T. Tamir

Theory of Periodic Dielect Waveguides

The propagation of electromagnetic waves along open periodic, dielectric waveguides is formulated here as a rigorous and exact boundary-value problem. The characteristic field solutions are shown to be of the surface-wave or leaky-wave type, depending on the ratio of periodicity to wavelength (d/lambda). The dispersion curves and the space-harmonic amplitudes of these fields are examined for both TE and TM modes. Specific numerical examples are given for the cases of holographic layers and for rectangularly corrugated gratings; these show the detailed behavior of the principal field components and the dependence of waveguiding and leakage characteristics on the physical parameters of the periodic configuration.

Unified theory of Rayleigh-angle phenomena for acoustic beams at liquid-solid interfaces

Various phenomena have been observed when a bounded acoustic beam is incident from a liquid onto the surface of a solid at or near the Rayleigh angle. These phenomena include: a shift of the reflected beam from the position predicted by geometrical acoustics, a null or minimum of intensity within the reflected beam, a 180° phase reversal of the field on either side of the null, a weak trailing field on only one side of the reflected beam and a frequency of least reflection when the solid is lossy. By carefully examining the reflection coefficient for angles in the vicinity of the Rayleight angle, and by taking into account the angular spectrum of plane waves that comprise a bounded beam, a model of the reflection process is developed that explains all of the observed phenomena. This model shows that the various critical-reflection effects result from the interference between a geometrically reflected field and the field of a leaky Rayleigh wave, which is excited by the incident beam. Moreover, this model resolves the conflict between various explanations made for these phenomena in the past; in particular, it is found that Schochs classical description of a laterally displaced reflected beam is valid only for beams having a large width.

Analysis and Design of Grating Couplers

Based on an accurate perturbation analysis of the guiding properties of dielectric gratings, simple design criteria are developed for grating couplers which transfer the energy of a beam into or out of an optical waveguide. Gratings having arbitrary groove shapes are considered and explicit formulae are given for the leakage parameters of gratings with symmetric profiles. The results cover TEv and TMv modes and they apply to both shallow and deep grating grooves. The variation of the leakage parameter α in rectangular gratings is examined in detail; these rectangular gratings are then used as basic configurations for predicting the characteristics of other grating profiles. Particular attention is given to trapezoidal and triangular profiles and gratings with asymmetric profiles are also discussed.

Frequency-selective reflection and transmission by a periodic dielectric layer

The feasibility of using a periodic dielectric layer, composed of alternating bars having dielectric constants epsilon /sub 1/ and epsilon /sub 2/, as a dichroic surface at millimeter-wave frequencies is examined. For oblique incidence, it is found that total transmission and total reflection can be obtained at different frequencies for proper choices of epsilon /sub 1/ and epsilon /sub 2/ and the geometric parameters. The frequencies of total reflection and transmission can be estimated from wave phenomena occurring in a layer of uniform dielectric constant equal to the average value in the periodic layers. For some of the frequencies of total transmission, the bandwidth for 90% transmission is found to be 40%. The bandwidth for 90% reflection is always found to be much narrower, the greatest value obtained being 2.5%. >

Lateral Displacement of Optical Beams at Multilayered and Periodic Structures

Many planar structures, including multilayered media and periodic configurations of the optical-grating type, are capable of supporting an electromagnetic field of the leaky-wave form. By exciting this field, an incident light beam transfers a portion of its energy into the leaky-wave structure; after being guided longitudinally for a certain distance along the structure, this energy is leaked back to form part of the reflected beam. Owing to the longitudinal energy flow, the complete reflected beam exhibits a lateral displacement that appears either as a forward beam shift, similar to the Goos-Hanchen effect along a single dielectric interface, or as a backward beam shift, which has not been identified before. By deriving a general expression for the field excited by a gaussian light beam incident upon a leaky-wave structure, we find that the reflected beam may undergo a lateral displacement of the order of the beam width; the magnitude of this beam shift may therefore be much larger than the maximum shift produced at a single dielectric boundary. In the case of periodic structures, all of the higher-order diffracted beams are shifted laterally whenever the specularly reflected beam is displaced. The dependence of the lateral displacement on the beam width, the angle of incidence, and the leakage distance is examined in detail and the relevance of the beam shift to optical-beam couplers is discussed.

Lateral Displacement of a Light Beam at a Dielectric Interface

The lateral (Goos–Hanchen) shift of a gaussian light beam incident from a denser medium upon the interface to a rarer medium is investigated by means of a rigorous integral representation comprising a continuous plane-wave spectrum. By applying a Fresnel approximation to that integral, we derive the lateral displacement for angles of incidence that are arbitrarily close to the critical angle of total reflection. Our results show that, in general, the lateral displacement is a function of the beam width, as well as the incidence angle; the classical expression appears as a limit case which holds only for large beam widths and for incidence angles that are not too close to the critical angle. An analysis of our expression for the beam shift reveals that, as the incidence angle approaches the critical angle of total reflection, the beam shift approaches a constant value that is strongly dependent on the beam width, in contrast to the classical expression, which predicts an infinitely large displacement; we also find that the maximum lateral displacement occurs at an angle that is slightly larger than the critical angle. Numerical results are presented in terms of normalized curves that are applicable to a wide range of realistic beams.

On radio-wave propagation in forest environments

Propagation of electromagnetic waves in forest environments at medium and high (1-100 MHz) frequencies is examined for the case where both the transmitting and receiving points are situated within the vegetation. A dissipative slab in the presence of a reflecting ionosphere is employed to describe the forest configuration. If the effect of the ground-forest interface is disregarded, the radiated field of an arbitrarily oriented, small dipole is found to consist primarily of two separate waves: a lateral wave which skims along the tree tops, and a sky wave which is produced by a single-hop reflection at the ionospheric layer. These two field constituents are compared and their domains of preponderance are calculated for a large range of the pertinent parameters; it is then found that the lateral wave plays the major role since the sky wave is restricted to a narrow frequency band and its amplitude is appreciable only at large distances. The lateral-wave field is examined in detail and is shown to yield a simple physical picture for the propagation mechanism in forests. Its features are found to be qualitatively consistent with the field behavior reported in the literature and the quantitative aspects agree well with the available experimental data. The observed variation of the field with distance, the height-gain effect, the vegetation factor, the basic path loss, and depolarization effects are separately examined and are all shown to express merely one or another of the intrinsic properties of a lateral wave. The ground-proximity effect produced by the presence of a planar-conducting ground is also estimated and shown to be of minor importance in most cases.

Scattering and guiding of waves by dielectric gratings with arbitrary profiles

Based on an exact solution of the pertinent boundary-value problem, a method is presented for finding the electromagnetic fields scattered or guided by lossy dielectric gratings having arbitrary profiles. This method unifies the treatment of both perpendicular (TE) and parallel (TM) polarizations by expressing the fields in terms of two coupled first-order differential equations. Their solution is obtained by resorting to difference equations in conjunction with the algorithm of Adams–Moulton, which easily leads to accurate results for a large variety of practical problems. To illustrate the application of this approach, quantitative results are presented for the scattering of plane waves by lossy corrugated structures and for the guiding of (leaky) surface waves by triangular gratings with symmetric or asymmetric profiles.

Nonspecular phenomena in beam fields reflected by multilayered media

Past studies have shown that beams reflected by a single dielectric interface exhibit lateral and focal shifts under total-reflection conditions or angular shifts if a partial reflection regime is maintained. We investigate these effects for Gaussian beams incident upon multilayered media by using an analysis that treats the three beam-shifting phenomena in a unified manner. This approach reveals a novel fourth effect that manifests itself as an expansion or a reduction of the beam waist. All the four nonspecular phenomena are evaluated for typical layered configurations, and simple approximate relations are derived. The results show that the reflected beam fields may be considerably different from those predicted by geometrical optics if incidence occurs at an angle around which the reflectance function varies rapidly.

The spectrum of electromagnetic waves guided by a plasma layer

The modal spectrum of a lossless, homogeneous and isotropic planar plasma layer is shown to contain contributions from surface waves and complex modes in addition to the usual continuous spectrum characteristic of open structures. These discrete contributions are only of the E-mode type and occur whenever the plasma dielectric constant e p is negative. The surface waves may be of the forward or the backward type and they carry power in opposite directions in the plasma and air regions. The complex modes are shown to appear always in degenerate pairs and as a consequence they carry no real power but may account for large reactive fields in the neighborhood of sources. For E modes with positive values of e p , and for all H modes, the spectrum is purely continuous; however, nonspectral leaky ways are then present which are significant in radiation considerations.