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The new compact polarization rotator in anisotropic graded index Ti:LiNbO3 channel waveguide is proposed and investigated by 3D beam propagation method (BPM). Device is based on a channel optical waveguide directed at small angle (about 5 degrees) with respect to Z-axis on Y-cut lithium niobate substrate. The polarization conversion from quasi-TE to quasi-TM guided modes (and backwards) along 8 mm long waveguide with an index contrast 0.015, has been numerically demonstrated. Device is intended for polarization diversity of integrated optic elements based on LiNbO3 structures.
©2008 Optical Society of America
1. Introduction
Usually, optical properties of integrated optical elements are polarization-dependent. The simplest way to eliminate this dependence is to use polarization rotators and polarization splitters, which help to make any optical element polarization independent. A thin polyimide half-wavelength plate embedded in a deep trench [1] is a good candidate for silica waveguides with small refractive index contrast and large cross section, providing waveguide small optical losses using an embedded rotator section. Polarization transformer/rotator in high index contrast semiconductor waveguides could be developed by manufacturing multi-section bend structures [2] or asymmetric angled-facet waveguide structures [3]. A mode-evolution-based polarization rotator can be formed by twisting a waveguide [4] that contains a pair of waveguide core layers. Unfortunately, all these technologies are not suitable for widely spread waveguides in lithium niobate (LiNbO3). The general aim of this paper is to propose and to investigate the polarization rotator that is compatible with common technology of lithium niobate integrated optical waveguides.
Twenty years ago, a great number of investigations were devoted for studying the anisotropic graded index waveguides in lithium niobate. It was shown that optical guided modes are strongly hybrid [5]. Besides, at particular angle of propagation (that is not far from the crystallographic Z-axis) the quasi-TE and quasi-TM guided modes could have a circular polarization [6, 7], with opposite directions of rotation. Similar types of hybrid modes with circular polarization could also exist in appropriately directed 3D Ti-diffused channel waveguides into LiNbO3. Thus, the input linear polarization could be rotated during the light propagation along the anisotropic channel waveguide [8] by means of two hybrid modes that exist in the optical waveguide with different effective indexes and opposite directions of rotation for their circular polarization. This effect of polarization conversion/rotation in anisotropic graded index channel waveguides has been studied in this paper for the first time by full-vectorial 3D beam propagation method (BPM) [9].
2. Simulated results and discussion
It has been examined the polarization rotation at variable orientation of an input linear polarization for different directions θ of the channel waveguide related to the crystallographic Z-axis of Y-cut LiNbO3. The waveguide width is w=13 µm, waveguide height is h=2.4 µm, maximum refractive index increase in the diffused waveguide is Δn=0.015, substrate main refractive indices are Ne=2.138 and No=2.212. All these parameters are relevant to a Ti-diffused LiNbO3 waveguide at the optical wavelength 1.55 µm. However, for simplicity we use the same value Δn for both extraordinary and ordinary increases of refractive indices. Graded index distribution of the refractive index across the waveguide depth has been typically used for the diffusion model and corresponds to the LiNbO3 simulated example [9]. Namely, waveguide refractive index distribution is derived as:
In our case we use hx=hy=h. Typical refractive index distribution is shown in Fig. 1.
Fig. 1. Simulated distribution of refractive index in channel waveguide (w=13 µm, h=2.4 µm, Δn=0.015).
Optical field distribution for the major and minor components of electric field of fundamental guided modes simulated by BPM are shown in Fig. 2 for a waveguide orientation along the crystal Z-axis (θ=0). It could be mentioned that for the chosen width w=13 µm the mode size in horizontal direction is close to the diameter of the single mode fiber core. In order to study the effect of polarization rotation in slanted (θ≠0) channel anisotropic waveguides, we use the optical fields of quasi-TE or quasi-TM polarizations as input, then examining by BPM the optical wave propagation through the anisotropic channel waveguide by determination of the overlap integral of the resulted field with the distribution of quasi-TE and quasi-TM modes determined for θ=0.
Fig. 2. Simulated distribution of optical field of guided modes in diffused waveguide of Fig. 1. (a) quasi-TE mode, (b) quasi-TM mode. (θ=0).
Typical behaviour of optical wave propagation along diffused channel waveguides directed at angle 5.27° with respect to Z-axis in Y-cut Ti:LiNbO3 is shown in Fig. 3 for the case of incidence quasi-TE fundamental mode.
Fig. 3. 3D BPM simulation of polarization conversion in anisotropic channel waveguide directed at angle θ=5.27°. Input polarizations: quasi-TE.
The left part of Fig. 3 demonstrates the propagation of quasi-TE mode along the waveguide. The right part of Fig. 3 shows behaviour of the power amplitude of both quasi-TE and quasi-TM guided modes.
One can see that the incident quasi-TE fundamental mode of optical beam has to change the polarization to quasi-TM mode while propagating along the waveguide. This effect of polarization rotation/conversion in an anisotropic channel waveguide could be explained in the following way. The incident optical beam excites two hybrid guided modes of circular polarization. Because of the phase delay due to the difference of effective refractive index of these modes, their superposition produces different polarization of the resulting field at the waveguide end, depending on the propagation length L.
It is worth noting that it has been impossible to achieve a constant level of the total power due to simulation problems, typical for the full-vectorial 3D BPM that currently works only under paraxial approximation [9]. Nevertheless, for our particular waveguides with small index contrast, this method could be also applied for the slanted waveguides (θ<7°) but at the expenses of a non constant level of the total power. However, this can be corrected by a simple power normalization procedure by means of the correction coefficient KC to the monitor values for quasi-TM and quasi-TE modes. This coefficient KC=(KC1·KC2)1/2=1.636 has been found in anisotropic channel waveguide directed at angle θ=5.27° by the determination the two amplitude ratios KC1 and KC2:
Incident mode is quasi-TE: KC1=A(TE)/A(TM)=1.647;
Incident mode is quasi-TM: KC2=A(TE)/A(TM)=1.625;
Amplitudes A for quasi-TE and quasi-TM modes, which has the notation A(TE) and A(TM), have been determined by the best fit of the data for different incident modes (similar to that presented in Fig. 3) by the analytic dependence: T=B+A·(sin(π/2·(pc-x/L0)))2, which is typically used to describe power exchange between the two modes.
To measure the actual conversion efficiency and the power transmittance T of different polarization, it is needed to multiply by KC the simulated results for quasi-TM mode or to divide by KC the simulated results for quasi-TE mode. Results of this power normalization are presented in Fig. 4. It is easily seen that, at optimal length L0=7.8 mm, this anisotropic channel waveguide produces a 90° rotation of the incident linear polarization from quasi-TE to quasi-TM [see Fig. 4(a)] or from quasi-TM to quasi-TE [see Fig. 4(b)].
Fig. 4. Normalized results of 3D BPM simulation of power transmittance T in anisotropic channel waveguide directed at angle θ=5.27°. Input polarizations: (a) quasi-TE; (b) quasi-TM.
The influence of waveguide orientation in the vicinity of the optimum angle θ0 has been investigated by the power transmittance analysis for quasi-TE and quasi-TM modes passing through a 7.8 mm long anisotropic channel waveguide. This length is close to the optimum for the 90° rotation, thus the input polarization has been chosen to have quasi-TE orientation. As a result, at optimum direction θ0 of the channel waveguide we have the maximum power transmittance for quasi-TM and the minimum transmittance for quasi-TE mode, respectively. Results of these simulations are presented in Fig. 5.
Fig. 5. 3D BPM simulation of polarization conversion from quasi-TE to quasi-TM at different angle θ relative to Z-axis in Y-cut Ti:LiNbO3. L0=7.8 mm. (a) quasi-TE; (b) quasi-TM.
One can see that the anisotropic channel waveguide in LiNbO3 is working as a good polarization rotator only within a small angle range, Δθ~0.1°, centered around the angle θ0=5.27° related to Z-axis. For another waveguide parameters, the optimal angle θ0 is different from this one but the optimum range Δθ is of the same order of magnitude. In general, the larger difference between the effective indices of fundamental quasi-TE and quasi-TM modes (measured along Z-axis), then the larger optimum value of the angle θ0 and the smaller length of the total polarization conversion.
The proposed optical element for the polarization conversion has the high extinction ratio (larger than -20 dB) in a wide transmitting band ~80 nm (see Fig. 6) that is very important for practical applications. For example, this polarization rotator/converter can be applied with the well known polarization splitter [10] for polarization diversity of the multiple photonic devices that can be monolithically integrated in lithium niobate substrate.
Fig. 6. 3D BPM simulation of polarization conversion from quasi-TM to quasi-TE modes at different optical wavelengths in an anisotropic channel waveguide directed at angle θ=5.27°. L0=7.8 mm. (a) quasi-TE; (b) quasi-TM.
3. Conclusions
This paper proposes and describes the results of theoretical investigation of novel integrated optics polarization rotator/converter based on the anisotropic graded index Ti-diffused channel waveguide in LiNbO3 substrate. The device operation is based on the hybrid nature of guided modes in 3D anisotropic waveguides. At a particular direction of the waveguide with respect to crystal axis, the two basic fundamental modes could have the circular polarization with opposite directions of rotation. Thus, the input linear polarization has to be rotated during the propagation along the anisotropic channel waveguide by means of two hybrid modes with the opposite directions of rotation. This effect of polarization conversion/rotation in anisotropic graded index waveguides has been studied in this paper for the first time by using a full-vectorial 3D beam propagation method. It has been examined polarization rotation at different launching polarizations for different waveguide orientations and optical wavelengths. It has been found that at particular waveguide direction (about 5° related to Z-axis of Y-cut LiNbO3), the condition of total polarization conversion from quasi-TE to quasi-TM mode (and backward) can be obtained by using a waveguide with index increase 0.015 and total length about 8 mm. The half length 4 mm is enough for the 45° polarization rotation. This optical element could find wide applications for the polarization diversity of photonic devices monolithically integrated in the LiNbO3 substrate.
Acknowledgments
The authors thank Company RSoft Design Group, Inc. for providing user license and technical support for Rsoft Photonic CAD Suite 8.0 including BeamPROP software for BPM simulations.
References and links
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