Integrated high-power electro-optic lens and large-angle deflector Kevin T. Gahagan, David A. Scrymgeour, Joanna L. Casson, Venkatraman Gopalan, and Jeanne M. Robinson

We present a theoretical discussion and experimental demonstration of what to our knowledge is a novel integrated electro-optic lens and beam deflector fabricated in lithium tantalate. The cylindrical lens collimates Gaussian beams as small as 4 ␮m in diameter, whereas the independently controlled deflector is capable of scanning the collimated beam through an angular range of nearly 20°. © 2001 Optical Society of America OCIS codes: 130.3120, 160.2100, 220.4000.

1. Introduction

Integrated micro-optical devices based in ferroelectric materials offer advantages for applications including optical data storage, communications, and optical computing. A variety of techniques for embedding optical waveguides and microengineering the ferroelectric domain structure have led to variable power lenses, beam deflectors, gratings, filters, frequency-conversion devices, interferometers, beam routers, multiplexers, and modulators.1–12 The rapid intrinsic electro-optic response 共gigahertz兲 and minimal leakage current 共nanoamperes兲 of these materials allow efficient high-speed operation in comparison with mechanical or liquid-crystal devices. In addition, large inexpensive wafers are available as substrates. Many optical systems, such as interconnects, scanners, and optical read–write heads, require the ability to rapidly control both the focusing and the deflection of a light beam. It is also useful to perform these functions on light exiting a waveguide or microcavity 共i.e., vertical-cavity surface-emitting lasers兲. Here we demonstrate a novel electro-optic deWhen this research was performed, K. T. Gahagan, J. L. Casson, and J. M. Robinson were with the Los Alamos National Laboratory, Los Alamos, New Mexico 87545. D. A. Scrymgeour and V. Gopalan were with Pennsylvania State University, University Park, Pennsylvania 16802. K. T. Gahagan 共gahagankt@ corning.com兲 can be reached at SP-AR-01-1, Corning Incorporated, Corning, New York 14831. Received 1 December 2000; revised manuscript received 13 July 2001. 0003-6935兾01兾315638-05$15.00兾0 © 2001 Optical Society of America 5638

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vice that integrates a high-power electro-optic collimating lens and a large-angle electro-optic beam deflector in a bulk single-crystal LiTaO3 wafer. The lens is capable of collimating light exiting from waveguides with diameters ranging from 4 to 40 ␮m. The collimated light is then deflected over an angular range of nearly 20° by the independently controlled deflector. The angular scan range of this device exceeds previously reported electro-optic continuous deflector performance characteristics by nearly a factor of 5 共Refs. 11 and 12兲 and is competitive with mechanical scanning systems. 2. Design and Fabrication

The refractive index of a ferroelectric linear electrooptic material in the presence of an applied electric field E is n共E兲 ⫽ n e ⫾ ⌬n ⫽ n e ⫺ 共1兾2兲n e3r 33 pˆ 䡠 E,

(1)

where ne is the linear refractive index of the medium, r33 is the electro-optic coefficient, and pˆ is a unit vector in the direction of the spontaneous ferroelectric polarization. The refractive index increases 共decreases兲 for an electric field antiparallel 共parallel兲 to the direction of spontaneous polarization. Domain poling techniques3,4 can be used to create a patterned ferroelectric domain structure. In the technique used here, a pulsed field exceeding the coercive field Ec of the material is applied to a set of shaped electrodes to selectively flip the spontaneous polarization in the desired regions. To operate the device, a uniform field is then applied across the patterned region, inducing a total refractive-index change of 2⌬n at the domain walls. To avoid destroying the domain

Table 1. Dimensions of Lenslets in the Collimating Lens Stack

Fig. 1. 共a兲 Diagram of a single biconvex lens of diameter D and radius of curvature R. 共b兲 Lens power per unit length for a biconvex lens as a function of the ratio of the radius of curvature to diameter. 共c兲 Diagram of the ferroelectric domain structure for the electro-optic lens portion of the integrated device.

structure, the device must be operated at or below the coercive field 共21 kV兾mm in LiTaO3兲. Thus to achieve a large absolute change in refractive index it is desirable to use a material with a high refractive index, a large electro-optic coefficient, and a high coercive field. This is in contrast to electro-optic modulators, which are operated at low field strengths well below Ec to achieve high modulation rates. The device described and demonstrated here consists of a lens component and a scanner component fabricated in LiTaO3. In typical operation, the lens component is used to collimate or focus light from a point-source or waveguide output. The collimated beam is then deflected by the scanner. The lens component consists of a 2.2-mm-long stack of biconvex parabolic lenses of varying diameters. To minimize the overall dimensions of the lens stack, it is useful to consider the lens power per unit length of a fixed-diameter biconvex lens as a function of the radius of curvature of the surfaces: ␾ 4⌬n 1 ⫽ , 2 2 l n e D C关C ⫺ 共C ⫺ 1兾4兲 1兾2兴

(2)

where D is the diameter of the lens, C ⫽ R兾D is the ratio of the radius of curvature to the diameter, and l is the length of the lens along the propagation axis. As shown in Fig. 1共a兲, ␾兾l rapidly approaches an asymptotic value of 4⌬n兾ne D2 for R ⬎⬎ D. Theoretically, if the separation between lenses in the stack can be made infinitesimally small, then the highest ␾兾l is achieved as C 3 ⬁ 共i.e., a gradient-index lens兲. Practical limitations on the number of lenses and a minimum lens separation distance of a few microme-

Lens Number

D兾2

Lens Number

D兾2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

50.0 50.0 50.0 50.0 50.0 50.0 50.0 50.0 50.0 50.0 50.9 53.5 56.2 58.7 61.2 63.5

17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

65.8 67.9 69.9 71.7 73.3 74.8 76.0 77.0 77.8 78.4 78.7 78.8 78.8 78.8 78.8 78.8

ters have led us to choose C ⫽ 1 for all the lenses in the stack. To reduce aberrations, the lenses were made parabolic, not cylindrical. For the C ⫽ 1 constraint, the parabolic curvature that approximates the cylindrical curvature in the paraxial region follows z ⫽ 共1兾D兲 x2. The procedure to optimize the diameter of each lens follows the general principle in which the diameter is monomized to be just large enough to accommodate an approximately Gaussian beam out of a waveguide of width 2w0. The diameter D of the first lens, located a distance s from the waveguide exit, is given by

冋 冉 冊册

D ⫽ 2r w w 0 1 ⫹

s z0

2 1兾2

,

(3)

where z0 ⫽ 1兾2kw02 and rw ⬃ 1.2–1.3 is a design variable describing how tightly the lens diameter is constrained to the 1兾e2 diameter of the beam. We designed the actual lens presented here assuming s ⫽ 250 ␮m and ␭ ⫽ 632.8 nm, with k ⫽ 2␲兾␭. From the dimensions of the first lens, subsequent lens diameters are determined by the ray matrix method13 to compute the beam diameter as it propagates through the lens stack. A minimum lens separation distance of ds ⫽ 5 ␮m and a refractive-index change across the domain wall of 2⌬n ⫽ 0.001 are assumed, consistent with a desired operating field of 7.6 kV兾mm to collimate a 4-␮m-diameter beam. In addition, a minimum lens diameter of 100 ␮m was chosen. The resulting lens stack 关see Fig. 1共b兲兴 has a total length of L ⫽ 2.2 mm and consists of 32 lenslets with the diameters given in Table 1. Optimization principles were also applied to the design of the scanner portion of the device. Here we followed the derivation presented by Chiu et al.14 to describe an idealized horn-shaped scanner with a slight modification. Lotspeich15 has shown that the deflection angle from a single prism can be approximated by ␪ ⫽ n 02r 33 E 共L兾D兲 , 1 November 2001 兾 Vol. 40, No. 31 兾 APPLIED OPTICS

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Fig. 3. Diagram of the ferroelectric device test apparatus. Fig. 2. BPM simulation of integrated device shown collimating a 4-␮m beam with the lens, then deflecting through an angle of ⬃10°. From the superimposed ferroelectric domain boundaries 共white lines兲, the split-horn design variation on a classical horn-shaped scanner can be seen.

where L is the length and D is the width of the device. A horn-shaped scanner follows the principle that each successive prism is just wide enough to accommodate the deflected beam. However, as the scanner widens toward the end of the horn, the additional deflection imparted by each successive prism is diminished. One way to improve performance is to split the prisms toward the end of the horn into pairs of prisms of equal width and approximately half of the width of the original horn 共see Fig. 2兲. By including the split in the scanner, we obtained as much as a 15% increase in the overall deflection angle compared with a horn-shaped scanner of the same length and entrance aperture. The penalty paid for this increased angular range is the introduction of a small amount of distortion to the beam when the scanner is operated at low voltages 共i.e., when the beam interacts with both sets of prisms in the split region.兲 We modeled the operation of the integrated lens and scanner device using a one-dimensional fast-Fouriertransform beam propagation method 共BPM兲.16,17 Figure 2 shows a simulation of a 4-␮m input beam being collimated by the lens, then deflected through an angle of 10°. A room-temperature in situ domain poling technique was used to pattern the ferroelectric domain structure to form the device. Briefly, a tantalum electrode forming a negative image of the device structure is lithographically deposited on the top surface of a 290-␮m-thick LiTaO3 crystal. Domain nucleation and growth in the patterned region are observed as a poling field 共E ⬵ 21 kV兾mm兲 is applied between the tantalum film and a transparent electrode on the bottom surface of the crystal.18 Once the desired domain structure is achieved, the tantalum film is removed and two pairs of rectangular electrodes covering the entire lens and scanner regions are lithographically deposited. Copper tape leads are attached to the electrodes with silver paste, and then the entire device is coated in roomtemperature vulcanizing silicone to prevent dielectric breakdown during operation. 3. Testing

The lens and scanner portion were tested independently. A schematic of the experimental setup is shown in Fig. 3. The 632.8-nm output of a He–Ne laser is collimated and then line focused onto the 5640

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entrance face of the crystal with a f ⫽ 100-mm cylindrical lens. The beam entering the crystal has Gaussian diameter dimensions of approximately 8 ␮m 共wide兲 ⫻ 200 ␮m 共high兲. Both the sample and an imaging CCD camera were mounted on separate precision translation stages. To characterize the lens performance, we first characterized the location and diameter of the input beam by recording a series of images over a range of distances from the waist. A least-squares fit to the measured beam diameter as a function of distance was performed to determine the input beam parameters. The device was then inserted, and a similar set of images was recorded for a range of distances between the input waist and the sample entrance face di 关see Fig. 4共a兲兴. The location and diameter of the output waist, located a distance do from the output face of the sample, along with the known distance

Fig. 4. 共a兲 Ray matrix diagram for analysis of lens performance. The input waist is located a distance di from the entrance face of the crystal. A transfer matrix M is calculated from known device geometry. 共b兲 Measured values of output beam waist versus di 共circles兲 plotted with a theoretical fit from ray matrix calculations.

Fig. 6. Representative beam profiles as a function of applied voltage for selected voltage levels.

Fig. 5. Measured deflection angle versus applied voltage for the scanner component of the integrated device.

from the lens to the output face of the crystal ds, are then used to calculate a ray transfer matrix M for the lens at a given operating voltage. This matrix can then be compared with a set of ray matrix parameters computed directly from the known geometry of the lens stack and the applied voltage. We found the measured parameters to be extremely sensitive to the measured input waist diameter and caused difficulty in the fitting procedure. By treating the input waist as the single adjustable parameter in the fitting procedure, we achieved a more reasonable fit. The fitted waist diameter of 9.1 ␮m differed by only 10% from the initial measured value of 8.0 ␮m. Figure 4共b兲 plots the measured output beam waist diameter as a function of the input waist to sample distance di for an applied voltage of 2.2 kV, along with a theoretical fit in which we used the calculated ray matrix parameters and assumed a fitted input waist diameter of 9.1 ␮m. The curvature in the theoretical curve, as compared with the apparently linear trend in the data, can be attributed to the tight constraints placed on the fit 共i.e., only a single adjustable parameter兲. The dependence of the scanner deflection on voltage was measured for a range of voltages from ⫺3 to 4 kV. We measured the deflection angle at each voltage by recording the position of the centroid of the laser spot at two distant planes. Beam trajectories were then extrapolated from these two points. Figure 5 plots the result of these measurements yielding an angular dependence of 36.5 ⫾ 5 mrad兾kV. This is slightly lower than the predicted value of ⬃40 mrad兾kV from BPM simulations, but is within the experimental uncertainty attributed to the uncertainty in the crystal thickness and electro-optic coefficient. It was observed that hand polishing of the end faces of the crystal imparted a surface curvature. Measurements of the deflection angle of a reflected beam as a function of surface position reveal an approximately cylindrical curvature of radius of 785 ⫾ 20 mm. This curvature will tend to reduce the external scan angle by 1–2% compared with theoretical calculations that assume a flat surface. It should be noted that, in principle, the relatively

large operating voltages required to access the entire scan range can be reduced by use of thinner bulk crystals, ferroelectric thin films, or other poled ferroelectric materials in which domain patterns can be formed. For example, a device fabricated in a 50␮m-thick crystal would require a total voltage range of ⫾750 V to achieve the ⫾15-kV兾mm maximum electric field range of the device. Similarly, use of a thin film with ⬃2-␮m electrode separation distance will require ⫾30-V applied voltage to utilize the entire scan range of the device design. As shown in Fig. 6, excellent beam quality is maintained over a range of almost 140 mrad. Distortion from the split-horn portion of the scanner 共not shown兲 was found to be minimal within ⫾100 V of zero and above ⫾400 V. However, between ⫾100 and 400 V, the distortion was severe with part of the profile reflecting in the opposite direction from the intended deflection. This degree of distortion was too large to permit meaningful deflection measurements and was greater than predicted by BPM simulations. This may be attributed to a slight misalignment of the scanner with the input beam axis and to domain wall overshoot in the poling process along the scanner axis in the split region. Both of these conditions would affect the range and severity of interaction of the deflected beam with the split region. Misalignment is also the likely cause of the slight increase in waist diameter observed at ⫺1200 and ⫺1900 V. Although we did not measure the insertion loss of this device directly, similar devices 共albeit with slightly fewer interfaces兲 are commercially available with insertion losses of ⬍5%.19 Typically, these commercial devices are antireflection coated for a specific wavelength range of interest. In our case, a nominal loss of ⬃25% from the uncoated entrance and exit faces is expected. Fresnel reflections applied to the domain boundaries contribute at most a 1–2% additional loss to the total. However, if residual strain at the boundaries is not annealed properly, scattering losses could increase the total loss considerably. 4. Conclusion

We have presented a theoretical and experimental analysis of the operation of a novel integrated electrooptic lens and beam deflector. The lens, consisting of a stack of 32 biconvex parabolic lenslets, was experimentally capable of collimating light from a 9.1␮m-diameter spot to a beam ⬃60 ␮m in diameter. The beam is then deflected by an integrated splithorn deflector consisting of a series of electro-optic 1 November 2001 兾 Vol. 40, No. 31 兾 APPLIED OPTICS

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prisms through an angular range of 18.9°. This scan range is nearly five times the previously reported highest range for a continuous-scanning electro-optic deflector and may provide a faster, more mechanically robust alternative to galvanometer-type and other mechanical scanning systems for some applications. References 1. K. Mizuuchi and K. Yamamoto, “Highly efficient quasi-phasematched 2nd-harmonic generation using a 1st-order periodically domain-inverted LiTaO3 wave-guide,” Appl. Phys. Lett. 60, 1283–1285 共1992兲. 2. Q. B. Chen, Y. Chiu, D. N. Lambeth, T. E. Schlesinger, and D. D. Stancil, “Guided-wave electro-optic beam deflector using domain reversal in LiTaO3,” J. Lightwave Technol. 12, 1401– 1404 共1994兲. 3. C. Baron, H. Cheng, and M. C. Gupta, “Domain inversion in LiTaO3 and LiNbO3 by electric-field application on chemically patterned crystals,” Appl. Phys. Lett. 68, 481– 483 共1996兲. 4. C. Baron, H. Cheng, and M. C. Gupta, “Periodic domain inversion in ion exchanged LiTaO3 by electric field application,” in Nonlinear Frequency Generation and Conversion, M. C. Gupta, W. J. Kozlovsky, and D. C. MacPherson, eds., Proc. SPIE 2700, 118 –121 共1996兲. 5. V. Gopalan, M. J. Kawas, M. C. Gupta, T. E. Schlesinger, and D. D. Stancil, “Integrated quasi-phase-matched 2nd-harmonic generator and electro-optic scanner on LiTaO3 single-crystals,” IEEE Photon. Technol. Lett. 8, 1704 –1706 共1996兲. 6. J. Li, H. C. Cheng, M. J. Kawas, D. N. Lambeth, T. E. Schlesinger, and D. D. Stancil, “Electro-optic wafer beam deflector in LiTaO3,” IEEE Photon. Technol. Lett. 8, 1486 –1488 共1996兲. 7. M. Yamada, M. Saitoh, and H. Ooki, “Electric-field-induced cylindrical lens; switching and deflection devices composed of

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