Abstract
Dispersion engineering of photonic crystal waveguides is attractive due to their potential applications in linear and nonlinear phenomena. Here, we present a comprehensive and systematic study to achieve the increased control over the dispersion curve of the waveguide, operating at telecom wavelengths. The effect of the radius of air cylinders, and their lattice position on the dispersion features is studied chiefly in a line-defect photonic crystal waveguide. For this purpose, perturbations were introduced in the radius and position of the air cylinders. With the help of MIT Photonic Bands software, group index and dispersion coefficients were calculated to characterize the features of the waveguide. Ring like structures were introduced in the innermost rows to increase the impact to further level. With this systematic study, one can tune the waveguide with desired range of group index and bandwidth with controlled dispersion properties. Present study resulted with a constant group index in the range of 31.42 to 7.64 over a bandwidth of 7.97 nm to 30.41 nm with very low dispersion. The developed structures may find applications in optical delays, optical buffers and nonlinear applications.
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References
Baba, T.: Slow light in photonic crystals. Nat. Photonics 2, 465-473 (2008). https://doi.org/10.1038/nphoton.2008.146
Bagci, F., Akaoglu, B.: Effects of innermost rows on slow light properties of photonic crystal waveguides. IEEE Xplore 1-3 (2013). https://ieeexplore.ieee.org/document/6608281
Casas-Bedoya, A., Husko, C., Monat, C., Grillet, C., Gutman, N., Domachuk, P., Eggleton, B.J.: Slow-light dispersion engineering of photonic crystal waveguides using selective microfluidic infiltration. Opt. Lett. 37, 4215-4217 (2012). https://doi.org/10.1364/OL.37.004215
Colman, P., Combrié, S., Lehoucq, G., De Rossi, A.: Control of dispersion in photonic crystal waveguides using group symmetry theory. Opt. Express 20, 13108-13114 (2012). https://doi.org/10.1364/oe.20.013108
Ebnali-Heidari, M., Grillet, C., Monat, C., Eggleton, B.J.: Dispersion engineering of slow light photonic crystal waveguides using microfluidic infiltration. Opt. Express 17, 1628-1635 (2009). https://doi.org/10.1364/OE.17.001628
Frandsen, L.H., Lavrinenko, A.V., Fage-Pedersen, J., Borel, P.I.: Photonic crystal waveguides with semi-slow light and tailored dispersion properties. Opt. Express 14, 9444-9450 (2006). https://doi.org/10.1364/OE.14.009444
Hamachi, Y., Kubo, S., Baba, T.: Slow light with low dispersion and nonlinear enhancement in a lattice-shifted photonic crystal waveguide. Opt. Lett. 34, 1072-1074 (2009). https://doi.org/10.1364/OL.34.001072
Hou, J., Gao, D., Wu, H., Hao, R., Zhou, Z.: Flat band slow light in symmetric line defect photonic crystal waveguides. IEEE Photon. Technol. Lett. 21, 1571-1573 (2009). https://doi.org/10.1109/LPT.2009.2030160
Johnson, S.G., Joannopoulos, J.D.: Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis. Opt. Express 8, 173-190 (2001). https://doi.org/10.1364/OE.8.000173
Krauss, T.F.: Slow light in photonic crystal waveguides. J. Phys. D. Appl. Phys. 40, 2666-2670 (2007). https://doi.org/10.1088/0022-3727/40/9/S07
Letartre, X., Seassal, C., Grillet, C., Rojo-Romeo, P., Viktorovitch, P., Le VassorD’Yerville, M., Cassagne, D., Jouanin, C.: Group velocity and propagation losses measurement in a single-line photonic-crystal waveguide on InP membranes. Appl. Phys. Lett. 79, 2312-2314 (2001). https://doi.org/10.1063/1.1405146
Li, J.T., Zhou, J.Y.: Nonlinear optical frequency conversion with stopped short light pulses. Opt. Express 14, 2811-2816 (2006). https://doi.org/10.1364/OE.14.002811
Li, J., White, T.P., O’Faolain, L., Gomez-Iglesias, A., Krauss, T.F.: Systematic design of flat band slow light in photonic crystal waveguides. Opt. Express 16, 6227-6232 (2008). https://doi.org/10.1364/OE.16.006227
Malik, J.V., Jindal, K.D., Kumar, V., Kumar, V., Kumar, A., Singh, K.S., Singh, T.P.: Effect of temperature on photonic band gaps in semiconductor-based one-dimensional photonic crystal. Adv. Opt. Technol. 2013, 798087 (2013). https://doi.org/10.1155/2013/798087
Notomi, M., Yamada, K., Shinya, A., Takahashi, J., Takahashi, C., Yokohama, I.: Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs. Phys. Rev. Lett. 87, 253902 (2001). https://doi.org/10.1103/PhysRevLett.87.253902
Pavan, V.D.R., Roy, S.: Temperature effects on dispersion tailoring of slow light engineered photonic crystal waveguide. IEEE Proceedings of 24th Microoptics Conference (MOC), pp. 268-269 (2019). https://ieeexplore.ieee.org/document/8982894
Petrov, A.Y., Eich, M.: Zero dispersion at small group velocities in photonic crystal waveguides. Appl. Phys. Lett. 85, 4866-4868 (2004). https://doi.org/10.1063/1.1815066
Roy, S., Chaudhuri, P.R.: Analysis of nonlinear multilayered waveguides and MQW structures: A field evolution approach using finite-difference formulation. IEEE J. Quantum Electron. 45, 345-350 (2009). https://doi.org/10.1109/JQE.2009.2013084
Roy, S., Willinger, A., Combrié, S., De Rossi, A., Eisenstein, G., Santagiustina, M.: Narrowband optical parametric gain in slow mode engineered GaInP photonic crystal waveguides. Opt. Lett. 37, 2919-2921 (2012a). https://doi.org/10.1364/OL.37.002919
Roy, S., Santagiustina, M., Colman, P., Combrié, S., De Rossi, A.: Modeling the dispersion of the nonlinearity in slow mode photonic crystal waveguides. IEEE Photonics J. 4, 224-233 (2012b). https://doi.org/10.1109/JPHOT.2011.2181942
Roy, S., Santagiustina, M., Willinger, A., Eisenstein, G., Combrié, S., De Rossi, A.: Parametric gain and conversion efficiency in nanophotonic waveguides with dispersive propagation coefficients and loss. J. Light. Technol. 32, 1177–1182 (2014)
Säynätjoki, A., Mulot, M., Ahopelto, J., Lipsanen, H.: Dispersion engineering of photonic crystal waveguides with ring-shaped holes. Opt. Express 15, 8323-8328 (2007). https://doi.org/10.1364/OE.15.008323
Schulz, S.A., O’Faolain, L., Beggs, D.M., White, T.P., Melloni, A., Krauss, T.F.: Dispersion engineered slow light in photonic crystals: a comparison. J. Opt. 12, 104004 (2010)
Soljacic, M., Joannopoulos, J.D.: Enhancement of nonlinear effects using photonic crystals. Nat. Mater. 3, 211-219 (2004). https://doi.org/10.1038/nmat1097
Tang, J., Wang, T., Li, X., Wang, B., Dong, C., Gao, L., Liu, B., He, Y., Yan, W.: Wideband and low dispersion slow light in lattice-shifted photonic crystal waveguides. J. Light. Technol. 31, 3188-3194 (2013). https://doi.org/10.1109/JLT.2013.2280716
Vlasov, Y.A., O’Boyle, M., Hamann, H.F., McNab, S.J.: Active control of slow light on a chip with photonic crystal waveguides. Nature 438, 65-69 (2005). https://doi.org/10.1038/nature04210
Willinger, A., Roy, S., Santagiustina, M., Combrié, S., De Rossi, A., Cestier, I., Eisenstein, G.: Parametric gain in dispersion engineered photonic crystal waveguides. Opt. Express 21, 4995–5004 (2013). https://doi.org/10.1364/OE.21.004995
Willinger, A., Roy, S., Santagiustina, M., Combrié, S., De Rossi, A., Eisenstein, G.: Narrowband optical parametric amplification measurements in Ga0.5In0.5P photonic crystal waveguides. Opt. Express 23, 17751-17757 (2015). https://doi.org/10.1364/OE.23.017751
Xuan, K.D., Van, L.C., Long, V.C., Dinh, Q.H., Mai, L.V., Trippenbach, M., Buczyński, R.: Influence of temperature on dispersion properties of photonic crystal fibers infiltrated with water. Opt. Quant. Electron. 49, 87 (2017). https://doi.org/10.1007/s11082-017-0929-3
Yang, D., Tian, H., Ji, Y.: The properties of lattice-shifted microcavity in photonic crystal slab and its applications for electro-optical sensor. Sens. Actuator A Phys. 171, 146-151 (2011). https://doi.org/10.1016/j.sna.2011.08.001
Acknowledgements
Authors sincerely thank Department of Science and Technology, Government of India for funding this work through INSPIRE fellowship program (IF160435).
Funding
This work is funded by Department of Science and Technology, Government of India (DST-GoI) under the INSPIRE fellowship with fellowship number IF160435. Authors sincerely thank DST-GoI for the same.
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VDRP has performed the simulations, collected the raw data, did the primary analysis and prepared the manuscript. SR has analyzed the results, drawn the conclusions and finalized the contents of the manuscript.
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Pavan, V.D.R., Roy, S. Analyzing dispersion properties of photonic crystal waveguides with hole and ring like lattice by introducing systematic shift and twist. Opt Quant Electron 53, 711 (2021). https://doi.org/10.1007/s11082-021-03333-9
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DOI: https://doi.org/10.1007/s11082-021-03333-9