Realization of true-time delay lines based on ... - IEEE Xplore

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Realization of True-Time Delay Lines Based on Acoustooptics Pál Maák, István Frigyes, Senior Member, IEEE, László Jakab, István Habermayer, Mihály Gyukics, and Péter Richter

Abstract—A true-time optical delay line for short radiofrequency (RF) pulses using path length dispersion is proposed. It is an optical implementation of the linear phase-shift theorem of the Fourier transformation. Acoustooptic signal processing is used for conversion into the optical frequency domain and for spatial Fourier decomposition of the pulse. The processing of the pulse is obtained by differentially phase shifting the particular frequency components, followed by a heterodyne reconversion into the RF domain. The optical system is intended to be used for delaying, but also for shaping and filtering of RF pulses, mainly in phased array radar antennas. Theoretical analysis of the system principle is given together with experimental results, demonstrating 2- s time delay of 0.5- s-long pulses with maximum optical phase shift of 1 2 . A detailed theoretical and experimental bandwidth analysis is carried out, pointing to the main technical problems and their solutions. Index Terms—Acoustooptic signal processing, delay effects, phase shifters, phased arrays, pulse measurements.

I. INTRODUCTION

O

NE of the most complex microwave components is a variable delay line, used in wide-band phased array systems. This statement is particularly true if the phased array antenna is very large, containing thousands or tens of thousands of radiating elements. Requirements in this case, to list only a few of them, are wide band, low loss, low weight, and small size. During the decades of their respective applications, very different designs were proposed and elaborated. Phased array antennas originally were intended to be used in scanning radar; this is their main field of application. However, potential application became wider with the increasing capacity (i.e., bandwidth) of wireless communications. And, as signal processing—besides matching guided waves into radiated waves—became one of the tasks of an array antenna, application of timed rather than phased arrays got a new perspective. With the advent of optical methods in microwave signal processing, it turned out that optical techniques in designing variable delay lines may have several advantages over their purely microwave counterparts. Perhaps the most important among these is their much lower weight and smaller size, as well as the virtually total lack of leakage, i.e., unwanted

interaction among components of the system. In the case of phased array antennas, this means no leakage between the delay–radiative elements. Publications reporting on various optical true-time delay (TTD) lines are abundant. In a tutorial review paper [1], many of the solutions published before 1995 were summarized. The number of papers on optical TTD lines did not decrease during the last five years [2]–[8]. A very interesting realization of optically generated TTD, based on the concept of path-length dispersion, was introduced in [9] and analyzed in [1] and [10], and some improvements were proposed in [11]. No experimental realization operating with pulse wave forms rather than with pure sinusoids has been reported yet, apart from two conference papers [12], [13]. The present paper gives a detailed description of the optical system of this type of optical variable TTD lines and describes the experimental results. Note that, although in this paper, only pulse delay is addressed, spatial decomposition of frequency components of a signal makes more general signal processing operations possible. Various spectral components can be attenuated in different ways, such as frequency-shifted and phase-shifted components. This can lead to more general photonic microwave signal processors forming a completely new class of systems. TTD can be regarded as one member of this class. The organization of the paper is as follows. In Section II, the need for delaying rather than phase shifting signals in wide-band phased arrays is briefly discussed and theoretical basis of TTD lines based on the concept of path-length dispersion is given. Section III describes our delay-system principle and presents an estimation of the required parameters. Numerical modeling of the new pulse delaying principle and related computational results are also included. In Section IV, experimental proof of the delay principle is presented, along with the comparison of the numerically calculated and experimentally measured pulse delay values. The transmission characteristics and bandwidth of the system are analyzed in detail in Section V, and the theoretical and experimental results are then concluded in Section VI. II. THEORETICAL BASIS

Manuscript received December 28, 2000; revised September 24, 2001. P. Maák, L. Jakab, M. Gyukics and P. Richter are with the Department of Atomic Physics, Budapest University of Technology and Economics, Budapest H-1111, Hungary (e-mail: [email protected]). I. Frigyes is with the Department of Microwave Technology, Budapest University of Technology and Economics, Budapest H-1111, Hungary. I. Habermayer is with the Department of Electron Devices, Budapest University of Technology and Economics, Budapest H-1111, Hungary. Publisher Item Identifier S 0733-8724(02)03344-3.

The variable delay line dealt with in this paper is based on two concepts: 1) optical processing of microwave signals and 2) path-length dispersion. Concept 1) is not dealt with in detail; it is mentioned only that if an electric (say, microwave) signal is converted, e.g., by modulation to the optical frequency band, phase shifted, and then coherently reconverted to the electric domain, then the phase shift

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introduced in the optical domain is maintained in the electric band. Of course, its frequency derivative, i.e., the group delay, is also maintained. The properties of coherent detection of optical signals, clarifying this characteristic, are dealt with in many optical textbooks; this property is discussed in some detail in [1]. Coming to concept 2), note that it is well known [14] that in wide-band phased arrays, a progressive time delay, rather than a progressive phase shift, must be applied in the excitation of a particular element. In order to point the beam of the antenna must be applied to the signal, in direction , a phase shift which excites radiating element

and so the delay can be expressed as (6) If the signal to be delayed is converted to some higher frequency band—in practice, into the optical frequency can be very large. This leads to the result that a band— , traveled by the particular spectral short variable length components, can be sufficient to yield the required . Take the simplest case when there is a linear dependence between and , with constants and

(1)

(7)

with being the location of element in the array, related to the . Thus, this phase specially chosen 0 element located at shift is related to the phase the 0 element. If the signal bandwidth can be adjusted by a frequency-independent phase is narrow, shifter, according to (1). This should be designed at the nominal carrier frequency. If the bandwidth is wide, it must be taken into account that the phase shift must be proportional to the frequency. However, a phase shift proportional to the frequency is equiv. In the present case, alent to a constant group delay this is

Here, subscript is used for marking the optical frequency are the lower and upper band band and, as before, and limits, respectively. is the bandwidth, in hertz, of the signal to be delayed; the bandwidth of the signal converted into the optical band is the same as that of the microwave signal. Applying (7) in (6), we get

(2) In the phased-array literature, this is called TTD. This must be realized in the entire frequency band of the signal, i.e., in the with subscripts and meaning lower range and upper frequency limits, respectively. Thus, in a wide-band phased array, the radiating element must be excited by a TTD line, where the phase shift at frequency must be

(8) Equation (8) leads to several conclusions. First, we see that, in contrast to what is required, is not constant, but a linear group delay variation is formed; its magnitude in the band of interest is (9)

In one possible realization of TTD, applied nearly exclusively, the signal is transmitted through a transmission line or free-space-section of length

If the relative optical bandwidth is very narrow, this distortion is very low and is negligible. Second, because the relative optical bandwidth (i.e., ) is very low, the second term in the bracket in (8) is of a very wide band microwave signal is very large, e.g., on the order of a few gigahertz per second whereas the optical frequency is in the order of hundreds of terahertz per second, is on the order of 10 . Thus, to a very so the ratio good approximation, the additive factor 1 in the bracket can be neglected and the group delay can be written as

(4)

(10)

(3)

with being the wave phase velocity within that line or freespace section, being equal to or different from the free-space velocity . To achieve the appropriate group delay, the length and of these sections must vary between a basic length , being the length of the array. In practical cases, this realization can be difficult, because the maximum length difference needed is usually high, on the order of 10 m. Note that, in this case, all spectral components of the signal travel through the same path of length . Applying a structure in which the length of the path is frequency dependent, the obtained phase will be (5)

Applying this technique, length can be, by orders of magnitude shorter than , the free space delay length of (4). Note also the following three points. 1) In a phased array, (3) must also be fulfilled, in addition to (2). This yields a unique magnitude for and for

(11) 2) As seen from the second part of (11), the principle of path length dispersion in phased arrays can only be applied if the signal is converted to a much higher frequency ). However, its reasonable application in (i.e.,

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Fig. 1. Scheme of the antenna array driven with pulses suffering TTD between the adjacent elements.

microwave delay lines is more or less restricted to opis not very large, the tical signal processing; if linear group delay distortion would be unacceptably high. Furthermore, it is mainly, if not exclusively, optical technology that can separate spectral components in relative bandwidths of the order of 10 . 3) From the conceptual point of view, it has been assumed, until now, that higher frequencies are traveling through longer paths; however, the opposite is also possible. Then, for example (12) and the delay would be (13) Of course, a net negative delay causing an advance of a signal cannot be realized. However, take into account that, whatever the physical realization of the delay structure may be, spectral components must be decomposed in order to achieve a dispersion of the path length; also, spectral decomposition causes an inherent delay. This delay can be decreased by the negative of (13), if the path length dispersion is realized as in (12). III. ACOUSTOOPTIC REALIZATION OF OPTICAL TTD LINES BASED ON PATH-LENGTH DISPERSION The operation of a phased array antenna with time-delayed pulses is depicted in Fig. 1. Based on (2), the maximum time with an array delay needed to achieve an angle range of of length will be (14) m of elements with an array of length ns delay time between two consecutive elements, ns over the entire array are needed for a deflecand tion angle of . In a classical phase-shifting system,

the needed maximum phase difference must be to achieve this angle variation [1]. In a TTD system, considering a bandwidth of 5 MHz, corresponding to about 200-ns pulse duration, for the required 30-ns the maximum phase shift would be delay, calculated with (6). phase shift corresponds to a free-space This small (at 633-nm waveoptical path length difference of length, this results in 95 nm). This small path length variation is in the range obtainable with piezoelectric crystals or electrooptic modulators. The most valuable solution is with a common phase-shifting spatial light modulator (SLM) driven at low (a few volts) control voltages. These systems usually operate at frequencies of 2–10 GHz. Therefore, practical importance of such a system would be in this frequency range. The useful bandwidth is also in the gigahertz range. We realized a preliminary system operating at 70-MHz carrier frequency in order to demonstrate the new signal processing principle. The architecture of the optical system, which demonstrates pulse delay, is presented in Fig. 2. In this form, this optical setup would provide the necessary time delay between two adjacent pixels of the radar antenna array. The same setup can be used, however, with minor changes for more complex processing of the pulse, such as filtering. This possibility is one of the main advantages of the processing in the spectral domain. The high resolution of the spectral decomposition, which allows adaptability to different functions, is a unique feature of this system, due to the acoustooptics. The acoustooptic cell performs simultaneously both the conversion of the driving signal into the optical frequency domain and the spectral decomposition of it [15]. The modulated RF signal to be processed is fed to the acoustooptic deflector. The frequency decomposition of the modulated signal is transformed into the angular distribution of the diffracted beam intensity. The diffracted beam emerging from the acoustooptic deflector has a divergence in the interaction plane proportional to the bandwidth of the signal. The divergent diffracted beam can be treated as a composition of particular beams, each having its frequency shifted by the RF frequency component corresponding to its deflection angle. As is well known, the propagation angle of the beams varies linearly with the diffracting acoustic (RF) frequency. These beams also conserve the optical characteristics of the input optical beam. The second crucial element of the system is the phase shifter, which shifts the relative phase of the different frequency diffracted beams. In an ideal TTD system, this phase shift varies linearly with the RF frequency carried by the beams, fulfilling (2). Ideally, the path length dispersion is a continuous function of the frequency. In practice, however, this function can be realized only if it is discrete. The resolution of the practical realization influences highly the shape of the pulse. After phase shifting, the beams are heterodyned with the reference beam on the detector surface. The detector signal contains the sum of different frequency heterodyne signals and rebuilds the processed RF signal. In our setup, the differential phase shift is obtained with a stepped mirror. The consecutive steps reflect different parts of the original spectrum, the double step height being the optical

MAÁK et al.: TTD LINES BASED ON ACOUSTOOPTICS

Fig. 2.

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Principle of the optical setup to realize the delay of a radiofrequency (RF) pulse between two consecutive segments of the radar antenna array.

Fig. 3. Calculated pulse delay achieved with the optical system at 70-MHz carrier frequency and an added linear phase shift of 3:9=MHz. The reference pulse located at the origin of the time scale suffered no additional phase shift.

path length difference between them. Because our system is not yet involved in a phased array antenna and serves only the concept demonstration, the realized time delay and phase shifts are not matched to the concrete application requirements. As seen in Fig. 2, one mirror step reflects a frequency band , called a sub-band. Here, steps would reflect the entire bandwidth. With designations introduced previously, sub-band center frequencies are given by (15) in hertz.) (Here, -s are given in radians per second, and In phased array applications, the phase shift and the group delay, applied to the radiating element at location , are given in (1)–(3). This phase shift and the group delay can be approximated by applying a discretized optical path length

(16) Using these results, the electrical transfer function of the entire device becomes

(17) where

is the transfer function of one mirror step.

One of the main limitations of this configuration is the fact that has transmission nulls at the crossover frequencies if is equal to . the phase-shift difference are defined as Crossover frequencies (18) To avoid excess linear distortion, one should conservatively choose (19) Condition (19) puts a lower limit on the number of sub-bands, in our simple case on the number of mirror steps. This number becomes higher as the antenna beamwidth becomes narrower and/or the bandwidth becomes wider. In order to give numerical values, we note that the requirements are the most severe at , the the extremely positioned radiating elements, i.e., at aperture length, and maximum beam steering. If we take as 60 , the application of (19) leads to (20) However, for a practical application, an electronically controllable differentially phase shifting device should be used instead of the stepped mirror. A good solution can be an SLM with small pixels allowing a large number of channels. The use of a multichannel electrooptic modulator, where different portions of the spectrum travel across different channels, would also be effective. Applying consecutively higher voltage to each

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Fig. 4. Experimental setup for demonstration of TTD. The system uses a stepped mirror as a differential phase shifting element. The rest of the optical system is fitted to achieve a maximum bandwidth transmission on the stepped mirror and an optimal heterodyne process at the detector surface.

Fig. 5. Experimental proof of the pulse time delay. The output pulses were captured with a 500-MHz bandwidth oscilloscope, with the input pulses used as reference. A flat mirror without differential phase shift alternatively replaced the stepped mirror. The time shift between the output pulses on traces 2 and D is the net delay obtained with the differential phase shift.

channel, a transversally increasing refractive index is obtained. When the gaps between the channels are small enough, the electric fields overlap and a refractive index increase within the gaps is expected. Thus, a quasicontinuous refractive index profile can be obtained, which results in a good approximation of the required phase shift distribution. The linear frequency dependence of the differential path length required for a given delay time can be easily computed. First, the Fourier transformation of the RF pulse should be taken; then, the linear phase shift of the form

calculation through the computation of (17) with an arbitrary resolution (arbitrary high number ). We simulated numerically the operation of the device including the effects of the acoustooptic cell and of the beam traveling through the optical system. In addition to the influence of the frequency dependent diffraction efficiency on the spectrum, the optical beams suffer additional phase shifts in the deflector and in the additional optical system. The frequency-dependent phase shift in the acoustooptic device can be expressed as

(21) should be applied, as well as the inverse Fourier transformation and are conresults in the time shifted pulse. Here, stants. The last two steps are realized in any discrete numerical

(22) where is the diffracting acoustic frequency, is the interaction length, and velocity,

is the acoustic is the angle

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Fig. 6. One output pulse of the system of Fig. 4 and its Fourier transform. This is not the shortest pulse transmitted, but the temporal distortions can be better examined. The maximum possible bandwidth is indicated by the presence of the secondary maxima in the spectrum.

difference between the incidence optical angle and the corresponding Bragg angle. This formula gives a linear dependence of the phase shift with the frequency, at a given optical incidence angle. With our acoustooptic cell of length 1.5 mm, acoustic velocity of 630 m/s, and incidence angle of 5 , the phase variation causes a phase shift of 10 rad/MHz. This variation corresponds to a time delay of 14 ns, mostly negligible. If the detection plane does not coincide with the image plane of the acoustooptic cell formed by the entire optical system, an additional frequency dependent phase shift will be added, as shown in Section V. In the numerical simulation, we used a linear frequency dependent optical path length difference, approaching the effect of the step mirror used in the experiment. The calculated pulse delay is shown in Fig. 3. The delay of 1.9 s is obtained with a linear phase shift of MHz, corresponding to a path delay of 1.2 with m/MHz. This path delay matches the step height of the sputtered stepped mirror. IV. EXPERIMENTAL RESULTS The experimental setup in which time delay of a pulse has been demonstrated is presented in Fig. 4. An optical system was chosen in which the image of the acoustooptic cell is created on the detector surface. Laser light of 633-nm wavelength is used, expanded to 5 5 mm to match the full aperture of the acosutooptic cell and to achieve the highest resolution. The TeO acoustooptic cell is driven at 70-MHz frequency modulated with a pulse of controllable width 0.01–100 s. It has 45-MHz bandwidth

Fig. 7. Calculated frequency-dependent transmission of the heterodyne detection, assuming complete overlap of the different frequency beams in the detector plane. It serves to visualize the pure effect of the incidence angle variation on heterodyning. The detector size is of 200 m, and the gradient of the angle variation with the carried frequency is of 1.6 mrad/MHz.

between 52 and 97 MHz. The diffraction efficiency in this frequency region is more than 50% related to the input beam intensity. The deflection angle varies linearly with the acoustic frequency with a slope of 1 mrad/MHz. The acoustooptic cell is placed in the back focal plane of lens , of 300-mm focal length, which ensures parallel propagation of the deflected beams. The individual beams are focused onto the stepped mirror, which provides the frequency dependent phase shift. For referencing at this position, a plane mirror replaces the stepped mirror. The reflected beams are then proand , onto the detector surface, jected through two lenses, so that the image of the deflector through the whole system (three lenses and three mirrors) appears approximately on the

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Fig. 8.

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Optical setup for characterization of systems that use the back focal plane of a lens as the detector plane.

detector surface. The individual elements are not diffraction limited, however, so the image formation is not accurate. The stepped mirror has five segments, each providing a 600-nm path difference relative to its neighbor. For accuracy, the steps were sputtered 0.6 mm wide. Thus, this arrangement approaches a linear frequency dependent optical path difference MHz. of 1.2 m/MHz, corresponding to a phase shift of The mirror is adjusted so that the path difference increases from lower to higher frequency components, providing a positive time shift of the pulse. In Fig. 5, the measured temporal characteristics of the input and output pulses are presented. The net delay obtained with the stepped mirror relative to the input pulse is compared with the delay time obtained by replacing it with a flat mirror. The net delay obtained with the stepped mirror (upper trace) is longer than that with the flat mirror (lower trace). The reference edge is the rising edge of the input pulse, the same in both cases. The pulse of the upper trace (D) encountered a positive time shift of 1.9–2 s relative to the pulse of the lower trace (2), corresponding exactly to the path-length gradient of the stepped mirror. The main parameters of the system, which determine the shape and minimum length of the output pulse, are bandwidth, transmission losses, and phase distortions. At this stage of the development, the most interesting parameter is the bandwidth, because it also determines the maximum radar scanning speed. Moreover, high bandwidth is the first advantage of the TTD principle.

the pulse is of about 0.35 s, but the asymmetry of it indicates phase nonlinearities, which make the correct estimation of the bandwidth difficult. The electronic components of the system do not to limit the bandwidth. The acosutooptic deflector and the detector have 45and 500-MHz bandwidth, respectively. The main bandwidth limitation is within the conversion from the optical to the RF domain. The heterodyning between the reference and the individual different frequency optical beams depends on the beam size matching, the relative phase, and the relative angle of the beams to be added. In an optical system, the spot size and the divergence angle are in tradeoff; therefore, the design must achieve optimal compromise. First, let us examine the effect of the different angles of propagation. The beam traveling at angle relative to the reference generates a sinusoidal intensity distribution. Its period is . The deflected beams in the detection plane can be of approximated as Gaussian beams with nearly plane wavefronts, which close the corresponding angle with the reference plane wavefront. Thus, the detected amount of light coming from the interference of one particular beam and the reference, corresponding to the component of frequency in the spectrum of the output signal, will be

V. BANDWIDTH ANALYSIS

represents the transfer function of the optical Here, is the angle of the system including the acoustooptic cell, is the beam diameter in the detector corresponding beam and plane. If the spot size of the particular beams is bigger than the must be replaced by the detector diameter detector surface, at the integration limits. In the system of Fig. 4, the angle variation of the different is of approximately frequency beams after the last lens 1.6 mrad/MHz, limiting the full-width at half-maximum (FWHM) of the heterodyne detection to about 6 MHz. Fig. 7 presents a calculation of the frequency dependent transmission, based on (23), considering the corresponding angle variation and the detector size of 200 m. The calculated bandwidth coincides with that estimated from the pulse transmission measurement (Fig. 6).

The bandwidth of the system of Fig. 4 is limited by several factors. In the following, we present a detailed analysis of the bandwidth limiting factors and of the bandwidth increasing possibilities. The bandwidth of the transmission was measured using a 500-MHz bandwidth oscilloscope, being also capable to complete temporal Fourier transformation. The duration and shape of the pulse transmitted through the optical system of Fig. 4 can be seen in Fig. 6. A longer pulse was captured in order to show the distortions of the pulse shape. The bandwidth of the transmission can be deduced from the presence of the sidelobes in the Fourier spectrum of the pulse. A bandwidth of about 6 MHz can be recognized, corresponding to a fractional bandwidth of 8.5%. The rise time of

(23)

MAÁK et al.: TTD LINES BASED ON ACOUSTOOPTICS

The detector size can limit the bandwidth also in a direct way, when part of the different frequency optical beams can miss it. This is not the case when the beams are completely overlapped on the detector in the image plane of the optical system. However, in this case, the beam size is usually much bigger than the detector size, and the angle variation limits the bandwidth, as described previously. To avoid high intensity losses due to the size mismatch between the detector and beam, the detection plane is usually not in the image plane. In the practical detection plane, the spectrum of the signal is spread along a line, and a part of it will not be detected. The fast detectors are usually small; therefore, this effect may cause a serious bandwidth limitation. The analysis of the simple system shown in Fig. 8 shows that, in such a case, decreasing the focal length of the focusing lens can increase bandwidth. The detection plane is placed in this experiment in the focal plane of the lens. The focused beam size is very small compared to the 200- m detector size. First, a 80-mm focal length lens was used. The reference beam was expanded to cover the whole spectrum. The detector could be shifted laterally to recover different parts of the spectrum, as shown in Fig. 9. The transferred pulse in the center of Fig. 9, representing the central part of the spectrum, corresponds to a bandwidth of about 3.5 MHz, i.e., 5% fractional bandwidth. The rise time of the pulse is 0.6 s, but the asymmetry of the pulse suggests the presence of nonlinear frequency dependent phase distribution, which avoids exact calculation of the bandwidth. With a 50-mm focal length lens, the bandwidth of the transmission increased to about 5.5 MHz, as shown in Fig. 10. This corresponds to a fractional bandwidth of 8%, and the pulse rise time decreased to about 0.4 s. The Fourier transform shows spectral sidelobes appearing in the corresponding frequency band. The experimental analysis of the system shown in Fig. 8 served to demonstrate that optimization of the optical system, here, mainly, the focal length reduction, can considerably increase the bandwidth. The system of Fig. 4 is optimized among the available resources of optical and optoelectronic elements. An optical system was chosen in which the detection plane is positioned between the image of the acoustooptic cell and the back focal plane. In this system, all bandwidth-limiting factors occur, yet a reasonable compromise can be found among them. The size of the image is about 3 mm, with an input aperture of 5 mm. The big difference between the image and detector sizes would introduce high intensity loss; therefore, the detector and the must be placed between the focal plane of lens image plane, at the position where the beam size is about 250 m, and most beams pass through the detector surface. Partial overlapping of the different beams gives rise to unwanted heterodyne signals, which are than filtered electronically from the output. For the desired applications, detectors operating in the gigahertz domain are required. Detectors of such speed are really of small size, but the diameter and speed do not have a linear relation. Detectors with 25- m diameter are available with 40-GHz bandwidth as well as 1-GHz bandwidth conjugated with 0.8-mm active area. It is clarified here that a bandwidth limitation caused by the detector size can be minimized

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Fig. 9. The spectrum of the pulse spatially distributed in the focal plane can be recovered by moving the detector perpendicular to the optical beam traveling direction. Here, the spectrum is spatially distributed in the detection plane in a larger area than the detector size. The signals were measured with an 80-mm focal length lens and a 200-m size detector.

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Fig. 10. Output pulse and its spectrum captured in the system of Fig. 8, using a focusing lens of 50-mm focal length. It should he compared with the middle image of Fig. 9, which was captured with an 80-mm focal length lens.

by shifting the detection plane toward the image plane. As an alternative, focal length decrease of the last lens also helps to overcome this problem. Actually, the frequency of the operation, from this point of view, is not limited to 10 GHz of the desired application. The distortion of the transmitted pulse, as shown in Fig. 6, has more reasons. One is the stepped mirror, in which the phase difference between two steps is more than . According to (17), this causes some frequency components to disappear from the output. The second reason is that the different frequency diffracted beams encounter different phase shifts while traveling through different optical paths. This phase shift causes a nonlinear frequency-dependent phase shift, which leads to signal distortion and bandwidth reduction. Simulation of the distortion effect has been also carried out. The frequency dependent nonlinear phase shift has been measured with a network analyzer. In this measurement, the linear phase shifts introduced by the system have been compensated. The measured phase distribution has been approximated numerically by a nonlinear function and applied to the numerical simulation of the system transmission. The obtained distorted pulse is shown in Fig. 11. The presented experiments and the theoretical considerations show that, from the point of view of the bandwidth and pulse distortion, the characteristics of the optical system are crucial. The bandwidth-limiting factors can be different, and a careful optical design should be carried out to optimize the optical elements for optimal time delay and bandwidth simultaneously. At the moment, the maximum achieved fractional bandwidth reaches 7%–8%, but we demonstrated experimentally that the limits of the optical system could be extended. An increase of the fractional bandwidth up to 50%, in a well-designed optical system, can be predicted.

Fig. 11. Calculated distortion of a pulse shape transferred through the system of Fig. 4, caused by the nonlinear phase difference between the particular frequency components. The pulse is compared with a pulse calculated assuming only linear frequency-dependent phase shift. The input pulse length is the same for both.

VI. CONCLUSION We demonstrated the possibility of TTD of short pulses by means of acoustooptic signal processing. Theoretical and experimental investigation of the delay principle has been carried out, and a good agreement for the delay of 0.5- to 5- s–long pulses was found. Time delays necessary for 60 radiation introduced angle range for 1-m size antenna require only phase dispersion with this method. This treatment shows that the bandwidth is limited by the properties of the optical system. Becausee theoretical and experimental analysis of different optical system concepts have been carried out, the bandwidth limiting factors were clearly recognized. It is expected that through careful optical design, the fractional bandwidth can be increased from the actual value of 7%–8% to the desired 50 .

MAÁK et al.: TTD LINES BASED ON ACOUSTOOPTICS

The main strength of the presented principle of optical realization is that it clearly operates in one plane. It uses the spatial spread of the signal spectrum along a line, allowing separately processing the particular frequency components in the same plane. This principle allows the realization of the system in an integrated optical form. The surface acoustic wave acoustooptic deflector and a multichannel electrooptic modulator can be integrated with some optical elements in a single LiNbO wafer on the order of 5–10 cm. Moreover, such a system would function most likely in the 2–10-GHz frequency range, which the most obvious application requires. We are planning to realize the system in the gigahertz range, first using bulk optics of smaller sizes, which is also possible, by simply reducing the characteristic distances. The size and number of steps of the stepped mirror mainly determine the actual size of the system, because the size of the spatially distributed spectrum must match its size. A crucial step in scaling down the system size is reduction of the channel size in the variable phase-shifting device. The use of an SLM with a pixel size of the order of 10 m will solve this problem. The desired optical system must assure an angle variation smaller than 0.5 mrad/MHz assuming an individual component spot size of 100 m. Here, the tradeoff between the beam diameter and the traveling angle of the different frequency components must be optimized. The size of the desired spectrum, spatially distributed in the detection plane, must be smaller than the detector size. To avoid intensity losses, the individual beam size should possibly also be smaller than the active part of the detector. The nonlinear phase distribution over the frequency spectrum must be avoided by controlling the phase of the different beams during the design and by ensuring diffraction limited transformation of the individual optical elements and wavefront matching. Further research is planned to extend the time delay capabilities for a number of independent antenna elements simultaneously. Use of a two-dimensional acoustooptical deflector as well as a diffractive beam splitter for antenna element selection will be experimentally investigated.

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[7] D. T. K. Tong and M. C. W. Multiwavelength, “Optically controlled phased-array antennas,” IEEE Trans. Microwave Theory Tech., vol. 46, pp. 108–205, Jan. 1998. [8] R. A. Minasian and K. E. Alameh, “Ultimate beam capacity limit of fiber grating based true-time-delay beam-formers for phased arrays,” in IEEE 1998 Int. Microwave Symp., June 1998, TH2C-4, pp. 1375–1378. [9] E. N. Toughlian and H. Zmuda, “A photonic variable RF delay line for phased array antennas,” J. Lightwave Technol., vol. 8, pp. 1824–1828, Dec. 1990. [10] I. Frigyes and G. Szporni, “Optically generated true time delay via pathlength dispersion,” in IEEE Top. Meet. OMI, Les Vaux, France, Nov. 21–23, 1994, Ma5, pp. 82–85. [11] I. Frigyes, O. Schwelb, and J. Bérces, “Investigations and improvements in microwave opto-electronic variable delay lines,” in IEEE 1996 Int. Microwave Symp., vol. 2, San Francisco, CA, June 1996, WE3F-20, pp. 887–890. [12] P. Maák, L. Jakab, P. Richter, I. Frigyes, and I. Habermajer, “True-time acoustooptic delay line for short pulses driving phased array antennas,” in Advances in Acousto-Optics, 4th AA-O, Florence, Italy, June 10–11, 1999, pp. 65–66. [13] P. Maak, J. Reményi, L. Jakab, P. Richter, I. Frigyes, and I. Habermajer, “True time acousto-optic delay line for short pulses based on optical path-length dispersion: Experimental proof,” in IEEE Int. Conf. Phased Array Systems Technology, Dana Point, CA, May 21–25, 2000, pp. 449–452. [14] M. I. Skolnik, Radar Handbook, 1st ed. New York: McGraw-Hill, 1970. [15] A. Korpel, Acousto-Optics, 2nd ed. New York: Marcel Dekker, 1996. [16] S. H. Lee, Ed., Optical Information Processing. Berlin, Germany: Springer Verlag, 1981.

Pál Maák, photograph and biography not available at the time of publication.

István Frigyes (M’87–SM’90), photograph and biography not available at the time of publication.

László Jakab, photograph and biography not available at the time of publication.

REFERENCES [1] I. Frigyes and A. J. Seeds, “Optically generated true-time in phased-array antennas,” IEEE Trans. Microwave Theory Tech., vol. 43, pp. 2378–2386, Sept. 1995. [2] N. A. Riza and N. Madamopoulos, “Microwave band demonstration of a re ective geometry fiber and free-space binary photonic delay line,” IEEE Microwave Guided Wave Lett., vol. 7, pp. 103–105, Apr. 1997. [3] A. Molony, L. Zhang, J. A. R. Williams, I. Bennion, C. Edge, and J. Fells, “Fiber Bragg-grating true time-delay systems: Discrete-grating array 3-b delay lines and chirped-grating 6-b delay lines,” IEEE Trans. Microwave Theory Tech., vol. 45, pp. 1527–1530, Aug. 1997. [4] M. Y. Frankel, P. J. Matthews, and R. D. Esman, “Fiber-optic true time steering of an ultrawide-band receive array,” IEEE Trans. Microwave Theory Tech., vol. 45, pp. 1522–1526, Aug. 1997. [5] R. A. Minasian and K. E. Alameh, “Optical-fiber grating-based beamforming network for microwave phased arrays,” IEEE Trans. Microwave Theory Tech., vol. 45, pp. 1513–1518, Aug. 1997. [6] M. Y. Frankel, P. J. Matthews, and R. D. Esman, “Two-dimensional fiber-optic control of a true time-steered array transmitter,” IEEE Trans. Microwave Theory Tech., vol. 44, pp. 2696–2702, Dec. 1996.

István Habermayer, photograph and biography not available at the time of publication.

Mihály Gyukics, photograph and biography not available at the time of publication.

Péter Richter, photograph and biography not available at the time of publication.