The term photonic crystals appears because of the analogy between electron waves in crystals and the light waves in artificial periodic dielectric structures. During the recent years the investigation of one-, two-and three-dimensional periodic structures has attracted a widespread attention of the world optics community because of great potentiality of such structures in advanced applied optical fields. The interest in periodic structures has been stimulated by the fast development of semiconductor technology that now allows the fabrication of artificial structures, whose period is comparable with the wavelength of light in the visible and infrared ranges.

http://ieeexplore.ieee.org/iel5/6354/16969/00781867.pdf

Photonic crystals

Preface 1. Planck's radiation law and the Einstein coefficients 2. Quantum mechanics of the atom-radiation interaction 3. Classical theory of optical fluctuations and coherence 4. Quantization of the radiation field 5. Single-mode quantum optics 6. Multimode and continuous-mode quantum optics 7. Optical generation, attenuation and amplification 8. Resonance fluorescence and light scattering 9. Nonlinear quantum optics Index

The quantum theory of light.

Resonantly absorbing media supporting electromagnetically induced transparency may give rise to specific periodic patterns where a light probe is found to experience a fully developed photonic band gap yet with negligible absorption everywhere. In ultracold atomic samples the gap is found to arise from spatial regions where Autler-Townes splitting and electromagnetically induced transparency alternate with one another and detailed calculations show that accurate and efficient coherent optical control of the gap can be accomplished. The remarkable experimental simplicity of the control scheme would ease quantum nonlinear optics applications.

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Optically tunable photonic stop bands in homogeneous absorbing media.

We show that the photonic analogue of the Korringa-Kohn-Rostocker method is a viable alternative to the plane-wave method to analyze the spectrum of electromagnetic waves in a three-dimensional periodic dielectric lattice. Firstly, in the case of an fcc lattice of homogeneous dielectric spheres, we reproduce the main features of the spectrum obtained by the plane wave method, namely that for a sufficiently high dielectric contrast a full gap opens in the spectrum between the eights and ninth bands if the dielectric constant $\epsilon_s$ of spheres is lower than the dielectric constant $\epsilon_b$ of the background medium. If $\epsilon_s> \epsilon_b$, no gap is found in the spectrum. The maximal value of the relative band-gap width approaches 14% in the close-packed case and decreases monotonically as the filling fraction decreases. The lowest dielectric contrast $\epsilon_b/\epsilon_s$ for which a full gap opens in the spectrum is determined to be 8.13. Eventually, in the case of an fcc lattice of coated spheres, we demonstrate that a suitable coating can enhance gap widths by as much as 50%.

Photonic Band Gaps of Three-Dimensional Face-Centered Cubic Lattices

We show that the photonic analogue of the Korringa-Kohn-Rostoker method is a viable alternative to the plane-wave method for analysing the spectrum of electromagnetic waves in a three-dimensional periodic dielectric lattice. Firstly, in the case of a fcc lattice of homogeneous dielectric spheres, we reproduce the main feature of the spectrum obtained by the plane-wave method, namely that for a sufficiently high dielectric contrast a full gap opens in the spectrum between the eighth and ninth bands if the dielectric constant of the spheres is lower than the dielectric constant of the background medium. If , no gap is found in the spectrum. The maximal value of the relative band-gap width approaches 14% in the close-packed case and decreases monotonically as the filling fraction decreases. The lowest dielectric contrast for which a full gap opens in the spectrum is determined to be 8.13. Eventually, in the case of a fcc lattice of coated spheres, we demonstrate that a suitable coating can enhance gap widths by as much as 50%.

https://iopscience.iop.org/article/10.1088/0953-8984/11/4/007/pdf

Photonic band gaps of three-dimensional face-centred cubic lattices

The band structure of absorptive dielectric photonic crystals is investigated. Provided the frequency-dependent electric permeability e(x,ω) satisfies certain analyticity requirements as a function of frequency, we show that no bandgaps exist in frequency regions where absorption takes place, i.e. where e(x,ω) has a non-zero imaginary part. In this case real eigenvalues of the Helmholtz operator in the Bloch-decomposed formalism are absent. Using a suitable analytic continuation procedure, we find that the former change into resonances, i.e. complex numbers depending on k, the wavevector from the first Brillouin zone, thus leading to complex bands in the lower half plane. This is confirmed numerically for a simple, one-dimensional example.

Band structure of absorptive photonic crystals

The band structure for an absorptive two-dimensional photonic crystal made from cylinders consisting of a Drude material is calculated. Absorption causes the spectrum to become complex and form islands in the negative complex half-plane. The boundaries of these islands are not always formed by the eigenvalues calculated for Bloch vectors on the characteristic path, and we find a hole in the spectrum. For realistic parameter values, the real part of the spectrum is hardly influenced by absorption, typically less than 0.25%. The employed method uses a Korringa–Kohn–Rostoker procedure together with analytical continuation. This results in an efficient approach that allows these band-structure calculations to be done on a Pentium III personal computer.

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Band structure of absorptive two-dimensional photonic crystals

For the case of a simple face-centred-cubic photonic crystal of homogeneous dielectric spheres, we examine to what extent single-sphere Mie resonance frequencies are related to band gaps and whether the width of a gap can be enlarged due to nearby resonances. Contrary to some suggestions, no spectacular effects may be expected. When the dielectric constant of the spheres is greater than the dielectric constant of the background medium, then for any filling fraction f there exists a critical above which the lowest-lying Mie resonance frequency falls inside the lowest stop gap in the (111) crystal direction, close to its midgap frequency. If , the correspondence between Mie resonances and both the (111) stop gap and a full gap does not follow such a regular pattern. If the Mie resonance frequency is close to a gap edge, one can observe a resonance-induced widening of a relative gap width by .

Resonance-induced effects in photonic crystals

https://web.science.uu.nl/scm/Articles/2001/Moroz_SyntheticMetals_2001.pdf

Adriaan Tip

Papers

Band structure of absorptive photonic crystals

Band structure of absorptive two-dimensional photonic crystals

Resonance-induced effects in photonic crystals

Absorption in periodic layered structures

On-shell T-matrices in multiple scattering