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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 1 — Jan. 13, 2014
  • pp: 987–994

Jacobi photonic lattices and their SUSY partners

A. Zúñiga-Segundo, B. M. Rodríguez-Lara, David J. Fernández C., and H. M. Moya-Cessa  »View Author Affiliations

Optics Express, Vol. 22, Issue 1, pp. 987-994 (2014)

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We present a classical analog of quantum optical deformed oscillators in arrays of waveguides. The normal modes of these one-dimensional photonic crystals are given in terms of Jacobi polynomials. We show that it is possible to attack the problem via factorization by exploiting the corresponding quantum optical model. This allows us to provide an unbroken supersymmetric partner of the proposed Jacobi lattices. Thanks to the underlying SU(1, 1) group symmetry of the lattices, we present the analytic propagators and impulse functions for these one-dimensional photonic crystals.

© 2014 Optical Society of America

OCIS Codes
(230.7370) Optical devices : Waveguides
(350.5500) Other areas of optics : Propagation
(230.4555) Optical devices : Coupled resonators
(230.5298) Optical devices : Photonic crystals

ToC Category:
Photonic Crystals

Original Manuscript: October 21, 2013
Revised Manuscript: November 13, 2013
Manuscript Accepted: November 14, 2013
Published: January 9, 2014

A. Zúñiga-Segundo, B. M. Rodríguez-Lara, David J. Fernández C., and H. M. Moya-Cessa, "Jacobi photonic lattices and their SUSY partners," Opt. Express 22, 987-994 (2014)

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  1. F. Cooper, A. Khare, U. Sukhatme, “Supersymmetry and quantum mechanics,” Phys. Rep. 251, 267–385 (1995). [CrossRef]
  2. D. J. Fernández C., N. Fernández-García, “Higher-order supersymmetric quantum mechanics,” AIP Conf. Proc. 744, 236–273 (2005). [CrossRef]
  3. D. J. Fernández C., “Supersymmetric quantum mechanics,” AIP Conf. Proc. 1287, 3–36 (2010).
  4. S. M. Chumakov, K. B. Wolf, “Supersymmetry in Helmholtz optics,” Phys. Lett. A 193, 51–53 (1994). [CrossRef]
  5. S. Tomić, V. Milanović, Z. Ikonić, “Optimization of intersubband resonant second-order susceptibility in assymetric graded AlxGa1−xAs quantum wells using supersymmetric quantum mechanics,” Phys. Rev. B 56, 1033–1036 (1997). [CrossRef]
  6. J. Bai, D. S. Citrin, “Supersymmetric optimization of second-harmonic generation in mid-infrared quantum cascade lasers,” Opt. Express 14, 4043–4048 (2006). [CrossRef] [PubMed]
  7. R. G. Unanyan, M. Fleischhauer, “Decoherence-free generation of many-particle entanglement by adiabatic ground-state transitions,” Phys. Rev. Lett. 90, 133601 (2003). [CrossRef] [PubMed]
  8. Y. Yu, K. Yang, “Simulating the Wess-Zumino supersymmetry model in optical lattices,” Phys. Rev. Lett. 105, 150605 (2010). [CrossRef]
  9. T. G. Tenev, P. A. Ivanov, N. V. Vitanov, “Proposal for trapped-ion emulation of the electric dipole moment of neutral relativistic particles,” Phys. Rev. A 87, 022103 (2013). [CrossRef]
  10. R. El-Ganainy, A. Eisfeld, M. Levy, D. N. Christodoulides, “On-chip non-reciprocal optical devices based on quantum inspired photonic lattices,” Appl. Phys. Lett. 103, 161105 (2013). [CrossRef]
  11. M.-A. Miri, M. Heinrich, R. El-Ganainy, D. N. Christodoulides, “Supersymmetric optical structures,” Phys. Rev. Lett. 110, 233902 (2013). [CrossRef]
  12. S. Longhi, G. Della Valle, “Transparency at the interface between two isospectral crystals,” Europhys. Lett. 102, 40008 (2013). [CrossRef]
  13. C. Daskaloyannis, “Generalized deformed oscillator and nonlinear algebras,” J. Phys. A: Math. Gen. 24, 789–794 (1991). [CrossRef]
  14. V. V. Dodonov, M. A. Marchiollo, Y. A. Korennoy, V. I. Man’ko, Y. A. Moukhin, “Parametric excitation of photon-added coherent states,” Phys. Scr. 58, 469–480 (1998). [CrossRef]
  15. A. A. Sukhorukov, A. S. Solntsev, J. E. Sipe, “Classical simulation of squeezed light in optical waveguide arrays,” Phys. Rev. A 87, 053823 (2013). [CrossRef]
  16. L. Infeld, T. E. Hull, “The factorization method,” Rev. Mod. Phys. 23, 21–68 (1951). [CrossRef]
  17. A. L. Jones, “Coupling of optical fibers and scattering in fibers,” J. Opt. Soc. Am. 55, 261–271 (1965). [CrossRef]
  18. D. N. Christodoulides, F. Lederer, Y. Silberberg, “Discretizing light behavior in linear and nonlinear waveguide lattices,” Nature 424, 817–823 (2003). [CrossRef] [PubMed]
  19. B. M. Rodríguez-Lara, “Exact dynamics of finite Glauber-Fock photonic lattices,” Phys. Rev. A 84, 053845 (2011). [CrossRef]
  20. A. Perez-Leija, R. Keil, A. Szameit, A. F. Abouraddy, H. Moya-Cessa, D. N. Christodoulides, “Tailoring the correlation and anticorrelation behavior of path-entangled photons in Glauber-Fock lattices,” Phys. Rev. A 85, 013848 (2012). [CrossRef]
  21. B. M. Rodríguez-Lara, F. Soto-Eguibar, A. Z. Cárdenas, H. M. Moya-Cessa, “A classical simulation of nonlinear Jaynes-Cummings and Rabi models in photonic lattices,” Opt. Express 21, 12888–128981 (2013). [CrossRef] [PubMed]
  22. M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions(Dover1970).
  23. B. M. Rodríguez-Lara, H. M. Moya-Cessa, D. N. Christodoulides, “Propagation, perfect transmission and trapping in three-waveguide axially varying couplers,” arXiv:1310.4754 [physics.optics] (2013).
  24. R. R. Puri, G. S. Agarwal, “Unitarily inequivalent classes of minimum uncertainty states of SU(1,1),” Int. J. Mod. Phys. B 10, 1563–1572 (1996). [CrossRef]
  25. I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series and Products (Academic, 2007).

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