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Principles of fiber optics technology

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1.1. Spectrum of light Light travels as an electromagnetic wave through a vacuum at a speed of c0 = 299,792.458 km/s. The spectrum of light spans a wide range from deep ultraviolet (UV) (wavelength λ = 100 nm) to the infrareds (IR) (λ = 200 mm), although visible light only occupies the range from 380 nm to 780 nm. Different types of optical waveguides are used at different wavelengths depending on their transmission properties. The majority of waveguide applications extends from the near UV (300 nm and above) to the low IR range.

Cosmic radiation

In a homogeneous medium, light travels in a straight line and is described by the laws of geometric optics. Geometric optics can also be used to explain the propagation behaviour in large waveguide structures, where there are many possible directions in which the light can travel (see Chapter 1.2.). However, as waveguide structures become ever smaller, the propagation of light can only be explained in terms of wave theory. The following chapters will describe the fundamental physical properties of those waveguide components manufactured by LEONI.

Visible light

TT radiation

UV radiation

IR radiation Microwaves, radar

X-rays 1020

Frequency (Hz)

1018

1016

1014

1012

250 THz

Wavelength (m)

Radio waves TV

1010

(1 THz)

VHF 108

(1 GHz)

SW 106 (1 MHz)

(1 pm)

(1 nm)

(1 µm)

(1 mm)

(1 m)

(100 m)

10-12

10-9

10-6

10-3

100

106

λ = Wavelength f = Frequency

C0 = 300,000 km/s C=λ*f

Ultraviolet radiation (UV) 0.2

Visible light (VIS) 0.4

0.6

0.8 650

780

1.0 850

940

1.2 1300/1310

POF PCF

1.4 1550 1625

Far infrared (FIR) 3.0 2940

MIR/FIR fibers GOF

UV – VIS VIS – IR

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Medium infrared (MIR)

Near infrared (NIR)

20

µm

Principles

1. Optical waveguides in general

Principles

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1. Optical waveguides in general

1.2. Propagation of light in an optical waveguide The basic principle of transmission in an optical waveguide is based on total internal reflection.When a light ray hits the boundary surface between a more optically dense medium with the refractive index n1 and a less optically dense medium with the refractive index n2, the ray is either refracted or totally reflected, depending on the angle of incidence α. sin α / sin β = n1 / n2 (α = angle of incidence, β = angle of reflection, n1 = refractive index of the more optically dense medium, n2 = refractive index of the less optically dense medium)

At the transition between the more optically dense medium and the less optically dense medium, the ray is refracted away from the perpendicular and a portion of the light, which increases with an increasing angle of incidence, is reflected at the boundary surface.The greater the angle at which the ray of light strikes the boundary is, the closer the refracted ray is to an angle of β = 90° towards the perpendicular of incidence. With an even greater angle of incidence of the light ray, instead of being refracted the ray is totally reflected. Above a certain angle the ray of light is reflected in its entirety; this angle is known as the critical angle of total internal reflection.The actual size of the critical angle of total internal reflection is a function of the difference between the refractive indices of the more optically dense medium and the less optically dense medium.

Total reflection in step-index profile - optical waveguide α critical

θ critical n0

1.3. Numerical aperture The numerical aperture is a crucial variable for the coupling of light into an optical waveguide. It is calculated from the difference between the refractive indices for the core and the cladding. The numerical aperture NA is calculated using the sine of the critical angle θcritical as follows:

n2 n1

Only those rays of light that enter the fiber within a certain range of angles ≤ θcritical are guided along the fiber. Typical values of the NA for commercial fibers are in the range from 0.1 to 0.5, corresponding to an acceptance angle of between 6 and 30°.

NA = sin θcritical = √(n12 – n22) NA = 0.37 ≈ α/2 = 21.72° NA = 0.29 ≈ α/2 = 16.86° NA = 0.22 ≈ α/2 = 12.71° NA = 0.20 ≈ α/2 = 11.54° NA = 0.15 ≈ α/2 = 8.63° NA = 0.10 ≈ α/2 = 5.74°

Typical acceptance angles of commercial glass fibers

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1. Optical waveguides in general

1.4. Under-excitation, over-excitation When light is launched into an optical waveguide, it often occurs that not all modes are excited equally. The critical angle or diameter of the incident ray often differs from the fiber parameters. Part of the ray which has an angle greater than the critical angle leaks out of the fiber and power is lost. This is known as over-excitation. In contrast, under-excitation is when the angle is smaller than the critical angle, i.e. the crosssection of the ray is smaller than the diameter of the core. When using gradient-index fibers (see Chapter 2.1.3.), marginally greater path attenuation values are achieved even with under-excitation. 1.5. Joining two fibers Two fibers can been joined together either by connecting the end faces of two fibers permanently, known as splicing, or by connecting two connectors in a coupling. Two identical connector types can be joined in a standard coupling and two different connectors can be joined in a hybrid coupling. The connection with the least influence (attenuation) on the guided light is a ‘fusion splice’, in which the two fiber ends are precisely aligned and then fused together using an electric arc.

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Principles

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Principles

2. Fiber types In LEONI’s product portfolio, a basic distinction is made between two types of fiber optic component: a) components in which the light is guided by an isolated fiber, and b) components in which the light is guided by a bundle of fibers. Individual fiber components also include components in which multiple buffered fibers are assembled in one cable. Individual fibers will be described first in the following sections, although certain fundamental properties also apply to fiber bundles. This will be followed by a specific description of the properties of fiber bundles.

The most commonly used singlemode fiber is the telecommunication fiber, which has a mode-field diameter typically of 9 to 10 µm and a cladding diameter of 125 µm.The light is guided primarily in the mode-field diameter, but with a small part being guided outside the actual core in an area of the cladding close to the core.The mode-field distribution corresponds to a Gaussian curve. The actual core diameter is usually 8.2 µm with a NA of 0.14.The singlemode transmission properties of a standard telecommunication fiber span a spectral range from 1280 to 1650 nm.The critical wavelength from which on a second mode is capable of being propagated is called the cut-off wavelength and is approximately 1260 to 1280 nm for a standard telecommunication fiber.

2.1. Individual fibers The illustration below shows the most important basic types of optical fiber: ■■ Multimode fiber with step-index profile ■■ Multimode fiber with gradient-index profile ■■ Singlemode fiber V = Const

Beam with longest delay time

r

θcritical

0

Core Cladding

n

Step-index profile

r

Beam with shortest delay time V2 > V1

θcritical

Utmost cleanliness of the fiber material (fused silica glass/doped silica glass) is a priority during the manufacture of standard telecommunication fibers in order to achieve maximum transmission.The typical attenuation of a modern singlemode fiber for telecommunications is 1310 or 1550 nm at Δf = 100 GHz corresponds to Δλ ≈ 0.8 nm in the third optical window. Standardised wavelength grid for a channel spacing of 100 GHz: fn = 193.1 THz + n x 0.1 THz, where n is a positive or negative integer (including zero).

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Principles

Physical definitions and formulae

286

Principles

Symbols and units of measure Symbols/units of measure

Definition

a

P

power in mW

P0

injected power

attenuation in decibels

PMD1

first-order PMD coefficient

a’

attenuation in neper

ps

picoseconds

a12 / a21

levels in a backscatter diagram in decibels rK

core radius in µm

B

bandwidth in GHz

R

bit rate in Gbit/s

BLP

bandwidth-length product in MHz km

R

reflection

RL

return loss: reflection attenuation in decibels

CR

coupling ratio  

d

radial misalignment in µm

s

axial misalignment in µm

D

directivity: cross-talk attenuation in decibels

S

D

chromatic dispersion in ps/nm

increase in the coefficient of chromatic dispersion in ps/nm2∙km)

D CD

coefficient of chromatic dispersion in ps/(nm∙km)

S0

DMAT

coefficient of material dispersion in ps/(nm∙km)

increase in the coefficient of chromatic dispersion at the zero-dispersion wavelength

S0max

maximum increase in the coefficient of chromatic dispersion at the zero-dispersion wavelength

T

pulse width

T

transmission

U

uniformity in decibels

v

propagation velocity in km/s

V

V number

VC

normalised critical frequency

w

mode-field radius

Z

number of modes that can be propagated

α

attenuation coefficient in dB/km

α

angle between incident ray and perpendicular

αcritical γ

critical angle of total internal reflection

η

coupling efficiency

λ

wavelength in nm

λ0

zero-dispersion wavelength in nm

λ0max

maximum zero-dispersion wavelength

λ0min

minimum zero-dispersion wavelength

λC Δλ

cut-off wavelength in nm

µm

micrometre

θcritical τ

maximum allowable angle of inclination to the optical axis

ΔτCD 〈Δτ〉

pulse spreading due to chromatic dispersion in ps

DWAV

coefficient of wavelength dispersion in ps/(nm∙km)

dB

decibel

dBm

unit of logarithmic power based on a milliwatt

dB/km

unit of attenuation coefficient

EL

excess loss in decibels

f

frequency in hertz

g

profile exponent

Gbit

gigabit

GHz

gigahertz

HWB

full width at half maximum

Hz

hertz

I

isolation in decibels

IL

insertion loss in decibels

km

kilometre

L

length in kilometres

m

metre

mW

milliwatt

n

refractive index

n0

refractive index of the medium between the end faces

nK

core refractive index

nM

cladding refractive index

NA

numerical aperture

nm

nanometre

tilt angle

spacing between adjacent wavelengths

group delay per unit of length in ps/km PMD delay in ps

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Term

Definition

Absorption  

Loss of light radiation when passing through matter as the result of conversion into other forms of energy, e.g. heat energy. With photodiodes, the absorption is the process that destroys a photon as it arrives and through its energy elevates an electron from the valence band to the conduction band.

Acceptance angle  

The largest possible angle within which light in the area of the fiber core can impinge on the end face, thus enabling it to be guided along the fiber core.

Add-Drop-Multiplexer

Functional module that makes it possible to add and drop partial signals to/from a multiplex signal.

Amplified spontaneous emission  

Amplification of spontaneous events in an optical amplifier when the input signal is missing. Causes the characteristic noise of the fiber amplifier.

Analyser

Component for checking the state of polarisation of the light. Differs from a polariser only with regard to its function in the selected optical design. The analyser is located on the observer side.

Bend loss  

Additional loss caused by micro- or macro-bending. An increased bend loss may be caused by the manufacture of the cable or by poor cable routing.

Bending radius  

Two different definitions: 1. Minimum radius of curvature by which a fiber can be bent without breaking. 2. Minimum radius of curvature by which a fiber can be bent without exceeding a certain predetermined attenuation value.

Bidirectional  

Propagation of optical signals in opposing directions along one optical waveguide.

Birefringence  

Property by which the effective propagation velocity of the light wave in a medium depends on the orientation of the light’s electrical field (state of polarisation).

Bit  

Basic unit of information in digital transmission systems. The bit is equivalent to the decision between two states, 1 and 0. Bits are represented as pulses. A group of eight bits is equal to one byte.

Bit error rate  

The ratio of the number of bit errors occurring on average in digital signal transmission over a relatively long period of time to the number of bits transmitted during this period. The bit error rate is a systemspecific index of error probability. The standard requirement is a BER