Modes In Dielectric Waveguides Research Articles

Thin-film metallized dielectric waveguides

An experimental study was made of the influence of metallic and dielectric coatings on the propagation of selectively excited TE and TM modes in thin-film dielectric waveguides. The theoretical and experimental results were obtained for different metals and different waveguide thicknesses.

Guided wave optics

Phenomena associated with the propagation and manipulation of light in thin-film dielectric waveguides are presently the object of considerable research effort, directed toward possible applications in communications and information processing. The theory of dielectric waveguide modes is reviewed, and the topics of directional coupling, input-output coupling, modulation, and distributed feedback laser sources are treated on the basis of coupled-mode theory. A summary of experimental results for each of the guided-wave optical phenomena covered by the theory is also presented.

Analysis of TEM modes in dielectric waveguides, by a variational method

In this paper, a method of analysis of dielectric waveguides using a variational method is presented. This method can be applied to dielectric waveguides with any general permittivity distribution. As examples, numerical calculations for dielectric waveguides with rectangular cross-sectional shape and quadratic inhomogeneous permittivity distribution are given.

The Stiles-Crawford effect—explanation and consequences

A complete electromagnetic analysis of human foveal cones is presented. We conclude that: (1) The physical properties (shape, size and refractive index) of an isolated human foveal cone completely determine the Stiles-Crawford effect of the first kind (SC—1) both in the sensitivity to angle of incidence in addition to the great variation of that sensitivity to wavelength. (2) The maxima and minima of the variations with wavelength in the SC—1 effect are due to diffraction and interference effects caused by dielectric waveguide mode propagation on the outer segments of the foveal cones. This correspondence provides direct psychophysical evidence for mode propagation on the human photoreceptors. (3) The measured increase in the SC—1 effect due to a high luminance adapting field is consistent with a photomechanical contraction of the human cone inner segments. We predict that in intense light the cone outer segments contract—increasing their diameter by a few per cent. (4) Small changes in the refractive index or diameter of the outer segment alters the location of the maxima and minima of Stiles' (1937) p (λ) curve. Changes in the diameter of the inner segment alter the magnitude of the p (λ) curve. Changes in the refractive index of the inner segment are more complicated. (5) Previous theories of the SC—1 effect have either been incomplete in their treatment of the receptors' physical parameters or incompatible with experimental evidence. We provide the only quantitative explanation for the variations of the SC—1 effect with wavelength.

Waveguide Laser Mode Patterns in the Near and Far Field

The difference in notations used by researchers in the dielectric waveguide field and those primarily interested in waveguide lasers is discussed, and the equations for the field components of the various modes in large radius hollow dielectric waveguides are rederived in terms of the more widely used notation. Certain linear combinations of these modes that give linearly polarized field distributions are then considered to be launched into free-space at a waveguide termination. The resultant Fresnel and Fraunhofer field distributions are useful in identifying the modes of oscillation and in choosing mirror apertures that will restrict oscillation on the fundamental waveguide mode.

The optical density of erythrolabe determined by a new method.

1. A new method is described for the determination of optical density by retinal densitometry based on an analysis of stray light.2. The basic assumption used is that the stray light present in retinal densitometry is independent of wave-length. The justification for this assumption is considered.3. The stray light and hence the optical density was determined by a method of successive approximations using a Linc 8 computer.4. The optical density of erythrolabe for the direction of maximum Stiles-Crawford efficiency was determined for five subjects, two deuteranopes, two deuteranomalous and one red-rich normal subject. The mean values for three of the subjects were close to the grand mean value of 0.42, but the other two subjects had considerably higher and lower values respectively.5. The results are in satisfactory agreement with optical density values determined by the self-screening method using retinal densitometry, and also with determinations using microspectrophotometry and psychophysics.6. The relevance of dielectric wave-guide modes in the outer segments is considered.

Investigation of the dielectric waveguide modes in homostructure GaAs laser

The investigation of the propagation modes in a homostructure GaAs laser and particularly of the spatial displacement of the TE and TM mode is reported. For this investigation, a homostructure GaAs laser was operated in an external optical cavity and experiments were performed where the resonator alignment was varied to displace the image of the p-n junction, formed in the optical cavity, from the p-n junction of the laser diode. The peak power of the laser radiation (which is in the TEM 00 mode), the delay, the optical waveform, and the polarization were measured at room temperature for different cavity alignments. For the evaluation of the propagation modes the experimental results are correlated with the computed field distributions of the modes in a three-layer dielectric waveguide.

Spectral Properties of the TE 0 and TM 0 Modes in Dielectric Thin Film Waveguides, Excited with a Prism Light Coupler

Spectral Properties of the TE 0 and TM 0 Modes in Dielectric Thin Film Waveguides, Excited with a Prism Light Coupler

Propagation Mode and Scattering Loss of a Two-Dimensional Dielectric Waveguide with Gradual Distribution of Refractive Index

An analytical discussion of the mode property and the scattering loss of a two-dimensional dielectric waveguide with gradual refractive-index distribution in the transverse direction is presented. To describe scattering loss, a transverse correlation as well as an axial correlation of the irregular variation of the refractive index have been used. The field distribution, the group delay, and the maximum film thickness of a single-mode waveguide scarcely depends on the shape of the distribution. The maximum value of the film thickness in the single-mode transmission region optimizes the scattering loss and the energy confinement. The scattering loss of a waveguide with a gradual index distribution is smaller than that of a three-layer waveguide when the transverse correlation is small, but it is not much altered when the transverse correlation is large.

Depolarization of plane-polarized light by light-guiding frog rods.

The light transmitted by a bleached rod in the unfixed frog’s retina is depolarized to a few percent. The depolarized light is transmitted along the edge of the outer segment. A significant part of this effect is caused by the differences of phase velocity of the guided dielectric-waveguide modes that are possible in the frog-rod outer segment.

The Coupling of Degenerate Modes in Two Parallel Dielectric Waveguides

Two parallel dielectric waveguides can exchange energy if the field carried by one guide reaches the other guide. We consider only the case of coupling between degenerate modes of dielectric waveguides (optical fibers, etc). Degenerate modes have equal phase velocities, but their transverse field distributions need not be identical. The coupling theory presented in this paper applies to dielectric waveguides of arbitrary shape and arbitrary distribution of refractive index. The dielectric media of the guides as well as the surrounding medium are allowed to be lossy. The coupling coefficient is obtained by means of perturbation theory. It is shown that whereas lossless degenerate modes can exchange their power completely, lossy modes tend to equalize their power. The theory is applied to the problem of crosstalk between cladded dielectric slab waveguides and cladded optical fibers embedded in a lossy medium. Since a lossy surrounding medium also causes an increase in the loss of the guided modes, formulas for this additional loss are presented. It is shown that additional mode loss results even for a lossless surrounding medium if n <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> k > β. (n <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> = index of surrounding medium, k = free space propagation constant, β = propagation constant of guided mode.)

Radiation Losses of the Dominant Mode in Round Dielectric Waveguides

The radiation loss theory that has been developed in a series of earlier papers is extended to the dominant mode of the round dielectric waveguide. The theory is applied to the calculation of radiation losses of abrupt steps, gradual tapers, and random wall perturbations of the round dielectric waveguide. The radiation losses caused by an abrupt step, and consequently the losses of tapers, are far higher for the dominant mode of the round dielectric waveguide than they are for corresponding steps and tapers of the dielectric slab waveguide. However, the losses caused by infinitesimal random wall perturbations of the round waveguide are nearly equal to the random wall losses predicted on the basis of the slab waveguide theory. In fact the losses of the dominate mode as well as the circular electric TE <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">01</inf> mode of the round rod due to random wall perturbations are very nearly the same. The theory is limited to circular symmetric distortions of the round dielectric rod (diameter changes). The radiation losses caused by steps of the round dielectric waveguide that carries the dominate guided mode have been verified by experiments at millimeter wave frequencies.

Electro-Optic and Waveguide Properties of Reverse-Biased Gallium Phosphidep−nJunctions

Observations of light transmitted along the plane of reverse-biased GaP $p\ensuremath{-}n$ junctions show the depletion layer to be birefringent and to produce mode confinement of the light. Extensive measurements were made on diodes having a variety of dopings (${N}_{D}\ensuremath{\approx}{10}^{17} \mathrm{to} {10}^{18}$ ${\mathrm{cm}}^{\ensuremath{-}3}$) and several crystalline orientations (${\mathbf{E}}_{J}\ensuremath{\parallel}[111]$ or [110] or [100]) with several laser wavelengths (632.8 nm and 1153 nm from a He-Ne laser and 896.5 nm from a GaAs laser). The measurements were mainly of three types: (1) measurement of the intensity on the exit face of the diode versus position, voltage, and polarization state; (2) measurement of the change of phase with junction voltage of each state of polarization by an optical heterodyne technique; (3) measurement of the phase difference between these two polarization states versus voltage and wavelength by optical compensation methods. We interpret these results in terms of a dielectric waveguide mode in which a higher optical dielectric constant exists in a layer whose width is fixed and approximately equal to the zero-bias junction width. The birefringence arises from the linear electro-optic (Pockels) effect within the junction width, which changes with bias. The optical dielectric constants on the $n$ and $p$ sides are assumed slightly different. Agreement with this model is generally satisfactory; a few discrepancies, including an anom alous modulation for ${\mathbf{E}}_{\mathrm{light}}\ensuremath{\parallel}{\mathbf{E}}_{J}\ensuremath{\parallel}[100]$, appear to be best explained by the presence of a small quadratic electro-optic (Kerr) effect. The origin of the higher dielectric constant that gives mode confinement is not known.

Dielectric-waveguide modes in laser diodes in the presence of a transverse magnetic field†

Dielectric-waveguide modes in laser diodes in the presence of a transverse magnetic field†

Electromagnetic Scattering by Obliquely Oriented Cylinders

Numerical results for scattering coefficients and extinction efficiencies for obliquely oriented infinite circular cylinders with index of refraction m=1.6 are presented. The extinction efficiencies for oblique incidence have a much more intense resonance structure than those for normal incidence. An analysis is made of these resonance modes for large angles of incidence and comparison is made with the propagation modes in cylindrical dielectric waveguides. A polarization reversal via extinction is noted for thin cylinders with sufficient tilt angles. By comparison with preliminary experimental results on finite cylinders it is shown that the theoretical solution for infinite cylinders may be usefully applied to the finite case as long as the angle of incidence of the radiation is small.

Radiation Characteristics of Circular Dielectric Waveguides

The radiation characteristics of isolated circular optical waveguides capable of supporting only low-order dielectric waveguide modes are studied both theoretically and experimentally for several combinations of modes, wavelength, diameter, and waveguide numerical aperture. Photographic and photoelectric measurements of the far-field intensities are compared with numerical predictions based on the equivalent current method of Schelkunoff. For a cross-sectional intensity distribution in the mode pattern of the approximate form Jn+12(ur/a) the predicted Fraunhofer pattern has the form: [Jn+1(x)−XJn(x)Jn+1(u)uJn(u)(u2−x2)(q2+x2)]2,where Jn is the Bessel function of order n, u(= k1a sinθ1) the mode eigenvalue, and x(= k0a sinθ) the customary diffraction parameter. θ1 is the characteristic angle of the mode in the fiber of core refractive index n1 and coating n2. Generally, the pattern has its strongest maximum at an angle slightly less than the Snell complement of θ1. However, the parameter q2 = (k0a)2(n12 − n22) − u2 becomes vanishingly small as the modes approach cutoff, giving rise to strong intensities in the forward direction. Photometric data show agreement with numerical predictions within experimental accurate limits.

Observed Dielectric Waveguide Modes in the Visible Spectrum*

The direct images and the radiation patterns of the first few lowest-order dielectric waveguide modes were observed in the visible region of the spectrum for fibers with core and cladding indexes of refraction of 1.56 and 1.52, respectively, and for core diameters from 0.1 to 5.5 μ. The cutoff wavelengths for the observed modes are in reasonably good agreement with theory. Photographs of the modes are shown.

Cylindrical Dielectric Waveguide Modes*

The propagation of cylindrical dielectric waveguide modes near cutoff and far from cutoff are considered. The relative amounts of Ez and Hz, and the transverse components of the field are determined for both sets of hybrid modes. With the radial dependence of the z components of the field in the central dielectric given by Jn(ur/a), the transverse components far from cutoff are given by Jn±1(ur/a), where u is a parameter found from the boundary conditions and which fixes the scale of the Bessel function relative to the boundary r = a. The two values n + 1 and n − 1 correspond to the two sets of modes. The designations of the hybrid modes are discussed. Field plots for the lower order modes are given.