal. Some parameters are constant, which are the DC voltage, (131)V and current, (3.80.1)A from the power supply, spacing,100 ns and width, 100 ns from the pulse generator and t , 25.3 ns and light source wavelength, (1553.80 0.01)nm from the light source.
45 The oscilloscope display obtained for the AOM investigated is shown in Figure 4.1. The display shows driving frequency almost 40 MHz.
f=39.999MHz
Figure 4.1: An oscilloscope trace showing the AOM driving frequency of 40 MHz
Table 4.1: Driving Signal Driving Signal
Frequency, (f 0.01)MHz
Modulating signal
0.16
Output signal
39.99
Table 4.1 shows the modulating signal at the frequency of 0.16 MHz. The output signal has the frequency of 39.99 MHz. This value is constant even though changes was done to minimize and maximize the signal amplitude.
46 4.2.2
Investigating the Characteristics of AOM
Table 4.2 list the data from the experimental setup for characteristic of the AOM. As the driving voltage increased the output voltage is increased until it reaches the value of -8.25 dBm. The increase in driving power will increase the efficiency of the interaction which is in good agreement with theory as indicated in Equation (2.9).
Table 4.2: The Characteristic of AOM
No.
1 2 3 4 5 6 7 8 9 10 11 12 13 14
Oscilloscope
Power Meter
Spectrometer
Vpeak to peak
Output Power
Amplitude
(V Volt 21.83 19.16 17.16 15.16 13.50 12.00 10.83 9.83 8.83 8.00 7.16 6.50 5.83 5.33
(P 0.01) dBm -10.07 -11.07 -12.07 -13.07 -14.07 -15.07 -16.07 -17.07 -18.07 -19.07 -20.07 -21.07 -22.07 -23.07
(A x 107) Counts 21.1838 16.4258 13.7020 10.7073 81.2149 7.2091 5.5313 4.2970 3.4362 2.6749 2.2420 1.6891 1.3540 1.0737
Output power, P0 = Output power from modulator V peak to peak
= Driving voltage from RF driver
(FWHM 0.0001) 10.1306 10.7317 10.7285 10.4506 10.3982 10.5604 10.6899 10.5903 10.4777 10.5521 10.3940 10.3616 10.4246 10.3328
Area (Ar x 107) Arbitrary unit 224.627 177.381 145.722 112.263 84.626 75.559 57.792 44.667 35.256 27.202 22.398 16.526 13.050 10.040
47 4.2.2.1Spectrums
Figure 4.2 shows the spectrum of output power from the modulator as given by the spectrometer using a special programming, OOIBase32 Software where data in Table 4.2 has been interpreted into it. The peak value of the output power optical power is 1556 nm which is similar to the input wavelength. Data given by the spectrum is plotted to observe the relationship between the amplitude of the voltage and output power level. The other spectrums are shown in Appendix A.
Figure 4.2: A sampel of spectrum from the spectrometer
48 4.2.2.2 Graphs
The variation of output power with driving voltage is shown in Figure 4.3.
Output power (dBm)
Output power change due to the peak to peak voltage 0 -5 0
5
10
15
20
25
-10 -15 -20 -25 -30 Peak to peak voltage (V)
Figure 4.3: Relation between amplitude of the voltage and output power level
The data from the spectrometer showed that there is increase in the area of the spectrum with optical power output. This corresponds to the variation of the output power as indicated in the above of result given in Figure 4.4. It shows that the increase in driving power will increase the intensity of output signal which is in good agreement with theory as indicated in Equation 2.9.
Figure 4.4: Relation between output power and spectrum area
49 4.2.3
Light Source Sensitivity
The data as shown in Table 4.3 are taken to observe the sensitivity of different light source towards the wavelength. The data has been taken using two types of light source; ELED and Newport -.)/ comes with the NIR Diode Array Spectrometer to investigate the sensitivity of each light source.
Table 4.3: Light source sensitivity Light Source E-LED, Newport Light Source,
0 ( 1) nm 1330
( 1) nm 1306
Vpeak to peak (V 0.001) Volt 3.583
Output Power (P 0.01) dBm -41.78
1553
1556
3.583
-25.04
( 0 1) nm = value given by factory setting ( 1) nm = value given by spectrometer
4.2.3.1 Spectrums
According to the spectrum given in Figure 4.5(a) and Figure 4.5(b), the wavelength of each light source given by the factory setting experienced an additional digit of 6 when it passes through an AOM. Spectrum given by the spectrometer for each light source is using the same scale and constant peak to peak voltage. This is due to the error in spectrometer setting and in need of calibration.
50
(a) Vpeak to peak, (V 0.001) Volt =3.583
Output Power , (P 0.01) dBm = -41.78
(b) Vpeak to peak, (V 0.001) Volt = 3.583
Output Power , (P 0.01) dBm = -24.07
Figure 4.5: Spectrum for 1550 nm and 1300 nm light source
51 4.2.4
Programming
A simple simulation, from Mat Lab, using Bragg equation, by inserting the values (f, n, , ), the Bragg angle, B can be determined. Figure 4.6 shows the variation of Bragg angle, B with driving voltage, f. From Figure 4.6, the Bragg angle obtained for the AOM is 0.1210.
Figure 4.6: Relation between Bragg angle and acoustic carrier frequency
A program using Visual basic is also design to make a calculation of shift angle, shift and Bragg angle, B for different light wavelength, acoustic frequency and speed of sound. Figure 4.7 shows the diagram of the program. By inserting the value of the wavelengh, speed of sound and acoustic frequency, the shift angle and Bragg angle was determine.
52
Figure 4.7: Screenshot of the Visual Basic Programming
4.3
Experimental result and discussion of an AOM
This section will present all the data of the experiments and the analysis of the data. The first part is data regarding to the calibration of the instrument, while the second part is the experiments that related to the objectives of this study.
4.3.2
Calibration Instruments
The results for the calibration of the instrument are presented in this section.
53 4.3.1.1 Tunable He-Ne Laser
Five different wavelengths were obtained by using both color selector and transverse adjustment knobs from tunable HeNe laser. Figure 4.8 shows the spectrum of the tunable HeNe laser at different wavelength. Table 4.4 shows the wavelength and power values for each color from He-Ne laser.
a) = 542.73 nm
b) = 592.28 nm
54
c) = 604.21 nm
d) = 612.24 nm
e) = 633.64 nm Figure 4.8: Spectrum of Tunable HeNe Laser
55 Table 4.4: Data Calibration for Tunable HeNe Laser Color of laser beam Green Yellow Orange Orange Red
Wavelength (nm) 542.73 592.28 604.21 612.24 633.64
P1 0.27 1.47 1.31 2.06 5.06
Power, P (mW) P2 P3 P4 0.28 0.29 0.28 1.46 1.49 1.46 1.32 1.29 1.28 2.07 2.09 2.06 5.04 5.04 5.06
P5 0.28 1.47 1.30 2.07 5.05
Table 4.5: Data from experiments and references value Color of laser beam
Green Yellow Orange Orange Red
Wavelength (nm)
542.73 592.28 604.21 612.24 633.64
References (manufactured) wavelength, (nm)
Average Power, P (mW)
543 594 604 612 633
0.28 1.47 1.30 2.07 5.05
References power (manufactured) (minimum output power) (mW) 0.3 0.6 0.5 2.5 4.0
From Table 4.5, all the five colors produced by the HeNe laser have wavelength approximately with the manufactured value. While the power of the light for each color is nearly the same with the references value except for color Orange 2 and yellow. The differences value maybe cause by the power losses during measument. So, the HeNe laser able to working properly and produced the laser beam as in the manual.
56 4.3.1.2 Determination of the Polarization of the Laser Light
Table 4.6 shows the reading of the power meter is decrease to 0.01mW at 180+ 0.02mW at 3600, while the intensity rise to a maximum which is 0.46mW at 900 and 0.45mW at 2700. This indicate that the beam is plane polarized.
Table 4.6: Determination the polarization of the laser light Position of polarizer(
Power(mW)
45
0.19
90
0.46
135
0.06
180
0.01
225
0.15
270
0.45
315
0.06
360
0.02
Zero intensity 180* 135*
Maximum intensity
225*
90*
270*
45
Maximum intensity
315* 360*
Zero intensity
Figure 4.9: Position of polarizer
57 4.3.2
Determination the Shifting of First Order Beam on the variation of Driving
Frequency
Table 4.7 and Figure 4.10 shows the increase in driving frequency (RF frequency) will increase the distance between zeroth order beam and first order diffracted beam (horizontal shifting). This is good agreement with theory that the RF frequency controlled the angle of deflected beam and diffracted beam.
Table 4.7: Effect of driving frequency on horizontal shifting, z RF Frequency(MHz) 72.79 75.95 80.17 82.94 86.99 89.61 90.14 91.67 96.56
Horizontal Shifting, d( 4130.60 4138.64 4204.43 4507.53 4585.74 5157.58 5373.90 5463.11 5564.44
Horizontal shifting, 6000 5500 5000 4500 4000 3500 70
80
90
100
RF
Figure 4.10: Effect of driving frequency on horizontal shifting, z
58
1st order diffracted beam
Zero order transmitted beam
z
4.3.3 Effects of input frequency on output frequency
Using the function generator, three types of signal were generated at various frequencies in order to determine the characteristics of AOM. The data for three types of signal from the function generator which is square wave, triangle wave and sine wave is shown in figure 4.11. The frequency was varied from 100 Hz to 1800Hz.
Input frequency (Hz)
Square wave
Triangle wave
Sine wave
102.4Hz
102.9Hz
102.2Hz
196.1Hz
196.9Hz
196.9Hz
100
200
59
Input frequency (Hz)
Square wave
Triangle wave
Sine wave
392.1Hz
394.3Hz
392.5Hz
598.1Hz
601.0Hz
598.1Hz
783.6Hz
786.6Hz
783.7Hz
1012Hz
1016Hz
1014Hz
1223Hz
1232Hz
1238Hz
400
600
800
1000
1200
60
Input frequency (Hz)
Square wave
Triangle wave
Sine wave
1435Hz
1441Hz
1433Hz
1693Hz
1647Hz
1639Hz
1827Hz
1838Hz
1825Hz
1400
1600
1800
Figure 4.11: Three types of output signal at input frequency 100 Hz to 1800Hz
Table 4.8 shows that, the output frequency is nearly equal to the input frequency. There are only slightly different between the input value and the output value. But, the output values still in the range of input value. Figure 4.12 shows the relation of output frequency with input frequency. It shows that, when the input frequency is increased the output frequency is also increased. Analysis of the graph was done by using the Least Square Method as shown in Appendix C.
61 Table 4.8: Values of output frequency for square wave, triangle wave and sine wave signals Input frequency (Hz)
Output frequency (Hz) from oscilloscope Square wave Triangle wave Sine wave 102.4 102.9 102.2 196.1 196.9 196.9 392.1 394.3 392.5 598.1 601.0 598.1 783.6 786.2 783.7 1012.0 1016.0 1014.0 1223.0 1232.0 1238.0 1435.0 1441.0 1433.0 1639.0 1647.0 1639.0 1827.0 1838.0 1825.0
100.0 200.0 400.0 600.0 800.0 1000.0 1200.0 1400.0 1600.0 1800.0
Graph of Input Signal vs Output Input Signal (Hz)
2500 2000 Square wave
1500
Triangle wave
1000
Sine wave
500 0 0
500
1000
1500
2000
Output Signal
Figure 4.12: Relation between input signal and output signal
62 4.3.4
Effects of Driving Power on Output Optical Power of First Order Beam
The amplitude of input frequency was varied from minimum value to maximum value. Some parameters were constant which is input frequency at 800 Hz, at the maximum value of RF power and at the maximum value of central frequency. By referring to the theory, Acousto-optic modulator is a linear analog modulator. It can produced output signal which have the same waveform like the input signal and the intensity of reflected signal is proportional to the incident light signal. Table 4.9 shows the data for these experiments. Input amplitude were varied from the minimum value which is 199 mV to the maximum value of 870 mV. From the table there is no change in output signal patent. For input amplitude more than 244 mV, there is no output produced by the modulator. The maximum value of input amplitude is 196 mV, where output signal still have the same waveform like the input signal .
Table 4.9: Value of input amplitude for 119 mV to 870mV No
Input signal
Output signal
119mV
2600mV
120mV
2700mV
1
2
63
3
121mV
2700mV
122mV
2600mV
176mV
1700mV
184mV
1200mV
196mV
400mV
4
5
6
7
64
8
244mV
100mV
870mV
200mV
9
Table 4.10: Value of input amplitude and output amplitude Input Amplitude
Output Amplitude
0.119
2.600
0.120
2.700
0.121
2.700
0.122
2.600
0.176
1.700
0.184
1.200
0.196
0.400
0.244
0.100
For input signal with amplitude less than 130 mV, the output amplitude is in the range of 2.6 V to 2.7 V which are around 21 to 22 times larger than the input amplitude.
65 Table 4.11: Ratio of output amplitude to input amplitude Input Amplitude 0.119 0.12 0.121 0.122 0.176 0.184 0.196 0.244
Output Amplitude 2.6 2.7 2.7 2.6 1.7 1.2 0.4 0.1
Ratio=Output/Input 21.85 22.50 22.31 21.31 9.66 6.52 2.04 0.41
From the graph in Figure 4.10, it is found that the value of output amplitude is decreased when the input amplitude increased. Analysis of the graph was done by using the Least Square Method. The graph equation is Equation 4.1. The RF driver can give frequency in range of 75 MHz to 100 MHz. This range can be achieved when the power level of RF driver fix at the center value. The power of RF driver must be selected with care to ensure the output frequency match with AOM. The AOM operating frequency is 80 MHz.
Amplitude output 22 2 Amplitudeinput 5.3 0.4
Where,
m 22 2 c 5.3 0.4
(4.1)
66
Graph Output Amplitude vs Input Amplitude 3 2.8 2.6 2.4
Amplitude for Output Signal(V)
2.2 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.22
0.24
0.26
Amplitude for Input Signal(V)
Figure 4.13: Graph of output amplitude at various input amplitude
4.3.6
Effects of RF power
The input frequency is constant at 800 Hz, and then the RF power was in-creased from the minimum value to maximum value. Table 4.12 and table 4.13 shows the data for this experiment. Tables show that power of first order will increase when the RF Power is increase. There are also the limitations of power in order to produce the desired signal. The minimum first order power to produce output nearly same like input signal where the diffraction of input signal was occurred, is 0.076 mW. If the RF power is less than this value, the diffraction of light was does not occured because the sound field does not produced any grating or the size of grating is too small. So, the diffraction occured at the very small angle, 0 zeroth order diffraction. Table 4.12 shows this phenomena.
67
Table 4.12: The first order power for minimum RF power to maximum RF power (position 1 to position 3) Position for RF power 1st Order Signal Power(mW) knobe from RF driver
1
0.0141"""!
250kHz
2
0.0141"""!
50kHz
0.0721"" "
3
250kHz
68 Table 4.13: The first order power for minimum RF power to maximum RF power (position 4 to position 14) Position for RF power Signal 1st Order Power(mW) knobe from RF driver
4
0.0761"""!
769.2Hz
0.1061"" "
5
801.3Hz
0.0641"" !
6
801.5Hz
0.1221"" "
7
801.3Hz
69
0.0721"" "
8
801.3Hz
0.1001"" "
9
801.4Hz
10
0.1281"""!
802.5Hz
11
0.1361"""!
802.1Hz
12
0.1341"""!
802.4Hz
70
13
0.1541"""!
801.3Hz
0.1701"" "
14
801.4Hz
Table 4.14:.The average power for RF power position, z z
Frequency out (Hz)
Average power (mW)
4
769.2
0.0761"""!
5
801.3
0.1061"" "
6
801.5
0.0641"" !
7
801.3
0.1221"" "
8
801.3
0.0721"" "
9
801.4
0.1001"" "
10
802.5
0.1281"""!
11
802.1
0.1361"""!
12
802.4
0.1341"""!
13
801.3
0.1541"""!
14
801.4
0.1701"" "
71
Figure 4.14: Graph of first order power from minimum RF power to maximum RF power
The increased of RF power will increase the efficiency of the interaction which in good agreement with Equation 2.9. By increased the acoustic driving power will increase the Bragg angle of the AOM.
CHAPTER V
CONCLUSIONS AND SUGGESTIONS
5.1
Conclusions
The objectives of this study were successfully achieved, which will contribute to a better understanding of Acousto- optic modulator.
A study on fibre coupled AOM using chalcogenide glass with refractive index of 2.6 has been done. This study focused on investigating the characteristics of AOM. The theory and working principle of AOM and other equipment in the experimental set up.were studied. The relationship between driving voltage from RF driver and output power from modulator was determined and the sensitivity of several light sources was carried out.
For the preliminary study, the 1550 nm light source was connected to the AOM and a fixed voltage of 13V from the dc power supply was applied to the RF driver. The driving frequency (RF frequency) for the AOM was 40 MHz. A pulse generator was used to generate the desired pulse with different pulse width at different pulse rate. The digital oscilloscope was connected to the RF driver to observe the driving voltage. The power meter was used to measure the output optical power and an infrared fiber optic spectrometer was used to display the spectrum.
The results shows as the driving voltage increased the output voltage increased reaching the value of -8.25 dBm. The increase in driving power will increase the efficiency
73 of the interaction which is in good agreement with theory as indicated in Equation 2.7. The peak value of the output power optical power is 1556 nm which is similar to the input wavelength. Data from the spectrometer showed that there is increase in the area of the spectrum with optical power output.
For the experimental set-up, Experiments were done in order to determine the polarization of the laser beam. Second, it is to investigate the relation between the type of input signals and output signals. It is also did to determine the change of output amplitude on varying the amplitude of input signals and also to measure the change of the first order power when the Radio Frequency power were increased.
The tunable HeNe laser with 632.8nm wavelength was used as the main light source. Light from the laser at certain wavelength was sent through the AOM with refractive index of 2.6. The 80 MHz driving frequency was used for the AOM the was precisely aligned at the Bragg angle, B to deflect the light beam. The angle of deflection of light was depending on the frequency of the sound wave (RF frequency) generated by the AOM Driver. The output signal was detected by using different detector system, namely a CCD Laser Beam Profiler to measure the beam profile, a photodetector (PDA 55) to measure the optical signal and a power meter to measure the optical output power.
Beam profile measurement have shown significant different between original light beam and modulated beam. The profile shows the beam have been diffracted into zero and first order. After modulation two spot were appeared in both two and three dimensional images. The size of the diffracted beam is smaller than the original beam. The increase in driving frequency (RF frequency) will increase the distance between zero order beam and first order diffracted beam (horizontal shifting), z which is in good agreement with theory.
Further analysis was carried out from the output optical signal with the input amplitude were varied in the range 199mV to 870mV. It can produced output signal which have the same waveform like the input signal and the intensity of reflected signal is proportional to the incident light signal. There is no change in output signal patent. The
74 output amplitudes were decreased when the input amplitude increased. For input amplitude more than 244 mV, there is no output produced by the modulator. The maximum value of input amplitude is 196 mV, where output signal still have the same waveform like the input signal. The power of first order will increase when the RF Power is increase. There are also the limitations of power in order to produce the desired signal. The minimum first order power to produce output nearly same like input signal where the diffraction of input signal was occurred, is 0.076 mW. If the RF power is less than this value, the diffraction of light was does not occurred because the sound field does not produced any grating or the size of grating is too small. So, the diffraction occurred at the very small angle and difficult to differentiate between the first order diffraction and zero order diffraction.
5.2
Suggestions
The experiment room is not fully shielded from external source. Light from surrounding may enter an AOM and LBP when reading is collected although background light has been shielded.
The incident light is not 100% go through into an AOM. Reflection by the surface may occur. This will cause the loss of transmitting light.
The future works of this project are the system of the AOM will be improved by recondition of output beam to get the good shape of beam.
75
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85 APPENDIX A The spectrums from the spectrometer
(a)Vpeak to peak ( 0.01 Volt) = 21.83
b)Vpeak to peak (0.01 Volt) = 19.16
Output Power (0.01 dBm) = -10.07
Output Power (0.01 dBm) = -11.07
86
(c)Vpeak to peak ( 0.01 Volt) = 17.16
(d)Vpeak to peak (0.01 Volt) = 15.16
Output Power (0.01 dBm) = -12.07
Output Power (0.01 dBm) = -13.07
87
(e)Vpeak to peak ( 0.01 Volt) = 13.50
Output Power (0.01 dBm) = -14.07
(f)Vpeak to peak (0.01 Volt) = 12.00
Output Power (0.01 dBm) = -15.07
88
(g)Vpeak to peak ( 0.01 Volt) = 10.83
(h)Vpeak to peak (0.01 Volt) = 9.83
utput Power (0.01 dBm) = -16.07
Output Power (0.01 dBm) = -17.07
89
(i)Vpeak to peak ( 0.01 Volt) = 8.83
Output Power (0.01 dBm) = -18.07
(j)Vpeak to peak (0.01 Volt) = 8.00
Output Power (0.01 dBm) = -19.07
90
(k)Vpeak to peak ( 0.01 Volt) = 7.16
Output Power (0.01 dBm) = -20.07
(l)Vpeak to peak (0.01 Volt) = 6.50
Output Power (0.01 dBm) = -21.07
91
(m)Vpeak to peak ( 0.01 Volt) = 5.83
Output Power (0.01 dBm) = -22.07
(n)Vpeak to peak (0.01 Volt) = 5.33
Output Power (0.01 dBm) = -23.07
92
(o)Vpeak to peak ( 0.01 Volt) = 5.00
Output Power (0.01 dBm) = -24.07
93 APPENDIX B Three types of output signal at input frequency 100 Hz to 1.8 kHz Input frequency (Hz)
Square wave
Triangle wave
Sine wave
102.4Hz
102.9Hz
102.2Hz
196.1Hz
196.9Hz
196.9Hz
392.1Hz
394.3Hz
392.5Hz
598.1Hz
601.0Hz
598.1Hz
100
200
400
600
94 Input frequency (Hz)
Square wave
Triangle wave
Sine wave
783.6Hz
786.6Hz
783.7Hz
1.012kHz
1.016kHz
1.014kHz
1.223kHz
1.232kHz
1.238kHz
1.435kHz
1.441kHz
1.433kHz
800
1k
1.2k
1.4k
95 Input frequency (Hz)
Square wave
Triangle wave
Sine wave
1.693kHz
1.647kHz
1.639kHz
1.827kHz
1.838kHz
1.825kHz
1.6k
1.8k
96
APPENDIX C Least Square Method- Equations
Calculation was using the equation as below: m
1 N xi yi xi yi
c
1 N xi2 yi xi xi yi
y interseption, c
Delta
N xi2 xi 2
Slope uncertainties, m
m N
2
- c
c
2 xi2
Graph Equations
By substitutes the value in the equation, the graph equation for all graphs are as below:
Square wave Graph f out 1.03 0.06 fin 13 6 Where,
m 1.03 0.06
97 c 13 6
Triangle wave Graph fout 1.031 0.006 fin 13 6 Where,
m 1.031 0.006
c 13 6
Sine wave Graph fout 1.024 0.006 fin 11 7 Where,
m 1.024 0.006
c 11 7
X(fin)
Y(fout)
100.0 200.0 400.0 600.0 800.0 1000.0 1200.0 1400.0 1600.0 1800.0 2000.0
102.4 196.1 392.1 598.1 783.6 1012.0 1223.0 1435.0 1639.0 1827.0 2036.0
x2 1.000E+04 4.000E+04 1.600E+05 3.600E+05 6.400E+05 1.000E+06 1.440E+06 1.960E+06 2.560E+06 3.240E+06 4.000E+06
y2 1.05E+04 3.85E+04 1.54E+05 3.58E+05 6.14E+05 1.02E+06 1.50E+06 2.06E+06 2.69E+06 3.34E+06 4.15E+06
xy 1.02E+04 3.92E+04 1.57E+05 3.59E+05 6.27E+05 1.01E+06 1.47E+06 2.01E+06 2.62E+06 3.29E+06 4.07E+06
mx+c 9.000E+01 1.930E+02 3.990E+02 6.050E+02 8.110E+02 1.017E+03 1.223E+03 1.429E+03 1.635E+03 1.841E+03 2.047E+03
y-mx+c 1.24E+01 3.10E+00 -6.90E+00 -6.90E+00 -2.74E+01 -5.00E+00 0.00E+00 6.00E+00 4.00E+00 -1.40E+01 -1.10E+01
(y-mx+c)2 1.54E+02 9.61E+00 4.76E+01 4.76E+01 7.51E+02 2.50E+01 0.00E+00 3.60E+01 1.60E+01 1.96E+02 1.21E+02
