On the Mode and Square Correspondence Between Circular Multimode Tapered Waveguides

In an axially straight multimode circular waveguide taper excited with a pure TE/sup /spl circle// /sub 11/ dominant mode, the first and only converted mode at and near cutoff is the TM/sup/spl circle// /sub 11/ mode. It is shown that in an axially straight multimode square waveguide taper excited with a pure TE/sup/spl square// /sub 10/ dominant mode, the TM/sup/spl square// /sub 12/ mode corresponding to the TM/sup/spl circle// /sub 11/ mode in circular case is not the only first converted mode at and near cutoff. The overall behavior or coupling mechanism of waveguides is similar whether the waveguide is rectangular, square, circular, or elliptical: i.e., the overall coupling coefficient at cutoff of a converted mode or modes approaches an ininfinity of the order 0/sup -1/4/.     

Equalization of Waveguide Delay Distortion

Microwave all-pass circuits, consisting of reactive networks used in conjunction with wide-band circulators or couplers, are described. An extremely useful all-pass circuit for minimizing phase distortion results when the restive network is a linear taper extending beyond cutoff. The delay characteristics of this circuit are well suited to the correction of the dispersive characteristics of TE or TM mode waveguides. Design formulas have been derived for the parameters of the tapers and a set of design curves is presented. The use of composite tapered sections and the use of tapers in conjunction with other equalizing circuits are described. Experimental results have been obtained for the phase of the reflection factor of a linear taper. Close agreement was observed between the results predicted by theory and the experimental data. Typical examples demonstrate that the time-delay variation of a length of uniform waveguide can be substantially reduced by linearly tapered waveguide equalizers.     

Leaky Waveguide: TE/sup cir//sub 01/ Circular Waveguide Periodic Array of Circular Apertures

This paper describes propagation characteristics of periodic leaky waveguides for helix waveguides and solid metal waveguides carrying a TE/sup cir//sub 01/ mode based primarily on experimental studies. For low-loss leaky waveguides, this type has not been considered feasible, because of the critical problem encountered in mode conversion-reconversion at the circular apertures. Additional loss due to the periodic array of the circular apertures and TE/sup cir//sub 01/ loss/frequency characteristics of the periodic leaky waveguide using helix waveguides and solid metal waveguides are measured by the shuffle-pulse method in the X-band. The periodic leaky waveguides using solid metal waveguides are seen to be acceptable for practical use as a low-loss leaky waveguide system, according to these measurements.     

Mode Coupling And Power Transfer In A Coaxial Sector Waveguide With A Sector Angle Taper

We report a theoretical study of mode coupling and power transfer in a coaxial sector taper. The power transferred from the desired TE /sub 01/ mode into other propagating modes is calculated as a function of taper length and operating frequency. Power transfer via mode coupling involves at least three other modes: TE/sub 21/, TE/sub22/, and TM/sub21/. Power transfer as a function of final sector angle is also shown. At sector angles greater than 180° the taper is highly over-moded. This type of waveguide taper is utilized to feed a wide-band input coupler for gyrotron traveling wave amplifiers.     

Modal Inversion in Circular Waveguides--- Part I: Theory and Phenomenology

Part I of this work investigates the phenomenon of mode reordering in circular waveguides containing one or more dielectrics. Specifically, conditions are established, be they ranges of dimensions, dielectric constants, or frequency, under which the sequence, TM/sub 01/, TE/sub 01/, TE/sub 11/, and TE/sub 21/ is obtained instead of the conventional TE/sub 11/, TM/sub 01/, TE/sub 21/, and TE/sub 01/. The desired effect is the reversal of the order of propagation between the normally dominant TE/sub 11/ mode and the circularly symmetric low-loss TE/sub 01/. Bandwidth regimes are drawn and the credibility of the dielectric model is examined and found to be satisfactory for the application of the phenomenon to the design of digital ferrite phase shifters operating in the TE/sub 01/ mode.     

Guided modes of a width-reduced photonic-crystal slab line-defect waveguide with asymmetric cladding

The authors fabricated GaAs-based width-reduced photonic-crystal (PC) slab line-defect waveguides with asymmetric cladding, characterized optically by broadband transmission spectral results. These waveguides were vertically sandwiched between air and oxide claddings. Transmission peaks originating from the guided mode located within the bandgap were observed, thereby showing the presence of a bandgap effect for the transverse-electric (TE)-like guided mode even with the coexistence of a fundamental transverse-magnetic (TM)-like mode. Propagation loss spectra were derived from transmission spectra for both TE and TM polarization inputs. Comparing the obtained spectra to band diagrams, the authors detected a mini-stopband effect in the transmission spectra arising from a folding of the fundamental TM-like mode at the Brillouin zone boundary. The coupling coefficient was then estimated to be /spl sim/0.01 [a/sup -1/] (with a being a lattice constant). Dips in spectral intensity were also observed and were attributed to TE-TM mode conversion based on a comparison to the band diagram.     

A Channel-Dropping Filter in the Millimeter Region Using Circular Electric Modes

A. channel-dropping filter in the millimeter region that transfers TE°/sub 01/ to TE/spl square//sub 10/ is described and analyzed. The important features are the use of TE/spl o deg//sub 011/ mode in the resonant cavities combined with a mode-selective coupling between circular symmetric and rectangular waveguides which make both heat loss and mode conversion low. Design formulas and experimental results on a model filter centered at 56 kMc are included. Finally, several possible mode transducers and filters based on the idea of mode-selective coupling are described.     

On the Optimum Design of Tapered Waveguide Transitions

It has been found experimentally that the conventional optimization of waveguide tapers for the interconnection of circular waveguides with different diameters fails if the ratio in the diameters becomes too large. With the aid of an accurate numerical analysis program, the reason for the failure was found to be the reconversion from the unwanted mode to the main mode, which is neglected in all known synthesis procedures. The performance of tapers can be considerably improved by the implementation of other design equations and establishing new design criteria. This results in somewhat longer tapers. Various tapers were designed according to these procedures for a maximum of -40-dB H/sub 02/-mode level between 40 and 110 GHz, and preliminary measurements on fabricated units substantiate the improvement. It is further shown that the mode conversion at cutoff does not exhibit any singularity.     

Design of a single-mode tapered waveguide for low-losschip-to-fiber coupling

The novel waveguide structures described in this paper have nonlinearly tapered shapes that result in low radiation losses despite their relatively short lengths. The core at the waveguide endface connected with the fiber has a very small cross section and an expanded mode field with a non-Gaussian shape. The taper structures are analyzed by using an improved step-transition method. This method is a based on the theory of enclosing a waveguide within electrical walls and that can therefore treat the radiation modes in a tapered waveguide as discrete mode spectra. Analyzing the relationships between the lengths and shapes of the tapers and the radiation loss due to the tapers show that appropriately tapered semiconductor waveguides operating at an optical wavelength of 1.55 μm and having a taper length of less than 0.7 mm can have a radiation loss of only 0.1 dB and a coupling loss with a conventional single-mode fiber of less than 0.5 dB     

Artificially integrated synthetic rectangular waveguide

A synthetic rectangular waveguide (SRW), which consists of two electrical sidewalls and two parallel periodical structures placed at the top and bottom surfaces of the waveguide, is presented. The SRW is made by multilayered integrated circuit processes, which typically have large ratios of SRW lateral dimensions to substrate thickness. Two theoretical methods, finite-element method and deembedding of composite structure consisting of SRW and mode converters, are applied to investigate the propagation characteristics of the SRW. Application of the dispersion characteristics of the two-dimensional periodical structures coupled with appropriate mode converter designs leads to results in SRW designs supporting TE/sub 10/, TM/sub 00/, and TM/sub 10/ modes. Measurements and the two theoretical approaches indicate that the slow-wave factor is 4.9 and Q-factor is 260 at 6.85 GHz for the TE/sub 10/ mode propagation with a cutoff frequency of 4.10 GHz (0.348 factor of cutoff frequency of conventional rectangular waveguide using the same material and dimensions). The theoretical data show the TM/sub 00/ mode to have a slow-wave factor of 1.8, Q-factor of 187.6 at 11.4 GHz, and cutoff frequency of 10.2 GHz. The TM/sub 10/ mode has a slow-wave factor of 1.98, Q-factor of 187.6 at 12.5 GHz, and cutoff frequency of 10.4 GHz.     

High-power TE11 and TM11 circular polarizers in oversized waveguides at 70 GHz

Elliptical deformation of oversized, smooth-wall circular waveguides can produce choosable elliptical or circular polarization from a linearly polarized TE11 or TM11 mode used as intermediate linearly polarized modes in TEO1 to HE11 mode conversion sequences in electron cyclotron resonance heating (ECRH) of magnetically confined thermonuclear fusion plasmas with high-power gyrotrons. Mode coupling in elliptically distorted overmoded circular waveguides has been studied theoretically and experimentally in order to optimize TE11 (and TM11) polarizers (I.D.=27.79 mm) for the 1 MW/70 GHz long-pulse (3s) ECRH system on the Garching Stellarator W VII-AS. Coupling coefficients for ellipticity coupling of non-degenerate modes are given (coupled-mode differential equations formalism). The polarization converters essentially consist of smooth-wall circular waveguides which are gradually squeezed. A sine-squared function of the length coordinate is used to get an almost elliptical crosssection in the middle and circular cross sections at both ends. Arbitrary elliptical polarization states can be generated introducing an extremely low level (<<1%) of undesired spurious modes. Well defined differential phase characteristics have been achieved.     

Optimized overmoded TE01-to-TM11 mode converters for high-power millimeter wave applications at 70 and 140 GHz

Mode coupling in bent, oversized, smooth-wall circular waveguides was studied by means of numerical integration of coupled-mode differential equations in order to optimize high-power TE01-to-TM11 mode transducers at 70 GHz and 140 GHz. Such mode transformers are used in the mode conversion sequence TEOn to TE01 to TM11 to HE11 for generating the almost perfectly linearly polarized Gaussian-like HE11 mode from circular electric TEOn gyrotron modes. This quasi-optical HE11 hybrid mode is in many respects ideal for electron cyclotron resonance heating (ECRH) of magnetically confined plasmas in thermonuclear fusion research and for other technical applications. Curvature and ellipticity coupling as well as ohmic attenuation of 6 coupled modes (TE01, TM11, TE11, TE12, TE21, TM21) are included in the coupling matrices. Integral expressions were used for deriving the coupling coefficients for arbitrary modes in bent, smooth-wall waveguide. Lowest level of unwanted spurious modes together with highest transmission efficiency (shortest arc length) is achieved with sinusoidal curvature distribution instaed of constant curvature. The calculated conversion efficiencies of 98.0% at 70 GHz and 95.2% at 140 GHz (interior waveguide diameter D=27.8 mm for 200 kW transmission lines) are in excellent agreement with the measured values of (97.6±0.4)% and (95±1)%, respectively.     

Rigorous Analysis of the Scattering of Surface Waves in an Abruptly Ended Slab Dielectric Waveguide

The reflection and the scattering properties of even TE and TM surface waves incident in an abruptly ended dielectric slab waveguide are analyzed. The discontinuity is regarded as a junction between two open waveguides namely the dielectric slab waveguide and the free space waveguide. The boundary conditions acting together with the orthogonality provide singular coupled integral equations on the discrete and the continuous wave amplitudes at the discontinuity. These singular coupled intergral equations with Cauchy kernels and infinite limits of integration are solved by iteration via the Neuman series. Numerical results are presented for the reflectivity of the even TE/sub 0/ and TM/sub 0/ fundamental modes, together with their mode conversion on even TE/sub 2/ and TM/sub 2/ in a slab where two guided modes can propagate. Reflectivity and mode conversion of higher order excitations are also investigated     

Design of Linear Double Tapers in Rectangular Waveguides

This paper considers the problem of a taper connecting two uniform waveguides of arbitrary dimensions and propagating a single mode; an approximate expression for the reflection coefficient is derived. The special case of a linear double taper in rectangular waveguide is examined in detail for propagation in the TE/sub 10/ mode. Approximate expressions for the reflection coefficient and voltage standing wave ratio as functions of the taper dimensions and free space wavelength are derived and experimentally verified.     

Scattering at Circular-to-Rectangular Waveguide Junctions

A formally exact solution is given for the problem of scattering at a circular-to-rectangular waveguide junction and at a thick diaphragm, with a centered circular aperture, in a rectangular waveguide. The method uses normal TE and TM mode expansions of the waveguide fields and traditional mode matching of the transverse electric and magnetic fields at the junction boundary. Exact closed-form expressions are obtained for the electric field mode-matching coefficients which couple the TE(TM) modes in the rectangular guide to the TE(TM) and TM(TE) modes in the circular guide. Numerical results are presented for the case of TE/sub 10/ mode propagation in the larger rectangular guide with all other modes cutoff. Convergent numerical results for the equivalent shunt susceptances of such junctions are obtained when about 12 modes (eight TE and four TM) are retained in the circular waveguide or in the circular aperture of the diaphragm. The results are graphically compared with formulas and curves due to the quasi-static theory of Bethe and the variational theory given in the Waveguide Handbook [2].     

Bandwidth Enhancement in Dielectric-Lined Circular Waveguides (Short Papers)

The increase in TE/sub 11/-TM/sub 01/ mode bandwidth obtained by inhomogeneously loading (dielectric lining) a circular waveguide is systematically documented. Maximum bandwidth is about 31.83 percent of center frequency (up from about 26.54 percent for fully filled or empty circular waveguides). This makes circular waveguides competitive with square waveguides (bandwidth/spl aprox/ 34.3 percent) as radiators in wide-band dual-polarization arrays. Certain interesting symmetries involving the TE/sub 21/-TM/sub 01/ modal inversion are also examined.     

Optimization of Waveguide Tapers Capable of Multimode Propagation

By converting Maxwell's equations, the general case of mode conversion in tapered waveguides is treated by matrix formulation in terms of an infinite set of coupled differential equations with nonuniform coupling coefficients and varying phase constants. An "orthogonalization" or "diagonalization" process is introduced through a nonlinear matrix transformation which is a function of taper length. The general matrix solution of the problem is obtained through a perturbation method in the form of an integral equation of the Volterra type, and the integral equation is solved by an iteration method. In view of the difficulties in finding eigenvalues, the problem is then reduced to the two-mode case, and the mode conversion is obtained in an explicit form revealing certain information which characterizes the choice of "mode-conversion distribution function." Optimization is first obtained through proper choice of the mode-converison distribution function. In an attempt to approximate a Tchebycheff mode-conversion response, further optimization is realized by creating "new zeros" and thereby changing the density of the distribution of zeros in the vicinity of the origin of the mode-conversion curve and the nature of the optimization procedure essentially becomes that of synthesis. Through using the optimized distribution function, a total reduction of about 50 per cent in taper length is realized (when compared with the cosine-squared distribution) for the case of 50-db prescribed-mode discrimination in a taper connecting a 7/8-in ID waveguide to a 2-in ID waveguide operating in the circular electric mode up to 75 kmc.     

Loss Increases in Multimode Rectangular Infrared Waveguides Due to Helical Deformations

The coupling coefficients for all TE/sub pq/ and TM/sub pq/ modes of multimode rectangular waveguides, caused by elementary rotations about the three axes of symmetry, are calculated in the microwave approximation. The modes b coupled to a common mode a by these independent rotations form three nonoverlapping families. Furthermore if a deformation consisting of no more than two of these rotations is considered, none of the modes b are coupled to each other by that deformation. These properties lead, in the case of mild deformations, to the formulation of a multimode coupling theory which shows that the loss increase due to such deformations can then be viewed as the result of multiple two-mode coupling. Explicit formulas are derived for the loss increase of TE/sub p0/ due to mild circular bending. Qualitative features of twists and helical deformations are also brought out.     

Reflection Coefficient of E-Plane Tapered Waveguides

This paper treats the reflection of linearly and sinusoidally tapered waveguides. In the first part, reflection coefficients of linearly tapered waveguides for dominant modes are calculated. Graphs of the vswr of tapers for different impedance ratios are plotted showing that the vswr does not go to unity at multiples of a half wavelength. In the second part, reflection coefficients of sinusoidally tapered waveguides are calculated. Experimental data verify the theory for both kinds of tapers of various lengths at 4 kmc band. Linear tapers perform almost as well as exponential tapers, and better than shorter hyperbolic tapers. The reflection coefficients of sinusoidal tapers can be about half as small as that of the linear tapers, and these tapers compare favorably with the Dolph-Tchebycheff and the Willis taper of improved design.     

8mm波段圆波导TE11模式过渡器的设计

模式过渡器是微波毫米波系统中的重要部件,它实现微波在两种尺寸不同的器件间传输。根据耦合波理论推导出耦合波方程,由该方程及模式过渡器设计原理提出一种线性渐变轮廓和两种非线性渐变轮廓的圆波导TE11模式过渡器。利用高频系统仿真软件HFSS分析比较了8mm波段内三种过渡器的具体长度、端口反射系数及相对功率分布,所得结果与设计要求符合,可以在工程中应用。