Theory of photonic crystals and of radiation-matter interaction

Photonic crystals (PhCs), namely materials with a periodic dielectric function in one, two or three dimensions, are the optical analog of usual crystal lattices for electrons. The occurrence of allowed and forbidden frequency bands for electromagnetic waves, as well as the possibility to introduce line and point defects, allows to control the propagation of light and to tailor radiation-matter interaction properties like diffraction, spontaneous emission, nonlinear effects, etc. Although three-dimensional (3D) photonic crystals are most suited in principle in order to "mold the flow of light" in all directions, the difficulties in fabricating 3D structures at near-infrared and optical wavelengths are not easy to overcome. It is, however, possible to obtain nearly complete control of light propagation in 3D by employing waveguide-embedded photonic crystals, or PhC slabs, which consist of 2D (or 1D) lattices realized in planar (slab) waveguides. Photonic crystal slabs support truly guided Bloch modes, that lie below the light line(s) of the cladding material(s) in the k-w plane and are not subject to propagation losses in a perfect material, and quasi-guided Bloch modes, that lie above the light line and are subject to intrinsic propagation losses due to diffraction out of the slab plane. Truly guided modes are subject to propagation losses in a real material, due to the presence of extrinsic disorder effects. The issue of intrinsic versus extrinsic (disorder-related) losses is a crucial one in the context of PhC slabs. Line and point defects in PhC slabs give rise to linear waveguide modes and cavity modes, respectively, whose propagation losses and quality factors are also determined by intrinsic as well as disorder-related effects. The possibility to obtain cavity modes with large Q-factor and small mode volume is crucial in order to tailor radiation-matter interaction and to be able to observe quantum-electrodynamical phenomena like the reduction of spontaneous emission lifetime (or Purcell effect), the strong-coupling regime for a two-level system in a cavity, etc.

Theoretical research of the group over the years has dealt with a number of problems related to the calculation of photonic bands in PhCs of different dimensionalities, propagation losses, optical properties, and radiation-matter interaction effects. Special attention has been given to a theoretical treatment of PhC slabs, by developing a method - called Guided-Mode Expansion (GME) - that leads to a fast and accurate calculations of photonic band dispersion both below and above the light line. The GME code is freely available on this web site. Including coupling to radiative PhC slabs modes by perturbation theory leads to a determination of intrinsic diffraction losses for propagating modes above the light line, and of cavity Q-factors in the case of point defects. Disorder-induced losses can also be included in the case of periodic lattices, linear waveguides and nanocavities, in the framework of suitable modes for disorder (e.g., random variation of the holes' radii or micro-roughness of the vertical hole sidewalls). Thus, intrinsic as well as disorder-induced diffraction losses can be treated and have been quantified in a number of situations like 1D and 2D lattices, linear waveguides, and nano-cavities. Theoretical results are being used to interpret experimental data and to design suitable samples. The GME method is complementary to general-purpose numerical techniques like finite-difference time domain (FDTD) or beam-propagation method (BPM) and to Fourier-modal expansion that rely on scattering-matrix formulations. Quite often, a good design of the samples and understanding of the experiments requires methods at different levels of complexity.

Semiclassical and quantum descriptions of radiation-matter interaction are also a subject of considerable interest within the group. Here the concept of photon confinement in low-dimensional dielectric lattices is linked to the analogous concept of electron confinement in semiconductor nanostructures. For examples, quantum-well (QW) excitons are quasi two-dimensional: QW excitons embedded in a PhC slab represent quasi-2D electronic excitations interacting with quasi-2D photons. We have shown that this situation may lead to photonic crystal slab polaritons, that are analogous to exciton-polaritons in bulk semiconductors or in semiconductor microcavities with quantum wells. Semiclassical and full quantum mechanical treatments of this situation have been formulated. Photonic crystal polaritons have been recently observed experimentally (see Quantum and nonlinear photonics). Also, quantum dot (QD) excitons are confined in all directions and represent zero-dimensional excitations. When quantum dots are embedded in a PhC slab nanocavity, 0D excitons interact with 0D photons and the interaction may lead to a strong-coupling regime. The theoretical conditions for the strong coupling regime have been analyzed and the experimental observation of strong exciton-photon coupling of QD excitons in nanocavities has been made by several groups. Our current activities are still focused on theoretical descriptions photonic and electronic nanostructures, with the aid of models as well as various numerical approaches. This allows us to attack different physical problems ranging from fundamental to applied ones, also in support of experimental developments.


L.C. Andreani, D. Gerace, M. Liscidini, C. Creatore, M. Agio, A. Balestreri, I. Maksymov, D. Mascoli, S. Ferretti

PhD Theses:

D. Mascoli, "Numerical studies of two-dimensional photonic crystals and waveguide-embedded cavity structures" (University of Pavia, 2009)

A. Balestreri, "Optical properties of opal-based photonic crystals" (University of Pavia, 2007)

M. Liscidini, "Nonlinear optical properties of planar microcavities and photonic crystal slabs" (University of Pavia, 2006)

D. Gerace, "Photonic modes and radiation-matter interaction in photonic crystal slabs" (University of Pavia, 2005)

M. Agio, "Optical properties and wave propagation in semiconductor-based two-dimensional photonic crystals" (University of Pavia and Iowa State University, 2003)

Key publications:

Q-factor optimization for TM-like modes in pillar-based photonic crystal cavities with planar slot waveguides,

D. Mascoli, D. Gerace, and L.C. Andreani,

Photonics and Nanostructures Fundam. Appl. 9, 63-69 (2011). PDF

Quasiguided surface plasmon excitations in anisotropic materials,

M. Liscidini and J. E. Sipe,

Phys. Rev. B 81, 115335 (2010). PDF

Quantum theory of spontaneous emission in multilayer dielectric structures,

C. Creatore and L.C. Andreani,

Phys. Rev. A 78, 063825 (2008). PDF

Scattering-matrix analysis of periodically patterned multilayers with asymmetric unit cells and birefringent media,

M. Liscidini, D. Gerace, L.C. Andreani, and J. E. Sipe,

Phys. Rev. B 77, 035324 (2008). PDF. Erratum.

Quantum theory of exciton-photon coupling in photonic crystal slabs with embedded quantum wells,

D. Gerace and L.C. Andreani,

Phys. Rev. B 75, 235325 (2007). PDF

Light-matter interaction in photonic crystal slabs,

L.C. Andreani and D. Gerace,

Phys. Status Solidi (b) 244, 3528-3539 (2007). PDF

Photonic crystal slabs with a triangular lattice of triangular holes investigated using a guided-mode expansion method,

L.C. Andreani and D. Gerace,

Phys. Rev. B 73, 235114 (2006). PDF

Strong exciton-light coupling in photonic crystal nanocavities,

D. Gerace, L.C. Andreani,

Physica Status Solidi (c) 2, 801-804 (2005). PDF

Effects of disorder on propagation losses and cavity Q-factors in photonic crystal slabs,

D. Gerace and L.C. Andreani,

Photonics and Nanostructures Fundam. Appl. 3, 120-128 (2005). PDF

Low-loss guided modes in photonic crystal waveguides,

D. Gerace and L.C. Andreani,

Optics Express 13, 4939-4951 (2005). PDF

Gap maps, diffraction losses and exciton-polaritons in photonic crystal slabs,

L.C. Andreani, D. Gerace, and M. Agio,

Photonics and Nanostructures Fundam. Appl. 2, 103 (2004). PDF

Disorder-induced losses in photonic crystal waveguides with line defects,

D. Gerace and L.C. Andreani,

Opt. Letters 29, 1897 (2004). PDF

Gap maps and intrinsic diffraction losses in one-dimensional photonic crystal slabs,

D. Gerace and L.C. Andreani,

Phys. Rev. E 69, 056603 (2004). PDF

Intrinsic diffraction losses in photonic crystal waveguides with line defects,

L.C. Andreani and M. Agio,

Appl. Phys. Lett. 82, 2011 (2003). PDF

Photonic bands and gap maps in a photonic crystal slab,

L.C. Andreani, M. Agio,

IEEE J. Quantum Electronics 38, 891 (2002)

(feature issue on Photonic Crystals, edited by T.F. Krauss and T. Baba).