Abstract
In this paper an accurate analysis of two-dimensional (2D) Photonic Crystal (PhC) based multimode resonant cavities is carried out. The analysis is performed with a robust and accurate Finite Volume Time Domain (FVTD) technique. The analysis proves the ability of the FVTD method to extract different resonant modes from a multimode PhC resonant cavity with the use of appropriate source profiles. A detailed explanation on how the source is engineered and used to excite different modes is given. Furthermore, parameters such as resonant frequency and quality factor for each resonant mode are accurately calculated.
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References
Andreozzi A., Jaluria Y., Manca O.: Numerical investigation of transient natural convection in a horizontal channel heated from the upper wall. Numer. Heat Transf. Part A-Appl. 9, 815–842 (2007)
Berenger J.P.: A perfectly matched layer for the absorption of electromagnetic waves. J. Comput. Phys. 114, 185–200 (1994). doi:10.1006/jcph.1994.1159
Borel, P.I., Frandsen, L.H., Harpøth, A., Leon, J.B., Liu, H., Kristensen, M., Bogaerts, W., Dumon, P., Baets, R., Wiaux, V., Wouters, J., Beckx, S.: Bandwidth engineering of photonic crystal waveguide bends. Electron. Lett. 40 (2004)
Chaiko M.A.: A finite-volume approach for simulation of liquid-column separation in pipelines. J. Fluids Eng. Trans. Asme 128, 1324–1335 (2006). doi:10.1115/1.2353271
Costa R., Melloni A., Martinelli M.: Bandpass resonant filters in photonic-crystal waveguides. IEEE Photon. Technol. Lett. 15, 401–403 (2003). doi:10.1109/LPT.2002.807953
Faraon A., Englud D., Bulla D., Luther-Davies B., Eggleton B.J., Stoltz N., Petroff P., Vučković J.: Local tuning of photonic crystal cavities using chalcogenide glasses. Appl. Phys. Lett. 92, 043123-1–043123-3 (2008)
Joannopoulos J.D., Meade R.D., Winn J.N.: Photonic Crystals: Molding the Flow of Light. Princeton University Press, NJ (1995)
Lohrengel, S., Remaki, M.: A FV scheme for Maxwell’s equations—convergence analysis on unstructured meshes. In: Third Symposium of Finite Volumes for Complex Applications, Porquerolles, France, 24–28 June 2002.
Mekis A., Meier M., DodaBalapur A., Slusher R.E., Joannopulos J.D.: Lasing mechanism in two dimensional photonic crystal lasers. Appl. Phys., A Mater. Sci. Process. 69, 111–114 (1999). doi:10.1007/s003390050981
Obayya S.S.A.: Finite element time domain solution of resonant modes in photonic bandgap cavities. J. Opt. Quantum Electron. 37, 865–873 (2005). doi:10.1007/s11082-005-1120-9
Ohkubo H., Othera Y., Kawakami S., Chiba T.: Transmission wavelength shift of +36 nm observed with Ta2O5-SiO2 multichannel wavelength filters consisting of three-dimensional photonic crystals. IEEE Photon. Technol. Lett. 16, 1322–1324 (2004). doi:10.1109/LPT.2004.826232
Painter O., Vučković J., Scherer A.: Defect modes of a two-dimensional photonic crystal in an optically thin dielectric slab. J. Opt. Soc. Am. B 16, 275–285 (1999). doi:10.1364/JOSAB.16.000275
Pinto D., Obayya S.S.A.: Improved complex-envelope alternating-direction-implicit finite-difference-time-domain method for photonic-bandgap cavities. IEEE J. Lightwave Technol. 25, 440–447 (2007). doi:10.1109/JLT.2006.886712
Pinto D., Obayya S.S.A.: Accurate perfectly matched layer finite-volume time-domain method for photonic bandgap devices. IEEE Photon. Technol. Lett. 20, 339–341 (2008). doi:10.1109/LPT.2007.913334
Piperno S. et al.: A nondiffusive finite volume scheme for 3-D Maxwell equations on unstructured meshes. SIAM J. Numer. Anal. 39, 2089–2108 (2002). doi:10.1137/S0036142901387683
Povinelli M.L., Johnson S.G., Fan S., Joannopoulos J.D.: Emulation of two-dimensional photonic crystal defect modes in a photonic crystal with a three-dimensional photonic band gap. Phys. Rev. B 64, 075313 (2001). doi:10.1103/PhysRevB.64.075313
Rao S.M.: Time Domain Electromagnetics. Academic Press, New York (1999)
Remaki M.: A new finite volume scheme for solving Maxwell’s system. COMPEL 19, 913–931 (2000)
Rodriguez-Esquerre V.F., Koshiba M., Figueroa H.: Finite-element analysis of photonic crystal cavities: time and frequency domain. J. Lightwave Technol. 23, 1514–1521 (2005). doi:10.1109/JLT.2005.843441
Taflove, A., Hagness, S.C.: Computational Electrodynamics: The Finite-Difference Time-Domain Method. Artech House, Norwood, MA (2005).
Villeneuve P.R., Fan S., Joannopoulos J.D.: Microcavities in photonic crystals: mode symmetry, tunability, and coupling efficiency. Phys. Rev. B 54, 7837–7842 (1996). doi:10.1103/PhysRevB.54.7837
Yu H., Yu J., Yu Y., Fan Z., Chen S.: Design, fabrication, and characterization of an ultracompact low-loss photonic crystal corner mirror. IEEE J. Quantum Electron. 43, 876–882 (2007). doi:10.1109/JQE.2007.904307
Zhou W., Qiang Z., Chen L.: Photonic crystal defect mode cavity modelling: a phenomenological dimensional reduction approach. J. Phys. D Appl. Phys. 40, 2615–2623 (2007). doi:10.1088/0022-3727/40/9/S01
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Pinto, D., Obayya, S.S.A. 2D Analysis of multimode photonic crystal resonant cavities with the finite volume time domain method. Opt Quant Electron 40, 875–890 (2008). https://doi.org/10.1007/s11082-009-9286-1
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DOI: https://doi.org/10.1007/s11082-009-9286-1