Frustrated Spontaneous Emission near the Edge of a Photonic Band Gap

Mesfin Woldeyohannes^1,

¹Department of Chemistry & Physics, Western Carolina University, 112 Apodaca Science Building, Cullowhee, NC, USA, 28723

Cite this paper:
Mesfin Woldeyohannes. Frustrated Spontaneous Emission near the Edge of a Photonic Band Gap. International Journal of Physics. 2023; 11(1):40-55. doi: 10.12691/ijp-11-1-5

Abstract

The novel dynamical and spectral features of (single photon) spontaneous emission from an atomic transition near a photonic band edge are investigated by frustrating these features by spontaneous emission through another atomic transition far from the photonic band edge and deep in the photon continuum, the two atomic transitions forming the two dipole-allowed transitions of a three-level atom in a Λ configuration. Though spontaneous emission through the atomic transition far from the photonic band edge (the “far” transition) is not directly affected by the photonic band gap (PBG), it is indirectly affected by the PBG through its coupling to the atomic transition near the photonic band edge (the “near” transition) via the Λ configuration. As a result of this coupling, spontaneous emission through the “far” transition can be used as a probe to measure the strength of the effects of the PBG on spontaneous emission through the “near” transition. We have shown that the effects of the PBG on spontaneous emission via the “near” transition are strongly affected (and, therefore, can be controlled by) not only by the detuning of the “near” transition from photonic band edge but also by the vacuum decay rate of spontaneous emission through the “far” transition which is coupled to the “near” transition through the Λ configuration. In particular, we have shown that the oscillatory behavior of spontaneous emission near a photonic band edge as well as the Autler-Townes doublet of the spontaneous emission spectrum (due to the splitting of the atomic level near the photonic band edge) are strongly dependent on the decay rate of spontaneous emission through the probe transition which is far from the band edge.

Keywords:
photonic band gap materials spontanoeous emission three-level atom

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References:

[1]	S. John, “Electromagnetic absorption in a disordered medium near a photon mobility edge,” Phys. Rev. Lett., 53, 2169 (1984).
[2]	S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett., 58, 2486 (1987).
[3]	E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett., 58, 2059 (1987).
[4]	S. John and J. Wang, “Quantum electrodynamics near a photonic band gap: photon bound states and dressed atoms,” Phys. Rev. Lett., 64, 2418 (1990).
[5]	S. John and J. Wang, “Quantum optics of localized light,” Phys. Rev. B, 43, 12772 (1991).
[6]	M. Woldeyohannes and S. John, “Coherent control of spontaneous emission near a photonic band edge: Ph.D Tutorial”, J. Opt. B, 5, R43-R82 (2003)
[7]	S. John and T. Quang, “Spontaneous emission near the edge of a photonic band gap,” Phys. Rev. A, 50, 1764 (1994).
[8]	T. Quang, M. Woldeyohannes, S. John, and G. S. Agarwal, “Coherent control of spontaneous emission near a photonic band edge: a single-atom optical memory device,” Phys. Rev. Lett., 79, 5238 (1997).
[9]	M. Woldeyohannes and S. John, “Coherent control of spontaneous emission near a photonic band edge: a qubit for quantum computation,” Phys. Rev. A, 60, 5046 (1999).
[10]	M. Boroditsky, R. Vrijen, T. F. Krauss, R. Coccioli, R. Bhat, and E. Yablonovitch, “Spontaneous emission extraction and Purcell enhancement from thin-film 2-D photonic crystals,” J. Lightwave Technol., 17, 2096 (1999).
[11]	T. Baba, K. Inoshita, H. Tanaka, J. Yoenkura, M. Ariga, A. Matsutani, T. Miyamoto, F. Koyama, and K. Iga, “Strong enhancement of light extraction efficiency in GaInAsP 2-D-arranged micro-columns,” J. Lightwave Technol., 17, 2113 (1999).
[12]	W. L. Barnes, “Electromagnetic crystals for surface plasmon polaritons and the extraction of light from emissive devices,” J. Lightwave Technol., 17, 2170 (1999).
[13]	S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High extraction efficiency of spontaneous emission from slabs of photonic crystals,” Phys. Ref. Lett., 78, 3294 (1997).
[14]	C. M. Soukoulis, Ed., “Photonic band gaps and localization,” in Proc. NATO Advanced Research Workshop on Localization and Propagation of Classical Waves in Random and Periodic Media, Heraklion, Crete, Greece, May 26-30, 1992; see also, Nato Advanced Studies Institute Series B: Physics. New York: Plenum, 1993, Vol. 308.
[15]	N. M. Lawandy and G. Kweon, “Molecular and free electron spontaneous emission in periodic three- dimensional dielectric structures,” in Ref [14].
[16]	N. Vats and S. John, “Non-Markovian quantum fluctuations and superradiance near a photonic band edge”, Phys. Rev. A, 58, 4168 (1998).
[17]	S. John and T. Quang, “Photon-hopping conduction and collectively induced transparency in a photonic band gap”, Phys. Rev. A, 55, 4083 (1995).
[18]	M. Woldeyohannes, I. Idehenre, and T. Hardin, “Coherent control of cooperative spontaneous emission from two identical three-level atoms in a photonic crystal”, J. Opt,, 17, 085105 (2015).
[19]	H. Autler and C. H. Townes, “Stark effect in rapidly varying fields,” Phys. Rev., 100, 703 (1955).
[20]	M. Woldeyohannes, S. John, and V. I. Rupasov, “Resonance Raman scattering in photonic band gap mate- rials,” Phys. Rev. A, 63, 013814 (2001).
[21]	L. Allen and J. H. Eberly, Optical Resonance and Two-level atoms. New York: Wiley, 1975.
[22]	P. Meystre and M. Sargent, Elements of Quantum Optics. New York: Springer-Verlag, 1991.
[23]	M.O Scully and S. Zubairy, Quantum Optics. London: Cambridge University Press, 1997.
[24]	D. F. Walls and G. J. Milburn, Quantum Optics. New York: Springer-Verlag, 1995.
[25]	W. H. Louisell, Quantum Statistical Properties of Radiation. New York: Wiley, 1973.
[26]	C. Cohen-Tannoudji, B. Diu and F. Lalo¨e, Quantum Mechanics, Vol.1. Toronto: Wiley, 1977.
[27]	M. R. Spiegel, Schaum’s Outline of Theory and Problems of Laplace Transforms. New York: McGraw-Hill, 1965.
[28]	J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals. Molding the Flow of Light. Princeton NJ: Princeton University Press, 1995.