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Design of switchable guided-mode resonant filters in zenithal-bistable liquid-crystal gratings Dimitrios C. Zografopoulos, Emmanouil E. Kriezis, and Romeo Beccherelli
Abstract—An electro-optically switchable infrared filter based on guided-mode resonances in a zenithal bistable liquid-crystal grating is designed and theoretically investigated. By proper selection of the material and geometrical parameters it is shown that the grating can switch between transparent and narrowband filtering operation. Switching times of few milliseconds are predicted owing to the employment of a dual-frequency nematic liquid crystal as the addressable material. The tunability of the resonant wavelength is also studied following two approaches, namely the adjustment of the angle of incidence of the impinging lightwave and the LC tuning by the electro-optic effect. Index Terms—Guided-mode resonance filters, zenithal bistable device, nematic liquid crystals, tunable optical filters.
I. I NTRODUCTION PTICAL notch filters are among the most widely used components in the photonic industry, as indispensable parts in spectrometers, lasers, and optical communication systems. A very efficient approach in the design and fabrication of high-quality reflective optical filters is based on the effect of guided-mode resonances (GMR). These occur from the coupling of diffracted waves generated by a periodic grating with photonic modes guided in a high-index waveguide, which can be either the grating itself or an adjacent dielectric slab [1]. Such filters yield high peak efficiency, low sideband, narrow linewidths, featuring a few-layer structure that is more compact and shows lower fabrication complexity compared to traditional filter designs based on multilayer mirrors [2]. The applicability of GMR filters can be substantially boosted by introducing an addressable material in the lightwave guiding region, capable of dynamically tuning the filter’s spectral response. By selectively opening or closing a spectral channel, such tunable filters are the key components in e.g. tunable laser cavities, optical limiting for sensor protection, or optical switching and memories. A promising solution for the design of functional GMR filters is the employment of liquidcrystals (LC), a class of anisotropic organic materials employed in both planar and fiber-based photonic industry thanks to their large reconfigurability and low power consumption [3], [4]. When combined with the extensive GMR sensitivity on the
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D. C. Zografopoulos and R. Beccherelli are with the Consiglio Nazionale delle Ricerche, Istituto per la Microelettronica e Microsistemi (CNR-IMM), Roma 00133, Italy (e-mail:
[email protected]). E. E. Kriezis is with the Department of Electrical and Computer Engineering, Aristotle University of Thessaloniki, Thessaloniki GR-54124, Greece. This report was made possible by a NPRP award [NPRP 7 - 456 - 1 - 085] from the Qatar National Research Fund (a member of The Qatar Foundation). The statements made herein are solely the responsibility of the authors. Copyright ©2017 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sending a request to
[email protected].
Fig. 1. (a) Schematic layout of the proposed zenithal bistable guided-mode resonant grating and definition of the material and structural parameters. (b) Nematic director profiles for the VAN and HAN states calculated for Λ = 1 µm and a0 = 0.7 µm. By proper design, the grating’s operation can switch between selective filtering (VAN state) and transparency (HAN state).
refractive index of the light-guiding material, the inherent large LC optical anisotropy leads to high tunability of the filter’s properties, such as resonant wavelength [5]–[7], bandwidth [8], [9] and/or intensity [10]. In this work, we propose a switchable GMR infrared filter based on LC zenithal-bistable (ZB) gratings, a particular class of LC components that combine the tunability of nematic LC materials with bistable operation. The latter eliminates the need for idle-power energy consumption, an unavoidable price paid for the tunable properties of previously demonstrated electro-optic LC-GMR filters. This concept has been thus far exploited in the development of passively addressed displays for image storing [11], as well as for the design of switchable beam steering [12], [13] or polarization control devices [14]. The ZB-LC grating is designed such that it acts as a selective reflective filter in one LC state, while it is optically transparent in the other. In addition, the tuning of the resonant wavelength via the control of the angle of incidence or via the electro-optic effect of the employed dual-frequency LC [15] is discussed.
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TABLE I P HYSICAL AND DIELECTRIC PROPERTIES OF THE DUAL - FREQUENCY NEMATIC LIQUID CRYSTAL MDA-00-3969. Parameter
Notation
Splay elastic constant Twist elastic constant Bend elastic constant Ordinary permittivity Extraordinary permittivity @ 1 KHz Extraordinary permittivity @ 50 KHz Rotational viscosity
K11 K22 K33 εos εL es εH es γ
Value
Ref.
18 pN [20] 10.8 pN [20] 21.1 pN [20] 7.3 [21] 10.3 [21] 4.55 [21] 310 mPa·s [24]
Fig. 3. Transmittance (θ = 0◦ ) of the ZB-GMRG in both VAN and HAN states for a = 400 and 700 nm. The insets show the electric field enhancement factor |Ey | /E0 at the resonant frequencies.
Fig. 2. Transmittance (θ = 0◦ ) of the ZB-GMRG in the VAN state for a grating height from 0 to 900 nm (step of 20 nm). The red dashed lines denote the wavelengths of the guided modes calculated as an eigenvalue problem.
Finally, the full switching dynamics between the two states are thoroughly investigated, demonstrating the device’s capability for reversible bistable filtering operation. II. G UIDED - MODE RESONANCE FILTERS IN ZENITHAL BISTABLE LIQUID - CRYSTAL GRATINGS The switchable ZB guided-mode resonant grating (ZBGMRG) is based on the layout of Fig. 1(a). The substrate is the BK7 Schott optical glass upon which a 50-nm layer of ITO is sputtered. The glass refractive index dispersion in the IR is described by the Sellmeier model [16], whereas the ITO permittivity by the Drude-Lorentz model [17]. The ITO serves as the electrode for the application of the low-frequency electric voltage needed to switch the LC molecules. A 500-nm PMMA buffer layer is spin-coated on the BK7/ITO substrate, on top of which a sinusoidal grating of pitch Λ=1 µm and peak height a0 is written, using holographic or other lithographic techniques employed in LC technology, such as liquid crystal on silicon (LCoS). The buffer layer optically isolates the lossy ITO from the region where the guided mode resonances are excited. The dispersion of PMMA is described via a Cauchy model [18]. The LC cell is formed by assembling two identical patterned substrates, separated by dielectric spacers at a distance of 2 µm, and it is infiltrated with the dualfrequency nematic mixture MDA-00-3969, whose relevant properties are summarized in Table I. Prior to LC infiltration, the grating surfaces are treated with a surfactant in order to induce strong homeotropic anchoring of the LC molecules
[19]. At the wavelength of 1550 nm, the isotropic materials are characterized by nBK7 = 1.501, εITO = 1.19 − j0.31, nPMMA = 1.492, and the LC ordinary and extraordinary indices are no = 1.482 and ne = 1.673, respectively. In such ZB gratings, the LC configuration can assume two stable states, termed as vertically-aligned nematic (VAN) and hybrid-aligned nematic (HAN), characterized by high and low, respectively, average tilt angle of the LC molecules, as shown in the profiles of Fig. 1(b). All calculations of the LC orientation were made by employing the tensorial formulation described in [12]. The tilt angle γ is defined as the angle between the nematic director, or equivalently the local axis of the LC anisotropy, and the x-axis in the x − y plane. It is stressed that both VAN and HAN profiles are planar, meaning that the LC axis lies exclusively in the x − y plane. Thus, the LC relative permittivity tensor is given by εo + ∆ε cos2 γ ∆ε cos γ sin γ 0 ε˜r = ∆ε cos γ sin γ εo + ∆ε sin2 γ 0 , (1) 0 0 εo where εo = n2o and ∆ε = n2e − n2o . The LC spatial distribution in the two stable states, combined with proper material selection, provides the conditions for the design of switchable GMR optical filters. Let us assume a planewave impinging on the ZB-GMRG at angle of incidence θ, as defined in Fig. 1(a). In the case of TEpolarized light, the electric field is polarized along the zaxis and it senses the ordinary LC index no in the LC bulk, which satisfies the condition no < nPMMA < nBK7 . As the grating refractive index is lower than that of the surrounding material, no GMR are excited and the grating is transparent in the spectral range of interest (1.5 − 1.65 µm), apart from some absorption in the ITO electrodes. In addition, diffraction effects are particularly weak, as the index contrast between the PMMA and the ordinary refractive index is vanishingly small. When it comes to TM-polarized light, a critical property of the grating in both LC states is that in the vicinity of the two sinusoidal gratings there are regions where the tilt angle obtains values between 0◦ and 90◦ , thus leading to a
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Fig. 4. Transmittance of the ZB-GMRG in the VAN state for an angle of incidence θ varying from 0◦ to 5◦ (step of 0.125◦ ).
Fig. 5. Transmittance (θ = 0◦ ) of the ZB-GMRG for an applied voltage from 0 to 25 V (step of 1 V) at a driving frequency of 1 KHz and 50 KHz.
non-zero εxy component of the permittivity tensor, as dictated by (1). Therefore, coupling between the x− and y−polarized components of the electric field is possible, even in the case of normal incidence. The y−polarized field component can excite TM guided modes, provided the LC permittivity εyy is high enough to create the sufficient index contrast. This condition is fulfilled only in the VAN state, where the LC acquires an tilt angle close to 90◦ in the LC bulk (εyy ∼ n2e ). On the contrary, in the HAN state the LC optical axis is mainly aligned along the x−axis, the y−polarized field component senses the low ordinary index and no resonances are excited. Therefore, by properly designing the grating for the VAN state, the ZB-GMRG can operate as a switchable optical filter at the target resonant wavelength. It is noted that this predominantly uniform LC alignment in the HAN state stems from the double-grating structure and it is not present in ZB gratings based on a single patterned surface as studied e.g. in [12]. In the latter case, a high-index zone is formed in both LC states for y-polarized light and thus, contrary to the proposed design, the device is not transparent in the HAN state. According to grating theory, GMR can occur in the interval
in the LC slab waveguide by fixing their propagation constant at β = 2π/Λ. All optical wave calculations were performed via the finite-element method, coupled with the LC orientation studies in COMSOL Multiphysics©. It is seen that in the range a0 = 300–500 nm the coupling to the fundamental mode decreases, while a second-order mode is also excited. This behavior is shown more clearly in Fig. 3, where the insets show the electric field enhancement factor between the excited y−component and the impinging field. For a0 = 700 nm, only the fundamental mode is excited, which leads to a deep resonance at λr = 1575.14 nm with an extinction of ∼ 19 dB and a 3-dB linewidth of 3.8 nm. The position of λr can be controlled either via adjusting the pitch, as already discussed, or the grating height, as shown in Fig. 2. Next, we investigate the means to dynamically tune the resonant wavelength λr . One approach is based on the rotation of the sample, that is by mechanically controlling θ. This approach has been widely employed for the mechanical tuning of grating structures in a very large scale of target frequencies, ranging from plasmonic gratings in the visible [22] to terahertz narrow-band GMR-based filters, as some of the authors have already demonstrated [23]. For θ 6= 0 the GMR wavelength for m = ±1 is no longer degenerate and it splits into two branches [2]. This behavior is investigated in Fig. 4, where it is clearly observed that by adjusting θ the filtering wavelength can be tuned in a wide range around λr toward both higher and lower wavelengths. An average shifting of 23 nm/deg is observed, in-line with the theoretical estimate ϑλr /ϑθ ≃ nBK7 Λ ≃ 26 nm/deg. Another road toward the dynamical tuning of the filtering wavelength, without the need for mechanical parts, is by exploiting the LC electro-optic effect. In this case, the dual-frequency LC offers two possibilities, according to the frequency of the driving signal. Starting from the VAN state, a driving voltage at 1 KHz, where the LC exhibits a positive ∆εs = εes − εos , further aligns the LC molecules along the y−axis, increases the average value of εyy and shifts the resonance to higher wavelengths. On the contrary, at 50 KHz one has ∆εs < 0, which progressively breaks the order of the VAN state and switches the LC molecules parallel to the
nBK7 ≤ |nBK7 sin θ − mλr /Λ| ≤ ng ,
(2)
where m is an integer denoting the diffraction order, λr the resonant wavelength, and ng the refractive index of the waveguiding region. For normal incidence, first-order diffraction, and the given material selection, Eq. (2) reduces to 1500 nm . λr . 1670 nm, hence the selection of Λ = 1 µm in order to place the GMR in the IR telecom window. By adjusting the pitch Λ, it is straightforward to shift the resonant wavelength at the desired wavelength. In the proposed ZB-GMRG the coupling strength to the GMR depends on the grating peak height a0 , the excited mode profile, and its overlap with the non-zero εxy regions. We have fixed the LC thickness at 2 µm in order to have one free design parameter, i.e. the height a0 . Figure 2 shows the evolution of the transmittance spectrum in the VAN state for increasing values of a0 up to 900 nm. The low transmittance path indicates the wavelengths were GMR are excited. These are in excellent agreement with the eigenvalue problem of defining the guided mode wavelengths
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Fig. 6. Dynamic response of the ZB-GMRG in terms of the average LC tilt angle and transmittance at the resonant wavelength. The insets show the tilt angle distribution at various time snapshots during the full switching cycle.
x-axis. Figure 5 summarizes the properties of the electrooptic tunability of the ZB-GMRG for a voltage up to 25 V. The low-frequency permittivity of PMMA was set to 3.6. For V > 10 V at 50 KHz the VAN LC orientation profile and the corresponding transmittance spectra are significantly distorted. For voltages up to 10 V a continuous shift of λr is observed at an average rate of ca. ±0.35 nm/V for the low and highdriving frequency, respectively. This fine-tuning of λr can be used e.g. for angle compensation [25]. The competitive advantage of the ZB device is that for a fixed λr it requires zero idle-power in either of the two states. Energy is consumed only when a pulse is applied so as to overcome the energy barrier and switch the LC state. The use of a dual-frequency LC provides a direct means of controlling the switching by using pulses of proper driving frequency, amplitude, and duration. In the case here studied, it was found that a 50 V pulse with a duration of 5 ms is sufficient to switch between both states, as shown in Fig. 6, which investigates the dynamics of a full switching cycle both in terms of the average LC tilt angle and the transmittance at resonance. It is stressed that here we aim only at demonstrating the proof of operation of the switchable filter. The performance of the device can be further improved, e.g. by reducing the thickness of the PMMA buffer or by opting for a LC with lower viscosity. III. C ONCLUSIONS We have presented the design of a switchable infrared filter based on a ZB-LC grating, which supports the excitation of GMR only for one of the two stable LC states. The filter shows high modulation depths, relatively small linewidth, and the potential for dynamically tuning its resonant wavelength either by mechanically rotating the device, as in static GMR optical filters, or via the LC electro-optic effect, which eliminates the need for mechanical parts. By employing a dual-frequency LC, switching between the two states of operation is performed when the device is subjected to pulses of few-millisecond duration and of properly selected driving frequency. R EFERENCES [1] R. Magnusson and S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett., vol. 61, pp. 1022–1025, 1992.
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