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We report polarization independent Bragg grating wavelength filter using polarization rotation. A non-vertical waveguide sidewall and antisymmetric grating structure can be used to generate the polarization rotation of the fundamental modes. The diffraction efficiencies and peaks becomes the same for two orthogonal input polarizations. The concept was verified by simulation and experiment.
© 2014 Optical Society of America
1. Introduction
Optical filtering devices have been demonstrated using Si wire waveguide technology [1–6]. Compact optical circuit can be obtained by tight light confinement in the waveguide. Usage of the CMOS process enables a mass production. Bragg grating is one of the important devices for wavelength filtering [7–14].
Polarization manipulation is important in telecommunication systems or interconnects for data center and supercomputers. The polarization becomes random after propagated through a long optical fiber transmission line. The wavelength filter used in these systems should be polarization independent. In this report, we describe a reflective Bragg grating which can convert the input polarization into another polarization of counter propagating light which can be used to achieve polarization independence [13, 15, 16].
One of the schemes to attain polarization independent Bragg grating is to use square cross section waveguide in which the effective indices of the TE (transverse electric) and TM (transverse magnetic) modes are equal [13, 14]. The same diffraction wavelength is obtained for the TE and TM modes due to the same effective indices for these polarization modes. We demonstrated this type of device in the previous report [14]. However, the diffraction wavelength peak height and the width tend to differ between polarizations because of a grating coupling coefficient difference. The TE and TM wavelength peaks becomes separated when the waveguide cross section deviates from the ideal shape. The wavelength peak and diffraction efficiency are expected to become the same when a polarization rotation Bragg diffraction [13, 15, 16] is used as will be shown. Schematic diffraction diagrams for these two types of Bragg diffractions are shown in Fig. 1. The grating period Λ can be designed for a Bragg wavelength λ as shown in Fig. 1. The grating period Λ is related to effective indices NTE NTM of TE and TM modes in different ways for two cases. The polarization independent peak wavelength is automatically achieved for polarization rotation diffraction so that the TE and TM diffraction peak is always the same irrespective of the waveguide size.
Fig. 1 Grating diffraction diagrams for polarization (a) independent and (b) rotation Bragg gratings.
Several studies have reported about polarization rotation in the Si waveguides [17–23]. These devices require waveguide structure non-symmetric in the depth directions. The air upper clad, rib waveguide and non-vertical side wall structures have been investigated. When the fundamental TM mode is converted to 1st order TE mode, it can be converted to the fundamental TE mode by a mode selective directional coupler. These waveguide cross sections can also be used in a polarization rotation Bragg diffraction.
We reported an experimental polarization rotation Bragg grating device using a rib waveguide structure [15, 16]. We also suggested several other possible device structures [15]. In this paper we report designing procedure and experiment for the device using a waveguide with non-vertical side wall. The non-vertical side wall can be fabricated by one-step etching process but a rib waveguide requires a two-step etching process. In the simulation and experiment we found that nearly vertical side wall can generate distinct Bragg diffraction peak accompanying polarization rotation.
In this report, firstly we suggest a required device structure based on the calculation of waveguide mode and coupling coefficient. Next, the grating characteristics are examined using the 3D-FDTD (finite difference time domain) method. And finally the measured results obtained from the fabricated device are described.
2. Waveguide and grating structures
The grating structure using non-vertical sidewall waveguide is shown in Fig. 2. The side wall grating is placed on both sides of the waveguide. The side wall corrugation can be fabricated simultaneously with the waveguide structure.
Grating and waveguide structures required for conversion between two polarizations can be deduced from the symmetries of the electric components of TE and TM mode fields. As indicated in the following, to achieve conversion between TE and TM fundamental modes, the mode field should be non-symmetric in the thickness direction and the grating on both sides should be shifted half period against each other [15]. The fabricated Si wire waveguides tend to have non-vertical sidewall and this can be used.
Waveguide thickness of 300 nm is chosen so that polarization independent 3dB coupler and curved waveguide with polarization independent losses are easily obtained.
2.1 Waveguide mode analysis and coupling coefficient
To describe the basis for the structure shown in Fig. 2, we study the coupling coefficient of the polarization rotation Bragg grating and waveguide mode used in it. The coupling coefficient of the Bragg diffraction is given by Eq. (1) [24]. Where normalized fields Eqr are for q = x, y, z components of r = TM, TE polarization modes. The grating corrugation generates dielectric permittivity perturbation Δε. The vacuum dielectric permittivity is ε0 and ω is the light frequency. Equation (1) indicates that the coupling coefficient for TE-to-TM KTETM and TM-to-TE KTMTE are the same.
The Ex, Ey and Ez components for the TE and TM fundamental modes are shown in Fig. 3. The mode fields of the waveguide calculated by the finite element method (FEM) are shown in Fig. 3 for 70° side wall angle. This side wall angle is chosen in Fig. 3 to emphasize the field shape conspicuous to this type of waveguide cross section. A 300nm thick and 500 nm wide Si wire waveguide is embedded in SiO2 clad.
By examining Fig. 2 we notice that ExTE∙ExTM, EyTE∙EyTM and EzTE∙EzTM in Eq. (1) are all antisymmetric about y axis. The integral of Eq. (1) becomes non-zero when the grating corrugations on both sides are shifted half period against each other so that Δε are antisymmetric about y axis. In Fig. 2, the largest Ex component of the TE mode, Ey component of the TM mode, and the secondary large Ez component of the TM mode have mirror symmetry about y axis. The secondary large Ez component of TE mode, small Ey component of TE mode and small Ex component of TM mode are antisymmetric about y axis. Coupling coefficient was estimated to be around 0.01 μm−1 for sidewall angle of 85~87° and100 nm corrugation depth.
Since the non-vertical side wall waveguide lacks the symmetry about x axis, all the components lacks the symmetry about this axis so that Eq. (1) becomes non-zero for side wall grating. If the waveguide was symmetrical about the x-axis the integral of Eq. (1) became zero, because ΔεExTE∙ExTM, ΔεEyTE∙EyTM and ΔεEzTE∙EzTM became antisymmetric about x-axis in this case. These considerations lead to a structure shown in Fig. 2.
2.2 Grating characteristics obtained by FDTD
The grating characteristics were examined using the 3D-finite difference time domain (FDTD) method. Examples of calculated wavelength response of the polarization rotation Bragg diffraction are shown in Fig. 4 for 85° and 89° sidewall angles. In this simulation, 300 nm thick and 500 nm wide waveguide was used. The grating length was 100 μm and corrugation depth of 150 nm was used. The corrugation period was 292 nm. A sinusoidal grating was used. Distinct wavelength peaks were observed. The TE-to-TM and TM-to-TE rotation diffraction wavelength peaks have the same wavelength characteristics as expected. The differences of the peak heights and wavelengths between polarizations are below detectable amount (0.2 dB and 0.2 nm respectively). The peak heights in Fig. 4(a) and 4(b) are −0.8 dB and −16 dB respectively. These heights are due to the short grating length which was limited by reasonable calculation time. Near 100% diffraction is obtained by longer grating.
Fig. 4 Wavelength response obtained using 3D-FDTD simulation for (a) 85° and (b) 89° side wall. The grating length is 100 μm.
The full width peak width [24] is Δλ = 2λB[|K2-(π/L)2|]1/2/[π(ngTE + ngTM)], which is polarization independent, where λB is the Bragg wavelength, K is the coupling coefficient, L is the grating length, ngTE and ngTM are group indices for the TE and TM modes respectively.
The diffraction wavelengths of the higher order modes are shown in Fig. 5 for main polarization conversion peak designed at 1490 nm wavelength. The high order mode diffraction becomes closer to the main peak in wider waveguide. There was no additional diffraction peak in wavelength range longer than 1490 nm. We chose 500 nm waveguide width to attain sufficient interval between diffraction peaks and width error tolerance simultaneously. Width error tolerance is needed to suppress peak widening due to width fluctuation.
The coupling coefficients of the polarization rotation grating are shown in Fig. 6 for 300 nm thick and 500 nm wide waveguide. In Fig. 6(a), the coupling coefficients were calculated for 85, 87 and 89° side wall angles each as a function of grating corrugation depth. In Fig. 6(b), the dependence on the side wall angle is shown. Figures 6 show that larger coupling coefficient is obtained by deeper corrugation. The coupling coefficient increases when the deviation from the vertical side wall is larger. For a sidewall angle of 85°, 100-200 μm long grating is sufficient. The 89° side wall demands 1-2 mm long grating. In most waveguide fabrication processes the condition is tuned to obtain near vertical side wall angle. In this case the 89° side wall is practical choice.
Fig. 6 Grating coupling coefficient as function of (a) corrugation depth and (b) side wall angle for 500 nm wide waveguide.
3. Experiment
As shown in Fig. 7, a pair of Bragg gratings is connected to the two output of the 3dB coupler. The structure is a standard scheme to separate the input and the diffracted lights. The Si core thickness was 300 nm. A 500 nm wide and 1 mm long waveguide was used in the Bragg grating section. The grating period of 292 nm and corrugation depth of 150 nm were used.
A light is injected into one input of the 3 dB coupler and the same amounts of light are sent to two Bragg gratings. The diffracted lights from the gratings are combined in the 3 dB coupler and ejected from the opposite port. We used a MMI (multi-mode interference) type coupler [14, 25] which is fabrication tolerant compared to directional coupler. The MMI coupler has 1.61 μm width to attain polarization independence at 1490 nm wavelength. The length of the 3dB MMI coupler is 10.1 μm. The 3 dB coupler should be polarization independent because both polarizations are input before and after rotated by the Bragg gratings. The 3dB MMI coupler excess losses obtained by 3D-FDTD simulation for the 1490 nm wavelength TE and TM modes were 0.11 and 0.05 dB respectively.
The device was fabricated using SOI (Silicon on insulator) wafer and standard fabrication process used in the foundry to obtain near vertical waveguide side wall. The waveguide pattern was written in resist layer by photo lithography. The Si layer was etched by RIE (reactive ion etching) to obtain waveguides. Usually, an 89° side wall is obtained by the fabrication process. The waveguide cross section obtained by TEM (transmission electron microscopy) is shown in Fig. 8(a). The side wall angle was 88.7°. The side wall angle is determined by the balance between ion bombardment and radical reaction processes. The former process is enhanced by high microwave power and bias voltage. The latter is enhanced by higher pressure and temperature. The ion bombardment is preferable for obtaining vertical sidewall, so a low pressure is used. Chlorine and HBr gases can be used in the etching process, which exhibits small radical reaction with Si.
In the measurement, super luminescent diode (SLD) was used as a wide band light source. The input polarization was controlled and injected to the sample by polarization maintaining fiber (PMF). The output is introduced into an optical spectrum analyzer through PMF and the polarization was determined by using a polarizer. The lensed fibers are used. The inverse width taper is used as spot size converters (SSC) at the waveguide input facets. The propagation losses of 1.7 and 3.0 dB/cm obtained using 285 nm wide reference waveguides, the SSC coupling losses of 1.7 and 3.6 dB/facet for the TE and TM modes respectively were taken into account. The chip length is 3.5 mm. Widened waveguide output was used at the end facet which exhibited polarization dependent coupling loss difference of 0.4 dB. The measured wavelength response is shown in Fig. 8(b). The diffraction peak wavelengths of the TE and TM polarization were the same within 0.1 nm. The peak height difference between polarizations was 0.7 dB and −2 dB peak height was obtained for the TE mode. The peak full-width-at-half-maximum was 1.5 nm.
4. Conclusion
We have reported polarization independent Bragg grating wavelength filter using non-vertical side wall waveguide. The grating characteristics were examined using 3D-FDTD. Distinct diffraction peak was obtained even for nearly vertical side wall angle of 89°. The diffraction peaks are almost the same for the TE and TM modes. The coupling coefficient of the grating was larger for smaller side wall angle and larger corrugation depth. A device was fabricated and tested. A 300 nm thick waveguide was used to obtain polarization independent 3 dB coupler and low loss curved waveguide. A 500 nm wide waveguide is used to attain sufficient separation between main and high order mode diffraction peaks. Polarizations rotating Bragg diffraction and polarization independent MMI 3dB coupler are used to achieve polarization independent wavelength filtering. The diffraction peak wavelengths of the TE and TM polarization were the same within 0.1 nm. The polarization dependent peak height difference was 0.7 dB.
Acknowledgments
This research is partly supported by New Energy and Industrial Technology Development Organization (NEDO).
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