1. Introduction

The technology of polarization beam splitting (PBS), which enables a spatial separation of the two orthogonal polarizations of light beam, can be widely used in optical systems, such as optical switches, data storage and image processing. Different from conventional methods which rely on the inherent birefringence of anisotropic materials or the Brewster angle effect, various configurations for PBS which utilize different responses of the structure for TE and TM polarizations have been proposed, such as embedded metal-wire nanograting [1], coupled plasmonic waveguide arrays [2], binary blazed grating coupler [3] and anisotropic metamaterial slab [4, 5]. Photonic crystals (PCs) are also used for PBS by employing polarization-dependent bandgaps [6, 7], anisotropies [8], as well as positive/negative refractions [9, 10]. However, since the functionalities of all these structures have been fixed at the fabrication, no further tuning of the optical properties can be performed, which is a limitation in many practical applications.

In this paper, we propose a tunable PBS via an electric field based on a symmetrical metal-cladding waveguide (SMCW) structure. Since the excitation of ultrahigh-order modes [11] in the SMCW is determined by the match of the incident parameter k _y0=2πn ₀sinθ/λ (n ₀, θ and λ denote the refractive index of the coupling material, the incident angle and the wavelength in vacuum, respectively) with the resonance condition, different resonance angles for TE and TM modes can be generated by using anisotropic coupling prism. High reflection is obtained for one polarization while the other polarization is largely transmitted. Moreover, the splitting of TE- and TM-polarized beams can be controlled via an electric field when optically active material is utilized in the guiding layer.

2. Structure of the SMCW

 

Fig. 1. Structure of the SMCW for tunable PBS.

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The nonlinear material LiNbO₃ is introduced in both the coupling prisms and the guiding layer of the SMCW, where the optical properties of polarization-dependent anisotropy and electro-optic (EO) effect are put to use, respectively. As shown in Fig. 1, two prisms, which act as the coupling layer, are made of x-cut LiNbO₃ crystal. It is easily seen that TE- and TM-polarized beams are the extraordinary and ordinary waves inside the prisms, respectively. So polarization-dependent k_{y 0} is obtained for the same light wavelength and incident angle owing to the different refractive indices of the prisms for the two orthogonal polarizations. And the z-cut LiNbO₃ slab, together with two air gaps, constitutes the guiding layers. The LiNbO₃ slab is the essential component for electrical tuning of the guiding layer properties, in which both TE- and TM-polarized beams can be considered as ordinary waves on condition of very small incident angles. The guiding layers are sandwiched between two gold thin films which are deposited on the bottom of the prisms. In the structure, the gold films not only serve as cladding layers but also work as electrodes, on which external electric field is applied. We assume n_j (ε _j), d_j as the refractive index (dielectric constant) and thickness of the jth layer, respectively. The parameters of the structure are as follows: n ₀=n ₆=2.170 (for TE mode) and 2.248 (for TM mode), ε ₁=ε ₅=-28+1.8i, n ₂=n ₄=1, n ₃=2.248, d ₁=26nm, d ₂=0.1mm, d ₃=0.5mm, d ₄=0.1mm and d ₅=30nm.

3. Principle

When a light beam incidents onto the structure at a small incident angle, an ultrahigh-order mode will be excited under the phase-matching condition. The reflectivity and transmissivity can be obtained by means of the characteristic matrix, which is given by [12]

with the effective admittance of the jth layer

where θ _j, δ _j=(2π/λ)n_jd_j cosθ _j represent the refractive angle and the phase thickness of the _jth layer, respectively, and λ is the light wavelength in vacuum. Then the reflectivity of the device can be express as

And the transmissivity is

As shown in Fig. 2 , we calculate the spectral responses of the SMCW structure for both TE-and TM-polarized beams at the light wavelength of λ=860nm. The reflectivity and transmissivity for each polarization strongly vary with the incident angle in the range of a guided mode. The coupling angles for TE and TM modes are staggered from each other, which give rise to different reflections and transmissions for different polarizations. It is seen that, at the coupling angle of TM mode (θ ₁=5.892°), TE-polarized beam is highly reflected, whereas TM-polarized light is largely transmitted. And it presents a reverse way of PBS at the coupling angle of TE mode (θ ₂=5.949°). When a dc voltage (U) is applied on the two gold films, the LiNbO₃ slab will alter its refractive index (n ₃) and thickness (d ₃) through the EO and piezoelectric effects, following the expressions Δn ₃=-n ³ ₃ γ ₁₃ E ₃/² and Δd ₃=d ₃₃ E ₃ d ₃, respectively, where γ ₁₃ is a component of the EO coefficient, d ₃₃ is a component of the piezoelectric coefficient, and E ₃ is the electric field on the LiNbO₃ slab. Besides, the air gaps will present a change of Δd ₂=Δd ₄=-Δd ₃/² in thickness. These changes of the structure parameters will modify the guided-mode resonance and lead to variations of the reflection and transmission. Consequently, the splitting effect of the two orthogonal polarizations can be controlled via the external electric field.

 

Fig. 2. Calculated reflectivity and transmissivity with respect to the incident angle for TE-and TM-polarized light.

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4. Experiments and discussions

Experiments are performed to demonstrate the tunable PBS effect in the SMCW, the setup of which is drawn in Fig. 3. An EO modulator is used to switch the polarization state of light beam (λ=860nm) from the laser source. After passing through two apertures, the well-collimated beam incidents upon the structure. Two photodetectors are used to measure the reflection and transmission intensities simultaneously. And the polarization extinction ratio is calculated by dB=10log₁₀ (P ₁/P ₂), where P ₁ is the power of primary polarization and P ₂ is the power of cross talk polarization.

 

Fig. 3. Experimental setup. PD: photodetector; EOM: EO modulator; AP: aperture.

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Initially, external voltage is not applied onto the structure and the incident angle is settled at θ=5.884°. This angle is a little smaller than the resonance angle of TM mode, where the guided mode is not excited yet. The PBS effect is indistinct at this operation point since both TE and TM polarizations are highly reflected (R _TE=89.9%, R _TM=91.1%). Then the applied electric field is adjusted to tune the PBS effect in the SMCW structure. As shown in Fig. 4(a), the status of TE polarization remains nearly invariant with the augmentation of applied voltage, whereas TM polarization gradually changes into large transmission. The transmission of TM polarization reaches T _TM=60.3% at U=2200V, where a high separation of polarization beams is achieved. The extinction ratios in reflection and transmission are 16.9dB and 15.7dB, respectively. The situation of θ=5.941°, which is a little smaller than the resonance angle of TE mode, is also measured in the experiment (Fig. 4(b)). Similarly, high reflections for both TE and TM polarizations (R _TE=90.4%, R _TM=91.5%) are demonstrated at U=0. But it presents an opposite way of PBS when adjusting the voltage, i.e., TM-polarized beam remains highly reflected while TE-polarized beam becomes largely transmitted. The transmissivity (reflectivity) of TE (TM) polarization is T _TE=60.0% (R _TM=90.8%) at U=2000V, with an extinction ratio of 17.0dB (18.6dB) in TM (TE) polarization. The EO and piezoelectric coefficients of the LiNbO₃ slab are γ ₁₃=8.27pm/V and d ₃₃=8pm/V at the wavelength in experiment. The ambient temperature is held constant at 25.2°C with the fluctuation of less than 0.2 °C during the experiment. In fact, the tuning of PBS in the SMCW is mainly determined by the refractive index change in the guiding layer. To keep stability of the device, the variation of temperature needs to be limited within 1 °C [13]. The operation voltage can be reduced to a much lower level if high efficient EO material is utilized [14].

 

Fig. 4. Experimental measurements of tunable PBS. (a) θ=5.884°; (b) θ=5.941°.

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5. Conclusion

In summary, a structure of SMCW is proposed to achieve a tunable splitting effect of TE and TM polarizations of the light beam via an electric field, which utilizes optically nonlinear crystal in both the coupling prisms and the guiding layer. Induced by the anisotropy of the coupling material, polarization-dependent reflection and transmission are obtained in the structure. Large transmission for TE (TM) polarization can be obtained at the resonance angle of TE (TM) mode, while TM (TE) polarization is highly reflected. Furthermore, the properties of the guiding layer can be changed by adjusting the applied electric field, which leads to the controllable splitting of polarization beams.