1. Introduction

The electro-optical or thermo-optical materials such as liquid crystal (LC) can be infiltrated into the hollow core waveguide or photonic crystal fibers (PCFs) to alter the optical properties of waveguide or PCFs by tuning the applying voltage or temperature. The waveguides with different optical characteristics have be studied such as Bragg optical waveguides [1], anti-resonant reflecting optical waveguides [2–5], liquid-liquid waveguides (L²s) [6], nanoporous cladding waveguides [7], Liquid-core waveguide (LCW) [8–10] and the LC filled PCFs [11–15], Liquid-crystal optical channel waveguide [16],the electrically tunable LC waveguide [17], LC in waveguides for tuning and sensing [18]. By infiltrating the LC or liquid into the hollow core waveguide or PCFs, the waveguide and PCFs can be the versatile devices such as optical modulator, optical attenuator [11,12,16,17] or biosensor [19–21]. Recently, we demonstrated the LC filled hollow waveguide formed by SiO₂ cladding [17]. The maximum optical attenuation of the device with the length of 0.4 cm is over 30 dB for the driving voltage of 5 volt. The corresponding optical attenuation per unit length and per voltage is 18.75(dB/cm/volt). The device is operated at the wavelength of 1550 nm. The color tunable device in visible has been proposed by T. T. Larsen et al. [11]. By heating the LC filled PCFs with the length of 2 cm between the temperature of 26.5 ^oC and 26.9 ^oC, the maximum optical extinction ratio is in excess of 60 dB. The color of the output light can be changed by varying the temperature to shift the photonic band gap (PBG) of the PCFs. The color of the output light can be tuned from green, yellow to blue.

In this paper, we demonstrate the LC filled waveguide based on the distributed Bragg reflectors (DBRs). The optical attenuation over 25 dB can be achieved for the driving voltage as low as 9 volt. The PBG of LC filled waveguide can be altered by changing the external voltage to varying the effective index of LC (n_core). The color of the output light can be tuned from white light to red, yellow or green.

2. Simulation

The DBRs used to form the hollow waveguide consist of six pairs of thin films in SiO₂ and Si₃N₄. The structure is schematically shown in Figs. 1(a) and 1(b). By using the photonic band gap of the thin film, the light can be confined in the core between the multilayer stacks. To design the multilayer structure, the transfer matrix method [22] is used. The refractive index of SiO₂ and Si₃N₄ at the wavelength of 532 nm is n_SiO2 = 1.5469 and n_Si3N4 = 2.0268, respectively. The substrate material is silicon with the index, n_Si, of 4.139 - 0.034i. The guiding material is liquid crystal, E7 (Merck), with the ordinary index of 1.52 and the extraordinary index of 1.75 denoted as n_o and n_e, respectively. For simplifying the calculation process, the indices of the materials at the wavelength of 532 nm are used for the calculation in the wavelength range from 500 to 800 nm. In Fig. 1(b), θ is the incident angle of the propagating light on the multilayer stack. The definition of the TE and TM polarization states is shown in Fig. 1(b). The thickness of SiO₂ and Si₃N₄ is calculated to be d_SiO2 = 335 nm and d_Si3N4 = 95 nm, respectively to obtain the largest photonic band gap. The thickness of one pair of SiO₂ and Si₃N₄ corresponds to the period Λ of DBRs is 430 nm.

 

Fig. 1 (color online) (a) Schematic structure of LC filled waveguide based on DBRs. The direction of applied voltage is along x-direction. (b) Cross-section view of LC filled waveguide based on DBRs. (c) PBG of DBRs obtained by the Bloch theorem.

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The width and the height of the hollow core are chosen to be d_core = 5 μm. The thickness of indium tin oxide (ITO), d_ITO, which is 0.5 μm, serves as the electrodes. We use the finite difference method to solve the Helmholtz equation to obtain the waveguide mode profile and the propagation constant as the refractive index of the LC core is 1.52. The propagation constant of the fundamental mode is used to calculate the incident angle of the light on the multilayer stack to be 88^o. By using the Bloch theorem, the complete band gap for the TE and TM modes can be obtained for different indices of LC as shown in Fig. 1(c), as the incident angle of the propagating light on the multilayer stack is 88^o. The blue region represents the complete band gap for the TE and TM modes in which the light can be confined in the LC filled waveguide. The result shows that the wavelength region for the light confinement can be altered due to the reorientation of LC director. The range of the index change of the LC is between 1.52 and 1.75 by varying the applied voltage. For the index range from 1.52 to 1.622, the light at short wavelength such as the yellow and the green light can be confined. For the index range from 1.622 to 1.654, no light at the wavelength region between 500 nm to 800 nm can be confined indicating that no light will be outputted (dark state). As the core index is changed from 1.694 to 1.75, the output light is changed from red to white light. The result shows that by applying the external voltage, the color of the output light can be changed from green to red. White light and no light at the output of the waveguide can also be obtained.

3. Sample fabrication

The hollow waveguide based on DBRs is fabricated on the (100) silicon wafer. The six pairs of multilayer stack (Si₃N₄/SiO₂) are deposited as the bottom cladding layer by employing the plasma-enhanced chemical vapor deposition (PECVD). The photo-resist, SU-8 is coated as sacrificial layer on the bottom cladding layer and patterned by the conventional photolithography process. Both of the width and the height of the sacrificial layer are 5 μm. The six pairs of multilayer stack (Si₃N₄/SiO₂) are deposited again as the top cladding layer by PECVD. The SiO₂ cover layer with the thickness of 2.5 μm is deposited on the top of the cladding layer to fortify the structure of device. The photo-resist remover is used to remove the photo-resist to form the hollow core. The transparent conductive film, indium-tin-oxide (ITO), with thickness of 0.5 μm is deposited as the electrodes on the top SiO₂ layer and the rear of silicon wafer for applying the voltage on the device. The image of scanning electron microscope of the end of the waveguide is shown in Fig. 2 . For infiltrating the LC into the hollow waveguide, the LC is heated to be the isotropic phase at 75 ^oC on the hot plate. By submerging the end of hollow waveguide into the LC, the LC can be infiltrated into the hollow waveguide by the capillary effect.

 

Fig. 2 SEM image of the cleaved waveguide facet.

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4. Results and discussion

The previous studies [12,23,24] about the LC filled photonic crystal fiber have reported that the orientation of LC director tends to be parallel along the waveguide or fiber axis after infiltrating the LC into the hollow core by capillary effect. Due to lack of aligning pretreatment, the orientation of LC director can be strongly affected by the interface between the LC and hollow core [12]. In this study, in order to investigate the orientation of LC director for different core geometries, we fabricate the LC filled waveguide with SiO₂ cladding (without DBRs) to facilitate the observation of the LC orientation. The core sizes of the waveguides are 5 μm × 50 μm, 5 μm × 10 μm, 5 μm × 5 μm and 10 μm × 10 μm. The polarized microscope is employed to analyze the orientation of LC director. The top view of the polarized micrographs of the hollow core waveguide after infiltrating the LC is shown in Fig. 3 . The symbol, P and A, represents the polarization direction of the polarizer and the analyzer, respectively. Figure 3(a) shows the micrographs of the waveguide with core size of 5 μm × 50 μm as the waveguide axis is parallel to the polarizer direction and as the waveguide axis is 45° to the polarizer direction, respectively. The center of waveguide is dark and bright for these two orientations, respectively, revealing that the orientation of LC director at the center of core is parallel to the waveguide axis. The LC near the SiO₂ cladding layer shows bright and dark for these two orientations, respectively indicating that the orientation of LC director near the SiO₂ cladding layer is orientated around 45^o with respect to the waveguide axis. For the LC infiltrated in the hollow core waveguide with core size of 5 μm × 10 μm, the polarized micrograph is shown in Fig. 3(b). The random distribution of the dark and bright region and the disclination lines [25,26] are observed in the LC filled waveguide. Therefore, the orientation of the LC is anisotropic. Figures 3(c) and 3(d) show the orientation of LC director in the hollow core waveguides with the square core size of 5 μm × 5 μm and 10 μm × 10 μm, respectively. The orientation of LC director can also be observed to be parallel to the waveguide axis. The disclination lines do not appear in the LC filled waveguides. Hence, the LC filled waveguide with the wider width of rectangle core (5 μm × 50 μm) and with the square core (5 μm × 5 μm and 10 μm × 10 μm) might provide self-alignment effect to the LC director for no alignment pretreatment.

 

Fig. 3 (color online) Top-view micrograph of LC filled waveguide without applying voltage for the LC filled waveguide with core size of (a) 5 μm × 50 μm (b) 5 μm × 10 μm (c) 5 μm × 5 μm and (d) 10 μm × 10 μm.

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To characterize the LC filled waveguide based on the DBRs, the supercontinuum broad-band light source by coupling the YAG laser into the PCFs is launched into the device. The wavelength range of the broad-band light source is from 500 nm to 1700 nm. Simultaneously, the external AC voltage with the frequency of 1 kHz is applied on the structure as shown in Fig. 1(a). The output light is collimated by the microscope objective with the magnification of 60X and the numerical aperture of 0.85 and is collected by the convex lens with the focal length of 12 cm. Finally, the spectrum of the output light is measured by the monochromator and the optical image is captured by the CCD. The average propagation loss is 1.15 ± 0.07 dB/mm. The propagation loss can be diminished by increasing the pair number of multilayer stack. The average coupling loss is 22.2 ± 4.7 dB. The large coupling loss is due to the residual LC on the facet of the waveguide which scatters the input light inducing the decrease of the light coupling.

Figure 4(a) shows the output images and the transmission spectra by varying the external voltage from 0 to 3.5 V_rms and from 25 to 30 V_rms. Since the intensity of the output light between 3.5 and 25 V_rms is significantly attenuated (dark state), the spectrum is not shown in Fig. 4(a). This state can be observed in the simulation result as shown in Fig. 1(c) when the refractive index is between 1.622 and 1.654. In Fig. 4(a), the color of the output light can be altered such as yellow, green, tangerine and white. As the applied voltage is 30 V_rms, the waveguide output shows white light. This corresponds to the simulation result as the refractive index is around 1.75 as shown in Fig. 1(c) where the light in the wavelength range from 500 to 800nm can be confined in the waveguide. The results show that the output color of the waveguide can be controlled by the applied voltage to obtain the green light to red light as well as the white light and the dark state.

 

Fig. 4 (color online) (a) Far-field image and transmission spectra of output light for different applied voltages. (b) Extinction ratio and output image of LC filled waveguide at the wavelength of 532 nm for different applied voltages.

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To investigate the polarization dependence of the waveguide, the linearly polarized laser light source at the wavelength of 532 nm is launched to the LC filled waveguide. The polarization of the input light is controlled by a polarizer. The power of incident light is 6 dBm. Simultaneously, the external AC voltage with the frequency of 1 kHz is applied on the structure. The applied voltage is varied from 0 to 15 V_rms. The power of the output light is measured by the power meter. The extinction ratio and the output image are shown in Fig. 4(b). The ϕ in Fig. 4(b) represents the angle between the x-direction [shown in Fig. 1(a)] and the linear polarization direction. We can observe that the attenuation of LC filled waveguide is almost independent of the polarization state. This is due to the fact that the linearly polarized light propagating in the LC filled waveguide can be depolarized by the multi-reflection in the rectangle waveguide [17].

As the applying voltage is zero, the light at the wavelength of 532nm is well confined in the LC filled waveguide. As the voltage increases, the intensity of the output light decreases when the voltage is varied from 5 to 9 V_rms. As the applied voltage is between 9 and 15 V_rms, the light cannot be confined in the LC filled waveguide. The extinction ratio is around 25 dB. The corresponding extinction ratio per unit length and per unit voltage is as high as 9.26 (dB/cm/voltage). This value is lower than our previous result 18.75(dB/cm/volt) [17]. This is mainly due to the fact that the thickness of the waveguide cladding layer is 2.5 times thicker than the structure in [17]. The corresponding electric field between the electrodes is reduced leading to the lower extinction ratio per unit length and per unit voltage.

5. Conclusion

In this study, the electrically tunable broad-band filter and attenuator has been fabricated by infiltrated the LC into the hollow core waveguide based on the DBRs. By applying the voltage from 0 to 30 V_rms, the wavelength of light confined in the LC filled waveguide can be varied. The color of the far-field output image is changed from green, yellow to white. Specifically, the guide mode for the whole visible range can be transformed to the leaky mode as n_core is between 1.622 and 1.654 for applying voltage from 3.5 to 25 V_rms. This property can be used to fabricate the broad-band tunable filter. Additionally, the light at the wavelength of 532 nm is also launched into the LC filled waveguide. By applying voltage between 9 V_rms and 15 V_rms, the light can radiate out of waveguide. The maximum extinction ratio of the LC filled waveguide of 25 dB can be achieved. This characterization can be employed to fabricate the optical attenuators or modulators. The device might be potentially applied for the scanning projection display or tunable dye-doped LC laser.