volume | PIER Journals

Abstract

We present a tool to aid the design of periodical structures, such as subwavelength grating (SWG) structures. It is based on the Fourier Eigenmode Expansion Method and includes the Floquet modes theory. Besides, the most interesting implemented functionalities to ease the design of photonic devices are detailed. The tool capabilities are shown using it to analyse and design {three} different SWG devices.

1. Rytov, S. M., "Electromagnetic properties of a finely stratified medium," Sov. Phys. JETP, Vol. 2, No. 3, 466-475, 1956.

2. Lalanne, P. and J.-P. Hugonin, "High-order effective-medium theory of subwavelength gratings in classical mounting: Application to volume holograms," J. Opt. Soc. Am. A, Vol. 15, No. 7, 1843-1851, Jul. 1998.
doi:10.1364/JOSAA.15.001843

3. Mateus, C., M. Huang, L. Chen, C. Chang-Hasnain, and Y. Suzuki, "Broad-band mirror (1.12--1.62 μm) using a subwavelength grating," IEEE Photonics Technology Letters, Vol. 16, No. 7, 1676-1678, Jul. 2004.
doi:10.1109/LPT.2004.828514

4. Halir, R., P. Cheben, S. Janz, D.-X. Xu, I. Molina-Fernández, and J. G. WangÄuemert-Pérez, "Waveguide grating coupler with subwavelength microstructures," Opt. Lett., Vol. 34, No. 9, 1408-1410, 2009.
doi:10.1364/OL.34.001408

5. Bock, P. J., P. Cheben, J. H. Schmid, J. Lapointe, A. Delâge, D.-X. Xu, S. Janz, A. Densmore, and T. J. Hall, "Subwavelength grating crossings for silicon wire waveguides," Opt. Express, Vol. 18, No. 15, 16146-16155, 2010.
doi:10.1364/OE.18.016146

6. Butt, H., Q. Dai, T. D. Wilkinson, and G. A. J. Amaratunga, "Photonic crystals & metamaterial filters based on 2D arrays of silicon nanopillars," Progress In Electromagnetic Research, Vol. 113, 179-194, 2011.

7. Shi, Y., "A compact polarization beam splitter based on a multimode photonic crystal waveguide with an internal photonic crystal section," Progress In Electromagnetic Research, Vol. 103, 393-401, 2010.
doi:10.2528/PIER10040402

8. Helfert, S. F. and R. Pregla, "The method of lines: A versatile tool for the analysis of waveguide structures," Electromagnetics, Vol. 22, No. 8, 615-637, 2002.
doi:10.1080/02726340290084166

9. Čtyroký, J., S. Helfert, and R. Pregla, "Analysis of a deep waveguide Bragg grating," Optical and Quantum Electronics, Vol. 30, 343-358, 1998.

10. Ortega-Moñux, A., I. Molina-Fernández, and J. G. Wangüemert-Pérez, "3D-scalar Fourier eigenvector expansion method (Fourier-EEM) for analyzing optical waveguide discontinuities," Optical and Quantum Electronics, Vol. 37, No. 1, 213-228, 2005.
doi:10.1007/s11082-005-1162-z

11. Hugonin, J. P., P. Lalanne, I. D. Villar, and I. R. Matias, "Fourier modal methods for modeling optical dielectric waveguides," Optical and Quantum Electronics, Vol. 37, 107-119, 2005.
doi:10.1007/s11082-005-1127-2

12. Alonso-Ramos, C., A. Ortega-Moñux, I. Molina-Fernández, P. Cheben, L. Zavargo-Peche, and R. Halir, "Efficient fiber-to-chip grating coupler for micrometric SOI rib waveguides," Opt. Express, Vol. 18, No. 14, 15189-15200, Jul. 2010.
doi:10.1364/OE.18.015189

13. Alonso-Ramos, C., A. Ortega-Moñux, L. Zavargo-Peche, R. Halir, J. de Oliva-Rubio, I. Molina-Fernãndez, P. Cheben, D.-X. Xu, S. Janz, N. Kim, and B. Lamontagne, "Single-etch grating coupler for micrometric silicon rib waveguides," Opt. Lett., Vol. 36, No. 14, 2647-2649, 2011.
doi:10.1364/OL.36.002647

14. Ortega-Moñux, A., L. Zavargo-Peche, A. Maese-Novo, I. Molina-Fernández, R. Halir, J. G. Wangüemert-Pérez, P. Cheben, and J. H. Schmid, "High performance multimode interference coupler in silicon waveguides with subwavelength structures," IEEE Photonics Technology Letters, Vol. 23, No. 19, 1406-1135, 2011.
doi:10.1109/LPT.2011.2161866

15. Cheben, P., P. J. Bock, J. H. Schmid, J. Lapointe, S. Janz, D.-X. Xu, A. Densmore, A. Delâge, B. Lamontagne, and T. J. Hall, "Refractive index engineering with subwavelength gratings for efficient microphotonic couplers and planar waveguide multiplexers," Opt. Lett., Vol. 35, No. 15, 2526-2528, 2010.
doi:10.1364/OL.35.002526

16. Chen, D., M.-L. Vincent Tse, and H.-Y. Tam, "Optical properties of photonic crystal fibers with a fiber core of arrays of subwavelength circular air holes: Birefringence and dispersion," Progress In Electromagnetic Research, Vol. 105, 193-212, 2010.
doi:10.2528/PIER10042706

17. Yariv, A. and P. Yeh, "Electromagnetic propagation in periodic stratified media. ii. Birefringence, phase matching, and x-ray lasers," J. Opt. Soc. Am., Vol. 67, No. 4, 438-448, 1977.
doi:10.1364/JOSA.67.000438

18. Scarmozzino, R., A. Gopinath, R. Pregla, and S. Helfert, "Numerical techniques for modeling guided-wave photonic devices," IEEE Journal of Selected Topics in Quantum Electronics, Vol. 6, No. 1, 150-162, 2000.
doi:10.1109/2944.826883

19. Besbes, M., J. Hugonin, P. Lalanne, S. van Haver, O. Janssen, A. Nugrowati, M. Xu, S. Pereira, H. Urbach, A. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. Baida, B. Guizal, and D. van Labeke, "Numerical analysis of a slit-groove diffraction problem," J. Europ. Opt. Soc. Rap. Public., Vol. 2, No. 07022, 1-17, 2007.

20. Collin, R. E., Field Theory of Guided Waves, 2nd Ed., IEEE Press, New York, 1991.

21. Watanabe, K. and K. Yasumoto, "Accuracy improvement of the Fourier series expansion method for Floquet-mode analysis of photonic crystal waveguides," Progress In Electromagnetics Research, Vol. 92, 209-222, 2009.
doi:10.2528/PIER09032704

22. Wangümert-Pérez, J., I. Molina-Fernández, and M. Luque-Nieto, "A novel Fourier based 3D full-vectorial beam propagation method," Optical and Quantum Electronics, Vol. 36, 285-301, 2004.
doi:10.1023/B:OQEL.0000015646.76059.58

23. Molina-Fernández, I. and J. Wangüemert-Pérez, "Variable transformed series expansion approach for the analysis of nonlinear guided waves in planar dielectric waveguides," Journal of Lightwave Technology, Vol. 16, No. 7, 1354-1363, Jul. 1998.
doi:10.1109/50.701417

24. Itoh, T., Numerical Techniques for Microwave and Millimeter-Wave Passive Structures, Wiley, 1989.

25. Cao, Q., P. Lalanne, and J.-P. Hugonin, "Stable and efficient Bloch-mode computational method for one-dimensional grating waveguides," J. Opt. Soc. Am. A, Vol. 19, No. 2, 335-338, 2002.
doi:10.1364/JOSAA.19.000335

26. Scott, A., P. Bock, C. A. Alonso-Ramos, B. Lamontagne, P. Cheben, M. Florjanczyk, I. Molina-Fernández, S. Janz, A. Ortega-Monux, B. Solheim, and D.-X. Xu, "Improved coupling to integrated spatial heterodyne spectrometers with applications to space," SPIE, Vol. 7928, No. 1, 79280K S. Garcia-Blanco and R. Ramesham (eds.), 2011.

27. Tamir, T., Guided-wave Optoelectronics, ser. Springer Series in Electronics and Photonics, Springer-Verlag, 1988.

28. Kim, D. W., A. Barkai, R. Jones, N. Elek, H. Nguyen, and A. Liu, "Silicon-on-insulator eight-channel optical multiplexer based on a cascade of asymmetric Mach-Zehnder interferometers," Opt. Lett., Vol. 33, No. 5, 530-532, Mar. 2008.
doi:10.1364/OL.33.000530

29. Halir, R., G. Roelkens, A. Ortega-Moñux, and J. G. Wangüemert-Pérez, "High-performance 90˚ hybrid based on a silicon-on-insulator multimode interference coupler," Opt. Lett., Vol. 36, No. 2, 178-180, 2011.
doi:10.1364/OL.36.000178

30. Implementation agreement for integrated dual polarization intradyne coherent receivers, Optical Internetworking Forum, 2010., Available: http://www.oiforum.com/public/documents/OIF_DP-C_RX-01.0.pdf.

Mr. Luis Zavargo-Peche

Dr. Alejandro Ortega-Monux

Dr. Juan Gonzalo Wanguemert-Perez

Dr. Inigo Molina-Fernandez