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Abstract
A novel design of a polarization controller based on “etch-less” Si3N4-loaded thin film LiNbO3 is described. Broadband operation in the spectral range between 1.45 and 1.65 µm is achieved by using a mode evolution TM/TE splitter/converter, two mode evolution 3-dB couplers, and two electro-optic phase shifters. Numerical simulations show that the on-chip insertion loss should not exceed 1 dB. A single TE-mode output can be adjusted by applying control voltages lower than 10 V for an arbitrary input polarization state.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Polarization controllers are important components of optical systems. While the polarization manipulation in an isotropic medium such as a free space can be performed by the combination of suitably adjusted $\lambda /4$ and $\lambda /2$ phase plates, in generally birefringent integrated-optic waveguides that support the (quasi)-TE and (quasi)-TM modes, the situation is somewhat different. For complete polarization control, the ability of the TE/TM conversion and controllable phase shifts are both required. The early guided-wave devices for polarization management [1–8] were mostly based on metal-diffused LiNbO3 waveguides because of their strong electro-optic properties enabling easy phase shifting. The realization of the TE/TM conversion in such waveguides was based on the coupling of the TE and TM modes; this may be challenging since the modes are nearly linearly and mutually perpendicularly polarized, and they also differ in the propagation constants due to the combined material and waveguide birefringence. The TE/TM coupling was typically mediated by an off-diagonal permittivity component introduced electro-optically, and the phase matching of the TE and TM modes was attained either by a periodic structure of electrodes, or by choosing the direction of propagation close to the optic axis of the LiNbO3 crystal.
Recent development of the thin-film lithium niobate technology (called also lithium niobate on insulator–LNOI) [9] has brought a disruptive change in the design of integrated-optic guided-wave LiNbO3 devices. This novel approach has led to the design of more compact devices with smaller footprint size and lower operation voltages. In order to localize light in the lateral direction, etched rib or dielectric-loaded channel waveguides are used. In these high refractive index contrast waveguides, the “minority” components of mode fields are strong enough to give rise to polarization coupling between the neighboring waveguides. Dispersion properties of such waveguides are more complicated than properties of traditional titanium-diffused LiNbO3 waveguides since the natural birefringence of the LiNbO3 crystal is now combined with the waveguide birefringence of the LiNbO3 crystal slab. As a result, one has to mitigate possible lateral leakage of TM polarized modes due to coupling with the TE polarized LiNbO3 slab mode [10,11], in analogy with the silicon on insulator (SOI) waveguides [12–15]. Nevertheless, various designs of polarization rotators and splitters on thin-film LiNbO3 platform have been recently published [16–21].
A complete electro-optic polarization control in a thin-film LiNbO3 device has been recently described in a very comprehensive paper [22]. Our present work is devoted to a similar though a more difficult problem–to design a broadband device operating in the wavelength range from 1450 to 1650 nm, capable of transforming an arbitrary polarized input wave into a TE polarized output mode, without the need of uneasy etching of a LiNbO3 slab. We thus consider waveguides laterally confined by silicon nitride loading stripes, similarly as in [23]. For efficient electro-optic control, the X-cut LiNbO3 film was chosen. Analogously to [22], the device is composed of a polarization mode splitter/converter, two 3-dB couplers, and two electro-optic phase shifters. To ensure broadband operation, adiabatic mode evolution components are applied. Their original design, rather analogous to [21,24–26], will be described in detail below. As a necessary pre-requisite of these designs, the properties of the silicon nitride-loaded thin film LiNbO3 waveguides will be briefly reviewed. For numerical simulations, COMSOL Multiphysics 6.1 mode solver [27] and our proprietary 3-D Fourier modal method (FMM) [28] were used.
2. Polarization controller
The configuration of the designed broadband polarization controller is schematically shown in Fig. 1. It consists of the input taper which prevents the bottom (narrower) waveguide from excitation and transforms the waveguide widths to the required input widths of the broadband adiabatic TM/TE splitter/converter. The upper waveguide is generally excited with a superposition of TE00 and TM00 modes with arbitrary amplitude ratio and relative phase shift. The adiabatic TM/TE splitter/converter transforms the input TM00 mode of the upper (wider) waveguide into the TE00 mode of the lower (narrower) waveguide. The aim of the first phase shifter is to adjust the relative phase shift between the input ports of the first broadband adiabatic 3-dB coupler to equalize the mode amplitudes at its output ports. The second phase shifter is used to adjust the relative phase of the input ports of the second 3-dB coupler in order to minimize the output from the bottom port and maximize the amplitude of the TE00 mode leaving the upper output port. Both the couplers are identical; however, to balance the upper and lower optical paths and thus possibly reduce the group velocity dispersion, the 3-dB couplers are mutually horizontally flipped.
Fig. 1. Schematic configuration of the polarization controller. The length dimensions are in micrometers.
The components of the controller–the TM/TE splitter/converter, the phase shifters and the 3-dB couplers–can be considered as linear four-ports, as it is shown in Fig. 2. The complex amplitudes ${a_{in}}$ and ${b_{in}}$ correspond to the input polarizations TE and TM, respectively, while the amplitudes ${a_m}$, ${b_m},m = 2, \ldots 5$ and ${a_{out}},\textrm{ }{b_{out}}$ represent complex amplitudes of the TE modes in the pertinent ports.
Fig. 2. Representation of the controller by a cascade of four-ports. SC—TM/TE splitter/converter, PS1, PS2—phase shifters, C1, C2—3-dB couplers. Symbols a and b (with subscripts) are explained in the text.
Due to negligible back-reflections, each component can be represented by the $2 \times 2$ transfer matrix. Neglecting losses, the matrices gain very simple forms shown in (1):
Here ${\varphi ^{TE}}$ and ${\varphi ^{TM}}$ are phase shifts due to propagation of the TE and TM polarized modes within the splitter/converter, respectively, ${U_1}$ and ${U_2}$ are control voltages of the phase shifters PS1 and PS2, respectively, and ${\varphi _w}$ and ${\varphi _n}$ are phase shifts of the modes entering the wider and narrower input ports of the 3-dB couplers, respectively. A straightforward analysis shows that for arbitrary input complex amplitudes ${a_{in}}$ and ${b_{in}}$ the voltage ${U_1}$ can be always adjusted within the limits $|{{U_1}} |\le {{{U_\pi }} / 2}$ in such a way that the absolute values of the complex amplitudes ${a_4}$ and ${b_4}$ are equal. In the lossless case, the optimum voltage ${U_1}$ depends only on the relative phase shift between the amplitudes of the input TE and TM modes ${a_{in}}$ and ${b_{in}}.$ Consequently, the voltage ${U_2}$ can be adjusted within the limits $|{{U_2}} |\le {{{U_\pi }}}$ to minimize the output amplitude ${b_{out}}$ and maximize the amplitude ${a_{out}}.$ Obviously, the interpretation of the operation of the polarization controller using the Poincaré sphere as in [22] can be alternatively used as well.
In the next sessions, the configurations of the broadband adiabatic components and phase shifters specifically designed for the Si3N4-loaded LNOI platform are described in detail.
3. Properties of Si3N4-loaded X-cut thin-film LiNbO3 waveguides
The cross-section of the silicon nitride-loaded thin-film LiNbO3 waveguide considered is shown in Fig. 3(a). The X-cut LiNbO3 slab thickness is 400 nm, the silicon nitride stripe thickness is 300 nm. Light propagates along the crystal axis Y. Figure 3(b) shows the dependences of the effective refractive indices of the TEm0 and TMm0 modes of the channel waveguide on the silicon nitride stripe width w at the wavelength of 1550 nm. Despite the fact that the extraordinary refractive index of the LiNbO3 crystal is lower than the ordinary one and the TEm0 modes are predominantly extraordinary polarized, their effective refractive indices are higher than those of the TMm0 modes of the same (lateral) order m due to the waveguide birefringence of the planar LiNbO3 thin film waveguide supporting the TE0 and TM0 modes. The TMm0 modes with the effective refractive indices lower than the effective refractive index of the TE0 mode, which takes place for narrower widths w, are extremely leaky due to the coupling with the TE0 mode via their minority field components parallel to the interfaces. Their radiation losses are shown in Fig. 3(c). From Fig. 3(b) it is evident that we can choose a particular pair of stripe widths for which the corresponding effective refractive indices of the TE00 and TM00 modes are identical (an example of such pair is indicated by dots on dispersion curves of the modes). This feature will be later utilized in the design of the TM/TE polarization splitter/converter as the key component of the polarization controller.
Fig. 3. (a) Cross-section of the Si3N4-loaded thin-film LiNbO3 waveguide. (b) Dependence of the effective refractive indices of supported modes on the silicon nitride stripe width w at the wavelength of 1550 nm. (c) Radiation loss of the TM modes due to coupling with the TE-polarized mode of the LiNbO3 slab planar waveguide. The data shown in (b) and (c) were calculated using COMSOL Multiphysics [27].
The electric field distributions of the relevant modes for the stripe widths 0.85 µm and 1.5 µm are shown in Fig. 4. Note that the mode fields are well localized in the transverse direction, and that the TE mode fields are concentrated mainly in the LiNbO3 slab which is important for efficient electro-optic control. The design does not make use of the bound modes in the continuum [29], which makes it independent of the limitations to the “magic widths” of waveguides and of reduced electro-optic efficiency of phase shifters [30].
Fig. 4. Distributions of the electric field (in relative units) of the waveguide modes for the silicon nitride stripe widths of 0.85 µm and 1.50 µm at the wavelength of 1.55 µm.
4. Broadband TM/TE splitter/converter
Design of adiabatic mode evolution components is not straightforward since adiabaticity is, in fact, an abstraction that can be achieved only approximately [31]. We used the procedure similar to that described in [21], adopted for the platform used. A narrow-band device can use a longitudinally uniform converter with the waveguide widths corresponding to the maximum hybridization of the supermodes of the pair of the waveguides, i.e., the configuration in which the difference between the effective refractive indices of the fundamental and the higher-order supermodes ${N_0},\textrm{ }{N_1}$ is the smallest. In this case, the polarization of the supermodes is strongly hybridized. The optimum coupling length of the uniform converter is obviously ${L_c}(\lambda ) = {\lambda / {[2({N_0} - {N_1})]}}.$
For a broadband operation, the coupling region has to be longitudinally tapered in such a way that the optimum hybridization can appear at different positions for different wavelengths. The converter parameters have to be varied slowly enough to reach the highest possible TM/TE coupling efficiency. In our design we fixed the edge-to-edge gap between the waveguides to 0.5 µm, to ensure sufficiently strong mode coupling without excessive fabrication demands, and decided to taper both waveguides of the converter. We set the widths ${w_1}$ and ${w_2}$ of the pair of the broader and narrower waveguides at the input and output of the adiabatic section to ${w_{1,\textrm{in}}} = 1.45\,\mathrm{\mu}\textrm{m}$, ${w_{2,in}} = 0.7\; \mathrm{\mu m,}$ ${w_{1,\textrm{out}}} = 1.3\,\mathrm{\mu}\textrm{m}$ and ${w_{2,\textrm{out}}} = 0.95\,\mathrm{\mu}\textrm{m}$, respectively. The input and output values correspond to the strongest mode hybridization at the wavelengths of ${\lambda _{\max }} = 1.65\,\mathrm{\mu}\textrm{m}$ and ${\lambda _{\min }} = 1.45\mathrm{\ \mu m,}$ respectively. Simulations showed that such waveguide widths depend approximately linearly on the wavelength,
As a consequence, the waveguide widths ${w_1}$ and ${w_2}$ are mutually linearly dependent, too. From (2) it follows that for the parameters given above, ${w_2}(\lambda ) \approx 3.6 - 2{w_1}(\lambda )$.
In Fig. 5(a) there are shown the dependences of the effective refractive indices of the supermodes on the wavelength widths in the vicinity of the strongest hybridization for several wavelengths. The wavelength dependence of the optimal length ${L_c}(\lambda ) = {\lambda / {[2({N_0} - {N_1})]}}$ of the uniform converter with the waveguide widths ${w_1}(\lambda )$ and ${w_2}(\lambda )$ leading to maximum hybridization is shown in Fig. 5(b). Numerical simulations confirmed the expectation that the function ${L_c}(\lambda )$ is approximately exponentially dependent on the wavelength, as shown in Fig. 5(b) by the red exponential fitting curve connecting the black simulated points. To enable numerical simulation of the adiabatic polarization splitter/converter with our FMM numerical code [28] (written in cartesian coordinates), we discretized the wavelength range into p wavelengths,
Fig. 5. (a) Dependence of the effective refractive indices of supermodes on the waveguide widths for several wavelengths. The black dashed line indicates the linear dependence of the “hybridization waveguide widths” on the wavelength. (b) Wavelength dependence of the optimum coupling length ${L_c}$.
The waveguide bends at the output of the adiabatic section ensure that the waveguides are separated, preventing them from further unwanted mode coupling. Their widths are simultaneously tapered from ${w_{1,\textrm{out}}}$ and ${w_{2,\textrm{out}}}$ to the identical width $w = 0.85\,\mathrm{\mu}\textrm{m}$ used in the electro-optic phase shifters. The shapes of the bends were designed as 5th-order polynomials which allow for smooth waveguide tapering without discontinuities in the waveguide edge slopes and curvatures. The length of the bends of 500 µm and the final edge-to-edge separation of the waveguides of 8 µm were chosen as a trade-off between the bend losses and the footprint size.
The configuration of the adiabatic TM/TE mode splitter/converter and the relative electric field distributions of the field within the waveguides under TM and TE mode excitations at several wavelengths are shown in Fig. 6.
Fig. 6. (a) Configuration of the adiabatic mode evolution TM/TE splitter/converter: I–input taper, II–adiabatic section, III–output bends; (b)–(f) electric field distributions inside the TM/TE splitter/converter (in relative units): (b) $\lambda = 1.55\mathrm{\ \mu m,}$TE00 input, ${|{{E_x}} |^2}$; (c) $\lambda = 1.45\mathrm{\ \mu m,}$ TM00 input, ${|{{E_y}} |^2}$; (d) dtto for $\lambda = 1.65\mathrm{\ \mu m;}$(e) $\lambda = 1.45\mathrm{\ \mu m,}$TM00 input, ${|{{E_x}} |^2}$; (f) dtto for $\lambda = 1.65\,\mathrm{\mu}\textrm{m}\textrm{.}$
The wavelength response of the power transmission and crosstalk of the whole TM/TE converter including the output bends was calculated with the FMM method [28]. The results are shown in Fig. 7. It is evident that the transmission is higher than –0.22 dB (i.e., $ > 95\%$) and the crosstalk is lower than –29 dB in the spectral range considered.
Fig. 7. Calculated wavelength response of the transmission and crosstalk of the broadband TM/TE splitter/converter.
5. Broadband 3-dB couplers
Broadband 3-dB couplers are indispensable components of many integrated-optic devices. Various designs have thus been proposed, fabricated, and tested [24,32–37]. Unfortunately, those based on subwavelength structures cannot be applied to laterally low-contrast Si3N4-loaded LNOI. A simple and elegant device using the concatenation of single-mode asymmetric and symmetric Y-junctions connected with the two-mode section, as shown in Fig. 8(a) (for which we were unfortunately unable to find any reliable reference), can be considered as an archetype of broadband adiabatic mode evolution 3-dB couplers. Since the correctly designed asymmetric Y-junction behaves adiabatically as a mode splitter/divider, light coupled into the wider input waveguide of the asymmetric Y-junction excites in the common two-mode section the fundamental, i.e., the symmetric mode while coupling into the narrower waveguide excites in the common section the antisymmetric mode. In both cases, light power is then divided symmetrically in the symmetric Y-junction into the output ports, which results in spectrally independent 3-dB coupling. Reciprocity of the device guarantees the 3-dB coupling in the opposite direction, too.
Fig. 8. (a) 3-dB coupler composed of the concatenation of asymmetric and symmetric Y-junctions (schematic view); (b) modified design: 1–input bends, 2–adiabatic mode evolution section, 3–symmetric output bends.
Unfortunately, this configuration suffers from important disadvantages. Sharp tips at the waveguide branchings make the fabrication of this device challenging. Moreover, in a broadband application, the third–symmetric–mode can be also supported and excited in the common central part at shorter wavelengths, and since it cannot propagate in the symmetric Y-junction, its power is radiated, which leads to transmission loss. Therefore, the design is usually modified by separating the waveguides, as shown in Fig. 8(b) for our case. Waveguide bends in section 1 (Fig. 8(b)) are tapered from identical widths at the input to different widths at the beginning of the adiabatic mode evolution section 2. Here the modes of the wider and narrower input waveguides evolve in linearly tapered waveguides into the symmetric and antisymmetric supermodes at its end. In the output bends (section 3), the waveguides are symmetrically separated, which results in symmetric power splitting of both input symmetric and antisymmetric supermodes. All bends are also shaped as 5th-order polynomials, ensuring continuity of waveguide edges, their slopes and curvatures.
Numerical simulation using the FMM [28] showed the propagation and splitting loss lower than 0.3 dB and the power imbalance lower than 0.4 dB in the spectral range considered. Broadband operation of the modified coupler is demonstrated by the samples of field distributions at the shortest and longest wavelength of the considered band, as shown in Fig. 9.
Fig. 9. ${|{{E_x}} |^2}$ field distributions in the 3-dB coupler (in relative units) at the wavelengths of (a) 1.45 µm and (b) 1.65 µm.
6. Electro-optic phase shifters
For the electro-optic phase shifters, a standard push-pull configuration is implemented. The X-cut Y-propagation arrangement allows utilization of the strong electro-optic coefficient ${r_{33}}$ of the LiNbO3 slab. Electrodes are designed as 6 µm wide, separated by 1 µm from the Si3N4 stripe, composed of the 150 nm SiO2 buffer covered with 200 nm of gold. The buffer is used to suppress light absorption in metal electrodes. Numerical simulations by COMSOL Multiphysics 6.1 [27] showed that the voltage of 1 V applied to the electrodes excites nearly uniform horizontal electric field intensity of 2 × 105 V/m in the LiNbO3 slab. Numerical simulations predicted optical absorption loss due to electrodes lower than 0.25 dB/cm. The absorption loss in both phase shifters, the total electrode length of which is 4 mm, is thus about 0.1 dB. The half-wave voltage ${U_\pi }$ of the phase shifters was estimated to be lower than 10 V. The distribution of the DC electric field calculated with COMSOL is shown in Fig. 10.
Fig. 10. Distribution of the DC electric field in the phase shifters. Arrows indicate the direction of the electric field.
7. Conclusions
A numerical proof of principle of an efficient broadband electro-optic polarization controller based on silicon nitride-loaded X-cut thin-film lithium niobate platform is presented. The device is designed to provide a single-mode TE polarization output from an arbitrary input polarization in the wavelength range of 1.45 to 1.65 µm without the need of uneasy etching of the LiNbO3 crystal. Original designs of the key adiabatic broadband components—the polarization splitter/converter and the 3-dB coupler—are described. Conventional two-electrode phase shifters utilizing the high electro-optic coefficient ${r_{33}}$ of the LiNbO3 crystal are designed for phase tuning. Numerical simulations indicate that the operation voltage of both phase shifters required for endless polarization control should lie within ${\pm} 10\textrm{ V}\textrm{.}$
The cumulative insertion loss of the controller obtained as a sum of calculated losses of individual components was found to be about 1 dB. Taking into account the typical background propagation loss in the silicon nitride-loaded LNOI of about 1 dB/cm, the total on-chip loss of the 1.5-cm long device should not exceed 2.5 dB.
Funding
Akademie Věd České Republiky (RVO 67985882); Vysoké Učení Technické v Brně (FSI-S-23-8389); České Vysoké Učení Technické v Praze (RVO 608407700); Ministerstvo Školství, Mládeže a Tělovýchovy (CZ.02.1.01/0.0/0.0/16_019/0000778).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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