Geodesic
Coupled dielectric waveguides with photonic crystal properties
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 11, pp. 1931-1937 
I. Yu. Popov; A. I. Trifanov; E. S. Trifanova. Coupled dielectric waveguides with photonic crystal properties. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 11, pp. 1931-1937. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_11_a6/
@article{ZVMMF_2010_50_11_a6,
     author = {I. Yu. Popov and A. I. Trifanov and E. S. Trifanova},
     title = {Coupled dielectric waveguides with photonic crystal properties},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1931--1937},
     year = {2010},
     volume = {50},
     number = {11},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_11_a6/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

A system of planar waveguides coupled through a periodic set of small windows is considered. It is shown that the weak periodic coupling of the waveguides leads to an additional eigenvalue band separated by a gap from the threshold of a continuous spectrum branch. Thus, the system has photonic crystal properties, which can be used to construct optical fiber devices. This system can also play the role of a SCISSOR device for reducing the group velocity of light, in optical delay lines, etc.

[1] Johnson S. G., Joannopoulos J. D., Photonic crystals, the road from theory to practice, Kluwer Acad. Publ., Boston, 2002

[2] Axmann W., Kuchment P., Kunyansky L., “Asymptotic methods for thin high-contrast two-dimensional PBG materials”, J. Light. Techn., 17:11 (1999), 1996–2007 | DOI

[3] Tip A., Moroz A., Combes J. M., “Band structure for absorptive photonic crystals”, J. Phys. A: Math. Gen., 33:35 (2000), 6223–6252 | DOI | MR

[4] Figotin A., Kuchment P., “Band-gap structure of the spectrum of periodic dielectric and acoustic media”, SIAM J. Appl. Math., 56:1 (1996), 68–88 | DOI | MR | Zbl

[5] Popov I. Yu., “Asymptotics of bound states and bands for laterally coupled waveguides and layers”, J. Math. Phys., 43:1 (2002), 215–234 | DOI | MR | Zbl

[6] Exner P., Vugalter S., “Asymptotic estimates for bound states in quantum waveguides coupled laterally through a narrow window”, Ann. Inst. Henri Poincare, 65:1 (1996), 109–123 | MR | Zbl

[7] Exner P., Vugalter S., “Bound-state asymptotic estimate for window-coupled Dirichlet strips and layers”, J. Phys. A: Math. Gen., 30 (1997), 7863–7878 | DOI | MR | Zbl

[8] Melnichuk O. P., Popov I. Yu., “Kvantovye volnovody, svyazannye cherez periodicheskuyu sistemu malykh otverstii: otsenka zapreschennoi zony”, Pisma v ZhTF, 28:8 (2002), 69–73

[9] Heebner J. E., Boyd R. W., Park Q.-H., “SCISSOR solitons and other novel propagation effects in microresonator-modified waveguides”, J. Opt. Soc. Amer., B19:4 (2002), 722–731

[10] Melnichuk O. P., Popov I. Yu., “Coupled dielectric waveguides: variational estimations”, J. Math. Phys., 46:7 (2005), 073501/1–073591/17 | DOI | MR | Zbl

[11] Lenz G., Eggleton B. J., Madsen C. K., Slusher L. E., “Optical delay lines based on optical filters”, IEEE J. Quant. Electron., 37 (2001), 525–532 | DOI

[12] Boyd R. W., Heebner J. E., “Sensitive disk-resonator photonic biosensor”, Appl. Optic., 40:31 (2001), 5742–5747 | DOI

[13] Mazurenko Yu. T., Merolla Zh.-M., Godzhebyur Zh.-P., “Kvantovaya peredacha informatsii s pomoschyu podnesuschei chastoty. Primenenie k kvantovoi kriptografii”, Optika i spektroskopiya, 86:2 (1999), 181–183

[14] Merolla J.-M., Mazurenko Y., Goedgebuer J.-P. et al., “Quantum cryptographic device using single photon phase modulation”, Phys. Rev. A, 60:3, 1899–1905 | DOI