Low-loss polynomial White cell optical true-time delay engine for wideband radio frequency array beam steering

Transcription

1 Low-loss polynomial White cell optical true-time delay engine for wideband radio frequency array beam steering Niru K. Nahar* and Roberto G. Rojas Department of Electrical and Computer Engineering, The Ohio State University, 2015 Neil Avenue, Columbus, Ohio 43210, USA *Corresponding author: osu.edu Received 16 March 2009; revised 12 June 2009; accepted 15 June 2009; posted 16 June 2009 (Doc. ID ); published 2 July 2009 An optical true-time delay (OTTD) engine based on a polynomial White cell (quadratic) is designed and simulated with commercially available components with a time delay increment of at least 25 ps for wideband beam steering in the frequency range of 2 18 GHz. The simulated quantification of aberration losses show for the first time that aberration losses in the null cell are about 5:0 db. However, for the longer delay arms, there is an additional loss of about 3:2 db=delay each time a beam travels an arm with a lens train used as a delay element compared with the same delay generated without a lens train. We present a design and simulation of a low-loss delay arms quartic cell without a lens train by using a separate field lens for each delay arm for efficient wideband beam steering Optical Society of America OCIS codes: , Introduction Optical true-time delay (OTTD) techniques are promising for squint-free beam steering of RF/ microwave phased array antennas (PAAs) that have wide frequency bandwidth (e.g., 2 18 GHz), are compact in size, lightweight, and are not prone to electromagnetic interference. Even though free-space OTTD systems have problems with collimation and loss, White cell [1] OTTD engines in combination with an array of micromirrors based on a microelectro-mechanical system (MEMS) have enormous potential for beam steering due to its minimal loss and scalability. White cell free-space OTTD can generate optical delays (by varying the length of the White cell arms) with very fine resolution [2]. Two types of White Cell OTTD engines, referred to as exponential and polynomial cells, have been demonstrated with one optical input beam/delay at a time [2,3]. For the polynomial cells [4] (e.g., the linear, /09/ $15.00/ Optical Society of America quadratic, quartic, and octic cells), the number of delays N is proportional to a power of the number of bounces m that the optical beam creates on an optical switching device, e.g., for a quadratic cell, N m 2 (see Fig. 1). Also in the polynomial cell, the switching engine to direct the beams into different path of the White cell and the delay engines are built as one single unit. Whereas, for the exponential cells [5] (e.g., binary and ternary cell), the lengths of the arms (attached to the switching engine) are the same, and the delays are created within a separate delay engine; on each bounce the MEMS switches the beam to a delay engine or a null path. Hence, the number of delays is proportional to some base number raised to the power of m, e.g., for a binary cell the number of delays grows as 2 m. In all White cell OTTD demonstrations to date, shorter delays (as small as 3 ps) have been produced using custom made glass blocks (also mounts), and lens trains have been used for longer delays (with mini mirrors for exponential cells) [3,4,6]. However, the shortest delay produced in free space (without any glass block) so far is 243 ps [6]. 10 July 2009 / Vol. 48, No. 20 / APPLIED OPTICS 3921

2 Fig. 1. Layout of the quadratic cell and its connectivity diagram (a) with and (b) without lens train. (c) Spot patterns of the input/output beams on the MEMS. However, the shortest delay needed for a wideband antenna array beam steering in the frequency range of 2 18 GHz is 50 ps. Previously, it has been shown that glass blocks do not produce as much material loss as the lens train in a White cell OTTD because the light beam travels through a fewer number of optical surfaces in a glass block than in a lens train [7]. Also, glass blocks cannot be used for delays longer than 125 ps due to the divergence of the beam as the block gets longer. On the other hand, we need at least two to three lenses to create a lens train. So, depending on the physical size and focal lengths of the lenses, there is a limitation on the minimum length of an optical path length we can create. Therefore, the shortest lens trains are too long to generate delays shorter than 500 ps [8]. Besides the loss, the glass blocks and the lens train make the White cell OTTD system bulky and expensive. This problem is circumvented in the exponential White cells by the use of large mode area photonic crystal fibers to create medium and longer delays [9], an approach not possible with polynomial cells because both the switching and the delay engines are built as one unit. Here, for the first time, to the best of our knowledge, we present a polynomial White cell designed to generate delays ( 50 ps) in free space (without using any glass blocks or lens train) that is suitable to demonstrate beam steering in the wideband frequency (e.g., 2 18 GHz). A typical overall White cell OTTD system for wideband beam steering is shown in Fig. 2. An IR laser generates an optical beam that is modulated by the RF signal by means of a modulator (Mach Zhender modulator). The microwave signal frequency can be generated by a Network analyzer Fig. 2. Schematic of an OTTD wideband beam steering system APPLIED OPTICS / Vol. 48, No. 20 / 10 July 2009

3 and varied from 2 to 18 GHz. The modulated optical signal is split into several signals (four in this case because we only had four photodetectors available) before it enters the TTD engine to produce four inputs for the four delays. At the output of the TTD engine, the four signals emerge with the proper delays and each signal is detected by a high speed photodetector. The outputs of the photodetectors are the delayed microwave signals, which can be fed to the network analyzer to measure the delays and thus test the accuracy and efficiency of the OTTD engine. Once the testing is completed, the desired delayed RF outputs are fed to the 4-element wideband antenna array (operating frequency 2 18 GHz) with high-quality coaxial cables to steer the beams. Any loss in the optical domain affects the efficiency of the system in the RF domain. Furthermore, it can result in a nonuniform excitation of the RF array elements. In other words, not all the signals will have the same magnitude. This could result in higher sidelobes and possibly a wider beam width. Misalignment and aberration losses in the OTTD engine for beam steering are two of the major important aspects to consider because the distorted and faint optical output beams will have less power when converted into RF signals. For a laboratory demonstration, the stability of the commercially available optical mounts available in our laboratory, in particular, the fixtures holding the input turning mirror (via which the input beams are brought into the OTTD) were marked as unreliable in the previous literature [6]. Therefore, optical mounts and fixturings with finer control and better accuracy will be helpful to reduce the misalignment loss in the White cell OTTD engine built with bulk optics. One current research and development effort (in industry) of White cell OTTD is concentrated in the microfabrication of the system. In other words, the whole system can be built in a dielectric volume with the MEMS mirrors being the only moving parts. This will be an excellent solution to the reduction of misalignment loss in the system. On the other hand, losses due to aberration in a White cell just by itself has been studied before [4,10]. However, losses due to the aberrations in a White cell OTTD with delay elements, such as lens trains, have not been studied to date. Therefore, the goals of this paper are to present the calculated material loss and the simulated aberration loss for each delay of the polynomial cells. The material loss includes both the reflection and transmission losses of the beam as it travels through the optical elements, such as the MEMS, lenses, and White cell mirrors. Furthermore, we present, for the first time to the best of our knowledge, a polynomial White cell designed to generate delays ( 50 ps) in free space without using any glass blocks or lens train. This system is suitable to demonstrate beam steering in the wideband frequency (e.g., 2 18 GHz). This newlydesigned polynomial cell makes use of commercially available optics and provides delays with equal minimized losses having separate field lenses for all the delay arms. It is important to note here that the main difference between the two polynomial cells we are discussing here is in the number of delays (N) they can produce with a certain number of bounces (m) on the MEMS. As an example, with six bounces the quadratic cell (N m 2 ) can produce 18 delays, whereas with the same number bounces, the quartic cell (N m 4 ) can produce 37 delays. In Section 2 we discuss the design and simulation results of a polynomial style (quadratic) White cell OTTD engine. We compare a quadratic cell that uses a lens train to produce long delays with one which does not use any lens train. Section 3 presents a design and analysis of a quartic cell with both short and long delays generated in free space and none of the delay arms share field lens with the other. The paper ends with conclusions in Section Low-Loss Quadratic White Cell A. Design of Quadratic Cell with MEMS The layout of two quadratic cells (for four simultaneous input beams) with and without a lens train along the long delay arm F is shown in Figs. 1(a) and 1(b), respectively. This cell has similar architecture as the quartic cell in [6] except for two fewer delay arms. The basic delay increment in a quadratic cell is m=2 because there are two delay arms in the cell, where m is the number of bounces for a beam on the MEMS surface. For a closed loop quadratic cell, a null cell consists of Mirror B and Mirror C, which have arms of equal length. There is a minimum delay increment of Δ as the beam goes from the null cell to the shortest delay arm E. Now if we go to arm E for m=2 times, then go to arm F, the delay assignment for this arm will be ðm=2 þ 2ÞΔ. For additional delays, the beam is directed into the delay arms E and/or F multiple times. Thus, the total number of delays, N, possible in this quadratic cell is m m N ¼ 2 2 þ 2 þ m 2 m ¼ þ m ð1þ 2 : ð1þ The connectivity diagram (permissible path to create desired delays) of the cell is shown in the upperleft corner of Fig. 1. The spot patterns of the input and output beams on the MEMS are shown in Fig. 1(c), where CCB and CCC represent the center of curvatures of the White cell mirrors B and C. The positioning of these centers of curvature determines the number of possible delays created in a White cell OTTD. In Fig. 1, the MEMS is shown in the left side and the field lens for the null/reference arms (BC) is labeled FLN. The delay arms (E and F) field lenses are labeled FLD1 and FLD2 for the short and long delays, respectively. In arm F, the system produces a conjugate image of the MEMS at the plane in 10 July 2009 / Vol. 48, No. 20 / APPLIED OPTICS 3923

4 Table 1. Delays and Free-Space Distances Along Each Arm of the Quadratic Cell Arm Mirror Bounce Delay (ps) d 0 (mm) d 1 (mm) d 2 (mm) d 3 (mm) Null CBCBC E once EBCBC E twice EBEBC F once CFCBC F LT once CFCBC between two lens train lenses (LT1 and LT2). This plane is used to bring in the input beam to the system and, once the delays are created, the output beams are relayed out of the system from the same plane. However, we must separate input and output arms (as shown in Fig. 1(a)) if there is no lens train along arm F. In that case, the input and output arms can be on two sides of the MEMS/cell. In this quadratic cell, we can have 18 different delays for six bounces. The delay arms of the quadratic cell are on two sides of the null arms to have closed loop connectivity among the cells. If the arms were on the same side of the null arms, we would have openloop connectivity because optical beams in a White cell are only allowed to travel from left to right (or top to bottom arm). This would require more bounces (10 bounces) to have the same number of delays, which would require a larger MEMS and may increase losses for the OTTD engine. In our design with 4 input beams, we use the MEMS that has a rectangular array with 100 μm square mirrors on a 250 μm pitch. Table 1 shows the desired delays of each arm and the free-space distances along the arms. Distance d 0 is between the MEMS and the field lens and d 1 is the distance between the field lens and the White cell mirrors, except for arm F with the lens train (LT) [Fig. 1(a)]. The field lens for arm F is the same as that of arm E when the delay is created with a lens train. If arm F does not have a lens train [Fig. 1(b)], it will use a different field lens to create the desired delay. All the optics used in these quadratic cell designs are commercially available and the details of the optical surfaces are tabulated in Table 2. The radii of curvature R of all four spherical mirrors are the same ( 750 mm). Table 2 also includes the central thickness t c of all the lenses used in the design. In the laboratory setup, arm E and F have to be folded using folding mirrors to accommodate the bulky housing of the MEMS and minimize the overall volume of the cell on the optics table. Next, we discuss results of the quadratic cell simulation done using the ray tracing software OSLO [11]. Table 2. Optical Surfaces of the Quadratic Cell Lens/Mirror R 1 (mm) R 2 (mm) t c (mm) B, C, E and F 750 FLN :8 5.0 ðfld1 and FLD2Þ LT LT : LT :0 8.3 FLD : B. Simulation of the Quadratic Cell A White cell is an off-axis optical system implying that some aberrations, especially astigmatism and coma, are unavoidable. Aberrations for both types of White cell OTTD systems without the delay elements have been studied before [4,5]. In this design, we use an input beam size of 25 μm to have a large enough beam to avoid divergence in free space and to capture 99.99% of the beam power on the MEMS pixels. Traditionally, the high speed InGaAs Schottky photodiodes (bandwidth of 25 GHz) used for the White cell OTTD system has a 25 μm diameter spot size as well. Once the delays are generated, the output beams might need to be demagnified to relay the beams onto the photodetectors without any power loss. The results of the aberration simulation of the quadratic cell for six bounces are tabulated in Table 3. The OSLO simulated aberration graphics for both the null arms and the shorter delay arm are shown in Fig. 3. Here, the ray analysis graphics [Fig. 3(a)] show the amount of coma (left), astigmatism (top-middle), and longitudinal spherical aberrations (top-right) for the null arms. The bottom-right of Fig. 3(a) shows the layout of the null cell in OSLO, which is comparable to the null cell (arms B and C) in Figs. 1(a) and 1(b). Figures 3(b), 4(a), and 4(b) show similar graphics for the shorter delay arm (arm E in Figs. 1(a) and 1(b)], the longer delay arm without lens train [arm F in Fig. 1(b)], and the longer delay arm with lens train (arm F in Fig. 1(a)], respectively. In Fig. 3(c) we also show the spotsize profile of the beam after six bounces. The vertical axis of Fig. 3(c) shows the object height normalized to one, and the horizontal axis represents the focus shift from the Gaussian image plane. We can see that the spot lies within the diffraction limited circle and there is almost no difference in the spot profile for all the object Table 3. Delay Arm Astigmatism and 3rd Order Seidel Spherical Aberration in the Quadratic Cell Delay (ps) Total Astigmatism (mm) 3rd Order Seidel SA Null (B and C) : Short (E) : Short (E twice) Long (F) Long ðfþ LT Long E and F : Long ðe and FÞ LT APPLIED OPTICS / Vol. 48, No. 20 / 10 July 2009

5 heights. The spot profile at the center (on axis) shows slight cometlike shape, which represents coma. As the spot experiences some focal shift, we can see positive and negative astigmatism and the spot shape becomes elongated instead of circular. In this quadratic cell design, we have used a meniscus lens as it was studied before, showing that this type of lens minimizes coma [4]. Therefore, the ray intercept graphics in all arms (on the left of Figs. 3(a) and 3(b), Figs. 4(a) and 4(b), and Figs. 5(a) and 5(b),) show negligible sagittal coma in the system. The layouts of the quadratic cell for the longest delay when a beam travels to both arm E and F, shown in Figs. 5(a) and 5(b), are comparable to the layouts of Figs. 1(a) and 1(b). The astigmatism graphics (on the left of Figs. 3(a) and 3(b), Figs. 4(a) and 4(b), and Figs. 5(a) and 5(b),) show the sagittal ( ) and tangential foci (þ), and the vertical axis is the position of the original object with respect to the optical axis, as a fraction of the object plane size normalized to 1. The horizontal axis is the distance in millimeters along the optical axis in the vicinity of the image. In general, astigmatism can be neglected as long as it is less than the depth of focus [5]. The depth of focus of this system is 2:533 mm, calculated using the beam size radius (25 μm) on the MEMS surface. As tabulated in Table 3, the astigmatism values show that astigmatism is two times higher for the longer arm with the lens train Fig. 4. Aberrations at the long arm for six bounces (a) without and (b) with a lens train. compared that with that of the longer arm without a lens train. The data for the longer arms with the lens train are denoted with LT subscripts. Fig. 3. Aberrations at (a) null arms, (b) shorter delay arm, and (c) spot profile after six bounces. Fig. 5. Aberrations along the long arm for six bounces going to both E and F once (a) without and (b) with a lens train. 10 July 2009 / Vol. 48, No. 20 / APPLIED OPTICS 3925

6 Table 4. Output Beam Size and Loss in a Quadratic Cell After Six Bounces Arm Delay (ps) ω y ðμmþ ω x ðμmþ Material Loss (db) Loss (db) Null (B and C) Short (E) Short (E twice) Long (F) Long ðfþ LT Long E and F Long ðe and FÞ LT The horizontal axis of the spherical aberration graphics is the longitudinal aberration (SA), i.e., the distance from the image surface to the intersection of the ray with the optical axis. The ordinate of the graph is the fractional pupil coordinate, ranging from 0 to 1. The 3rd order Seidel spherical aberration coefficients are tabulated also in Table 3, and we see that spherical aberrations are negligible for the null, short, and long arms (without the lens train). However, spherical aberration builds up for the lens train arm delays [see changes in the horizontal axis from 0.5 to 75 mm at top right of Fig. 4(a) to Fig. 4(b)] and for even the longer delays that require the beam to visit both delay arms E and F [comparing Figs. 5(a) and 5(b)]. Table 3 shows that the 3rd order SA coefficient for the free-space quadratic cell after six bounces is about a thousand times lower than that of the one with the lens train. Next, we examine the output beam size because spherical aberration causes the imaged beam to be blurred. Therefore, we do not expect the beam to be the same size (25 μm) and shape (circular Gaussian) after six bounces as the input beam we started with. Table 4 tabulates the skewed and magnified spot size of the output beam after six bounces in both vertical (ω y ) and horizontal (ω x ) axes. There are some unwanted ( 5 μm) magnifications in the skewed output beam size. Introduction of the lens train increases the output beam size and, hence, increases loss (which includes both material loss and coupling loss to the high speed photodetector) along the arms as well. The longer arm, if it consists of a lens train (LT), has about 3:237 db more loss than the arms without the lens train. Figure 3 to Fig. 5and Table 4 also show that, if we do not use any lens train, the loss per delay stays constant for both short and long delays. For example, loss for 1Δ (going to arm E once), 2Δ (going to arm E twice), 3Δ (going to arm F once), and 4Δ (going to arm E and F once) is around 1:8 db for material and 6:8 db for material and aberration combined. By comparison, in free space without any lens train added, there is about 4:9 db loss just due to aberration in all arms; with a constant material loss of 1:8 db. Once the lens train is included, the material loss increases only by 0:16 db; however, the aberration loss increases by 3:0 db. The material loss can be cut down with better antireflecting coating, and the aberration loss can be lowered by using free-form optics that correct the image distortions and reduce the optical element count in a system [12,13]. Fewer optical element counts also assure lesser misalignment and better reproducibility. 3. Low-loss Quartic White Cell An optical system is mechanically robust if the optical element count is as low as possible, the fixturings are stable, and the system is easy to align assuring the reproducibility of the results. In all the previous White cell OTTD demonstrations, mechanical stability was one of the major problematic issues [6,14]. Therefore, if we can design a White cell OTTD without glass blocks and lens trains, it will be more mechanically robust. Hence, this cell will also allow us to decrease aberration, material and misalignment losses, as well as the cost to build the cell. In terms of fixturing, there is not much that can be done other than coming up with more precise commercially available holders with finer tuning. As an example, in a quartic cell, Nαm 4, to create eight delays with glass blocks and lens trains as delay elements, the Table 5. Delays and Free-Space Distances in the Quartic Cell Delay Arm Delay (ps) d 0 (mm) d 1 (mm) Null (A and B) C E D F Fig. 6. OSLO simulated ray-trace schematic of a free-space quartic cell APPLIED OPTICS / Vol. 48, No. 20 / 10 July 2009

7 Table 6. Optical Surfaces of the Free-Space Quartic Cell Lens/Mirror R 1 (mm) R 2 (mm) t c (mm) D R (mm) D S (mm) A and B C D E F FLAB : FLC : FLD FLE : FLF material losses are about and 2:343 db, respectively. These delay elements also increase the optical element count in the White cell OTTD. Here we propose a quartic cell, Nαm 4, design unlike those in [2,6] without any delay elements (to change the optical path length) to generate both short and long delays. This design uses one field lens for the two null arms but will have separate field lenses for all the delay arms. Separate field lenses for the delay arms allow the system to use spherical mirrors with different radii of curvatures and, hence, create different delays in each arm in free space. Table 5 shows the possible delays and the freespace distances for the cell. Figure 6 shows the ray-trace schematic of the new quartic cell simulated in OSLO. Here the delays were picked to show that both very short and long delays can be produced with this system just by choosing different field lenses and spherical mirrors for each delay arm. Using a separate field lens and the White cell mirror will allow us to vary the optical path length of each delay arm independently. Fig. 7. Output of quartic cell after ten bounces: (a) ray-trace curves and (b) spot profile. Table 6 tabulates the radii of curvature, thicknesses, and the diameters of the field lenses and mirrors. In this table we also see that the calculated (using Maple) required diameters, D R, for the mirrors and lenses that satisfy the paraxial imaging condition are much smaller than the diameter used in the simulation, D S, because of the commercial availability of the lenses and their mounts. The diameters of the field lenses on the delay arms are half Fig. 8. Eight-element isotropic array: (a) broadside and (b) beam steering at 115 for Δt ¼ 25 ps. 10 July 2009 / Vol. 48, No. 20 / APPLIED OPTICS 3927

8 Fig. 9. Eight-element isotropic array beam steering with optical loss for Δt ¼ 25 ps: (a) at broadside and (b) scanned at 115. of the diameter of the null arms to make sure of the spacing in the actual laboratory setup. At the same time, the diameter of the lenses satisfies the condition that all the power of the beam goes through the field lenses. In this quartic cell, we can produce delays as small as 5 ps and as long as 2000 ps with only a total of 10 bounces. In Fig. 7, we present the quartic cell aberration losses after ten bounces with the ray-trace graphics [Fig. 7(a)] and the spot profile within the diffraction limited spot size [Fig. 7(b)], in the same manner we presented losses of the quadratic cell in the last section. The graphics show much smaller aberration losses for ten bounces compared to the six bounce quadratic cell with lens train described in Section 2. The astigmatism (top-middle of Fig. 7(a)] at the output is 1:268 mm. This is still an acceptable error because it is only half of the depth of focus of the system (2:533 mm). In this system we are using separate field lens for each arm so the 3rd order spherical aberration is much smaller (4:845e 7) than that of the quadratic cell. Considering the input beam radius of 25 μm, the output spot size along xðω x Þ and yðω y Þ axes are and 27:73 μm, respectively. The total loss of this quartic cell is only 6:833 db=delay. It is important to note here that in the earlier polynomial cells, delay arms consisting of the lens train were used as the entrance plane of the input to the cell and the exit plane of the output [6]. In this newly proposed quartic cell we do not have any lens trains. Therefore, we can bring the input beam (with required spot size) directly to the MEMS pixels at the location shown in Fig. 6 and the output beam exit plane is shown in the opposite side of the cell. As the input beam does not need to travel through the lens train for each delay, more delays can be produced with fewer bounces. Also, having separate input and output arms will allow us to fine tune the input/output beam sizes without disturbing the delay arm alignment as well as minimize any aberrations in the input/output beams. Therefore, all the arms of the polynomial cell will generate delays with beams of equal strength that are transformed from the optical domain to the RF domain of the antenna array. This will result in a uniform excitation of all the RF array elements. 4. Summary and Conclusions To illustrate how the losses in the optical system affect the RF array, we present some simulated beam steering. In Fig. 8 we show simulated results for a 4 element array (each element is a 2 element subarray). The interelement separation and the subarray element separation are 2.3 and 3:0 cm, respectively. In this case, we show the array factor which implies each antenna element is assumed to be an isotropic radiator. This simulation does not include any optical aberration or mutual coupling loss for the frequency range of 5 12 GHz at broadside. The table at the bottom of Fig. 8 shows the ideal and actual delays and the relative magnitude (in db) of the beams. In Fig. 8(a), the sidelobe level is about 13 db lower than the main beam at the frequency of 7 GHz. Here, the main beam is strong for the whole range of frequencies 5 12 GHz, and the strongest grating lobe appears at around 11 GHz. The major grating lobes on both sides of the main beam became tapered due to the additional cosine factor introduced by the subarrays. Figure 8(b) shows the case when the beam is scanned to an angle of 3928 APPLIED OPTICS / Vol. 48, No. 20 / 10 July 2009

9 115 for a delay step of 25 ps. The difference between the actual and ideal delay varies from 1.75 to 5:2 ps as the delay becomes longer. For the scanned beam, the difference between the main beam and the first sidelobe is about 9 db. The dotted vertical marker at left in Fig. 8(b) shows that the actual scan angle is 114 ; the discrepancy between the actual and the scanned angles is only 1. Next, we introduce the weighted optical loss (shown in the table at the bottom of Fig. 9) in Section 2 due to the lens train calculated in OSLO. The magnitude of the main beam is down about 6 db due to optical loss. At the frequency of 7 GHz for the case of no beam scanning (broadside), the grating lobe [shown in Fig. 9(a)] shows up at the same positions and at about the same level with the main beam as shown in Fig. 8(a). The sidelobe level is still approximately 13 db below the main beam. Once we scan the beam at 115 [Fig. 9(b)], the main beam magnitude goes down even further to a value of 13 db compared to the broadside case. There is only an 8 db difference between the main beam and the first sidelobe. As expected, the grating lobe level exceeds the main beam at this point. This simple example illustrates the effect that the optical losses can have in the RF array. We have presented the design of a low-loss truetime delay engine based on a polynomial White Cell optical true-time delay engine for application to beam steering of wideband RF antenna arrays. Instead of using conventional delay elements in the delay arms, the optical path length of the OTTD engine was varied in free space. This modification of the polynomial cells will decrease the material loss to about 0:16 db and aberration loss to about 3:2 db to create any long delay by eliminating lens trains. It was also shown that using separate lenses in each arm decreases the spherical aberrations drastically. References 1. J. White, Long optical paths of large aperture, J. Opt. Soc. Am. 32, ). 2. R. Mital, C. M. Warnky, and B. L. Anderson, Design and demonstration of an optical true-time-delay device based on an octic-style white cell, J. Lightwave Technol. 24, (2006). 3. B. L. Anderson, D. J. Rabb, C. M. Warnky, and F. Abou-Galala, Binary optical true-time delay based on the White cell: design and demonstration, J. Lightwave Technol. 24, (2006). 4. B. L., S. A. Collins, R. Mital, N. K. Nahar, and B. R. Stone, The Octic White cell true- time delay device, in Government Microcircuit Applications and Critical Technology Conference-2003, Tampa, Florida, 31 March 3 April 2003; 5. R. Higgins, N. K. Nahar, and B. L. Anderson, Design and demonstration of a switching engine for a binary true-timedelay device that uses a White cell, Appl. Opt. 42, (2003). 6. C. M. Warnky, R. Mital, and B. L. Anderson, Demonstration of quartic cell, a free-space true-time-delay device based on White cell, J. Lightwave Technol (2006). 7. S. Kunathikom, B. L. Anderson, and S. A. Collins,Jr., Design of delay elements in a binary optical true-time-delay device that uses a White Cell, Appl. Opt (2003). 8. B. L. Anderson, S. A. Collins, R. G. Rojas, G. Valco, C. M. Warnky, D. J. Rabb, F. Abou-Galala, N. K. Nahar, and G. Hughes, Binary optical true-time delay based on the White cell: final report phase I, (ElectroScience Laboratory, The Ohio State University, 2004). 9. N. K. Nahar and R. G. Rojas, Coupling loss from free-space to large mode area photonic crystal fibers, J. Lightwave Technol. 26, (2008). 10. W. H. Kohn, Astigmatism and White cells: theoretical considerations on the construction of an anastigmatic White cell, Appl. Opt. 31, (1992). 11. Lambda Research Corporation, OSLO leading lens design software, A. Y. Yi, C. Huang, F. Klocke, C. Brecher, G. Pongs, M. Winterschladen, A. Demmer, S. Lange, T. Bergs, M. Merz, and F. Niehaus, Development of a compression molding process for three-dimensional tailored free-form glass optics, Appl. Opt. 45, (2006). 13. W. T. Plummer, J. G. Baker, and J. V. Tassell, Photographic optical systems with nonrotational aspheric surfaces, Appl. Opt. 38, (1999). 14. B. L. Anderson and C. D. Liddle, Optical true time delay for phased-array antennas: demonstration of a quadratic White cell, Appl. Opt. 41, (2002). 10 July 2009 / Vol. 48, No. 20 / APPLIED OPTICS 3929