Fabricating Dual-Sided Micro Lenses and High Frequency Talbot Diffraction Gratings Using Binary Masks

and Introduction: Binary photomasks are a way of approximating 3D structures when using photolithography. Multiple masks are used and the surface of a substrate is etched into a number of distinct heights. A Fresnel lens was made employing this method, and was etched into both sides of a quartz substrate; the advantage of using a phase mask on both sides of a lens is that the diffraction effects that take place inside of the medium can be taken advantage of. This idea eventually was carried over to make a diffraction grating that used what is called the “Talbot Effect. ” This effect describes the phenomenon where light that passes through a periodic grating repeats the grating pattern in the near field at certain distances termed the Talbot length (ZT). The frequency of the pattern doubles at a quarter of ZT. By creating relatively shifted diffraction gratings on either side of the substrate, we effectively created a higher frequency grating. Experimental Procedure: The Fresnel lens was simulated in MATLAB by first simulating the phase of a conventional lens [1] with a focal length of 50 cm; then the mod function was used on this phase to turn the lens into a Fresnel lens. Masks transferred into Clewin software would approximate the three dimensional surface in eight distinct heights. These binary masks were made on a single chromium photomask in the Heidelberg DWL 66FS and were used to expose our substrate in the SUSS MJB3 Maskaligner. Our substrate consisted of a fused silica slide with a 40 nm coating of chromium (Cr) on one side, which aided in alignment. Negative resist (NR9) was used in the photolithographic process to create the first Fresnel lens. First an aperture was created in Cr by etching it with a chemical known as CR-7S. The fused silica was etched in the Plasma-Therm reactive ion etch II (RIE II), which etched the surface using a plasma. A 3:1 mixture of tetrafluoromethane and trifluoromethane gases was used at a temp erature of 25°C giving an etch rate of 12 nm per minute. For a material of refractive index n(λ), the etch depth for a phase difference of 2π is given by h2π = λ/(n(λ)-1). The etch time for the ith photomask is given by t2π/2 i, where t2π is the etching time for h2π. This lens was made again on the other side of the substrate, opposite of the Cr coated side effectively creating a lens of focal length of 25 cm when using HeNe laser light. Our Talbot grating was also simulated using MATLAB software. Our substrate for these gratings was a 1 mm thick quartz substrate, which also had a 40 nm coating of Cr on one side. We used the equation provided by Lord Rayleigh [2] in Figure 1 to determine our grating period so that the ZT would be four times the substrate thickness; this meant that at 1 mm, the intensity pattern of the grating would have twice the frequency as the original grating. The photolithographic process for making the Talbot grating was the same as earlier, except we only needed one etch into the quartz on each side to make the phase grating. The same grating was made four times on the Cr side of the one-inch square substrate in a 2×2 array. On the opposite side, two gratings were made; one grating was shifted by one fourth of a period, and the other was shifted by one half. This was so the effect on the diffraction pattern of the two could be compared against the grating etched on a single side. Figure 1: Equation to determine ZT. The letter a represents the grating period. Figure 2: Top view of the MATLAB simulation of the Talbot grating.