The dispersion of electromagnetic waves in molecular crystals has been studied using the second quantization formalism. The excitation spectrum, the Green's functions for the optical exciton and photon field, as well as the corresponding distribution functions, are calculated and discussed. The ground state energy of the crystal is derived in a closed form with the polarization of the medium taken into account explicitly. In the low-density limit the expression for the ground state energy corresponds to the summation of an infinite sequence of terms in a perturbation-theory approach.
The dispersion of electromagnetic waves in molecular crystals has been studied using the second quantization formalism. The excitation spectrum, the Green's functions for the optical exciton and photon field, as well as the corresponding distribution functions, are calculated and discussed. The ground state energy of the crystal is derived in a closed form with the polarization of the medium taken into account explicitly. In the low-density limit the expression for the ground state energy corresponds to the summation of an infinite sequence of terms in a perturbation-theory approach.
The theory of the coherent pairing of excitons in the presence of a resonant electromagnetic field is generalized to describe the biexciton spectra of molecular crystals, which contain several molecules (atoms) in the unit cell. The excitation spectrum for crystals like anthracene having two molecules per unit cell is discussed in detail. It is found that, at high exciton densities and under resonance of near-resonance conditions and at temperatures below some value T c , the formation of four biexciton states is feasible provided that the dielectric gaps induced by the electromagnetic field are less than those of the corresponding biexciton states. Expressions for the absorption coefficient describing optical transitions to the biexciton states are derived.
The theory of the coherent pairing of Frenkel excitons in the presence of a resonant electromagnetic field is generalized to include the effect of the electron spin. It is shown that at high exciton densities and when the electromagnetic field is at resonance or near resonance, the removal of the spin degeneracy of the exciton pairs results in generating two fields, the singlet and the triplet biexciton fields, respectively. The gap functions ${\ensuremath{\Delta}}_{+}$ and ${\ensuremath{\Delta}}_{\ensuremath{-}}$ due to the singlet and triplet biexciton fields, respectively, are calculated and they are found to be independent of one another only in the limit when the exchange interactions between the charges disappear. In this limit, the energy modes for singlet and triplet biexciton fields have well-defined meaning and propagate through the crystal independently. A dielectric gap is induced by the electromagnetic field, which produces the energy splitting in the singlet biexciton spectrum, and it must be less than that of ${\ensuremath{\Delta}}_{+}$ for the singlet biexciton state. For finite values of the exchange interaction, the gap functions ${\ensuremath{\Delta}}_{+}$ and ${\ensuremath{\Delta}}_{\ensuremath{-}}$ depend strongly on each other and consequently the singlet and triplet biexciton fields are strongly mixed together. Optical transitions to the singlet and triplet biexciton states are considered and the corresponding expressions for the absorption coefficient are derived. The ground-state energy describing the binding energy arising from the singlet and triplet biexciton fields is calculated and discussed. Numerical estimates indicate that at high exciton densities, namely, for exciton concentrations 1018-1019 ${\mathrm{cm}}^{\ensuremath{-}3}$ and when the ratio of the average exciton-exciton interaction over the average kinetic energy is between 0.7 and 2 (strong-coupling limit), the energy gap due to the singlet biexciton state is in the range 40-650 ${\mathrm{cm}}^{\ensuremath{-}1}$, the corresponding transition temperature is 33-534 \ifmmode^\circ\else\textdegree\fi{}K, while the binding energy is 22-684 ${\mathrm{cm}}^{\ensuremath{-}1}$.
These notes, intended to be self contained and tutorial, present a direct, macroscopic approach to quantizing light inside a linear-response dielectric material when both spectral dispersion and spatial nonuniformity are present, but the spectral region of interest is optically transparent so that explicit treatment of the underlying physics of the medium is not needed. The approach taken is based on the macroscopic Maxwell equations and a corresponding Hamiltonian, without the use of Lagrangians or any dynamical model for the medium, and uses a standard mode-based quantization method. The treatment covers: energy density and flux in a dispersive dielectric; a summary of the inverse permittivity formalism; a new derivation of the mode normalization condition; a direct proof of the nonorthogonality of the modes; examples of quantized field expressions for the general case and various special cases; the relationship between group velocity and energy flux; the band approximation and the continuum limit; and quantum optical treatment of waveguide modes.
The dephasing of a high-frequency intramolecular vibrational mode in a molecular crystal is successively investigated by the cumulant perturbation expansion method as in the preceding papers in this series, I and II. The dephasing of the high-frequency mode is brought on by the thermal excitation of a low-frequency mode in the same molecule as in I and II. In this paper, however, the intramolecular vibrational modes are expressed by the bands of the exciton waves traveling through the crystal (in I and II, the intramolecular vibrational modes are expressed by the localized excitation in one molecule). The calculation shows that the spectrum becomes considerably broad as the temperature increases, while the narrowing is observed as the band widths of the exciton waves increases.
The theory of optical birefringence is discussed from the point of view of the scattering of polarized photons by molecules using the framework of formal scattering theory and quantum electrodynamics. In Part One, those features from noncovariant quantum electrodynamics relevant to the molecular scattering of photons are reviewed. Chapter One contains an outline of classical electrodynamics in the Coulomb gauge, including the Stokes parameter and density matrix formulations of polarization. Chapter Two deals with the quantization of the radiation field, and the occupation number representation is defined. The quantum mechanical description of polarized light is outlined in Chapter Three: operator equivalents of the density matrix and Stokes parameters are invoked, the parameters themselves being obtained from the expectation values of the Stokes operators with the state vector of the photon. The Stokes parameter and density matrix are then applied to the polarization of a general beam containing an arbitrary number of photons, and some new methods are developed. The interaction of the electromagnetic field with bound electrons is formulated in Chapter Four in terms of a canonically transformed interaction Hamiltonian in which the multipole terms are explicit. Since each term is then gauge-invariant, this Hamiltonian is particularly suited to the application of diagrammatic perturbation theory which follows from the iteration of the scattering matrix in the interaction representation (Chapter Five). Also the extension of the theory to multiphoton processes is facilitated "because the field strength is explicit in the transformed Hamiltonian. The S-matrix connects the initial and final asymptotic states of the scattering system, and in Chapter Six the state vector and density operator of the scattered photon beam are obtained from those of the incident beam. Part Two contains the application of the above methods to a variety of linear and nonlinear optical birefringence effects in the absence or presence of external fields. In Chapter Seven, general equations are obtained for the polarization changes imposed on a forward scattered photon in terms of matrix elements of the reaction operator between plane polarized photon base states; whereas Chapter Eight extends this treatment to an n-photon beam, thereby encompassing the hyperpolarizability contributions to the polarization changes of the forward scattered beam. It is then demonstrated that the fundamental process in optical birefringence can be interpreted as an infinitesimal unitary transformation of the polarization spinor. Also the S-matrix approach to birefringence is compared with the methods used in crystal optics, and with the classical treatments of the scattering of polarized light by molecules. The general equations obtained for the polarization changes of the forward scattered beam are subsequently interpreted in the light of the physical circumstances appropriate to the bire- fringence effect of interest. In Chapters Nine, Ten, and Eleven, diagrammatic perturbation theory is used to obtain explicit expressions, in terms of molecular polarizability and rotation tensors, for the linear and nonlinear contributions to the polarization changes involved in natural optical activity, and in birefringence phenomena induced by static and optical electric and magnetic fields. The nonforward scattering of polarized photons by molecules is discussed in Part Three. General equations are calculated in Chapter Twelve for the azimuth, ellipticity, and depolarization ratio of the Rayleigh beam at any scattering angle and for any polarization of the incident beam. Explicit expressions in terms of molecular quantities are then obtained for the polarization at scattering angles of 90° and almost zero from both optically inactive and optically active molecules. It is demonstrated that a determination of the precise polarization state of the scattered beam can provide useful molecular information additional to that obtained from depolarization ratios alone. This is because the depolarization ratio depends on only the diagonal elements of the polarization density matrix and so does not convey all the information about the system. Raman scattering processes are contained in the formulation and the polarization of the Raman light at any scattering angle can be obtained. This is shown to be particularly useful for predicting the polarization of stimulated Raman light for any Raman-active liquid placed within a laser cavity. By extending the nonforward scattering formulation to incorporate multiphoton processes, equations are obtained in Chapter Thirteen for the ellipticity, azimuth, and depolarization ratio of the second harmonic wave at any scattering angle as a function of the incident polarization. Several specific situations are subsequently investigated. Finally, it is shown in Chapter Fourteen that the near-forw- ard Rayleigh and Raman scattering formulations provide an explanation for the observed polarization, as a function of the initial polarization, of the self-trapped filaments that arise from the self-focusing of an intense laser beam.
We present a formalism for the description of fluorescence from optically active materials embedded in a photonic crystal structure possessing a photonic band gap or pseudogap. An electromagnetic field expansion in terms of Bloch modes of the crystal is used to develop the equations for fluorescence in terms of the local density of photon modes available to the emitting atoms in either the high or low dielectric regions of the crystal. We then obtain expressions for fluorescence spectra and emission dynamics for luminescent materials in photonic crystals. The validity of our formalism is demonstrated through the calculation of relevant quantities for model photon densities of states. The connection of our calculations to the description of realistic systems is discussed. We also describe the consequences of these analyses on the accurate description of the interaction between radiative systems and the electromagnetic reservoir within photonic crystals.