Dielectric Meta-Reflectarray for Broadband Linear Polarization Conversion and Optical Vortex Generation

Transcription

1 Supporting Information Dielectric Meta-Reflectarray for Broadband Linear Polarization Conversion and Optical Vortex Generation Yuanmu Yang, Wenyi Wang, Parikshit Moitra, Ivan I. Kravchenko, Dayrl P. Briggs, Jason Valentine 1. Device Fabrication Amorphous silicon (Si) (n=3.7) was chosen as the resonator material due to its high index contrast. In order to incorporate the silver mirror while also using low pressure chemical vapor deposition (LPCVD) for the Si layer, we reversed the conventional fabrication steps by first depositing silicon on quartz, followed by patterning the cut-wires and addition of the low index spacer and silver mirror. Amorphous Si was deposited on quartz using an LPCVD horizontal tube furnace. A quartz caged boat was used to contain the wafer to improve cross wafer uniformity. Deposition temperature was 550 C and process pressure was 300 mtorr. Process gases were introduced into the tube furnace via mass flow controllers by flowing 50sccm s of 100% SiH4. The silicon cut-wire patterns were created by a sequential process of electron beam lithography (EBL), mask deposition, lift-off and reactive-ion etching (RIE). In the EBL process, we coated a 10 nm chrome charge dissipation layer on top of PMMA resist to avoid surface charging, and the chrome layer was subject to chemical removal prior to the resist development. The total pattern size was ~1 mm x 1 mm for the polarization converter and 3 mm x 3 mm for the vortex beam generator, both patterns were written using a JEOL 9300FS 100kV EBL tool.

2 We used a fluorine-based RIE recipe to etch the silicon with 80 W RF, 1200 W ICP power and C4F8, SF6, O2 and Ar gas flows. PMMA was then spin-coated on the sample, followed by soft baking (180 degrees for 2 minutes) and reflowing at 300 C for 2 minutes to reach the desired thickness and flatness. In the last step, 150 nm of silver was thermally deposited on top of the sample, serving as the ground plane mirror. The entire process is summarized in Figure S1. Figure S1. (a) LPCVD silicon on quartz. (b) EBL patterning. (c) Etch mask deposition and liftoff. (d) RIE. (e) PMMA spinning and silver deposition. 2

3 2. Modeling a. Reflectance and phase simulations Numerical simulations presented in Fig. 2 and Fig. 3 of the manuscript were carried out using a commercially-available software (CST Microwave Studio 2013) using the finite-element frequency-domain (FEFD) solver with periodic boundary conditions for each unit cell. We calculated the complex reflection (transmission) coefficient for both cross- and co-polarized light with a TE (transverse electric) or TM (transverse magnetic) mode at the incident port followed by probing reflection (transmission) in both the TE and TM modes. b. Device Performance With Varying PMMA Thickness The optimal PMMA thickness is determined through a though parameter sweep using FEFD simulations. Here we provide the waveplate performance as a function of the PMMA thickness (Figure S2). As can be observed, the highest polarization conversion efficiency occurs at a PMMA thickness of 200nm, though the metasurface maintains >90% efficiency for thicknesses ranging from 150 nm to 225 nm over the wavelength span of 1400 nm to 1700 nm. Figure S2. (a) Cross-polarization reflectance and (b) polarization conversion efficiency of the meta-reflectarray half waveplate with varying PMMA thickness. 3

4 c. Device Performance With Changing Incident Angle Here, we provide the angle-dependent response of the meta-reflectarray for both s- and p- polarized light (Fig. R3). From the result, we find two interesting features. First of all, the bandwidth of the response is reduced with increased angle of incidence and at off-normal incidence a high Q-factor guided mode resonance is excited. This sharp resonance is in fact a Fano resonance arising from interference of the free space excitation and a photonic crystal mode in the film 1,2. This will limit the use of the surface to normal incidence when using broadband illumination. However, if narrowband illumination is used, the surface can still be used for illumination angles up to 10 while still preserving a near-unity polarization conversion. Figure S3. Cross-polarization reflectance as a function of incident angle for (a) s- and (b) p- polarized light. 4

5 d. Multiple Reflection Theory and Resonance Positions The linear to linear polarization conversion can be explained with a multiple reflection model, as is shown in Figure S4. The resonator array, the PMMA spacer and the metal ground plane are each treated as an individual layer. For the resonator layer, light incident onto the top surface can couple into the resonators and then radiate back to the environment with the amplitude and phase being modified differently for co- and cross-polarized fields. The layer of resonators can then be regarded as an effective layer with the light being re-radiated treated as being reflected or transmitted. The complex reflectivity and transmissivity from the resonator layer is obtained from FEFD simulations from an array of resonators embedded in PMMA without the metal ground plane. The reflectivity and transmissivity are expressed as r and t where =0 for co-polarized fields and ρ = 1 for cross-polarized fields. Based on the multiple reflection model, the reflected field, E ', j (j represents the jth pass), from each individual pass is given by where E ', j 1 Eincr ' 2 2 E ' 0, j 2 Einc( t0 t1 )exp( i2 k0n0d) rm E E tt exp( i2 k n d) r 2 E E t C r r t C r r tt C r ' 1, j 2 inc m j 2 j 2 j 2 l j 2 l l 2 l j 2 l l l j 2 l l j 1 ' 0, j,( j 3) inc( 0 j j j 2 0 r1 )exp( i2 k0n0d) rm l 0 l 0 l 1 ( l even) ( l even) ( l odd ) j 2 j 2 j 2 2 l j 2 l l 2 l j 2 l l l j 2 l l j 1 ' 1, j,( j 3) inc( 0 j j j )exp( ) m l 1 l 1 l 0 ( l odd ) ( l odd ) ( l even) E E t C r r t C r r tt C r r i k n d r E inc is the incident electric field, k 0 is the free space wave number, n 0 is the refractive index of PMMA, d is the spacer thickness, l is an integer number smaller than (j-2) and represents the number of times that the polarization is rotated upon reflection at the bottom surface of resonator layer in the jth pass. As a field being cross-polarized twice will return to a 5

6 co-polarized field, the requirement for the jth path, E ', j to be co-polarized is that 1 appears an even number of times in the equations. The same is true for cross-polarized field where 1 can only appear an odd number of times. The overall reflection for both co- and crosspolarization is the sum of individual passes E ' E ',j. The simulated overall reflected field and the calculated sum of the reflected field of each pass are plotted in Figure S4b. The result from the FEFD simulation and the calculation shows good agreement in both co- and crosspolarization, which corroborates the theory. j Figure S4. (a) Schematic of the multiple reflections. (b) Comparison between the calculated reflected field from multiple reflections and the simulated overall reflected field. The bandwidth of the metasurface can be partially understood by the fact that we are working between the long and short axis resonances of the unit cell. To illustrate this fact, we have plotted the scattering cross-sections of isolated resonators (a = 250 nm, b = 500 nm) for illumination along the short and long axis in Fig. S5(a,b), respectively (λ0 = 1550 nm). The positions of these resonances for the case of the periodic reflect-array are also shown in Fig. S5(c,d) where we have denoted their position in both the S11 and reflected phase plots. In addition to working between the resonances, the multi-reflections within the spacer layer result 6

7 in smoothing of the phase variation across the resonances, ultimately resulting in the ~200 nm bandwidth across which a π phase variation is maintained. Figure S5. (a,b) Scattering cross-sections of isolated resonators when illuminated along the short and long axis, respectively. (c) S 11 of the reflect-array formed from the resonators showing the resonance positions. The blue and red dashed lines correspond to illumination along the long and short axis, respectively. (d) Phase advance in reflection for illumination along the long (blue) and short axis (red) demonstrating broadening of the resonances and the fact that the polarization conversion region is occurring primarily between L1,S1 and L2,S2. e. Realizing 2π phase control at visible frequencies It is of great interest to realize 2π phase control in the visible frequencies. However, due to the lack of transparent high index materials at visible frequencies, this becomes difficult as a high index contrast (and thus sharp resonance) is required to achieve 2π phase control with one layer of resonators. However, the index contrast requirement can be greatly relieved if we incorporate the metal ground plane because in that case we get multiple light passes through the 7

8 resonator. Therefore, transparent materials at visible wavelengths, such as TiO2, can be applied as the resonator material. Since high quality TiO2 can be deposited using techniques such as electron beam evaporation, the fabrication process can be simplified from that of the Si based process. Figure S6. (a) Schematic of the TiO2-based visible frequency device. (b-c) simulated reflection (b) amplitude and (c) phase for the cross-polarized light with varying dimensions at a fixed wavelength of 632 nm. The unit cell period is 425 nm, the resonator height is 100 nm, and the Al2O3 spacer thickness is 25 nm. The dimension of resonators 1-4 are 1) a=160nm, b=280nm; 2) a=175nm, b=290nm; 3) a=200nm, b=300nm; 4) a=215nm, b=325nm, and resonators 5-8 are simply rotated by 90 with respect to resonators 1-4. Figure S6a shows a schematic of a TiO2-based reflect array, and the simulated reflectance and phase are shown in Figs. S6b-c. The four phase elements we chose all have a cross-polarized reflectance greater than 85%, and the phase increment is kept at π/4. The illumination wavelength is 632 nm and the period of the array is 425 nm. The lower conversion efficiency compared to silicon is primarily due to loss in the silver backplane rather than an intrinsic inefficiency in the resonator design. 8

9 3. Vortex Beam Characterization Figure S7. Schematic of the Michelson interferometer. In order to characterize the quality of the generated vortex beam as well as the polarization conversion efficiency of the reflectarray, a Michelson-type interferometer was employed (Figure S7). A fiber-based diode laser was passed through a linear polarizer, P1, with its transmission axis oriented along x-axis of the sample, after which it was separated into two beams which were directed to the sample and reference arm. The recombined beams were ensured to have the same polarization by placing a quarter waveplate in the reference arm. Finally, an indium gallium arsenide camera was used to measure the interference patterns with and without a second polarizer, P2, which was used to filter out co-polarized light, as discussed in the main text. For the tilted interference pattern obtained in Figures 4(f) (h), we tilted the 9

10 beam in the reference arm and made sure the E-field of the Gaussian beam is always along the transmission axis of polarizer P2 to ensure that the reference beam is not filtered out. 4. Anomalous Reflection Figure S8. (a-c) Cross-polarized electric field profile of the beam deflector at 1500 nm, 1550 nm and 1600 nm, respectively. (d-f) Comparison of the far-field profile of the beam deflector for cross-polarized and co-polarized light at 1500 nm, 1550 nm and 1600 nm, respectively. Here we numerically demonstrated broadband beam deflection by the resonators, laid out side by side, with a π/4 phase variation between neighboring antennae (refer to the designed structure in main text). A Gaussian beam with beam waist diameter of 7 μm was incident normally onto the meta-reflectarray. The cross-polarized reflected electric fields at multiple wavelengths (1500 nm, 1550 nm and 1600 nm) are plotted in Figs. S8a-c, respectively. The 10

11 simulated anomalous reflection angle (11.1 for 1500 nm, 11.5 for 1550 nm, 11.8 for 1600 nm) matches exactly with the calculated result from the equation arcsin np r, where r is the reflection angle, 0 is the free space wavelength, n0 is the refractive index of PMMA and p0 is the period of the 8-resonator-supercell. The directivity of scattered co- and cross polarized reflected light is plotted in Figs. S8d-f, demonstrating high conversion efficiency from co -to cross- polarized light. The 1 st order diffraction efficiencies for 1500 nm, 1550 nm, and 1600 nm are 80%, 83%, and 82%, respectively. 5. References 1. Fan, S. & Joannopoulos, J. Analysis of guided resonances in photonic crystal slabs. Phys. Rev. B 65, (2002). 2. Lee, J. et al. Observation and Differentiation of Unique High-Q Optical Resonances Near Zero Wave Vector in Macroscopic Photonic Crystal Slabs. Phys. Rev. Lett. 109, (2012). 11