Abstract
We demonstrate that the dispersion of guided propagating modes in certain Photonic Crystal Waveguides (PCWGs) can be kept constant when the waveguide’s structure changes along the propagation direction. This suggests that the principle of constant group velocity matching may be utilized to improve impedance matching between different types of PCWGs while at the same time providing significant design flexibility. We illustrate this principle through the design of several efficient coupling structures between two different PCWGs via a local density of states and Fourier transform analysis of the associate electromagnetic fields. The couplers consist of heterostructures whose individual sections exhibit rather distinct structural parameters. Furthermore, we compare these structures to an adiabatic coupler.
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References
Akahane Y., Asano T., Song B.S., Noda S. (2003) High-Q photonic nanocavity in a two-dimensional photonic crystal. Nature 425, 944–947
Asatryan A.A., Busch K., McPhedran R.C., Botten L.C., de Sterke C.M., Nicorovici N.A. (2003) Twodimensional green tensor and local density of states infinite-sized two-dimensional photonic crystals. Waves in Random Media 13, 9–25
Bache M., Nielsen H., Lægsgaard J., Bang O. (2006) Tuning quadratic nonlinear photonic crystal fibers for zero group-velocity mismatch. Opt. Lett. 31, 1612–1614
Biswas R., Li Z.Y., Ho K.M. (2004) Impedance of photonic crystals and photonic crystal waveguides. Appl. Phys. Lett. 84, 1254–1256
Boscolo S., Conti C., Midrio M., Someda C.G. (2002) Numerical analysis of propagation and impedancematching in 2-D photonic crystal waveguides with finite length. J. Lightwave Tech. 20, 304–310
Boscolo S., Midrio M., Krauss T.F. (2002) Y junctions in photonic crystal channel waveguides: high transmission and impedance matching. Opt. Lett. 27, 1001–1003
Chan Y.S., Chan C.T., Liu Z.Y. (1988) Photonic band gaps in two dimensional photonic quasicrystals. Phys. Rev. Lett. 80, 956–959
Chaloupka J., Zarbakhsh J., Hingerl K. (2005) Local density of states and modes of circular photonic crystal cavities. Phys. Rev. B 72, 085122
Horiuchi N., Segawa Y., Nozokido T., Mizuno K., Miyazaki H. (2004) Isotropic photonic gaps in a circular photonic crystal. Opt. Lett. 29, 1084–1086
Imeshev G., Arbore M.A., Fejer M.M., Galvanauskas A., Fermann M., Harter D. (2000) Ultrashort-pulse secondharmonic generation with longitudinally nonuniform quasi-phase-matching gratings: pulse compression and shaping. J. Opt. Soc. Am. B 17, 304–318
Jafarpour A., Reinke C.M., Adibi A.,Yong X., Lee R.K. (2004) Anewmethod for the calculation of the dispersion of nonperiodic photonic crystal waveguides. IEEE J. Quant. Electron. 40(8): 1060–1067
Janssen T. (1988) Aperiodic crystals: a contradictio in terminis?. Phys. Rep. 168, 55–113
Jin C., Cheng B., Man B., Li Z., Zhang D., Ban S., Sun B. (1999) Band gap and wave guiding effect in a quasiperiodic photonic crystal. Appl. Phys. Lett. 75, 1848–1850
Johnson S.G., Bienstman P., Skorobogatiy M.A., Ibanescu M., Lidorikis E., Joannopoulos J.D. (2002) Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic crystals. Phys. Rev. E 66, 066608
Kaliteevski M.A., Brand S., Abram R.A., Krauss T.F., Millar P., de La Rue R.M. (2001) Diffraction and transmission of light in low-refractive index penrose-tiled photonic quasicrystals. J. Phys. Condens. Matter 13, 10459–10470
McNab S.J., Moll N., Vlasov Y.A. (2003) Ultra-low loss photonic integrated circuit with membrane-type photonic crystal waveguides. Opt. Express 11, 2927–2939
Michaelis D., Wächter C., Burger S., Zschiedrich L., Bräuer A. (2006) Micro-optically assisted high-index waveguide coupling. App. Opt. 45, 1831–1838
Notomi M., Shinya A., Mitsugi S., Kuramochi E., Ryu H.-Y. (2004) Waveguides, resonators and their coupled elements in photonic crystal slabs. Opt. Express 12, 1551–1561
Olivier S., Weisbuch C., Benisty H. (2003) Compact and fault-tolerant photonic crystal add drop filter. Opt. Lett. 28(22): 2246–2248
Petrov A.Yu., Eich M. (2004) Zero dispersion at small group velocities in photonic crystal waveguides. Appl. Phys. Lett. 85(21): 4866–4868
Sanchis P., Bienstman P., Luyssaert B., Baets R., Marti J. (2004) Analysis of butt coupling in photonic Crystals. IEEE J. Quant. Electron. 40, 541–550
Skorobogatiy M., Jacobs S.A., Johnson S.G., Fink Y. (2002) Geometric variations in high index-contrast waveguides, coupled mode theory in curvilinear coordinates. Opt. Express 10(21): 1227–1243
Wang Y., Cheng B., Zhang D. (2003) The density of states in quasiperiodic photonic crystals. J. Phys. Condens. Matter 15, 7675–7680
Zarbakhsh J., Hagmann F.,Mingaleev S.F., Busch K., Hingerl K. (2004) Arbitrary anglewaveguiding applications of two-dimensional curvilinear-lattice photonic crystals. Appl. Phys. Lett. 84, 4687–4689
Zarbakhsh J., Isfahani F.G., Chaloupka J., Rinnerbauer V., Hingerl K. (2005) Geometric freedom for constructing variable size photonic bandgap structures. Proceeding of 31st European Conference on Optical Communication (ECOC) 3: 509–510
Zarbakhsh, J., Mohtashami, A., Hingerl, K.: Geometrical freedom for constructing variable size photonic bandgap structures. Submitted to Opt. Quant. Electron. (2007) doi:10.1007/s11082-007-9081-9
Zoorob M.E., Charlton M.D.B., Parker G.J., Baumberg J.J., Netti M.C. (2000) Complete photonic bandgaps in 12-fold symmetric quasicrystals. Nature (London) 404, 740–743
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Mohtashami, A., Zarbakhsh, J. & Hingerl, K. Advanced impedance matching in photonic crystal waveguides. Opt Quant Electron 39, 387–394 (2007). https://doi.org/10.1007/s11082-007-9080-x
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DOI: https://doi.org/10.1007/s11082-007-9080-x