Electromagnetic Waveguide

Abstract

This disclosure deals with a novel electromagnetic waveguide particularly adapted for the transmission of a range of waves from submillimeter through optical wavelengths having a finite-conductivity tube of dielectric constant greater than unity surrounding a medium of lesser dielectric constant and of cross dimension of a value preferably very much greater than the wavelength of the waves propagated along the waveguide.

Description

The present invention relates to electromagnetic waveguides being more particularly (though not exclusively) directed to the improved wave-guided propagation of a range of waves from substantially submillimeter wavelengths down through optical wavelengths.

Prior waveguides have been of three basic types: metallic or other substantially infinitely conducting tubes bounding a dielectric medium, such as air or any other gas or dielectric medium; dielectric rods; and dielectric-coated metallic guides. The efficiency of the metallic tube type is limited by the conductivity of the metal , since the confining of the electromagnetic energy is dependent upon the high reflectance of the metallic shield. The efficiency of the dielectric rod type of guide or the dielectric-coated metallic guide, on the other hand, is limited by how low the conductivity of the dielectric can be made, the field-confining action being dependent upon critical reflection at the dielectric interface. External fields, moreover, affect the wave propagation along such dielectric structures.

In accordance with the present invention, improved transmission efficiency (lower attenuation), lighter weight and better field-confining properties are all attained, particularly for submillimeter and lower wavelength energy ranging down into the optical region, with a novel waveguide structure having, in summary, a low or finite conductivity tubular member of dielectric constant greater than unity surrounding a medium of lesser dielectric constant and of cross section very large compared to the wavelength of the waves propagated therealong. Underlying this structure is the discovery that a high reflectance to electromagnetic waves travelling at small angles can be presented by a partially lossy dielectric under such critical conditions of appropriate dielectric constant and dimensional relationships.

An object of the invention, accordingly, to provide a new and improved electromagnetic waveguide structure.

Other and further objects will be hereinafter pointed out and more particularly delineated in the appended claims.

The invention will be further described in conjunction with the accompanying drawing, the single figure of which illustrates a embodiment diagrammatically. As shown in the drawing, the waveguide of the invention comprises a low or finite conductivity (i.e. partially conducting) tubular dielectric member of dielectric constant greater than unity (preferably in some instances, as later mentioned, equal to or greater than two), surrounding and bounding a dielectric medium or core of less dielectric constant and of cross section much larger than the wavelength of the waves being propagated therealong. The thickness of the tubular member, to attain the optimum results with the energy mainly confined to the medium, must be sufficient that fields at the outer periphery are at least an order of magnitude less than (and thus negligible with respect to) the fields at the interface between the inner periphery of the tubular member and the said dielectric medium. The loss tangent of the tubular member should, moreover, approximately be equal to unity for effective attainment of this end of minimum attenuation.

In accordance with the invention, the efficiency of propagation is a complex function of the dielectric constant and low or finite conductivity of the partially conducting dielectric tubular member and the lesser dielectric constant of the inner medium. The restriction for operation in accordance with the phenomenon underlying the same that said medium must be of cross section much larger than the wavelength of the propagated waves causes the most practical applications of the invention to be restricted to fractional millimeter wavelengths and below into the optical spectrum.

Considering, for example, a cylindrical circular cross section tubular member and internal medium, though waveguides of any other geometry may also be employed, we have shown that, as the frequency increases (or the wavelength decreases), the attenuation characteristics of the waveguide of the present invention become increasingly better than those of an equivalent metallic or conductive-walled waveguide.

Specifically, a copper-walled air-filled waveguide of 0.5 cm. diameter will produce the same 0.73 db./meter attenuation at a wavelength of 0.16 mm. (dominant TE.sub.11 mode) as a similiar-dimensioned air-filled guide constructed in accordance with the invention and having an outer dielectric tube of dielectric constant equal to three (equivalent EM.sub.1 mode). As the wavelength .lambda. decreases, the attenuation constant .alpha. of the waveguide of the invention becomes improved over the attenuation .alpha..sub.m of the metal waveguide at a rate determined by the 5/2 power, as follows:

In the optical range where .lambda.=0.6.mu., for example, the attenuation of the invention is a million times better than that of the shielded waveguide for these EM.sub.1 and TE.sub.11 modes.

Thus, the invention is well adapted to such uses as the optical link in laser communication systems or even as the gas-containing and energy-confining oscillation cavity or container between the mirrors of, for example, a Fabry Perot gas laser oscillator.

Continuing with the illustrative example of circular cross section guides, it has been determined that, unlike prior art guides, there is only a finite number of modes which are confined substantially to the dielectric medium within the dielectric tubular member of the invention to produce the results herein described with, for example, circularly symmetric transverse electric waves, circularly symmetric transverse magnetic waves, and waves of other field components and angular variations of order p, where p is an integer greater than or equal to unity. The number of possible modes thus confined to the inner dielectric medium is dependent upon the material parameters, the order of the angular variation, the wavelength and the radius of the inner cylindrical dielectric medium. When the tubular member radius is many wavelengths in diameter, the approximate root-locations u of the Bessel function J'.sub.o (u) =0 for transverse electric (TE) and transverse magnetic (TM) circularly symmetric waves have been found to be as follows:

u.sub.1 .apprxeq.3.832 for TE.sub.01 ; TM.sub.01 ;

u.sub.2 .apprxeq.7.016 for TE.sub.02 ; TM.sub.02 .

The longitudinal attenuation is found to reach a minimum in the TM case for a loss tangent in the dielectric tube of unity. The depth of penetration of the modes, i.e. the distance of the field into the tubular member for which the fields fall to 1/e of their value at the inner interface with the inner dielectric medium, increases as the dielectric constant of the tubular member approaches that of the inner medium and also as the loss tangent of the tubular member decreases. In fact, there exists a value of loss tangent dielectric constant and frequency for each mode for which the penetration depth actually becomes infinite. This behavior is totally unlike that of the shielded cylindrical dielectric waveguide, through more akin to the cylindrical dielectric waveguide. It has been determined, interestingly, that these modes do not exist, however, when the tubular member becomes a perfect insulator at which the prior art well-known modes will exist and are mainly confined to the tubular member and not the inner medium.

The lossy cylindrical dielectric waveguide herein disclosed is thus readily distinguishable from the metal-shielded cylindrical dielectric waveguide, the cylindrical dielectric rod waveguide, and the dielectric-coated cylindrical metallic waveguide because its tube has a low conductivity and a dielectric constant preferably of the order of 2 or larger. The waves which propagate along such a waveguide , furthermore, have behaviors which distinguish them from those waves associated with such prior art structures; namely, the fields are mainly confined to the region of lesser dielectric constant and the attenuation of the TM circularly symmetric and the EM waves is lowest for a specific value of conductivity and relative dielectric constant of the tube with respect to the inner dielectric medium. The cross-dimensional size of the lossy dielectric waveguide of the invention, in addition, has been determined to be a critical factor in determining the attenuation. Only when the diameter is much larger than a wavelength in the inner dielectric medium is the attenuation low and improved over such prior waveguides.

Theoretical analysis for the guides of the invention have been experimentally verified in the 7.6 to 12 gHz. frequency range. The lossy dielectric finite conductivity tubular member was chosen as a 15 inches i.d., 17 inch o.d. unreinforced concrete pipe with an air-filled dielectric medium. The17 inch cross section of the air medium (of lesser dielectric constant than the value 5.1 of the concrete) is from 11 to 17 times the wavelengths of the above frequency range. The 2-inch thickness of the tubular pipe has been found to be sufficient for the external field at the outer periphery thereof to be negligible with respect to that at the inner periphery, at least an order of magnitude less. Two lengths of pipe were chosen; four sections of 8 ft. pipe (or 32 ft.), and eight sections of 8 ft. pipe (or 64 ft.). Sectoral horns were used for the receiving and transmitting antennae at the ends of the pipe. Several of the above-mentioned excited modes were identified and their attenuation satisfactorily checked with the theory. It was found that the guide offered a 10 db. improvement over the free space transmission between the horns at the same distance, including even the mismatch losses introduced in coupling to the modes.

In connection with such circular cross section guides, moreover, waves of all field components and p angular variations (not just TE or TM), generically referred to herein as EM.sub.p waves, it has been found that the approximate root location of the Bessel function J.sub.o (u)=0 (characterizing the field distribution and phase velocity of the waves as is well known) is

u.sub.1 =2.405 for the EM.sub.1 mode.

Further modifications will occur to those skilled in the art and all such are considered to fall within the spirit and scope of the invention as defined in the appended claims.

Claims

What we claim is:

1. A waveguide for the propagation of electromagnetic waves of wavelengths extending from the millimeter range down through optical wavelengths having, in combination, a tubular member of finite conductivity, of loss tangent substantially unity, and predetermined dielectric constant greater than unity surrounding a medium of dielectric constant less than said predetermined dielectric constant through which electromagnetic waves of one of said wavelengths may propagate, the cross section of said medium being adjusted to a value large compared with said one of said wavelengths, and the thickness of said tubular member being adjusted such that field external thereto is negligible compared with that at the interface between said tubular member and said medium.

2. A waveguide as claimed in claim 1 and in which said medium is a gas.

3. A waveguide as claimed in claim 1 and in which the said cross section is substantially circular and the approximate root locations u of the Bessel Bessel function J'.sub.0 (u)=0 for the following transverse electric and magnetic waves are

u.sub.1 =3.832 for TE.sub.01 and TM.sub.01 modes

and

u.sub.2 =7.016 for TE.sub.02 and TM.sub.02 modes

4. A waveguide as claimed in claim 1 and in which the cross section is substantially circular and the approximate root location u of the Bessel function J.sub.o (u)=0 for EM.sub.1 mode is

u.sub.1 .apprxeq.2.405.

5. A waveguide as claimed in claim 1 and in which said predetermined dielectric constant is substantially equal to at least two.