Background technology
Rectangular waveguide is a hollow metal tube, and its cross section is a rectangle, is a kind of common electromagnetic transmission structure of microwave, millimeter wave frequency band.Rectangular waveguide is compared with microwave transmission structures such as microstrip line, coaxial lines, has that loss is little, power capacity is big and advantage such as firm in structure.In addition, can also form radio antenna---the slot antenna of a class uniqueness by on rectangular waveguide, cracking.Generally speaking, rectangular waveguide is with a wide range of applications in microwave, millimeter-wave technology field.But rectangular waveguide has a very big shortcoming: the width of rectangular waveguide cross section (suppose width more than or equal to height, down with) must be greater than 1/2nd of transmission electromagnetic wavelength, otherwise electromagnetic wave just can't be propagated in rectangular waveguide.Also can be understood as: the electromagnetic wave of propagating in rectangular waveguide, its operation wavelength must be less than two times of the width of rectangular waveguide cross section (these numerical value be otherwise known as the cut-off wavelength of rectangular waveguide, its corresponding frequency then is called as cut-off frequency).Therefore, the development width is less than the transmission operation wavelength and have important use greater than the electromagnetic miniaturized rectangular waveguide of cut-off wavelength and be worth.
Supernormal medium is a kind of novel artificial composite electromagnetic material that is risen 20 end of the centurys, it has periodic structure, form by the periodic arrangement of supernormal medium construction unit in the space, described supernormal medium construction unit comprises substrate and C type fracture annulus, as shown in Figure 5.Supernormal medium has very special electromagnetic property, and especially the effective dielectric constant of supernormal medium or effective permeability can be negative value.Supernormal medium is owing to possess special electromagnetic property, and supernormal medium is widely used in the performance of improving existing radio frequency, microwave, millimetric wave device, dwindles their volume.2005, people such as Hrabar utilize supernormal medium to realize a kind of rectangular waveguide of miniaturization, as shown in Figure 4, it comprises a hollow rectangle waveguide, and in the inside of rectangular waveguide, place anisotropy supernormal medium construction unit along the central axis of waveguide, and this supernormal medium construction unit perpendicular to the effective permeability component on the waveguide axis direction for negative, the effective permeability component on other direction and the effective dielectric constant component on all directions be on the occasion of.This miniaturized rectangular waveguide can transmit the electromagnetic wave of operation wavelength greater than cut-off wavelength (just operation wavelength is greater than two times of rectangular waveguide cross-sectional width).That is to say that this miniaturization waveguide under 1/2nd the situation of cross-sectional width less than the electromagnetic wave operation wavelength, still can be transmitted electromagnetic wave.Because the cross-sectional width of common waveguide must be greater than 1/2nd of operation wavelength, therefore, this rectangular waveguide is a kind of rectangular waveguide of miniaturization, and it is compared with common waveguide has littler cross-sectional width, but can transmit the electromagnetic wave of same wavelength.
Yet, above-mentioned miniaturized rectangular waveguide based on supernormal medium, a more special place is arranged: electromagnetic wave phase velocity direction therein opposite with the group velocity direction (phase velocity is a negative value, and the electromagnetic wave of Chuan Boing is called as backward wave by this way) aspect transmission characteristic.And for normal rectangular waveguide or other transmission structures (coaxial line, microstrip line etc.) and comprise for most homogeneous mediums of air, electromagnetic wave phase velocity direction therein identical with the group velocity direction (phase velocity be on the occasion of, the electromagnetic wave of Chuan Boing is called as forward wave by this way).Special even so electromagnetic property can make this miniaturized rectangular waveguide bring beyond thought benefit in several applications, but it also can bring very big inconvenience in general traditional application simultaneously.For example, when using this miniaturization waveguide when realizing leaky-wave antenna, this leaky-wave antenna is radiated electromagnetic wave and radiated electromagnetic wave forwards rearward.
Embodiment
Embodiment one: specify present embodiment according to Figure of description, the controlled miniaturized rectangular waveguide of the described a kind of electromagnetic wave phase velocity direction of present embodiment, it comprises a hollow rectangle waveguide 1, a plurality of supernormal medium construction units 2, described miniaturized rectangular waveguide also comprises a plurality of cylindrical control rods 3, each supernormal medium construction unit 2 is positioned at described hollow rectangle waveguide 1 inside, each cylindrical control rod 3 penetrates described hollow rectangle waveguide 1 along the y that is parallel to described hollow rectangle waveguide 1 to axis, and described each cylindrical control rod 3 forms a line to axis along z, the partial fixing of described each cylindrical control rod 3 in described hollow rectangle waveguide 1 has a supernormal medium construction unit 2, described each cylindrical control rod 3 is used for along self cylinder axis rotation, the supernormal medium construction unit 2 that is fixed on described each cylindrical control rod 3 with drive all rotates to x direction or the z direction that is parallel to hollow rectangle waveguide 1, described supernormal medium construction unit 2 is being a negative value perpendicular to the effective permeability component on the direction of described supernormal medium construction unit 2 real estates, the effective permeability component on other direction and the effective dielectric constant component on all directions be on the occasion of, the height of the cross section of hollow rectangle waveguide 1 is less than or equal to the width of described cross section, and described width is less than 1/2nd operation wavelengths.
Embodiment two: specify present embodiment according to Figure of description 2 and 3, when the described supernormal medium construction unit 2 that is fixed on described each cylindrical control rod 3 of present embodiment all rotates to the x direction that is parallel to hollow rectangle waveguide 1, described supernormal medium construction unit 2 is a negative value at the magnetic permeability component of described x direction, in the described hollow rectangle waveguide 1 transmission the electromagnetic wave phase velocity be on the occasion of; If the supernormal medium construction unit 2 that is fixed on described each cylindrical control rod 3 all rotates to the z direction that is parallel to hollow rectangle waveguide 1, then described supernormal medium construction unit 2 the magnetic permeability component of described z direction be on the occasion of, the electromagnetic wave phase velocity of transmission is a negative value in the described hollow rectangle waveguide 1.
The theoretical foundation of present embodiment is:
Suppose that the waveguide axis direction is the z direction, the cross-sectional width direction is the x direction, and short transverse is the y direction, then this moment the supernormal medium construction unit effective permeability
, effective dielectric constant is
At this moment, the electromagnetic field in this rectangular waveguide satisfies the Maxwell equation of no source space
Will
Bring (1) formula into, obtain corresponding scalar equation and be
Mutual substitution just can obtain only relevant with longitudinal field component electromagnetic field expressions with (2b) formula with (2a) formula, shown in (3) formula
For the TE pattern, (3) formula can be reduced to
On the other hand, (1b) formula being updated to (1a) formula can obtain
(5)
(5) formula is launched, can be obtained
(6)
Again (4) formula being updated to (5) formula can obtain
Can utilize the separation of variable to find the solution the above-mentioned differential equation.The result is
(8) formula (4) formula that is updated to just can be obtained filling the field equation in the rectangular waveguide of anisotropy supernormal medium
Can obtain separating of phase constant and find the solution (9) formula
Can reach a conclusion thus:
1. work as
The time, the cut-off frequency of rectangular waveguide disappears, and that is to say, and electromagnetic operation wavelength that waveguide can be propagated and rectangular waveguide size are irrelevant.Simultaneously, because
The time,
And
So this moment, electromagnetic wave is to propagate with the form of forward wave, that is to say that phase velocity is for just in this rectangular waveguide.
2. work as
The cut-off frequency of rectangular waveguide still exists, but opposite with the cut-off frequency effect of normal rectangular waveguide just: the effect of normal rectangular waveguide cut-off frequency is, below cut-off frequency, electromagnetic wave can not be propagated, more than cut-off frequency, electromagnetic wave just can be propagated, so the width of rectangular waveguide must be greater than 1/2nd of operation wavelength; For
The time rectangular waveguide, the effect of its cut-off frequency is, more than cut-off frequency, electromagnetic wave can not be propagated, below cut-off frequency, electromagnetic wave just can be propagated, so therefore the width of rectangular waveguide must realize miniaturization less than 1/2nd of operation wavelength.Simultaneously, because this moment,
With
Set up simultaneously,, that is to say that phase velocity is negative in this rectangular waveguide so electromagnetic wave is to propagate with the form of backward wave.
Embodiment three: specify present embodiment according to Figure of description 2, present embodiment is further specifying embodiment two, be fixed on supernormal medium construction unit 2 on described each cylindrical control rod 3 in the embodiment two when all rotating to the x direction that is parallel to hollow rectangle waveguide 1, described each supernormal medium construction unit 2 becomes to be staggeredly placed along the z direction both sides metallic walls of hollow rectangle waveguide 1.
Embodiment four: present embodiment and embodiment one, two or threes' difference is that the material of the substrate of the described supernormal medium construction unit 2 of present embodiment is a Teflon.
Embodiment five: the difference of any one execution mode is in present embodiment and the embodiment one to four, the height of the substrate of the described supernormal medium construction unit 2 of present embodiment is 12 millimeters, the width of described substrate is 6 millimeters, the thickness of described substrate is 0.7 millimeter, and the relative dielectric constant of described substrate is 2.6.
Embodiment six: the difference of any one execution mode is that the inside radius of the C type fracture annulus of described supernormal medium construction unit 2 is 1 millimeter in present embodiment and the embodiment one to five, the outer radius of described C type fracture annulus is 2 millimeters, and the fracture width of described C type fracture annulus is 0.5 millimeter.
In the present embodiment, opposite in the fracture site of the C type fracture annulus on the substrate two sides of supernormal medium construction unit 2.
Embodiment seven: the difference of any one execution mode is that described each supernormal medium construction unit 2 is divided into two groups and is staggeredly placed along the z direction both sides metallic walls of hollow rectangle waveguide 1 period pitch with 6 millimeters in present embodiment and the embodiment one to six.
Carry out numerical simulation at present embodiment, the numerical simulation result of the transmission coefficient of the described supernormal medium miniaturized rectangular waveguide of acquisition present embodiment can see as shown in Figure 6, a passband occurred about 8.2GHz.Fig. 7 and Fig. 8 have described the effective dielectric constant and the effective permeability of the described supernormal medium miniaturized rectangular waveguide of numerical simulation acquisition respectively, from Fig. 7 and Fig. 8, can see, corresponding near the passband the 8.2GHz among Fig. 6, this moment the effective dielectric constant of described supernormal medium miniaturized rectangular waveguide and magnetic permeability be on the occasion of, that is what, transmit in this supernormal medium miniaturized rectangular waveguide this moment is forward wave (phase velocity is positive electromagnetic wave).