Planar Dielectric Interface Research Articles

Fresnel studies of reflected beams

It is shown that standard numerical methods based on the Fresnel equation accurately model the reflection of a collimated TE-polarized Gaussian beam from a planar dielectric interface when the beam is incident on the interface at arbitrary nonnormal angles. >

Time-domain analysis of horizontal dipoles in front of planar dielectric interface

Time-domain solutions for fields due to an impulsive horizontal magnetic and electric dipole above a planar dielectric interface are studied analytically. General time-domain expressions for the Hertzian potentials corresponding to the electromagnetic fields in the upper medium are analyzed in a novel way by exploiting exact image theory. Analytic closed-form solutions are derived for certain special locations of the source and observation points. Some of the results are new, while the rest agree with the solutions in the literature.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Angular shift of an electromagnetic beam reflected by a planar dielectric interface

A mathematical procedure for obtaining theoretically an expression for the fields of a beam reflected by a planar interface separating two lossless, linear, isotropic, homogeneous media is presented. Comparison of this expression with that obtained when the beam undergoes reflection from a perfect conductor leads to the expression for the angular shift of the beam reflected by a planar dielectric interface. The cases of normal and parallel polarization of a microwave beam are considered. In the last case, a complete study for angles of incidence far and near the Brewster angle is made.

Light emission by magnetic and electric dipoles close to a plane dielectric interface III Radiation patterns of dipoles with arbitrary orientation

We have derived analytic expressions for the angular distribution of light emitted by an atomic system, e.g., a fluorescent molecule, located in a dielectric medium 1 at distance z0 from the interface to a different dielectric medium 2. The theory is rigorously valid for electric and magnetic dipole transitions with arbitrary orientation of the dipole transition moment. (In Paper II [ J. Opt. Soc. Am.57, 1615– 1619 ( 1977)], only the special case of dipoles oriented perpendicular to the interface had been treated.) The radiation patterns of dipoles located on the interface (z0 = 0) and oriented parallel to it, and ensembles of such dipoles radiating incoherently with randomly oriented dipole moments were examined in particular. They differ greatly from the corresponding well-known dipole radiation patterns in an unbounded medium 1, due to the wide-angle interferences of emitted plane waves, and radiation from evanescent waves in the dipole’s near field into medium 2, if this is denser than medium 1.

Errata: Light emission by magnetic and electric dipoles close to a plane dielectric interface II Radiation pattern of perpendicular oriented dipoles

Get PDF Email Share Share with Facebook Tweet This Post on reddit Share with LinkedIn Add to CiteULike Add to Mendeley Add to BibSonomy Get Citation Copy Citation Text W. Lukosz and R. E. Kunz, "Errata: Light emission by magnetic and electric dipoles close to a plane dielectric interface. II. Radiation pattern of perpendicular oriented dipoles," J. Opt. Soc. Am. 68, 1155_2-1155 (1978) Export Citation BibTex Endnote (RIS) HTML Plain Text Citation alert Save article

Light emission by magnetic and electric dipoles close to a plane dielectric interface II Radiation patterns of perpendicular oriented dipoles

We have derived analytical expressions for the angular distribution P(α) of the power radiated by magnetic or electric dipoles located at distance z0 from a dielectric interface and oriented perpendicular to it. For dipoles in the rarer medium very close to the interface, evanescent waves in the dipoles’ near field give rise to strong radiation into the denser medium. The resulting large maximum of P(α) shows characteristic differences for magnetic and electric dipoles when the relative refractive index of the two dielectrics is greater than √2. For dipoles lying on the interface a symmetry relation is established connecting the power distributions P(α) for the values n and 1/n of the relative refractive index.

Directional change of beams undergoing partial reflection*

When a beam of finite width is partially reflected at a planar dielectric interface, there is in general a shift in the reflected beam direction away from that predicted by the simple application of the geometrical optics relfection law. We give a simple derivation of this shift, clarifying the underlying physical mechanism. The Gaussian beam is studied in detail.

External reflection from dielectrics at microwave frequencies

3 cm microwave are being used to investigate the beam shifts which occur for external reflection from a planar dielectric interface. The adaptation of a planar wave theory to the microwave case has proved successful in predicting the magnitudes and direction of such shifts.

Quantum electrodynamics in the presence of dielectrics and conductors. IV. General theory for spontaneous emission in finite geometries

A quantum-electrodynamic theory of spontaneous emission in presence of dielectrics and conductors is developed. The theory makes use of the master-equation techniques and the response-function formalism of part I of this series of papers. Various observable entities such as damping coefficients (lifetimes), Lamb shifts, and frequency shifts are related to the appropriate surface-dependent response functions. The results are valid for arbitrary geometries (involving linear dielectrics) and naturally contain, as a special case, the usual results of spontaneous emission in free space. As explicit examples we consider a two-level atom (also the multilevel atom) in presence of a plane dielectric interface and between two conducting plates. Formulas for the shifts and widths are given and their asymptotic behavior for large and short distances is discussed. The behavior when the atom is embedded inside the dielectric is different than when the atom is outside the dielectric. The origin of coherence in the present model is discussed and the coherence effects in this model are contrasted with those in Dicke's model. The results are also compared with those obtained by the image method. Exact expressions for the operator radiation-reaction fields are obtained in terms of the atomic polarization operators and response functions. Approximate results for such fields are also given. The far-zone behavior of the radiation fields is obtained in terms of response functions and the polarization operators. Some of the normally ordered correlation functions are also calculated. The connection of some of the theoretical results with a recent experimental work of Carniglia, Mandel, and Drexhage is discussed. The effect of anisotropy of the dielectric function on the lifetimes as well as on the far-field correlation functions is also considered. Finally the contribution to the shifts and widths due to the excitation of surface polariton modes is computed and the results are compared with those obtained by the quantization of surface polariton field. It is found that such surface modes contribute significantly to widths.

Short range electrostatic interactions in dielectric media

The electrostatic theory for a dielectric sphere with arbitrary charge distribution within it is presented. The sphere is located in a dielectric medium which either contains another similar sphere or is separated from another dielectric medium by a planar interface. It is shown that the case of two dielectric spheres is simply related to that of a sphere near a planar interface. The cases of a point charge or a point dipole at the center of the sphere are analyzed in detail. For the point charge case, the numerical results for both the electrostatic potential energy and forces for a wide range of values of the ratio of dielectric constant of sphere to that of medium are given. In addition, approximate analytical expressions are given and constrasted with the exact numerical results. The asymptotic expression occasionally used is shown to provide a good approximation for equal and oppositely charged cavities embedded in a medium of very high dielectric constant. An analytical expression, similar in structure to the exact one for metallic spheres, is derived and shown to provide an excellent approximation over the whole range of dielectric constants and arbitrary charge combinations. Approximate expressions using Padé approximants and simple variational approaches are also given. For the point dipole case, extensive numerical results are presented. It is shown that, for the case of a dielectric cavity, embedded in a medium of high dielectric constant and in contact with another similar cavity with the dipoles oriented along the lines of centers, the potential energy can be expressed in terms of tabulated analytical functions. This also applies for a dielectric cavity in contact with a planar dielectric interface with dipoles oriented perpendicular to the interface.

A generalized approach to beam wave interaction with a dielectric interface

New phenomena have been reported recently in connection with Gaussian beam interaction with a plane dielectric interface, namely, the deterioration of the reflected and refracted beams from shapes predicted by geometric optics, and the generation of higherorder components that cause angular beam deflection. Any bounded, symmetric beam, which is not necessarily Gaussian, can be comprised in terms of an angular spectrum of plane waves. Utilizing such a modal expansion, a model of the interaction process that seems to point out the generality of the phenomena involved for bounded symmetrical beams with any cross-section is presented. The procedure is applied to a Cauchy profile, and analytical results are given. Comparison with previous results obtained for the Gaussian beam and careful examination of the respective spectral functions demonstrate close correspondence between the results. This adds credence to the general approach presented here which can be applied to bounded symmetrical beams of general shape.

Generation of complex Gaussian beam modes in beam interaction with a planar dielectric interface

The problem of Gaussian beam interaction with a planar interface separating two semi-infinite homogeneous isotropic lossless media is considered for regular incidence, i.e., excluding the case of total internal reflection. The reflected and refracted fields are expressed in terms of the fundamental and higher order complex beam modes. These newly identified complex beam modes differ from the conventional beam modes and they describe the structure of the reflected and transmitted fields in a more convenient manner.

Evanescent fields produced by totally reflected beams

When the coordinates of a line source are assigned complex values in the free-space Green's function, the resulting field represents a bounded beam. This property is employed to formulate an integral expression for the field transmitted across a plane dielectric interface. Asymptotic evaluation of the integral requires detailed study of the saddle point and steepest descent path configurations, especially when the incident beam is totally reflected. The asymptotic results in that case are employed to chart the power flow lines and to deduce the lateral shift of the reflected beam.

Relation between beam displacement and phase shift upon total reflection at a plane dielectric interface

Relation between beam displacement and phase shift upon total reflection at a plane dielectric interface

Reflection and Transmission of Beams at a Dielectric Interface

When complex values are assigned to the source coordinates in the expressions for the fields radiated by a line or point source in a homogeneous medium, the resulting fields have the form of a two- or three-dimensional Gaussian beam. This fact may be utilized to develop results for beam propagation and scattering in inhomogeneous regions from corresponding results for point or line source fields. After justifying the analytic continuation procedure to derive rigorous integral solutions for the (two-dimensional) beam fields reflected by and transmitted through a plane dielectric interface, asymptotic results are obtained by the saddle point method; it is found that the analytic continuation to complex source coordinates can be performed directly on the asymptotic expressions for reflected, refracted and lateral wave constituents of ordinary line source fields. Interpretation of the reflected fields reveals that they incorporate directly the lateral beam shift, a phenomenon usually regarded as a diffraction...