## Efficient Computation of Longitudinal Lasing Modes in Arbitrary Active Cavities: The Bidirectional Time Evolution Method

Journal of Lightwave Technology, Vol. 27, Issue 15, pp. 3000-3009 (2009)

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### Abstract

In this paper, we develop the Bidirectional Time Evolution Method (BTEM) as an efficient technique to determine the frequencies of the longitudinal lasing modes in arbitrary 1-D active cavities. The BTEM is based on a mathematical property of linear Maxwell equations for active media at real frequencies: the backward Fourier transform of their frequency-domain solution provides nonphysical time-reversed fields when the threshold condition is fulfilled (i.e., the round-trip gains overcome the round-trip losses). Although such time-reversed fields are not physically feasible, they can be easily computed and their spectrum provides all the (real) frequencies at which the threshold condition is fulfilled. On the other hand, the phase condition is given by the peaks of the cavity transmittance modulus. Numerical examples of Fabry--Pérot, distributed Bragg reflector, DFB, random, and metamaterial active cavities illustrate the capabilities of our method.

© 2009 IEEE

**Citation**

Manuel Perez-Molina, Luis Carretero, and Salvador Blaya, "Efficient Computation of Longitudinal Lasing Modes in Arbitrary Active Cavities: The Bidirectional Time Evolution Method," J. Lightwave Technol. **27**, 3000-3009 (2009)

http://www.opticsinfobase.org/jlt/abstract.cfm?URI=jlt-27-15-3000

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### References

- D. Findlay, R. A. Clay, "The measurement of internal losses in 4-level lasers," Phys. Lett. 20, 277-278 (1966).
- J. H. Osmundsen, N. Gade, "Influence of optical feedback on laser frequency spectrum and threshold conditions," IEEE J. Quantum Electron. 19, 465-469 (1983).
- A. Olsson, C. L. Tang, "Coherent optical interference effects in external cavity semiconductor lasers," IEEE J. Quantum Electron. 17, 1320-1323 (1981).
- R. Lang, K. Kobayashi, "External optical feedback effects on semiconductor injection laser properties," IEEE J. Quantum Electron. 16, 347-355 (1980).
- H. Kogelnik, C. V. Shank, "Coupled-wave theory of distributed feedback lasers," J. Appl. Phys. 43, 2327-2335 (1972).
- T. Makino, "Threshold condition of DFB semiconductor lasers by the local-normal-mode transfer-matrix method: Correspondence to the coupled-wave method," J. Ligthw. Technol 12, 2092-2099 (1994).
- X. Wu, J. Andreasen, H. Cao, A. Yamilov, "Effect of local pumping on random laser modes in one dimension," J. Opt. Soc. Am 24, A26-A32 (2007).
- H. Cao, "Lasing in random media," Waves Random Media 13, R1-R39 (2003).
- R. J. Hawkins, J. S. Kallman, "Lasing in tilted-waveguide semiconductor amplifiers," Opt. Quantum Electron 26, 207-217 (1994).
- A. Taflove, Computational Electrodynamics: The Finite Difference Time Domain Method (Artech House, 1995).
- M. Kretschmann, A. A. Maradudin, "Lasing action in waveguide systems and the influence of rough walls," J. Opt. Soc. Am. B 21, 150-158 (2004).
- A. S. Nagra, R. A. York, "FDTD analysis of wave propagation in nonlinear absorbing and gain media," IEEE Trans. Antennas Propag. 46, 334-340 (1998).
- W. H. P. Pernice, F. P. Payne, D. F. G. Gallagher, "A finite-difference time-domain method for the simulation of gain materials with carrier diffusion in photonic crystals," J. Light. Tech 25, 2306-2314 (2007).
- S. C. Hagness, R. M. Joseph, A. Taflove, "Subpicosecond electrodynamics of distributed Bragg reflector microlasers," Radio Sci 31, 931-941 (1996).
- R. W. Ziolkowski, J. M. Arnold, D. M. Gogny, "Ultrafast pulse interactions with two level atoms," Phys. Rev. A 52, 3082-3094 (1995).
- M. Born, E. Wolf, Principles of Optics (Cambridge Univ. Press, 1999).
- J. Skaar, "Fresnel equations and the refractive index of active media," Phys. Rev. E 73, 026605 (2006).
- M. Perez-Molina, L. Carretero, "Comment on resolving the wave vector and the refractive index from the coefficient of reflectance," Opt. Lett. 33, 1828-1828 (2008).
- G. Guida, P. Stavrinou, G. Parry, J. Pendry, "Time-reversal symmetry, microcavities and photonic crystals," J. Modern Opt. 48, 581-595 (2001).
- A. D. Boardman, Y. G. Rapoport, N. King, V. N. Malnev, "Creating stable gain in active metamaterials," J. Opt. Soc. Am. B 24, A53-A61 (2007).
- L. Carretero, M. Perez-Molina, P. Acebal, S. Blaya, A. Fimia, "Matrix method for the study of wave propagation in one-dimensional media," Opt. Exp. 14, 11385-11391 (2006).
- M. Perez-Molina, L. C. Lopez, "Polynomial fixed-point algorithm applied to the electromagnetic analysis of one-dimensional continuous structures," J. Opt. Soc. Am. B 24, 1354-1364 (2007).
- B. Nistad, J. Skaar, "Simulations and realizations of active right-handed materials with negative refractive index," Opt. Exp. 15, 10935-10946 (2007).
- L. Brillouin, Wave Propagation and Group Velocity (Academic Press, 1960).

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