1. Introduction

The function of a conventional waveplate is to transform the polarization state of an electromagnetic wave. These are commonly used to convert a linearly polarized beam into a circularly polarized beam (quarter wave retarders), or to rotate the polarization axis of a linearly polarized beam (half wave retarder). In general, waveplates can be either reflective or transmissive, with most commercial products falling into the transmissive variety due to the relative ease of use in optical setups. However, transmissive waveplates are not necessarily possible to develop at arbitrary wavelengths as material birefringence needs to be appropriately tailored in order to achieve the desired polarization control. This cannot only be difficult to achieve, even over a narrow wavelength range, but can also come at the expense of excessive losses.

In the midwave infrared, there are currently a limited number of waveplate options available and material issues make reflective elements appealing. For transmissive operation, birefringent materials e.g. semiconductor crystals like cadmium thiogallate or chalcogenide glasses [1] have shown potential as phase shift materials over broad chromatic operation ranges. Another example of the transmissive variety is a one dimensional dielectric grating, which has been demonstrated in both silicon [2] and diamond [3], though there are direct tradeoffs between efficiency and spectral range. In recent years, both reflective [4] and transmissive [5, 6] waveplates relying on plasmonic resonances have been demonstrated, though efficiency and bandwidth are somewhat limited. In the reflective category, meanderline structures [7] inspired by microwave technology have been applied to the long wave infrared and terahertz frequency ranges as quarter wave phase shifters.

A reflective waveplate used often in the Terahertz which exhibits tunable phase retardation consists of a wire grid polarizer suspended above a metallic ground plane [8]. In these structures, the gap between the components is air filled and the separation distance and induced phase shift can be mechanically controlled. The same phase shift mechanism is employed in this work; however, mechanical tuning of retardation is impractical for the midwave infrared as phase shift is very sensitive to small variations in the sub-micron gap distance. We explore a static system in which a subwavelength one dimensional wire grid polarizer is fabricated on a fixed height dielectric film and an optically thick gold ground plane. By varying the incidence angle and subsequent path length through the device, we numerically and experimentally demonstrate phase shift tuning of a linearly polarized beam, and show precise half wave operation over a ~300 nm wavelength range. With less stringent phase shift standards, ~5% tolerance, the tuning range is extended to ~500nm centered at 3.1 μm. Additionally, we demonstrate near quarter wave retardation at ~2.4 μm wavelength using the same structure, though improvements could be made by proper design for precise quarter wave operation. From the presented work, it is clear that through proper material and geometrical design, the structure can be modified for highly efficient and tunable quarter or half wave operation in arbitrary frequency ranges.

2. Operational principle

The reflective waveplates presented herein operate by generating a path length difference between the orthogonal electric field components of a reflected light beam (See Fig. 1). The upper layer of the structure is a subwavelength grating akin to a conventional wire grid polarizer. When an incident light beam is linearly polarized and oriented such that the electric field makes a 45° angle with the polarizer lines, the parallel component is reflected while the perpendicular is passed. Upon crossing the grating, Snell’s law determines the angle of ray traversal through the spacer layer by the perpendicular polarization component. The additional path length experienced by the perpendicular component of the electromagnetic wave is then defined by angle of incidence as well as the material properties and thickness of the spacer layer. From the incidence angle θ₁,material index n, and spacer thickness h, one can employ ray optics to calculate the effective phase shift, Δφ, generated between the components using Eq. (1) at a given wavelength λ.

 

Fig. 1 Schematic of device with ray trace demonstrating path length difference for orthogonal polarization components. Light with E field parallel to grating (black dot) is efficiently reflected while that with E field perpendicular (arrow) propagates through the dielectric spacer.

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Equation (1) indicates that there is potential for tuning of the phase shift by varying the incidence angle of the beam. However, this simplistic analysis of the device is not strictly accurate as reflection efficiencies for the two polarization components can differ and there can also be multiple reflections within the spacer. In order to better predict behavior and determine device fabrication requirements, numerical simulations were conducted using Lumerical Solutions ltd. FDTD commercial software that will be detailed in section 3. Figure 2 shows simulated phase shift and ray analysis predictions from Eq. (1) versus wavelength for an example structure. While these show reasonable agreement for phase delay in this particular example, Eq. (1) does not take into account reflection efficiencies of real materials which are easily incorporated into the numerical simulations.

 

Fig. 2 Phase shift predictions of FDTD simulation and ray path model for 45 degree incidence angle.

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3. Device simulations

Extensive FDTD simulations were conducted to optimize design and predict performance. The optical properties of the constituent materials, PECVD deposited silicon nitride as dielectric spacer and gold were taken from Infrared-Variable Angle Spectroscopic Ellipsometer (Woollam IR-VASE) measurements and Palik [9] respectively. Simulations were performed using assuming periodic boundary conditions on a unit cell consisting of a single period of the structure. Initial simulations were conducted at a 45 degree incidence angle for a wavelength of 3.1 μm where power and electric field monitors were employed to measure efficiency and induced phase shift. Narrowband pulses at the design wavelength were used as sources in the simulation and the propagation of the pulses was monitored in the time domain. The phase shift was quantified by analyzing the time delay between the orthogonal polarization components shown in Fig. 1.

Device geometry optimization began by sweeping wire grid polarizer periodicity and line width. From these results, a periodicity of 220 nm and line width of 70 nm was found as the optimum combination for total reflection efficiency and the minimization of dichroism. Next, sweeps of spacer height were performed while monitoring phase shift which indicated a value of ~400 nm for half wave operation, with results shown in Fig. 3. Lastly, with grating periodicity, grating width and spacer height fixed from the above results, the incidence angle of the beam was varied from 25 to 65 degrees along with the wavelength (2.8-3.4 μm) to determine the extents of the tuning range of the structure, the results of which are shown in Fig. 4. As can be seen from the figure, precise half wave operation of the device can be tuned over a wavelength bandwidth of ~300 nm while a 5% tolerance on phase shift allows for tuning over a 500 nm bandwidth.

 

Fig. 3 Phase shift and reflection efficiency FDTD simulation results versus dielectric spacer height.

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Fig. 4 FDTD predicted phase shift versus incidence angle for various wavelengths of interest.

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4. Fabrication and characterization

The device was fabricated on a silicon substrate. Ground plane metallization of 10 nm titanium adhesion layer and 100 nm gold was followed by deposition of PECVD silicon nitride to a thickness of ~400 nm. Next e-beam lithography was performed to pattern the 220 nm period 70 nm line width grating pattern and another e-beam metallization of a 5 nm titanium adhesion layer and 50 nm gold deposition followed by liftoff was used to make the final grating structure. The wire grid patterning was performed over a 5 mm x 5 mm area to simplify optical measurements. An SEM image of a device profile is shown in Fig. 5.

 

Fig. 5 SEM image of device profile.

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Device characterization was conducted using an M Squared Firefly–IR OPO laser system with idler output tunable between 2.4 and 3.6 μms. The OPO power was first attenuated with a combination of neutral density filters and then passed through a wire gird polarizer resulting in a linearly polarized beam oriented at 45 degrees with respect to the grating lines. The beam was passed through an optical chopper set to 650 Hz and was shaped with 2 mm iris aperture to only interact with the patterned surface. After striking the sample, the reflected signal was passed through a second analyzing wire grid polarizer mounted on an automated rotation stage before being collected with a Kolmar technology InSb detector, which was monitored with a signal recovery 7550 lock in amplifier.

From the FDTD simulations of reflection efficiencies for the orthogonal electric field components and the phase shift induced between them, the output of the final polarizer was calculated in order to be compared with the collected data. In this analysis, we define the x-axis to be along the grating lines of the structure and normal to the plane of incidence. Given a beam with intensity I₀ linearly polarized at some angle α with respect to the x-axis, the optical intensity passed by a linear polarizer at angle θ with respect to the x-axis is given by

However, when an elliptically or circularly polarized beam is incident upon a linear polarizer, the transmitted power is given by a linear combination of Eq. (2) applied to the major and minor axis of the ellipse, i.e.

 

Fig. 6 (a) Normalized measured signal versus polarizer angle. (b) FDTD simulated normalized results.

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Fig. 7 (a) Simulated and measured intensity radar plots for (a) 3.1 μm light at 45° incidence angle, (b) 3.3 μm light at 25° incidence, (c) 3.0 μm light at 55° incidence, and (d) 2.4 mm light at 25 ^o incidence.

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Phase shift tuning was demonstrated by repeating the experiment for both 25° and 55° incidence angles. Figure 7(a) shows the recorded data and FDTD simulation results for half wave operation of 3.3 μm radiation at 25° incidence angle. Similarly, Fig. 7(b) and 7(c) show measured and simulated data plots for 3.3 μm at 25° incidence and 3.0 μm at 55° incidence respectively, again exhibiting half wave operation.

This device design has the potential to be tuned to arbitrary wavelength and phase shift ranges thorough judicious choices in materials and geometry. However, the data trends of Fig. 4 imply that for a sufficiently short wavelength, the induced phase shift would be 0.75 ⋅2π. Rather than construct a new sample with optimized dichroism and reflection efficiencies for first order quarter wave operation, we demonstrate nearly first order quarter wave performance of the structure by repeating the measurement for 2.4 μm light at an incidence angle of 25°, as shown in Fig. 7(d) along with simulations of the structure. Though perfect quarter wave retardation would result in a clean circular radar plot, the suitability of the structure for modification to that end is evident.

Efficiency measurements of the structures were performed in a similar manner as the optical activity measurements but without neutral density filters and using a pyroelectric power meter as the detector. The reflected power was measured without an analyzing polarizer and back ground corrected with the power meter placed in the optical path preceding the sample surface. Figure 8 shows the FDTD predicted efficiencies versus those measured for an incidence angle of 45° over the OPO’s entire tuning range.

 

Fig. 8 FDTD simulated and measured reflection efficiency of fabricated device over OPO tuning range.

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The modest offset for the measured sample is attributed to the imperfect metallization (roughness evident in Fig. 5) and a possible variation in complex refractive index between the measured values used in simulation and those of the employed materials. Efficiencies for half wave operation at 3.3 μm for incidence angle 25° and 3.0 μm for incidence angle 55° were simulated to be 94% and 92% and measured to be 89% and 87.5% respectively. While further optimization can be performed, it is clear that reasonable efficiency can be obtained using this approach.

5. Conclusion

In this work, an incidence angle tunable reflective waveplate for the midwave infrared wavelength range was studied. Using extensive FDTD simulations device performance was analyzed and shown to agree well with values measured on fabricated devices. The general device design was shown to be capable of operating as a quarter or half waveplate polarizing structure with the possibility of high efficiency enabling high power density applications. In addition, the possibility of nano-imprint lithography as a replacement for e-beam lithography could reduce costs and make such a device a viable and affordable alternative to current commercially available devices.