The birefringence (double refraction of light into polarized ordinary and extraordinary rays) of liquid crystals (LC) is well known and used extensively to manipulate optical radiation in visible and near-IR light. Recently, we showed that several LCs are relatively transparent (extinction coefficient of 2cm-1) and exhibit substantial birefringence magnitude, Δn=0.1, in the terahertz (THz)—or sub-millimeter wavelength—region. Thus, it should be feasible to produce new THz photonic elements with LC-enabled functionalities such as phase shifters, modulators, attenuators, and polarizers.
To illustrate, we present the principle and performance of an LC-based Lyot filter. It has two phase retarder elements, A and B, separated by a linear polarizer (see Figure 1). Each retarder element consists of a fixed retarder (FR) and a tunable retarder (TR). The FR consists of a pair of permanent magnets sandwiching a homogeneously-aligned LC cell (i.e., the LC molecules align parallel to the substrate). The homogeneous cells in FRA and FRB supply fixed phase retardations, GA and GB, for THz waves. The tunable retarders, TRA and TRB—see Figure 1(b)—are homeotropically-aligned LC cells (i.e., LC molecules align perpendicular to the substrate) at the center of a rotatable magnet. TRA and TRB are used to achieve the desired variable phase retardation, ΔGA and ΔGB.
Figure 1. Schematic diagram of a liquid-crystal-based tunable terahertz (THz) Lyot filter. LC: liquid crystal. P: polarizer. N: north pole. S: south pole.
Because of the birefringence of LC, the THz waves that pass through each element separate into extraordinary and ordinary rays (e-ray and o-ray) with corresponding time delays between the e-ray and o-ray, ΔtA and ΔtB, respectively. This Lyot filter is designed such that ΔtB=2ΔtA. The first maxima of the transmittance of the Lyot filter, T(f), occur when ΔtA·f=1, where f is frequency of the THz wave. The homogeneous LC layer in FRA and FRB are 4.5 and 9mm thick, respectively. The LC layers in homeotropic cells for TRA and TRB, are 2 and 4mm thick, respectively. The retardation of THz waves transmitted through the homeotropic cells is tuned by rotating the magnets. The retardation provided by the homeotropic cells, TRA and TRB, is zero when the LC molecules are parallel to the propagation direction of THz waves and increases with reorientation of the LC molecules as the magnets rotate.1,2
Figure 2. An example of the transmitted spectrum of the broadband THz pulse through the LC THz Lyot filter, obtained by taking the fast Fourier transform of the time-domain transmitted THz signal, which is shown in the inset.
An example of the transmitted THz spectrum through the filter, normalized to the maximum of transmittance, is shown in Figure 2. The transmitted peak frequency and the bandwidth of the filter are 0.465THz and ~0.10THz, respectively. The corresponding THz temporal profile with total retardance, ΔG=0, is shown in the inset of Figure 2. Note that the four peaks have peak-to-peak separations of ΔtA. This is explained as follows: The THz wave is separated into an o-ray and an e-ray after passing the first element. These two waves are further separated into an o-o-ray, e-o-ray, o-e-ray, and e-e-ray, respectively, again after passing through the second element. The transmission spectrum manifests the interference among the four peaks of the THz signal.
The filter is tuned by rotating the magnets in TRA and TRB synchronously to maintain ΔtB=2ΔtA. The temporal THz profile is split from one peak into four peaks after passing through the two elements of the filter. The equal time difference, ΔtA, between each peak can be observed from measured data. The frequency-dependent transmitted spectrum comes from the interference of these four parts of the THz signal and is obtained by applying a fast Fourier transform (FFT) to the temporal signals. The peak transmission frequency of the filter decreases with increasing ΔtA. The tuning range of the filter is from 0.388 to 0.564THz, or a fractional tuning range of ~40%. The bandwidth of the present device is 0.1THz. Adding elements can narrow the bandwidth even more. Extending the LC-based Lyot filter to the 10–30THz range or mid-IR is straightforward, with shorter wavelengths providing the additional benefit of a larger tunable range.
We have demonstrated the design of an LC-based, tunable Lyot filter with potential applications in the THz frequency region as phase shifters, modulators, and other photonic devices.