Mode Conversion Loss Research Articles

Calculation of radiation loss in integrated-optic tapers and Y-junctions

Mode conversion and radiation loss in integrated-optic tapers and Y-junctions are calculated by means of the beam propagation method combined with the effective refractive-index method. Simple design rules for the tapers and Y-junctions are derived from the obtained results.

Cyclotron harmonic absorption via the Green’s function for the mode conversion-tunneling equation

Cyclotron harmonic absorption is included in the analysis of the mode conversion-tunneling process by solving for the Green’s function of the fourth-order mode conversion-tunneling equation. For the first cyclotron harmonic where ω≈2ωci and the wave propagates exactly across the magnetic field, the solution is given in closed form in terms of the basic homogeneous solutions. For finite k∥, the solution is given by solving an integral equation where the kernel is not self-adjoint since the basic mode conversion-tunneling equation is not self-adjoint. For cavity modes, it appears that mode conversion losses are generally greater than harmonic cyclotron absorption losses although both are of the same order, and the result implies that electron heating may dominate ion heating for these processes.

Scattering of optical surface waves by a covered groove

The reflectionjand modeconversionbehavior is considered for both TE(0) and TM(0) modes at a covered groove, which is cut in the substrate surface and covered by a thin film. With a numerical example, the scattering behavior of covered and surface grooves is presented here. It is found that a covered groove produces much less radiation loss than a surface groove of the same shape. Therefore, it is preferable as a reflector element in applications which require minimum mode conversion loss. On the other hand, surface grooves are preferable for grating couplers as they provide stronger coupling from surface to space waves as observed in this study.

Mode conversion and radiation loss caused by refractive-index fluctuations in an asymmetric slab waveguide

The purpose of this paper is to show how much power is converted from an incident TE 0 mode to other guided and radiation modes due to random fluctuations of the refractive index in the core region of an asymmetric slab waveguide. Power conversion is calculated by using a perturbation technique with the assumption that the perturbed field can be expanded in terms of higher guided modes together with radiation modes (air and substrate modes). Curves are presented for mode conversion and radiation loss as a function of thickness of the core region, inhomogeneity scale of the refractive index, and refractive-index difference between the core and substrate. It is shown that the radiated power depends greatly on the refractive-index inhomogeneities, and it exceeds the power of guided mode conversion at short correlation length of the medium fluctuations.

Measurement on positive-permittivity metal-clad waveguides

A few metals exhibit a permittivity whose real part is positive at \lambda_{0} = 632.8 nm, in contrast to most metals which have a permittivity with a large, negative real part. The effects of two metals, chromium and germanium, have been measured when used as claddings on polystyrene asymmetrical waveguides. The measurements confirm recent theoretical predictions, and indicate attenuations greater than an order of magnitude over measured attenuations in silver, aluminum, and gold. Techniques used in making measurements of attenuations up to 100 dB/cm are described, and experimental values are compared with predicted attenuations. They are shown to agree with calculated values when additional mode-conversion losses are taken into account. The measured mode-index data also confirm the presence of guided modes which have a mode index less than that of the second cladding region (air). Such a propagating wave has been shown to exist in both of the metal claddings examined.

Mode conversion and radiation losses in a step-index optical fibre due to bending

Wave propagation in a step-index optical fibre with a curved section is treated theoretically. Mode conversion and radiation take place. The mode coupling coefficients which depend on the polarization of the incident mode are calculated. Radiation losses at the transition between a straight and a curved fibre section and total losses including the continuous radiation loss due to a uniform bend are evaluated. Comparisons are also made between singly and doubly clad fibres. It is shown that the doubly clad fibre can tolerate a sharper bend.

Mode conversion losses of randomly bent, singly and doubly clad waveguides for single mode transmission

Mode conversion effects take place when a dielectric optical guide is bent and its curvature varies along the guide. This paper considers and compares such conversion losses of singly and doubly clad slabs (adopted as analogs of corresponding fibers) for single mode transmission. It is shown that the conversion loss of a W-type slab is much smaller than that of a singly clad slab, provided that the beamwidths of both guides are equal. This property is the consequence of the wider mode spacing of the W-guide.

Analysis of Optical Waveguide Consisting of a Square-Law Lenslike Medium and its Analogies to Circular TE/sub 01/ waveguide

Propagation behavior of light beams along sinusoidal and serpentine bends as well as circular bends and linearly tapered bends of optical waveguides consisting of a square-law Ienslike medium is investigated in detail, both theoretically and numerically, on the basis of the approximate wave theory. A new design method of the circular bend for removing the effects of the bend is proposed and numerical results are presented. The divergence phenomena of the beam trajectory in both the sinusoidal and serpentine bends of the optical waveguide are discussed in comparison with mode-conversion phenomena occurring in the circular TE/sub 01/ waveguide with the same bends. Several design conditions to eliminate undulations of the beam trajectory and/or the spot size which would occur at a circnlar bend of the optical waveguide are also studied, and interesting analogies to the design conditions proposed so far to prevent mode-conversion losses at a circular bend of the TE/sub 01/ waveguide are shown.

A Class of Waveguide Filters for Over-Moded Applications

As the frequency spectrum extends to the millimeter wave range, the rapid rise in intrinsic loss and the diminishing physical dimensions greatly curtail the usefulness of conventional waveguide filters in dominant mode waveguide. The incentive for designing filters in over-moded waveguide is all too apparent. However, filter design in over-moded waveguide faces challenging design criteria, such as mode conversion loss and intrinsic loss, ease of being analyzed and synthesized, and feasibility for economical fabrication. A filter structure is presented which fulfills all aspects of the design objectives. The structure involves a type of discontinuity which is not only free from mode conversion but also extremely simple to characterize analytically. The latter renders feasible the use of available filter synthesis techniques. While the proposed filter structure can be designed either as a bandpass filter, a bandstop filter or a low-pass filter in an over-moded uniform waveguide of arbitrary cross section, for illustration purposes only the low-pass filter in over-moded circular waveguide is discussed in great detail. Design theories are presented which allow the proposed structure to be designed either by the image method or by operating parameter filter synthesis. Excellent agreement between the theory and measurements made on filter models is shown.

Mode Conversion Reduction in Curved Circular Waveguide*

ABSTRACTKnowledge of the frequency-phase constant diagram of the TE01mode and the TE/TM1n hybrid mode in circular circumferentially corrugated waveguide enable curvature mode conversion losses to be determined. Theoretical and experimental curves are given for the frequency-phase constant diagrams. For a given bend, mode conversion to the TM/TE11 hybrid mode is virtually eliminated. Bandwidth and mode conversion loss are then determined by coupling to the TE/TM12 hybrid mode.

Mode Conversion Caused by Diameter Changes of a Round Dielectric Waveguide

This paper presents the theory of mode conversion and radiation losses of the lowest order circular electric mode in a dielectric rod (fiber) waveguide and its confirmation by a microwave experiment. The theoretical results were obtained from a theory whose detailed development has been presented in an earlier paper. The microwave experiment was carried out at approximately 50 GHz. The optical fiber with imperfect walls was simulated by a teflon rod of 1 cm diameter and 1 m length with a periodically corrugated wall. Mode conversion was observed in excellent agreement with theory. The observed radiation losses are somewhat less than the prediction of the perturbation theory, but the agreement is quite good. The direction and width of the far-field radiation pattern was observed in agreement with theory.

Measured TE01Attenuation in Helix Waveguide with Controlled Straightness Deviations

A helix circular waveguide 380 feet long has been deformed into three different curves. The added mode conversion loss for a TE <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">01</inf> signal mode has been measured and calculated theoretically, with good agreement. For a curve with 30-inch deflection over a distance of 100 feet, peak-to-valley (200-ft period), the measured added loss at 55.5 kmc was 0.23 db/mile, the calculated 0.20 db/mile.

E- and H-Plane Bends for High-Power Oversized Rectangular Waveguide

A study is presented of theoretical and experimental results of E- and H-plane bends for high-power oversized rectangular waveguide having cross-section dimensions in the range between 1..5 and 2.5 free space wavelengths. It is expected that waveguides having these dimensions will be able to transmit 50 to 100 kW of average power at X-band without water cooling. The transmission of at least 5.0 MW of peak power at X-band without pressurization is also a design objective. Dimensions for bends having low-mode conversion loss were determined by numerical integration of the coupled transmission line equations. The dominant TE/sub 10//spl square/ mode and four spurious modes were considered in these calculations. The results obtained for both constant curvature and sinusoidally shaped E- and H-plane bends are presented. A compact H-plane constant curvature bend is described for which the ratio of centerline radius to waveguide width is equal to 1.48. The measured mode conversion loss to the TE/sub 20//spl square/, TE/sub 30//spl square/, and TE/sub 40//spl square/ modes for an experimental model having a width equal to 2.25 inches was less than -20 dB in the frequency range from 7.0 to 11.0 Gc/s.

Mode-conversion loss in a sequential confocal lens system

A sequence of equally spaced confocal lenses can be used for guiding electromagnetic energy. It has modes in which the field pattern is repeated at successive lenses. Each mode is effectively confined within a cylinder whose axis is the common axis of the system.The cylinder diameter is smaller for the lower modes and for close spacing of the lenses. At visible wavelengths a spacing of as much as a fraction of a mile may yet be small enough to make overspill of the lowest mode negligible and the attenuation virtually zero.For wider spacing or for higher modes the cylinder diameter may become comparable with the lens diameter, with consequent attenuation. For high enough modes, the attenuation may be so great that the mode virtually does not exist.If the lenses are perturbed from their correct positions, coupling between modes occurs. Sideways (off-axis) displacements seem most likely to be troublesome. The low-loss lowest mode tends to degenerate into higher modes with higher loss.If the sideways displacements are random, a distribution of power between a number of modes occurs, and a pattern exists that is repetitive. This power pattern replaces the modal amplitude pattern.The attenuation, which can be reduced in the simple case by close spacing of the lenses, can no longer be so reduced. Calculation for a numerical case at a visible wavelength shows that, if it is assumed that the r.m.s. offset cannot be expected to be less than 0.1–0.15 in, owing to instability of the lens mountings, then it would be necessary to have some form of automatic beam centring to reduce the attenuation below about 1 dB/mile. To this must be added the transmission losses of lenses and beam benders.

Noncylindrical Helix Waveguide

Small uniform deformations of the cross section of helix waveguide perturb the circular electric waves slightly. From these perturbations the added circular electric wave loss is found in a uniformly deformed helix waveguide. For a nonuniformly deformed helix waveguide Maxwell's equations are converted into generalized telegraphist's equations. By an approximate solution for small deformations, mode conversion and circular electric wave loss are found. Random imperfections with small correlation distance cause an average circular electric wave loss that is nearly independent of the wall impedance which the helix jacket presents to the waveguide interior. It is therefore nearly the same as in metallic waveguide. Near 50 kmc, the rms value of elliptical diameter differences should not be more than 0.0015 inch in order that on the average not more than 10 per cent of TE <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">01</inf> loss in a perfect 2-inch inside diameter copper pipe is added to the TE <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">01</inf> loss in a helix waveguide of the same inside diameter.

Monotonic multi-section tapers for over-moded circular waveguides

The results of a detailed analysis of the propagation of circular electric modes, H0n, is extended, approximated and eventually adapted to the design of monotonic multi-section conical tapers.The formulae and graphs obtained are directly applicable to the calculation of mode conversion loss encountered when two colinear waveguides are connected together by means of a multi-section taper, and the conversion loss is related to the wavelength and the geometry of the structure.The design procedure is illustrated in detail by several numerical examples. It is thereby clearly demonstrated that, for a given mode conversion loss and bandwidth, a considerable reduction in the overall taper length is possible if a multi-section taper of suitable proportions is used in preference to a simple linear taper.

Circular Electric Wave Transmission in a Dielectric-Coated Waveguide

The mode conversion from the TE <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">01</inf> wave to the TM <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</inf> wave which normally occurs in a curved round waveguide may be reduced by applying a uniform dielectric coat a few mils thick to the inner wall of the waveguide. Such a dielectric coat changes the phase constant of the TM <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</inf> wave without affecting appreciably the phase and attenuation constants of the TE <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">01</inf> wave. Thus, relatively sharp bends can be negotiated to change the direction of the line or deviations from straightness can be tolerated. For each of these two cases a different optimum thickness of the dielectric coat keeps the TE <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">01</inf> loss at a minimum. At 5.4-mm wavelength a bending radius of 8 ft in a ⅞-inch pipe or 50 ft in a 2-inch pipe can be introduced with 0.2 db mode conversion loss. Deviations from straightness corresponding to an average bending radius of 300 ft can be tolerated in a 2-inch pipe at 5.4-mm wavelength with an increase in TE <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">01</inf> attenuation of 5 per cent. Serpentine bends caused by equally spaced supports of the pipe may, however, increase the mode conversion and cause appreciable loss at certain discrete frequencies. Compared with the plain waveguide the dielectric-coated guide behaves more critically in such serpentine bends. The mode conversion from TE <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">01</inf> to the TE <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">02</inf> , TE <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">03</inf> , … waves at transitions from a plain waveguide to the dielectric-coated guide is usually very small.

Mode Conversion Losses in a TE01 Type Cavity Resonator with Tilted End-plate

A cylindrical cavity resonator of TE 013 mode was constructed and Its Q-value was measured at the frequency of 3075 Mc/sec. It was found that the Q-value is reduced, when the end-plate of the cavity is slightly tilted. The optimum Q-value (Q 0 =7.53×10 4 ) agrees well to that calculated from the d.c. conductivity of the wall material (copper). It may be considered that some other modes (TE 11 , TE 12 and TM 11 modes) of waves are generated from the primary TE 01 mode and they are lost as heat and radiation, when the end-plate is tilted. Thereby the resonance of TE 01 mode is damped by mode conversion which is calculated assuming the deformation of the cavity wall is small. The calculated result agrees well to the observed Q-value of the cavity with tilted end-plate.

Mode Conversion Losses in Transmission of Circular Electric Waves through Slightly Non-Cylindrical Guides

A general expression is derived for the effective attenuation of circular electric (TE01) waves owing to mode conversions in a section of wave guide whose shape deviates slightly in any specified manner from a perfect circular cylinder. Numerical predictions are in good agreement with experiment for the special case of transmission through an elliptically deformed section of pipe. The effect of random distortions in a long wave guide line is analyzed in terms of the mean-square values of the Fourier coefficients describing the distortions; and from the general formulas it appears that the mode conversion losses depend in large measure upon the statistical distribution of the various types of distortion. Under certain rather arbitrary simplifying assumptions about this distribution, it is calculated that mode conversions in a 4.732-inch copper pipe whose radius deviates by 1 mil r.m.s. from that of an average cylinder will increase the attenuation of the TE01 mode at 3.2 cm by an amount equal to 8 percent of the theoretical copper losses. The dependence on frequency of mode conversion losses in such a guide is discussed.