Light Propagation In Crystals Research Articles

Electro-optical effects in anisotropic crystals: I. The Pockels effect

The perturbation-theory method is proposed to calculate the induced anisotropy optical effects in crystals with different symmetries. On its basis, the influence of the Pockels effect on the light propagation in crystals with different symmetries is analyzed using Fedorov’s approach of invariant vector fields. This approach has many advantages over known methods in calculating different versions of Pockels effect application for different purposes. Calculation schemes are presented that make it possible to select longitudinal and transverse versions of electro-optical sensors and modulators, which can be used, in particular, to design optical measuring transformers and electric field sensors in high-voltage power lines.

Nature and energy structure of impurity and intrinsic defects in V-doped Cd1−xHgxTe

The nature and the energy structure of impurity and intrinsic defects, including the formation of anisotropic impurity centres, are determined in V-doped semi-insulating Cd1−xHgxTe (x ⩽ 0.037) crystals which were grown by the Bridgman technique for the first time. From detailed analysis of the spectral dependence of the photodiffusion current data obtained for the different directions of light propagation in crystals as well as the impurity absorption spectra, we established that for the investigated crystals anisotropic V2+ and V3+ centres are formed. Two mechanisms of the electron photogeneration from the ground impurity state to the conduction band (direct photoionization and auto-ionization from the excited state V2+ ions) are established. It is shown that the efficacy of the auto-ionization of electrons depends on the position of the excited state relative to the conduction band bottom. The photoinduced impurity centres are formed as a result of the illumination of the crystals with the light with energy about 1.50 eV. The nature and photoionization energy of these photoinduced centres are determined. The scheme of the impurity and intrinsic defects energy levels in the energy gap of the investigated crystals is presented.

Dispersion and Propagation of Light in Crystals in the Exciton Absorption Region

Analogues are obtained of Fresnel's formulas for the reflectivity and transmission of light in the exciton absorption range. Boundary conditions for electromagnetic waves in absorbing media obtained in a previous paper and following from them the law of light refraction are used. Calculation of the light propagation in the An = 1-exciton absorption range in CdS crystals is in good agreement with the experiment. Es werden Analogua der Fresnelschen Formeln fur das Reflexionsvermogen und die Transmission von Licht im Exzitonenabsorptionsbereich erhalten. Dabei werden die Grenzbedingungen fur elektromagnetische Wellen in absorbierenden Medien aus einer fruheren Arbeit und daraus folgend das Lichtbrechungsgesetz benutzt. Die Berechnung der Lichtausbreitung im An = 1-Exzitonenabsorptionsbereich von CdS-Kristallen ist in guter Ubereinstimmung mit dem Experiment.

On crystal optics with spatial dispersion

Publisher Summary This chapter focuses on crystal optics with spatial dispersion. The theoretical development of crystal optics of electrodynamics devoted to the propagation of light in crystals. The longitudinal waves will get a group velocity different from zero only if one takes spatial dispersion into account. The angle between the group velocity vector and the wave vector can be larger. Crystal optics with spatial dispersion accounts for a whole series of new effects and peculiarities with respect to classical crystal optics. The microscopic approach to crystal optics on the present level is closely associated with the theory of excitons, in which spatial dispersion is an organic and quite essential element. The phenomenological approach of crystal optics develops crystal optics on the basis of spatial dispersion before going over to classical crystal optics.

Optical Absorption near Excitonic Resonance of MOCVD‐Grown ZnSe Single Crystals

AbstractThe exciton and band‐to‐band absorption spectra of monocrystalline ZnSe films produced by MOCVD‐technique on GaAs substrates are studied in the temperature interval 80 to 300 K by laser spectroscopy technique. Violation of the Bouguer law and the temperature dependence of the integral absorption coefficient in the region of the excitonic band are revealed. The distinctive features of the transmission spectra near the excitonic resonance are interpreted in terms of the polaritonic approach to light propagation in crystals.

Polariton Theory of Light Propagation in Crystals I. Connection between the Microscopic Theory of Exciton—Phonon Polaritons and Maxwell Equations

AbstractThe light propagation in a crystal is considered as a polariton propagating through the crystal assuming no polariton damping. With the use of the Legendre transforms a set of nine independent exact equations is derived for the corresponding vertex and Green's functions. All possible correlation and screening effects are included in principle. Knowledge of the solutions of the above equations provide the excitation energies of the quasi‐particles (polaritons) formed by coupling of excitons with photons and phonons. Examination of the poles of the two‐particle electron—hole Green's function leads to an equation for the Bethe‐Salpeter amplitudes, as well as to the microscopic derivation of the Maxwell equations.

The coherent non-linear light propagation in crystal in the exciton range of the spectrum

The phenomenon of self-induced transparency (SIT) in the exciton range of the spectrum consists of the propagation through the crystal of solitary wave packets of coherent excitons and photons with anomalous small losses. In the running frame of reference at the site occupied by the soliton a single aperiodic transformation of photons into excitons and a reverse motion of the energy into the field takes place. The solutions of the SIT equations have been received in the slowly-varying amplitude approximation. Taking into account the phase modulation, the authors have shown the appearance of the branch of the carrier wave frequency with anomalous dispersion not only at the given pulse width but at the given pulse amplitude. They have also found the exact solution of the above mentioned equations taking into account the effect of saturation of the dipole momentum transition from the crystal ground state to the exciton state. It leads to the increasing of the soliton time width, to the decreasing of its amplitude and worsens the SIT observation.

Treatment of optical propagation in crystals using projection dyadics

The propagation of light in crystals has many features that suggest an eigenvalue problem involving a real symmetric dyadic, such as the occurrence of two distinct phase velocities vo and ve for the ordinary and the extraordinary waves and the orthogonality of their polarizations. The usual treatment by the use of Fresnel’s formulas, however, does not reveal an eigenvalue problem. It is shown in this paper that there is indeed an eigenvalue problem but that it relates, not directly to the permittivity dyadic ?, but to the dyadic P↘⋅?−1⋅P↘, where P↘ is the projection dyadic onto a plane orthogonal to the propagation vector k↘. The displacement vectors ?o and ?e for the ordinary and extraordinary waves act as eigenvectors of this dyadic with eigenvalues 1/εo and 1/εe. These effective permittivities εo and εe determine the phase velocities vo= (μεo)−1/2 and ve= (μεe)−1/2 of the ordinary and extraordinary waves, respectively.

Reflection Spectra of PbCl2in the Exciton Region

The reflection spectra of orthorhombic PbCl 2 crystals are studied in the exciton region with linearly polarized light at 2 K. It is found that the exciton band splits into two in the spectra obtained with the polarized lights along b - and c -axes. This splitting is explained as due to a combined effect of the crystal field and the Davydov-type interaction of the excitons. The latter effect arises from the fact that the unit contains four PbCl 2 molecules different in their orientation. When light propagation in crystal does not coincide with any of crystal axes, an additional structure appears on the higher energy side of the main band, which is attributed to a complex exciton polariton mode peculiar to anisotropic crystals.

D. Macromolecules Optical rotation in helical polymers

Our knowledge of the circular dichroism of helical molecules like polypeptides and nucleic acids has advanced enormously in the last ten years, yet the theoretical problem of calculating the optical rotation of molecules with several coupled chromophores has a long history, going back to the beginning of this century. It starts when Oseen (1915) and Born (1933) developed the concept of coupled elec­tronic oscillators in great detail to explain the propagation of light in crystals. After the development of the quantum theory by Rosenfeld (1928) and Kuhn (1932), chemists tended to stress the role of single electrons making transitions in an asymmetric environment as the main source of optical activity (Condon, Altar & Eyring 1937; Condon 1937). But the subject continued to develop (Boys 1934) and the next important landmark is Kirkwood’s famous quantum mechanical theory of coupled chromophores (Kirkwood 1937). He showed how the Coulomb interaction between electronic transitions in neighbouring, but non-overlapping, parts of a molecule gave rise to new terms in the rotatory dispersion, which were proportional to the electric polarizabilities of the groups. Kirkwood’s final formulae were remarkably like those of the old classical theory. Now there is a pause of nearly twenty years until Moffitt (1956 a, b ) and Kirk­wood’s (Fitts & Kirkwood 1956, 1957) brilliant work revived interest in the optical rotation of polymers. His theory laid a sure foundation for all the advances which have been made since his time and came at a most opportune moment.