Methods

Chapter II: Single-shot quantitative phase gradient microscopy using a system

2.8 Methods

Simulation and design

The simulation results presented in Fig.2.A.4were obtained by finding the transmis- sion coefficients of corresponding periodic metasurfaces using the rigorous coupled wave analysis technique [95]. The amorphous silicon nano-posts were assumed to be 664 nm tall and the square lattice constant was 380 nm. The nano-posts are capped with an 8-𝜇m-thick SU-8 polymer layer. Refractive indices of amorphous silicon, fused silica, and SU-8 for the operation wavelength of 850 nm in the simu- lations were 3.56, 1.44, and 1.58, respectively. Side lengths of the nano-posts, 𝐷_𝑥 and 𝐷_𝑦, were varied in simulations to achieve full and independent phase control over the 2𝜋 range for𝑥 and 𝑦 polarizations (see Figs.2.A.4a-2.A.4dfor the simu- lation results) [13]. Next, we optimized 𝐷_𝑥 and 𝐷_𝑦 as functions of𝜙_{𝑇 𝐸} and 𝜙_{𝑇 𝑀} to provide high transmission and desired phase shifts. The optimized maps of the side lengths as functions of the phase delays for TE and TM polarized light are plotted in Figs. 2.A.4e and2.A.4f (see Figs.2.A.4g and2.A.4h for the simulated transmittance corresponding to TE and TM polarizations). For the double-sided metasurface device, while the metasurface layer 2 is designed by the same lookup table in Figs. S4e and S4f, the metasurface layer 1 was composed of nano-posts having a 60-nm-thick Al₂O₃layer on top of the amorphous silicon layer. To consider the presence of the Al₂O₃layer, we performed additional simulations with the new condition. In particular, the refractive index of Al₂O₃for the operation wavelength in the simulation was 1.76. The optimized results are plotted in Figs.2.A.4i-2.A.4l.

We used the wave propagation method for the numerical studies of Fig. 2.A.1 to calculate the optical fields for TE and TM polarized light. Then, the interference intensity patterns at the image plane can be directly calculated from the TE and TM polarized fields. Metasurfaces are treated as phase plates in simulations, and their phase profiles used in the numerical simulations are given in Appendix 2.1. It is worth noting explicitly that the optimal phase profiles of the two metasurface layers in

19 Fig.2.A.1ewere obtained through optimization with the ray-tracing technique using a commercial optical design software (Zemax OpticStudio, Zemax) to minimize geometric aberrations.

Device fabrication

The metasurface layers 1 and 2 shown in Fig.2.2dwere fabricated on two different 1-mm-thick fused silica substrates. A 664-nm-thick layer of amorphous silicon was deposited using the plasma enhanced chemical vapor deposition technique. For nano-patterning, a∼300-nm-thick positive electron resist (ZEP-520A) was used. In addition, a∼60-nm-thick water soluble conductive polymer (aquaSAVE, Mitsubishi Rayon) was spin-coated for charge dissipation. The patterns were generated using electron-beam lithography (EBPG-5000+, Raith). The conductive polymer was then dissolved in water and the resist was developed in a resist developer solution (ZED- N50, Zeon Chemicals). A 60-nm-thick Al₂O₃layer was deposited by electron beam evaporation. The pattern was transferred to the Al₂O₃layer by a lift-off process in a solvent (Remover PG, MicroChem). The patterned Al₂O₃layer worked as a hard mask to etch the amorphous silicon layer. The dry etching step was performed in a mixture of SF₆ and C₄F₈ plasmas using an inductively coupled plasma reactive ion etching process. The Al₂O₃mask was dissolved in a 1:1 mixture of ammonium hydroxide and hydrogen peroxide heated to 80^◦C.

The double-sided metasurfaces shown in Fig.2.4bare patterned on both sides of a 1-mm thick fused silica substrate. Two 664-thick layers of amorphous silicon were deposited on both sides of the substrate using the plasma enhanced chemical vapor deposition technique. Then, the metasurface layer 2 was first fabricated using the same process employed for the single-sided metasurfaces. Then, metasurface 2 was cladded by an SU-8 polymer layer (SU-8 2002, MicroChem), which served to protect metasurface 2 during the fabrication of the metasurface 1. A 4-𝜇m-thick layer of SU-8 was spin-coated on the sample, baked at 90^◦C for 4 minutes, and reflowed at 200^◦C for 5 minutes to achieve a completely planarized surface. The SU-8 polymer was then exposed with ultraviolet light and cured by baking at 200^◦C for another 90 minutes. To align the metasurface layers 1 and 2, a second set of alignment marks were patterned on the side of the metasurface 1 and aligned to the alignment marks on the side of the metasurface layer 2 using optical lithography. Next, metasurface 1 was fabricated by the same method as the single-sided metasurfaces. However, the Al₂O₃ mask was not removed from the top of the metasurface layer 1 because a mixture of ammonia and hydrogen peroxide at 80 ^◦C would damage the SU-8

both sides to protect the apertures.

Measurement procedure

The imaging performance of the QPGM was characterized using the setups shown schematically in Fig. 2.A.6. An 850-nm LED (Thorlabs LED851L) was exploited as the light source. A linear polarizer (Thorlabs, LPVIS100-MP2) was placed in front of the LED and set at 45^◦ to confirm the polarization state of the input light.

The sample image was captured by the two metasurface layers which are mounted on three-axis translation stages to enable alignment. The field at the image plane of the QPGM was captured by a custom-built optical microscope. The microscope consists of an objective lens (Olympus, LMPlanFL 10×) and a tube lens (Thorlabs AC254-150-B-ML, focal length of 15 cm). The second linear polarizer, set at - 45^◦, was inserted between the objective lens and the tube lens to form interference between𝑥- and𝑦- polarized light. An optical band pass filter (Thorlabs, FL850-10) in front of the camera was used to limit the bandwidth of the LED and remove the background. For the double-sided metasurface devices, the optical system is almost the same as the one used for the two separated metasurface layers. The double-sided metasurface device was mounted on one three-axis translation stage instead of two.

For the setup shown in Fig.2.A.11a, a CMOS image sensor (MT9J001, Arducam) replaces the custom-built microscope. A 260-𝜇m-thick linear polarizer (LPVIS100- MP2, Thorlabs) is attached on top of a glass substrate protecting the CMOS image sensor by a double-sided tape. As shown in Fig. 2.A.11a, the band-pass filter is placed between a LED and a lens (LB1761-C, Thorlabs).

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