1. Introduction

Liquid crystals (LCs) have long been used for wavelength tuning in optical communication systems, laser oscillators, and spectrometers [1–3]. LC devices usually need polarizers, since efficient tuning functions are induced by a great birefringence of LC molecules. Although LCs are used widely in the visible and near-infrared (IR) regions, applications to mid- or far-IR measurements have been limited until now [4–7]. A reason that hinders the application-field extension is lack of efficient IR polarizers. Dichroic films and birefringent prisms, for example, absorb long-wavelength IR radiation, and hence, inefficient, undurable, expensive wire-grid polarizers have to be used in the spectral range beyond 2 μm wavelength [8, 9]. In addition, both lack of strong lamps and unavoidable disturbance by thermal radiation noise require IR devices that exhibit a low insertion loss. Polarization-insensitive LC devices are therefore desired keenly for advancing the IR technology. In this study we prepared a Fabry-Perot interferometer by using a cholesteric LC and evaluated a polarization dependence of its refractive index in the IR region, aiming at development of a polarizer-free tunable filter.

2. Principle

Conventional LC filters are based on a Fabry-Perot interferometer that consists of two reflective plates (cavity mirrors) and a nematic LC layer. As Fig. 1(a) shows, columnar molecules of the LC are oriented in the direction parallel to the alignment coatings on the plates. When an electric voltage is applied on the LC layer, the molecules are reoriented in the direction perpendicular to the plates, as shown in Fig. 1(b). Consequently, a light beam that is polarized in the direction parallel to the original orientation (↕) takes a refractive index n that decreases from $n_e$ (extraordinary index) to $n_o$ (ordinary index) as the voltage increases. This index change causes interference-peak shift, since peak wavelengths ${\lambda }_m$ are

 

Fig. 1 (a) A nematic LC that is oriented in the direction parallel to the alignment coatings on the cavity plates. The refractive index of the LC is $n_o$ or $n_e$ depending on the polarization direction. (b) Reorientation of the LC during a voltage application process. The refractive index is $n_o$ independent of the polarization direction. (c) Rotation of the polarization direction in a cholesteric

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Various methods have been proposed to create polarization-insensitive filters; e.g., beam division by the use of polarization beam splitters [2, 6, 11], conversion of linear polarization to circular polarization by the use of quarter-wave plates [2, 12], and stacking of orthogonally-oriented LC-layers [13, 14]. Complicated LC alignments were also studied for elimination of polarization dependence [15–17]. Recently cholesteric LCs are attracting interests for constructing optical switches [18, 19]. As Fig. 1(c) shows, a cholesteric LC (a mixture of nematic and chiral LCs) exhibits a phase in which the molecular direction (director) makes a periodic revolution with a chiral pitch p. As a linearly-polarized beam propagates in this phase, the polarization direction rotates according to the director, if the pitch is longer than light wavelength. This transmission mode is used in flat-panel displays (twisted nematic LC). If the pitch is comparable with wavelength, the cholesteric LC acts as a 1-D photonic crystal that exhibits a stop-band in a particular spectral range. This characteristic is useful for tuning laser oscillation [3]. As the pitch decreases further, the chiral structure becomes difficult to recognize with optical wavelength. According to the effective medium theory, a mixed material, e.g., a solution or a nanoparticle suspension, exhibits an average refractive index of the components if its microstructure (refractive index distribution) is smaller than light wavelength $\text{λ}$ [20]. This happens with a short-pitch LC; i.e., if $\text{λ}\gtrsim \text{Δ}np (\Delta n=n_{\text{e}}-n_{\text{o}})$, the LC exhibits an average dielectric constant or an average refractive index $n_{\text{AV}}=\sqrt{\left(n_{\text{o}}{}^2+n_{\text{e}}{}^2\right)/2}$ independent of the polarization direction. However, this isotropic property is difficult to attain in the short wavelength range ($\text{λ}<\Delta n p$). It was reported, for example, that $\Delta n$ had to be reduced to 0.02 for eliminating polarization dependence at 1.5 μm wavelength [21].

It is known that LC exhibits a polarization-independent refractive index when it takes a nano-sized domain structure (a blue-phase) [22]. The blue phase, however, appears only in a limited temperature range (<1 K), and hence, stable device operation is difficult to attain by using this phase. This problem was solved by stabilizing the blue-phase LC with a photo-curable polymer [23, 24]. Those polymer-stabilized LCs were used successfully for controlling a divergence or a phase distribution of an optical beam [25–27]. For example, a flat lens with a suitable index-distribution was fabricated by using a polymer-stabilized LC, and focal-length variation was demonstrated with a He-Ne laser beam (633 nm wavelength). This polymer–LC composite, however, requires an electric voltage of 100 V for inducing a refractive-index change of 0.05, since the rigid polymer matrix restricts reorientation of LC molecules. In another research, a complicated design theory was worked out to realize a polarization-independent Fabry-Perot filter with twisted LC molecules [28]. In the IR region, however, neither the composite creation nor the complicated filter design is needed to attain a polarization-independent refractive index, since a cholesteric LC naturally exhibits isotropic properties for long-wavelength light. It is expected that a cholesteric LC with a large birefringence will realize both low-voltage device operation and great refractive-index change in the IR region.

In the current experiment we used a cholesteric LC (JNC Corporation, JD-1036LA) with a chiral pitch of 5 μm. According to manufacturer’s data the refractive indices of this LC were $n_{\text{o}}$ = 1.52 and $n_{\text{e}}$ = 1.76 at 0.59 μm wavelength. As Fig. 1(d) shows, this LC was injected into a gap of two silicon (Si) plates (20 mm square) that were adhered to one another via glass spacers [29]. No alignment coating was achieved on these plates, since polymer coatings caused absorption in the IR region. With no alignment coatings, the cholesteric LC takes a random domain structure, as illustrated in Fig. 1(d) [18, 19]. The refractive index of this random structure is assumed to be

3. Experiments and results

The phase change of the cholesteric LC was observed by injecting it between two glass plates, since the Si cell was opaque in the visible spectral range. The glass plates were coated with an indium-tin-oxide (ITO) film for attaining electric conductivity, but no alignment coating was achieved in order to simulate the condition of the Si cell. The cell gap was adjusted to 20 μm by using glass spheres. Figure 2 shows micrographs that were taken by placing the LC cell between orthogonally oriented polarizers (crossed Nicols). As Fig. 2(a) shows, the LC exhibits domains of 10–50 μm size at 0 V. Although orthogonal polarizers usually create dark images, this photograph shows a bright image, which indicates that the LC induces strong scattering or polarization rotation (retardation) for visible light. It is expected, however, that both scattering and polarization-state change become negligible in the long-wavelength IR range. As Fig. 2(b) shows, a fingerprint pattern appears, when an electric voltage of 10 V is applied between the glass plates. This is a typical pattern of the cholesteric phase, in which notable scattering takes place due to a large number of defects. As Figs. 2(c) and 2(d) show, this fingerprint pattern disappears when the voltage exceeds 20 V. At the same time the image becomes dark, indicating that a polarization state of light is preserved in this reoriented molecular phase. The bluish color of these images suggests that scattering or birefringence remains only in the short wavelength range. In other words, this LC phase is expected to exhibit a polarization-independent property in the long-wavelength IR range. Although the LC phase in the Si cell cannot be observed, a similar phase change is assumed to take place in the IR Fabry-Perot filter.

 

Fig. 2 Polarized optical microscopic images of the cholesteric LC. The LC was injected in a 20 μm gap between two glass plates. Polarizers were oriented orthogonally with one another. A sinusoidal electric signal (1 kHz) of (a) 0, (b) 10, (c) 20, or (d) 30 V (peak voltage) was applied between the ITO films on the glass plates.

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A Fourier-transformation IR spectrometer was used for measurements of the Fabry-Perot filter. The black line in Fig. 3(a) shows a transmission spectrum of the Si cell that contained no LC (before LC injection). Since the outer surface of each Si plate caused a reflection loss of ~30%, the maximum transmittance of the cell was ~50% (0.7 × 0.7). The gray line shows peak wavelengths that were calculated by using Eq. (1) with n = 1.00 (air). (The vertical position of the gray line has no meaning, since it was drawn at a suitable height for comparison of the peak wavelengths.) The calculated peaks fitted to those of the measured spectrum when the spacing was assumed to be d = 16.4 μm. Figure 3(b) shows the spectrum that was measured after injecting the LC into this Si cell. No polarizer was used in this measurement. The spectrum was disturbed by the LC absorption in the wavelength ranges around 3.4 μm and beyond 5.5 μm [30]. As the gray line shows, the best fitting was attained when the refractive index was assumed to be n = 1.58. This value was close to n_R that was evaluated by using Eq. (2), indicating that the LC took the randomly-oriented domain structure. Figure 3(c) shows spectra that were measured by placing a BaF₂ wire-grid polarizer (Edmund, WGP8203) in front of the sample. Transmittance was evaluated as a ratio of light intensities that were measured before and after the LC cell was put on the sample stage lest the insertion loss of the polarizer affected the measurement. Spectra for vertical and horizontal polarizations (solid and dotted lines) overlapped one another. Although the transmittances were slightly lower than that for non-polarized light, both peak wavelengths and evaluated index (1.58) were unchanged. These results confirm the prediction that the cholesteric LC exhibits an isotropic refractive index in the IR region. The lower transmittance seems to be caused by scattering in the LC layer, since the transmittance decreases as wavelength becomes short. A possible reason for this scattering increase is enhancement of the beam coherency; i.e., linearly polarized light is possibly scattered or diffracted more notably than non-polarized light. Further experiments are needed, however, to clarify the origin of this phenomenon.

 

Fig. 3 (a) Transmission spectrum of the Si cell before LC injection. The gray line indicates peak positions of a cavity with n = 1.00 (air) and d = 16.4 μm. (b) Transmission spectrum that was measured after injecting the LC into the Si cell. Non-polarized light was used in this measurement. (c) Transmission spectra that were measured by using a probe beam with linear polarization (horizontal or vertical to the ground). Peak positions (the gray lines) in (b) and (c) were calculated for n = 1.58 and d = 16.4 μm.

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The spectra in Fig. 3, which were measured at the sample center, possibly depend on the sample position, since the domain structure takes a random distribution. Figure 4 shows the spectra that were measured at four different positions in the sample. As the insets show, a probe beam of 2 mm diameter was transmitted through a position that was 3 mm apart from the sample center (A, B, C, or D). The spacing d was evaluated at each position before LC injection. Although peak wavelengths changed slightly due to a position-dependent variation of the spacing (d = 16.4–16.8 μm), the evaluated refractive index was the same (1.58) at all positions. This fact indicates that the director distribution of the domain structure is random enough to induce a uniform, isotropic index n_R in the entire sample. As these spectra show, peak wavelengths of the interferometer change notably by variation of the spacing. If the spacing d increases from 16.4 to 16.5 μm, for example, the peak wavelength changes from 2.59 to 2.61 μm according to Eq. (1) (n = 1.58 and m = 20). Consequently, the spacing variation within the beam diameter (2 mm) causes superimposition of spectra with different peak wavelengths, which leads to a reduction of the transmittance contrast (amplitude of the spectral oscillation). This contrast reduction is notable in the short wavelength range, since the peak spacing becomes smaller as wavelength becomes shorter. This is the reason why the transmittance contrast becomes small at the positions A and D, where the spacing variation is larger than that in other positions.

 

Fig. 4 Transmission spectra that were measured at different positions (A–D) of the LC cell. The gray lines show peak wavelengths that were calculated by using a measured spacing d and a suitable refractive index n.

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Next, we examined voltage dependence of the refractive index. As Fig. 1(b) shows, an electric signal of 1 kHz was imposed between the Si plates. A peak voltage was adjusted between 0 and 60 V. Figures 5(a)–5(d) show the spectra that were measured at the sample center by using non-polarized light. In comparison with the original spectrum (0 V) in Fig. 3(b), the transmittance decreased heavily in the short-wavelength range when the voltage was 10–16 V. This phenomenon was caused by light scattering that became notable as the domain structure collapsed during the reorientation process [18, 19, 31]. The transmittance, however, recovered to the original level at 20 V, corresponding to the phase change shown in Fig. 2(c). The refractive index began to decrease when the voltage exceeded 10 V, and reached 1.49 at around 20 V. As the voltage increased further to 30 V, both the transmittance and its contrast became a little higher than those of the original spectrum (0 V) shown in Fig. 3(b). No spectral change took place when the voltage increased exceeding 30 V.

 

Fig. 5 Voltage dependence of the transmission spectrum. The probe beam was (a–d) non-polarized or (e) linearly-polarized in the horizontal or vertical directions. The fitting curves (the gray lines) were drawn by using a suitable n value.

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Polarization dependence was also examined by placing a polarizer in front of the sample. Transmittance was evaluated as a ratio of light intensities that were measured before and after placing the sample, and hence, the insertion loss of the polarizer did not affect the measurement. As Fig. 5(e) shows, spectra for two orthogonal polarizations overlapped one another during the voltage application process. In addition, the transmittance for polarized light was the same as that for non-polarized light, as shown by the spectra in Figs. 5(d) and 5(e). This fact contrasted with the results for no voltage application, in which the sample exhibited a lower transmittance for polarized light than non-polarized light [Figs. 3(b) and 3(c)]. The parallel orientation structure probably induces a lower scattering loss than the domain structure (0 V) particularly in the short wavelength range.

Figure 6(a) shows the peak-wavelength change by voltage application. The peak shift is close to or greater than the free spectral range (the spacing between two adjacent peaks). Figure 6(b) shows the corresponding refractive-index change. The refractive index decreases from 1.58 to 1.49 in the 12–18 V range. These values are smaller than the predicted values ($n_R$ = 1.60 and $n_o$ = 1.52 at 0.59 μm), since refractive indices of materials usually decrease as wavelength becomes longer (wavelength dispersion) [30]. Although the refractive index stops deceasing at 18 V, the transmittance continues to increase until the voltage reaches 30 V, as shown in Figs. 5(c) and 5(d). Probably a slight fluctuation of the refractive index remains at 18 V, and it decreases as the voltage rises to 30 V, leading to reduction of the scattering loss.

 

Fig. 6 (a) Peak shift during the voltage application process. Peak wavelength (the vertical axis) is indeterminate in the absorption band (3.3–3.5 μm). (b) Refractive index of the LC as a function of the applied voltage. The straight lines show indices ($n_o$,$n_e$, and $n_R$) that were predicted at 0.59 μm wavelength.

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Figure 7 shows polarization states of the transmitted beam. As the inset in Fig. 7(f) illustrates, transmittance was measured with the output polarizer being rotated by Δθ with reference to the input one. The blank spectrum (100% intensity) for the transmittance evaluation was measured through the parallelly oriented polarizers before inserting the sample. In the wavelength range beyond 6 μm, a polarization state of the input light (linear polarization) was preserved regardless of the applied voltage. In the 4–5 μm range, the polarization direction deviated by 5–10 deg at 0 V. In the range below 3 μm, both retardation and polarization rotation occurred below 10 V.

 

Fig. 7 Polarization states of the transmitted light. Wavelengths are (a–f) 2–7 μm. The horizontal axis shows the angular difference of the polarizer directions ($\Delta \theta$), as illustrated in (f). The numerals beside the lines denote the applied voltage.

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4. Discussion

As Fig. 7 shows, the polarization state was disturbed slightly in the 2–3 μm wavelength range when the LC took the poly-domain structure (at low voltage). As Figs. 3 and 5 show, however, a polarization-independent transmittance is attainable even at 2 μm wavelength. Further the refractive-index change that was measured in the current experiment (0.09 = 1.58 ‒ 1.49) was greater than that of the polymer-stabilized blue-phase LC [25]. The required voltage (18 V) was also lower than that of the blue-phase LC (100 V). These results indicate usefulness of the cholesteric LC for creating an IR tunable filter. The chiral pitch, which is p = 5 or $\Delta np$ = 1.2 μm in the current LC, has to be reduced for both improving the beam quality (preservation of the polarization state) and extending the transmission range to shorter wavelengths (the optical communication band). We are currently evaluating optical properties of a short-pitch LC.

As Figs. 3–5 show, the maximum transmittance of the current sample ($T_{\text{max}}$) was ~50%, and the interference contrast ($\text{Δ}T=T_{\text{max}}-T_{\text{min}}$) was ~20%. The reflection loss at the outer surface of the Si plate is responsible for the reduction of the maximum transmittance. On the other hand, the contrast $\text{Δ}T$ is determined by the reflectance at the inner surface of the Si plate. According to the Fresnel equations [32], the reflectance at the Si–air boundary is $R_{\text{OUT}}\cong$30%, since the refractive index of Si is 3.4. The reflectance at the Si–LC boundary is $R_{\text{IN}}\cong$20%, since the refractive index of the LC is ~1.5. Figure 8(a) shows the transmission spectra that were calculated by using these reflectances ($R_{\text{IN}}\cong$20% and $R_{\text{OUT}}\cong$30%) and the cavity thickness d = 20 μm [33]. The refractive index of the LC was assumed to be 1.58 (0 V) or 1.49 (18 V). The maximum transmittance of the calculated spectra was 50%, which was close to the experimental results. As regards the interference contrast $\text{Δ}T$, the calculated spectra exhibited an oscillation of ~30%, whereas the measured spectra exhibited a smaller variation (~20%). This discrepancy was probably caused by a fluctuation of the cavity length (thickness d) and the divergence (inclination) of the probe light beam. The performance ($T_{\text{max}}$ and $\text{Δ}T$) of the current filter can be improved by both enhancing the inner reflectance ($R_{\text{IN}}$) and reducing the outer reflectance ($R_{\text{OUT}}$). Figure 8(b), for example, shows the transmission spectra that were calculated for $R_{\text{IN}}\cong$90% and $R_{\text{OUT}}\cong$0%. Sharp peaks ($T_{\text{max}}=\text{Δ}T=100\%$) are expected to appear by changing the reflectances in this manner. We are currently preparing Si plates whose surfaces are coated with high-reflection and anti-reflection films.

 

Fig. 8 Calculated transmission spectra of the Fabry-Perot filer consisting of Si plates and the cholesteric LC. Reflectances at the inner and outer surfaces of the plates were assumed to be (a) R_IN = 20% (Si–LC boundary) and R_OUT = 30% (Si–air boundary) or (b) R_IN = 90% (high-reflection coating) and R_OUT = 0% (anti-reflection coating). The LC layer thickness was fixed at 20 μm. The refractive index of the LC was assumed to be 1.58 (the gray line) or 1.49 (the black line). As the arrows show, the interference peaks shift to a shorter wavelength by voltage application.

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5. Conclusion

A cholesteric LC with a 5 μm pitch exhibited a polarization-independent refractive index at wavelengths longer than 2 μm. The refractive index changed from 1.58 to 1.49 by 18 V application. This tunable, isotropic property is useful for extending the application field of LC devices in the IR spectral region.