We discuss the design, fabrication and optical performance of a broadband form-birefringent quarter-wave plate for the 3.5 to 5 µm wavelength region. Rigorous coupled wave analysis (RCWA) was used to design the requisite subwavelength grating for silicon substrates in ambient air. Fabricated samples yield a measured phase retardation of 89° to 102° over the desired wavelength range.
©1999 Optical Society of America
Subwavelength gratings are attractive for compact implementations of polarization-sensitive devices such as wave plates [1–3] and polarizing beam splitters [4,5]. In particular, wave plates for single wavelength operation have been previously fabricated as surface relief structures in silicon nitride , GaAs [2,4], and amorphous silicon . Recently, Kikuta et al.  proposed a method of creating achromatic form birefringent wave plates by compensating for the usual 1/λ dependence of the phase retardation with the strong dispersion exhibited by form birefringence when the grating period is on the order of the optical wavelength. For example, in one of their design studies a retardation error of only 3° is predicted for a ±10% change in wavelength . In this paper, we report the first physical implementation of a broadband form birefringent wave plate that makes use of form birefringence-based dispersion. In this case we have designed, fabricated, and tested a quarter-wave plate for the 3.5 to 5 µm wavelength region. The resultant device represents a potentially attractive alternative to the only other mid-infrared achromatic wave plate currently available, which involves the use of two uniaxial materials .
In designing a broadband form birefringent quarter-wave plate, we used rigorous coupled wave analysis (RCWA) to examine the effects of several parameters on the phase retardation and transmission characteristics of a subwavelength grating. As illustrated in Fig. 1, these parameters include the grating period, Λ, fill factor, F=a/Λ, and thickness, t. The substrate is silicon with air as the ambient medium. Normally incident illumination is assumed, and TE (TM) polarization is defined as the electric field parallel (perpendicular) to the grating ridges. The refractive index of Si as found in Ref. 9 was used in the RCWA calculations reported in this paper. All simulations included dispersion.
Based on our original application, we desired to achieve a phase retardation of 0.5π±0.1π over the 3.5 to 5 µm wavelength range. By systematically varying the values of the grating period, fill factor, and thickness, we found that a grating period of 1 µm, a fill factor of 66% (i.e., trench width of 340 nm), and an etch depth of 1.25 µm yield a satisfactory dispersion in the effective refractive index with which to compensate the 1/λ dependence of the phase retardation. We then determined the sensitivity of the retardation to small fabrication errors in the grating fill factor and thickness. For example, as shown in Fig. 2, only a narrow range of fill factors (64–68%, which corresponds to a trench width tolerance of +/-20 nm) satisfies the desired phase retardation criteria while the etch depth tolerance is less severe. Clearly, tight control of the fill factor is essential for the successful fabrication of a broadband structure.
Our fabrication process began with 75 mm diameter p-type <100> silicon wafers with a resistivity of 1–20 ohm-cm. Photolithography was done with a contact mask aligner (made by AB-Manufacturing) that had a mercury arc lamp source. We used a 5″×5″ dark field photomask with a grating region that consisted of 500 nm wide chrome lines and spaces within a 1.3 cm×1.3 cm area in the center of the mask. Wafers were prepared for photolithography by first spin coating an aqueous-based adhesion promoter (Surpass 1000 from DisChem, Inc.) followed by a 500 nm thick layer of Shipley 1805 photoresist. Samples were then softbaked at 115°C for one minute on a vacuum hotplate.
Vacuum contact printing of small feature sizes, such as the 500 nm lines and spaces of the photomask used here, poses significant challenges. We have, however, been able to achieve uniform and well-defined grating patterns in photoresist over nearly the whole 1.3 cm×1.3 cm grating area defined on our mask. A critical factor is turning off the substrate vacuum prior to exposure, which allows better vacuum contact between the mask and the wafer. Furthermore, by carefully controlling the exposure, we are able to tightly control the photoresist fill factor which is a critical precursor to achieving the desired silicon grating fill factor. For example, as shown in Fig. 3(a), we found that an exposure of 3.3 seconds (for measured intensities at 365 nm and 405 nm of 16 mW/cm2 and 9.9 mW/cm2, respectively) and a 1 minute development time in Microposit 352 developer resulted in a grating pattern with an approximately 30% photoresist fill factor.
After photoresist patterning, a lift-off method was used to create a chrome etch mask on the silicon substrate. To assure good adhesion between the chrome and the substrate, a short oxygen plasma etch is employed to remove any residual photoresist present after development. A 250 nm thick chrome layer is deposited over the patterned photoresist, following which the wafer is immersed in acetone and gently wiped with a foam-tip applicator to aid in achieving lift-off. Typical results are shown in Fig. 3(b).
The grating pattern is transferred into the silicon substrate by reactive ion etching in a Plasma-Therm 790 system with 9.5″ diameter electrodes. We used a graphite electrode cover plate. CHF3 and SF6 were used to achieve an anisotropic etch based on polymer sidewall passivation . The process parameters include gas flow rates of 34 and 6 sccm for the CHF3 and SF6, an RF power of 125W (0.27W/cm2), and a pressure of 10 mTorr. This results in a Si etch rate of 16 nm/min. A typical grating cross section is shown in Fig. 4. The etch depth is approximately 1.23 µm and the sidewalls are slightly sloped. There is also some evidence of a small amount of redeposited silicon on the upper sidewalls.
The fabricated subwavelength grating was optically tested using an FTIR-based spectropolarimeter. The phase retardation and the transmission coefficients of the TE and TM modes were measured at normal incidence. A comparison between these measurements and RCWA simulations of the etched grating profile, which was approximated by a 6-layer binary grating stack, is shown in Fig. 5. The grating stack parameters used in the simulation are listed in Table 1. As illustrated in Fig. 5(a), the measured phase retardation of the quarter-wave plate over the 3.5 to
5 µm wavelength range varies from 0.49π to 0.57π (89° to 102°), and the RCWA simulation result compares well with experimental measurement. Note that the measured phase retardation is flatter over the left-hand third of the retardation curve than the simulation results shown in Fig. 2(a) would suggest. Our simulation experience indicates that this beneficial effect is likely due to the slightly sloped sidewalls of the etched grating profile.
The transmission measurements and corresponding RCWA results are shown in Fig. 5(b). Since the backside of the silicon wafer was not anti-reflection coated, the RCWA transmission values are adjusted to include a 30% Fresnel loss at the backside of the wafer to facilitate direct comparison with measurement. The measured transmission coefficients of the TE and TM modes vary between 52% and 60%. In comparison with RCWA simulation, one can see that RCWA agrees qualitatively with the measured values, although there is some quantitative difference at shorter wavelengths.
We have designed, fabricated, and measured the optical performance of a subwavelength grating for use as a broadband quarter-wave plate over the 3.5 to 5 µm wavelength region. Dispersion of the effective refractive indices when the grating period is on the order of the wavelength is clearly an effective method of compensating for the usual 1/λ dependence of the phase retardation as long as the grating parameters are carefully controlled in the fabrication process. Such grating structures offer an attractive and flexible method of implementing broadband wave plates in the infrared.
G. P. Nordin acknowledges support by National Science Foundation CAREER Award ECS-9625040 and grant EPS-9720653. P. Deguzman acknowledges support by a National Science Foundation Traineeship (grant GER-9553475). The authors also wish to thank Lynn Deibler and Dr. Matthew H. Smith for performing the spectropolarimeter measurements.
References and links
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