Non-mechanical beam steering with a dynamic lithography of tunable metasurface

Tamelia Ali1, Ada-Simona Popescu1, Igor Bendoym3, Simeon Bikorimana1, Roger Dorsinville1, Linda Marchese4, Alain Bergeron4, Marc Terroux4, Andrii B. Golovin1,2, David T. Crouse1,2.

1Department of Electrical Engineering, The City College of New York, New York, New York 10031

2Center for Metamaterials, 160 Convent Avenue, Steinman Hall, New York, New York 10031 3Phoebus Optoelectronics, New York, New York 10031

4Institut National d'Optique INO, Quebec, Canada

Abstract— Beam steering has been traditionally achieved by mechanical means. Even though these mechanical techniques have evolved over the past few decades, non-mechanical approaches, due to benefits such as increased speed, lower costs and reduced complexity, have gained considerable interest. In this work, we propose a non-mechanical beam steering of terahertz radiation method using a transient, or dynamic lithography process. The experimental setup is based on a pump-probe technique, with a Ti:Sa pulse laser at 800 nm wavelength as laser source. The high power pump beam is used to “write” a metasurface pattern composed of v-shaped antennas on a high purity float zone silicon substrate. The wavefront of the pump beam is modulated by a liquid crystal spatial light modulator (LCSLM), such that, by the time the beam reaches the silicon substrate, the illumination pattern has the appearance of an array of antennas. Upon incidence on the silicon substrate, the beam generates electron-hole pairs in the illuminated areas, therefore creating structures with metallic-like properties. The presence of carriers and implicitly the metallic quality of the structures are ensured as long the radiation is incident on the substrate. This process was named transient or dynamic lithography, due to its non-destructive property relative to the silicon wafer. The probe beam, less powerful, is used to generate the terahertz signal. This is achieved by a photo-conductive antenna. Subsequently, the terahertz beam probes the pattern projected on the silicon substrate by the pump beam. Due to the electron-hole pairs previously generated in the substrate, the antenna structures will respond to the terahertz radiation in a way similar to metallic antennas. The terahertz beam is therefore steered by the pseudo-metallic antenna array. The detection is achieved with an un-cooled bolometer terahertz video camera. This beam steering technique is very promising due to its flexibility in quickly changing the direction of the steered beam, by “rewriting” the antenna arrays on the silicon substrate, without any mechanical movement of optical elements.

Keywords- spatial light modulator, 0-th order of diffraction, metasurface, pump-probe technique, non-mechanical beam steering, THz generation, THz detection.

I. INTRODUCTION Over the past two decades, terahertz technology has

received a growing interest from researchers in a wide variety of scientific disciplines: communications, biology, homeland security and many more[8]. While the generation and detection

techniques of terahertz radiation have been increasingly evolving, the real time manipulation of the terahertz radiation requires substantial development.

In this paper, an innovative method of beam steering in terahertz regime is proposed. This method is based on a so-called “dynamic lithography” procedure, which allows for rapid change of the direction of terahertz beam.

II. BEAM STEERING METASURFACE In the microwave regime, a well-known beam steering

technique is the point-by-point control of the phase of a beam along a surface, as in phased array antennas. Such phased arrays are composed of a set of phase shifters connected to radiators as depicted in Fig.1. The phase shifters achieve a gradient of phase shift for each antenna. Therefore, the wavefront of the radiating beam is tilted, achieving beam steering in a desired direction.

Figure 1. Phased array of linear retarders [2].

In this project, instead of the phased array as a steering device, a metasurface composed of metallic radiating elements has been used. The v-shaped antennas that compose the metasurface introduce various phase shifts in the phase of the incoming wave front, as a function of the dimensions of the arms, the angle between the arms and their spatial orientation. This type of metasurface has been first introduced and investigated by Capasso et. al.[1].

The metasurface used in this work is an array of v-shaped antennas, as depicted in Fig.2. The unit cell of the array contains eight subwavelength antenna elements, where each

antenna introduces an additional 45 degrees phase relative to the previous one, such that the whole unit cell introduces a 2π phase shift. This allows for a full control on the radiated wavefront, just like in the case of the microwave phased arrays. In this metasurface structure, each antenna works as a phase shifter and radiator at the same time.

Figure 2. The metasurface structure consists of sub-wavelength sized v-shaped

antennas.

Figure 3. The gradient of the phase retardation, from Φo to Φo +2π

introduced by a unit cell , where ∆Φ = π/4.

The electromagnetic behavior of the v-shaped antenna structure was done by using the High Frequency Structural Simulator (HFSS) from ANSYS. Each antenna element has been simulated individually.

The v-shaped antenna is a sub-wavelength resonator, responding to a characteristic resonant frequency. Each antenna introduces a phase shift that is the phase difference between the excitation plane wave and the scattered wave by the antenna, as depicted in Fig.4.

The metasurface is composed of a collection of unit cells, each containing the eight v-shaped antennas, as depicted in Fig. 3. In order to provide full wavefront control from each unit cell, the phase differences between the eight antennas are equally distributed. The computer design is achieved by performing sweeps of the parameters of antennas: length of arms, width etc.

The modeling process design was performed in two steps: first, the antennas were modeled with air as a surrounding medium, and second, real experiment conditions were taken in an account, therefore antennas on a silicon substrate were modelled. The main consequence is that antenna magnitudes and resonant frequencies were downshifted after adding the silicon substrate to the simulations.

In Fig.4, the simulation results are presented for the first two antennas in the group of eight antennas composing a unit cell. Each v-shaped antenna was simulated by varying

dimensions, while monitoring the magnitude and phase shift of the resonance. This allowed for the selection of the dimensions of the all eight v-shaped antennas such that they exhibit almost identical scattering amplitudes and a π/4 radians phase shift between neighbors, thereby achieving controllable refraction at and by the metasurface.

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Figure 4. HFSS snapshots of the v-shaped antennas resonances when having the antennas surrounded by vacuum. Straight-line antenna (a) and v-shaped antenna with 60 degrees angle between the arms (b). Solid and dashed lines

correspond to amplitude and phase shift, respectively.

Furthermore, the metasurface composed of the v-shaped antennas was modelled. Simulations validated the physics of the metasurface structure and the operation of individual antennas.

III. DYNAMIC LITHOGRAPHY The experimental setup for the non-mechanical beam

steering is a modified version of a "pump-probe" technique. In this setup, the source beam is split in two by using a beam splitter, as shown in Fig.6. The pump beam is the stronger beam, carrying most of the power of incident light, whereas the probe beam is the weaker one. The wavefront of the pump beam is shaped by a spatial light modulator (SLM) and then projected on the silicon substrate. The wavefront of the pump beam is modulated in such a way that when it reaches to the substrate, the intensity profile has the same pattern as the antenna array in Fig.2 Since the wavelength of the radiation incident on the silicon is 800 nm, the energy of the photons in the light beam is higher than the band gap of silicon. Therefore, electron-hole pairs are generated for a short time interval. Due to these free carriers, the antenna structures exhibit metal-like properties.

Figure 6. Schematic diagram of dynamic lithography.

The generation of terahertz radiation is achieved with a photoconductive antenna. The probe beam triggers the operation of the photoconductive antenna, which in turn generates a terahertz signal.. The terahertz radiation is then used to probe the “pseudo-metallic” antenna array. The presence of free carriers in the areas illuminated by the pump beam on the silicon surface create regions of high conductivity that can support a changing current . The incident terahertz radiation produces a current in these conductive areas. As a direct consequence, the antennas will radiate and introduce a phase shift in the wavefront of incident terahertz radiation. Thus, the terahertz beam is both reflected and refracted.

The main advantage of this proposed method of dynamic lithography is that the antenna array is not patterned permanently. A certain pattern is present as long as the expose to the radiation of the pump beam is maintained. By simply changing the phase profile in SLM we are able to change the direction of the steered beam.

IV. OPTICAL SETUP The full schematic of the experimental setup is depicted in

Fig. 7. A Ti:Sa pulse laser of 800 nm wavelength is used as source which is able to produce the average power of 400 mW. The incoming beam from this ultra short pulse laser is then split by the beam splitter (BS) in two parts: pump and probe beam. The pump beam is carrying approximately 90% power of the incident beam, whereas the probe beam is carrying the rest 10%. The wavefront of the incoming pump beam is modulated by the spatial light modulator (BNS, Colorado, USA) such that the illuminated part of reflected beam has the appearance of v-shaped antenna containing metasurface structure as it reaches to the silicon substrate. In this experiment, a high purity float zone silicon wafer of 1 mm thickness is used as sample substrate. When the reflected beam from SLM has reached to silicon substrate, due to the enough power of incident beam free carriers are generated in the illuminated part of the silicon. Therefore, the v-shaped antenna structures shows metal like properties for a short time interval. This time interval depends on the exposure time of laser pulse and carrier life time of silicon substrate.

For the silicon sample, used in this experiment the carrier life time is approximately 1.2 millisecond.

The probe beam is focused by lens L1 to a photoconductive antenna (PCA) which generates the terahertz radiation. The terahertz radiation exhibits in a high divergence profile, therefore a parabolic mirror M7 is used to collimate the terahertz beam and to project terahertz radiation from PCA on the silicon substrate. Due to the metallic property of the v-

Figure 7. Experimental setup: The laser is a Ti:Sa pulsed laser, M1 - M6 are silver coated flat mirrors, M7 and M8 are silver coated parabolic mirrors, BS is a beam splitter, L1 and L2 are lenses, PCA is a photoconductive antenna (Batop Optoelectronics, Germany), RR is a retroreflector, P1 and P2 are polarizers, Si is a silicon substrate, SLM is a spatial light modulator (BNS, Colorado), THz camera is a uncooled bolometer based video camera (INO,

Quebec, Canada).

shaped antennas, terahertz radiation has reflected as well as refracted in a angle determined by the gradient of phase retardation inscribed in the metasurface. The second parabolic mirror M8 is used to focus the refracted terahertz beam to the THz video camera.

One major concerns through this entire experiment is to eliminate the difference between the path length of the pump beam and the probe beam from beam splitter to silicon substrate. Because of the short existing time of the v-shaped antennas on the silicon substrate, path length of the pump beam has to be slightly shorter than probe beam such that the terahertz beam is incident on the substrate right after the metasurface structure has been created. To control this distance a computer controlled delay stage containing retro reflector is used.

A. Gerchberg-Saxton algorithm The Gerchberg-Saxton algorithm is a well-known phase

retrieval algorithm which is used to generate the phase profile of the metasurface structure. It is a recursive algorithm, based on Fast Fourier Transform (FFT) of Cooley and Tukey[3], which is implemented in our programs.

The algorithm starts with a random phase map at the SLM plane, with given intensities in the planes of the silicon substrate and the input image, as depicted in Fig.8. After several iterations, the phase map at the SLM plane is recalculated such that evaluated intensity map in the plane of silicon substrate matches the desired pattern of v-shaped antennas.

Figure 8. Diagram of the optical setup which allows for the projection of the v-shapped antenna pattern onto the silicon substrate in the setup depicted in Fig.7. SLM is the spatial light modulator, f is the focal length of lens L2 and

Si is the silicon substrate.

B. Spatial Light Modulator The spatial light modulator (SLM) from Boulder Nonlinear

Systems (Lafayette, Colorado) used in our experiments operates in reflection mode. Technical parameters of SLM are: the pitch of pixels is 15x15 µm2, the number of pixels in the array is 512x512 pixels, the spatial resolution is 33lp/mm and the array size is 7.68x7.68 mm2 [5]. The SLM is optimized for operating at the wavelength λ=800 nm: the front surface of the SLM is coated with an antireflection coating, with maximum

transmission at 800 nm and the backplane of the SLM is coated with a dielectric mirror with maximum of reflection also at 800 nm.

The main limitation of working with SLM is the intensity for zeroth order of diffraction. In order to reduce this intensity of the zeroth order, two steps were followed: first, the recalibration the SLM and the second one is applying correction coefficients[6] to the phase profile generated by Gerchberg-Saxton algorithm.

1) Calibration of the Spatial Light Modulator: In order to calibrate the SLM, a calibration table called Look-up table is used. The look-up table provided by the manufacturing company is created for normal incident light. But in the experimental setup depicted in Fig. 7, the incoming light from 800 nm pulse laser is incident at an angle of approximately 9.5 degrees relative to the front plane of SLM. Therefore, the recalculation of that look-up table is needed. The calibration procedures include measurements of the phase retardation as a function of gray level for two angles of incident beam, namely 0 (normal incident light) and 9.5 degrees (off-normal incident light). These calibration procedures were performed by using Mach-Zehnder interferometer optical setup.

Figure 9. Experimental setup with Mach-Zehnder interferometer: laser is a mini cw laser diode at wavelegnth λ=785 nm, Ms are silver coated flat

mirrors, O1 and O2 are lenses of spetial filter, Ph is a pinhole, I is an aperture iris, P1 and P2 are two polarizers used to attenuate intensity of light, BS1 and

BS2 are beam splitters, SLM is a spatial light modulator and BP is a beam profiler.

The phase shift of the SLM is measured as a function of the gray level, which represents the amplitude of the applied voltage in the SLM’s software. Varying the applied voltage to the SLM produces change in the orientation of the liquid crystal, which results in the variable index of refraction. Thus the phase shift is measured as a function of gray level.

In order to apply varriable voltage to the liquid crystal molecules in SLM, the gray level of one half of the loaded image is fixed, whereas in the other half gray level is increased from 0 to 255, as demonstated in Fig. 10.

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Figure 10. Examples of three patterns, which demonstrate the fixed gray level 0 on the right hand side and have gray levels of 0 (a), 122 (b), and 255 (c) all

on the left hand side.

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(b)

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Figure 11. Interference patterns captured with Mach-Zehnder interferometer when SLM was loaded with patterns depicted in Fig.10.

Figure 12. Phase shift versus applied gray level based on the data collected with the beam profiler attached to Mach-Zehnder interferometer.

The interference pattern created by the interferometer was recorded with a beam profiler camera BC 106-VIS from Thorlabs. Fig.11 demonstrates three experimental pictures of interference patterns captured when the SLM was loaded with three images depicted in Fig.10. The phase shifts between the two sides of the interference patterns are measured and recorded for all the 255 gray levels.

The phase shifts introduced with normal and tilted incident beams are different, as illustrated in Fig.12. The maximum phase shift is of 4.9π radians in the case of normal incident beam, whereas in case of the 9.5 degree incident angle it is 4.71π radians.

From the phase measurements achieved using the Mach-Zehnder interferometer, a new 16-bit Look-up table is created which allows for the control the phase shift of the tilted incident wavefront from 0 to 2π.

2) Correction coefficients: In order to further reduce the intensity of zeroth diffraction order, a set of correction coefficients is calcualted by using the procedure described by Ronzitti, et. al[6]. These correction coefficients are then applied to the phase map generated with the Gerchberg-Saxton algorithm, which is to be loaded in the SLM.

Vertical, horizontal and checkerboard gratings with spatial frequencies of 2, 4 and 6 pixels are generated and loaded into the SLM. For these gratings, one half of the period is kept with constant phase retardation Φo and the phase of other half of the period is varied from Φo to Φo+2π. The intensities of the zeroth order and first order of diffraction for all these gratings are then measured, which allows for the assessment of the diffraction efficiency and cross talk between the pixels. These values are used to calculate the correction coefficients that allow for higher diffraction efficiencies. By applying this correction to the phase profiles of the gratings, the intensity of zeroth order is minimized significantly, as demonstrated in Fig.13, where a comparison of the v-shaped antennas pattern recorded with the beam profiler is presented for three different situations: using the BNS’s LUT, LUT created with Mach-Zehnder interferometer for off-normal incident angle, and lastly, LUT for off normal incident angle together with applied correction coefficients.

C. Generation of terahertz radiation

A photoconductive antenna, model PCA-44-06-10-800-h from BATOP Optoelectronics, Germany, is used for the terahertz generation in this experimental setup. The wavelength of laser excitation for this PCA model is 800 nm. The arm length of the PCA is 44μm and the gap in between arms is 6μm. The PCA is equipped with a hyperhemispherical

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Figure 13. Images of the v-shaped antenna patterns recorded with the beam profiler after applying: BNS’s LUT (a), LUT created with Mach-Zehnder interferometer (b), LUT created with Mach-Zehnder interferometer and correction coefficient (c).

silicon lens to initially collimate the emitted terahertz radiation.

Figure 14. Schematic of the PCA antenna used to generate THz radiation.

Figure 15. Spectrum of terahertz signal emitted by the PCA antenna. measured with a detection scheme which included a second PCA antenna as a detector.

The short pulse from Ti:Sa laser is focused by lens L1 into the gap between the of the antenna’s metallic contacts. (depicted in Fig.7). The radiation of the pulse generates carriers in the area between the two contacts , therefore closing the circuit. Concurrently, a biasing voltage is applied to the contacts of the antenna, which allows the carriers to be accelerated. The current generated in this antenna radiates a terahertz wave.

D. Detection of terahertz radiation

Detection of the terahertz radiation is performed with a terahertz camera, model IRXCAM-INO384, designed and fabricated by Institut National d'Optique (INO), Canada. The main component of the camera is the uncooled bolometric terahertz detector that allows for a resolution of 384x288 pixels [7].

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Figure 16. Photo of the terahertz video camera [7] (a) and snapshot of terahertz beam (b) generated by PCA antenna.

V. DISCUSSION At this stage in our experiments, the beam steering

produced by the v-shaped antenna pattern excited with the terahertz radiation is under development. The main drawback is the insufficient power of our laser system. The limitation introduced by the SLM, namely the zeroth order of diffraction, has been minimized.

The most important feature of this method of dynamic lithography is that it allows a rapid change of metasurface structures on a semiconductor substrate, which results in the non-mechanical beam steering of terahertz radiation.

VI. CONCLUSION This paper presented an overview of the current stage of

experiments involving dynamic lithography of metasurfaces for beam steering applications in the terahertz range carried out at lab of the Center for Metamaterials, City University of New York.

ACKNOWLEDGMENT

This work is supported by the NSF Industry/University Cooperative Research Center for Metamaterials (IIP-1068028). The authors thank Isroel Mandel for his help with HFSS simulations.

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