We review basic quantum electrodynamics and quantum optics aspects in microstructures that exhibit a gap in the spectrum of the electromagnetic radiation they support, known as photonic crystals. After a brief sketch of the properties of such materials we discuss the behaviour of few-level atoms or collections thereof with transition frequencies inside and in the vicinity of the gap. The discussion is cast in terms of a unified formalism which facilitates the comparison with standard cavity-atom physics.

https://iopscience.iop.org/article/10.1088/0034-4885/63/4/201/pdf

Fundamental quantum optics in structured reservoirs

Photonic crystals are promising systems for application in the fields of optoelectronics and optical communications. Understanding of their underlying physical principles and techniques for fabrication and characterization has progressed significantly during the last decade. This paper outlines the main achievements in these areas, and gives an overview of various photonic crystal systems, including those fabricated in semiconductors by traditional tools of microelectronics, and those fabricated from glasses, resins and other materials using novel non-traditional techniques.

Tailoring and characterization of photonic crystals

An overview of the most relevant properties of photonic crystals is presented considering 1D, 2D and 3D structures. The emphasis is on nonlinear properties both of the second and third order. Different processes like second harmonic generation and parametric processes are considered. Nonlinearities of composite materials are also presented. Finally quantum effects and the control of spontaneous emission in PBG (photonic band gap) are discussed.

Wave interactions in photonic band structures: an overview*

An extension of the second quantization scheme based on the quasinormal-modes theory to one-dimensional photonic band gap (PBG) structures is discussed. Such structures, treated as double open optical cavities, are studied as part of a compound closed system including the electromagnetic radiative external bath. The electromagnetic field inside the photonic crystal is successfully represented by a new class of modes called quasinormal modes. Starting from this representation we introduce the Feynman's propagator to calculate the decay rate of a dipole inside a PBG structure, related to the density of modes, in the presence of the vacuum fluctuations outside the one-dimensional cavity.

Second quantization and atomic spontaneous emission inside one-dimensional photonic crystals via a quasinormal-modes approach.

We develop a consistent mathematical theory of weakly nonlinear periodic dielectric media for the dimensions one, two and three. The theory is based on the Maxwell equations with classical quadratic and cubic constitutive relations. In particular, we give a complete classification of different nonlinear interactions between Floquet–Bloch modes based on indices which measure the strength of the interactions. The indices take on a small number of prescribed values which are collected in a table. The theory rests on the asymptotic analysis of oscillatory integrals describing the nonlinear interactions. (Some figures in this article are in colour only in the electronic version; see www.iop.org)

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Nonlinear photonic crystals: I. Quadratic nonlinearity

We present results of theoretical and experimental investigations into spontaneous emission alteration and nonlinear optical effects in thin-film multilayer devices. We begin with a brief section on one-dimensional photonic band gaps (PBGs) and photonic band edges. We then introduce the concept of nonlinear optical effects in PBG structures with the outline of the method of operation of an all-optical PBG switch. Next, we model a device that exhibits passive anisotropic optical transmission—the analogue of the electronic diode. This structure is designed to exhibit a greater shift in the location of the photonic band edge for light incident from one direction than from the opposite direction. Finally, we show enhancement of the spontaneous emission power spectrum of an emitter that is localized within a PBG structure—without the use of a typical microcavity—for frequencies near the photonic band edge. Two slightly different AlAs/AlGaAs/GaAs semiconductor PBG light emitting diodes (LEDs) were designed and fabricated. The emission spectra of these structures were measured and compared with that of a reference GaAs LED. We use a novel method for modeling the emission rate from within the structures.

/pdf/spontaneous-emission-and-nonlinear-effects-in-photonic-2jexvlig5j.pdf

Ishella S Fogel

Papers

Spontaneous emission and nonlinear effects in photonic bandgap materials