**5. Characterization setup**

Series of devices in the frequency range of 0.2-1 THz are fabricated. The devices are being prepared to be characterized using Agilent Millimeter-wave PNA-X network analyzer (up to 500 GHz). The characterization setup is simulated using HFSS v.11 and SEMCAD (Bayat et al., 2010). In this section, full HFSS simulation results are presented that are considered strong validations of expected measurement outcomes. In the new setup, sub-mm metallic waveguides are employed as the interface between the PNA coaxial cables and input/output (I/O) tapers of the PC-slab waveguide devices. For example for central frequency of 200 GHz, WR-5 is utilized with size of 0.0510" × 0.0255" (1.295mm × 0.647mm). The total thickness of the polarization rotator assuming that 200 GHz corresponds to normalized frequency of a/λ=0.263 would be 0.0155" (0.395 mm); thus, there is a good match between WR-5 and input taper. A single-defect line PC slab waveguide is employed as the calibration reference. The waveguide is designed to guide both TE-like and TM-like wave (Bayat, et al., 2007).

Fig. 19(a) shows the sketch of the setup designed to couple electromagnetic wave in and out of the waveguide utilizing sub-mm metallic waveguides. To couple the electromagnetic wave to the defect line, a taper structure is utilized as shown in Fig. 19(a). The geometry of the I/O tapers must be designed properly to maximize the coupling efficiency to the defect line of PC slab waveguide.

In HFSS (v.11) simulations, the input wave is TE10 mode of the rectangular transition waveguide that has been polarized along y direction. The structural parameters of the PC slab waveguide are as follows: w=0.6a, t=0.8a, a=0.378 mm, nsi=3.48 and tanδ=1×10-4; where a, w, t, nsi, tanδ are the unit cell, width of square holes, thickness of the PC slab waveguide, refractive index and loss tangent of silicon, respectively. The central frequency is set to 200 GHz corresponding to the normalized frequency of a/λ=0.252. The power transmission takes place through the PC defect line. The frequency response of the setup is plotted in Fig.

Fig. 18. SEM picture of (a) square hole PC polarization converter (b) circular hole PC and

Series of devices in the frequency range of 0.2-1 THz are fabricated. The devices are being prepared to be characterized using Agilent Millimeter-wave PNA-X network analyzer (up to 500 GHz). The characterization setup is simulated using HFSS v.11 and SEMCAD (Bayat et al., 2010). In this section, full HFSS simulation results are presented that are considered strong validations of expected measurement outcomes. In the new setup, sub-mm metallic waveguides are employed as the interface between the PNA coaxial cables and input/output (I/O) tapers of the PC-slab waveguide devices. For example for central frequency of 200 GHz, WR-5 is utilized with size of 0.0510" × 0.0255" (1.295mm × 0.647mm). The total thickness of the polarization rotator assuming that 200 GHz corresponds to normalized frequency of a/λ=0.263 would be 0.0155" (0.395 mm); thus, there is a good match between WR-5 and input taper. A single-defect line PC slab waveguide is employed as the calibration reference. The waveguide is designed to guide both TE-like and TM-like

Fig. 19(a) shows the sketch of the setup designed to couple electromagnetic wave in and out of the waveguide utilizing sub-mm metallic waveguides. To couple the electromagnetic wave to the defect line, a taper structure is utilized as shown in Fig. 19(a). The geometry of the I/O tapers must be designed properly to maximize the coupling efficiency to the defect

In HFSS (v.11) simulations, the input wave is TE10 mode of the rectangular transition waveguide that has been polarized along y direction. The structural parameters of the PC slab waveguide are as follows: w=0.6a, t=0.8a, a=0.378 mm, nsi=3.48 and tanδ=1×10-4; where a, w, t, nsi, tanδ are the unit cell, width of square holes, thickness of the PC slab waveguide, refractive index and loss tangent of silicon, respectively. The central frequency is set to 200 GHz corresponding to the normalized frequency of a/λ=0.252. The power transmission takes place through the PC defect line. The frequency response of the setup is plotted in Fig.

(a) (b)

circular hole polarization converter.

**5. Characterization setup** 

wave (Bayat, et al., 2007).

line of PC slab waveguide.

19(b). S11 (reflection) and S21 (transmission) are depicted by dashed and solid lines, respectively. The graphs show that the insertion loss is less than 2 dB in the entire band from 190 to 210 GHz. The return loss is higher than 20 dB. Thus, the waveguide can be employed as a wide band low loss transmission line.

Fig. 19. (a) The schematic of the characterization setup consisting of PC slab waveguide, input/output tapers and rectangular waveguides (b) S11(blue line)-S21(red line) (return lossinsertion loss) plots of the PC slab waveguide

The same setup as in Fig. 19(a) has been used to characterize the polarization rotator. The input wave is TE10 mode with electric field pointing in y direction (Ey). For 90o polarization rotator, the input polarization rotates by 90o so that at the output plane the x-component of electric field is dominant. The output rectangular metallic waveguide is to be rotated by 90o to support Ex field. Fig. 20(a) shows the schematic of the polarization rotator with two alternating top loaded layers. Previously, it was shown that for this design the rotation angle for each top loaded layer is 6.5o; therefore, the polarization rotator with two top loaded layers rotates the input polarization by an angle of 22\*6.5o=26o. In this design, normalized frequency of a/λ=0.263 (where a and λ are the unit cell size and free space wavelength) is assigned to 200 GHz; thus, it is expected to see approximately 26o polarization rotation in the frequency band of 196-204 GHz corresponding to normalized frequency band of a/λ=0.258-0.267.

If the output taper shown in Fig. 19(a) was placed at the output, Ex component of the field would have been exposed to the geometry variation of the output taper imposing reversed rotation; the width of the taper in x-direction is decreasing along the propagation. To improve the polarization extinction ratio and enhance the coupling of Ex component to the rectangular metallic waveguide, the output taper was rotated by 90o, shown in Fig. 20 (a). Having rotated the output waveguide, it supports only Ex component and Ey component of the field reflects back. Thus, S21 and S11 parameters would provide a good measure of the polarization extinction ratio.

Photonic Crystal for Polarization Rotation 323

Fig. 20(b) shows S11 and S21 plots from the HFSS simulations. It shows that within the frequency band of 196-206 GHz, S21 is higher than -4 dB and S11 is less than -10 dB. The bandwidth is in a good agreement with the design results presented in Sec. 3. The electric field distribution at the input and output ports are shown in Fig. 21. The input and output electric fields are laid out in x and y-direction, respectively. The electric field distribution

The structure shown in Fig. 22(a) is designed to rotate the input polarization by 90o. The 4.5 top loaded layers provide 90o rotation. The output taper has not been rotated 90o because of the fabrication limits and feasibility issues of such taper. Thus, we would expect to observe lower coupling efficiency of Ex component to the output rectangular waveguide. Due to the computational limits of HFSS, SEMCAD was employed to simulate the structure using 3D-

y

(a)

(b)

Fig. 22. (a) Schematic of the polarization rotator with an angle of rotation of 90o (b) S11 (blue

clearly pictures the electric field rotation.

dashed line) and S21 (solid red line) plots.

FDTD method.

Fig. 20. (a) The schematic of the polarization rotator with the rotation angle of 26o with input/output tapers and waveguides (b) S11 (blue dashed line) and S21 (solid red line) plots of the structure.

Fig. 21. Field distribution at the (a) input, and (b) output ports of the polarization rotator at 200 GHz.

(a)

(b)

Fig. 21. Field distribution at the (a) input, and (b) output ports of the polarization rotator at

Fig. 20. (a) The schematic of the polarization rotator with the rotation angle of 26o with input/output tapers and waveguides (b) S11 (blue dashed line) and S21 (solid red line) plots

(a) (b)

of the structure.

200 GHz.

Fig. 20(b) shows S11 and S21 plots from the HFSS simulations. It shows that within the frequency band of 196-206 GHz, S21 is higher than -4 dB and S11 is less than -10 dB. The bandwidth is in a good agreement with the design results presented in Sec. 3. The electric field distribution at the input and output ports are shown in Fig. 21. The input and output electric fields are laid out in x and y-direction, respectively. The electric field distribution clearly pictures the electric field rotation.

The structure shown in Fig. 22(a) is designed to rotate the input polarization by 90o. The 4.5 top loaded layers provide 90o rotation. The output taper has not been rotated 90o because of the fabrication limits and feasibility issues of such taper. Thus, we would expect to observe lower coupling efficiency of Ex component to the output rectangular waveguide. Due to the computational limits of HFSS, SEMCAD was employed to simulate the structure using 3D-FDTD method.

Fig. 22. (a) Schematic of the polarization rotator with an angle of rotation of 90o (b) S11 (blue dashed line) and S21 (solid red line) plots.

Photonic Crystal for Polarization Rotation 325

The focus of this chapter was on design and fabrication of PC slab waveguide based polarization

 A novel compact PC slab waveguide based polarization rotator was introduced and designed. PC based coupled-mode theory was developed to design the structure. Coupled-mode theory provides with a simple yet closed form method for initial design. Square-hole PC was preferred in order for simplicity of the closed-form formulations. The design was refined using rigorous electromagnetic numerical method (3D-FDTD). 3D-FDTD simulation results verified the robustness of coupled-mode theory for design

 To extend the design to more general shape PC based polarization rotator, a design methodology based on vector-propagation characteristics of normal modes of asymmetric loaded PC slab waveguide was introduced. The vector-propagation characteristics of normal modes of the structure were calculated utilizing 3D-FDTD method combined with SFT. Profile and propagation constants of slow and fast modes of asymmetric loaded PC slab waveguide were extracted from 3D-FDTD simulation results. The half-beat length, which is the length of each loaded layer, and total number of the loaded layers are calculated using aforementioned data. This method provides

 SOI based PC membrane technology for THz application was developed. PC slab waveguide and polarization rotators were fabricated and characterized employing this

Barwicz, T. & Watts, M.R. & Popović, M.A. & Rakich, P.T. & Socci, L. & Kärtner, F.X. &

Bayat, K. & Safavi-Naeini, S. & Chaudhuri, S.K. (2007). *Polarization and thickness dependent guiding in the photonic crystal slab waveguide,* ,Optics Express, Vol. 15, Issue 13, pp. 8391-8400. Bayat, K. & Safavi-Naeini, S. & Chaudhuri, S.K. (2009). *Ultra-compact photonic crystal based* 

Bayat, K. & Safavi-Naeini, S. & Chaudhuri, S.K. & Barough, M.F. (2009). *Design and* 

Bayat, K. & Rafi, G.Z. & Shaker, G.S.A. & Ranjkesh, N. & Chaudhuri, S.K. & Safavi-Naeini,

Microwave Theory and Tech., IEEE Trans., Vol. 58, Issue 7, pp. 1976-1984. Bayat, K. & Safavi-Naeini, S. & Chaudhuri, S.K. (2007). *Polarization and thickness dependent guiding in the photonic crystal slab waveguide,* ,Optics Express, Vol. 15, Issue 13, pp. 8391-8400. Chan, P.S. & Tsang, H.K. & Shu, C. (2003). *Mode conversion and birefringence adjustment by focusedion-beam etching for slanted rib waveguide walls,* Opt. Lett., Vol. 28, No. 21, pp. 2109-2111. Deng, H. (2005). *Design and characterization of silicon-on-insulator passive polarization converter* 

El-Refaei, H & Yevick, D. (2003) *An optimized InGaAsP/InP polarization converter employing asymmetric rib waveguides*, J. Lightwave Tech., Vol. 21, No. 6, pp. 1544-1548.

Ippen, E.P. & Smith, H.I. (2007) *Polarization-transparent microphotonic devices in the* 

*simulation of photonic crystal based polarization converter* ,J. Lightwave Technol., Vol.

S. (2010). *Photonic-crsytal based polarization converter for terahertz integrated circuit*,

processor devices. A summary of the key achievements are highlighted as following:

with exact values of the parameters of the polarization rotator structure.

*strong confinement limit,* Nature Photonics, Vol. 1, pp. 57 - 60.

*polarization rotator* ,Optics Express, Vol. 17, Issue 9, pp. 7145-7158.

*with finite-element analysis,* Ph.D Thesis, University of Waterloo.

and analysis of PC based polarization rotator.

27, Issue 23, pp. 5483-5491.

**6. Conclusions** 

technology.

**7. References** 

Fig. 22(b) shows the spectrum of S-parameters. It is very similar to S-parameters graph presented in Fig. 20(b). In Fig. 22(b), within the frequency band of 199-208 GHz, S21 and S11 are higher and less than -5 dB and -15 dB, respectively. Since the structure was designed for 90o rotation, higher polarization extinction ratio was expected in comparison with the polarization rotator with 26o angle of rotation. The S-parameter plot in Fig. 22(b) has large fluctuation and it is not as smooth as the S-parameter shown in Fig. 20(b). These fluctuations are due to the numerical noise of 3D-FDTD analysis.

Snap shots of Ex and Ey components at f=205 GHz is presented in Fig. 23. Fig. 23(a) shows that the TE10 mode has launched Ey –fields in the left side and it is well-confined inside the input taper and then couples into the defect line of the PC slab waveguide. On the other hand, Ex–field component in Fig. 23(b) is weak at the left (input) side of the defect line; the color bar shows that it is one order of magnitude smaller than Ey component. As Ey –field mode propagates inside the defect line of PC slab waveguide based polarization rotator, it gradually rotates and converts to Ex component. At the other end of the PC slab waveguide, Ex component seems to be one order of magnitude larger than Ey. At the output taper, Ex will expose to the geometry variation of the taper resulting in reverse polarization conversion. Thus, the polarization conversion efficiency would decrease.

Fig. 23. Snap shots of (a) Ey and (b) Ex componnets obtained using 3D-FDTD analysis.
