DE1924994B2 - Dielectric wave rider - Google Patents

Description

is chosen, where λ is the wavelength of the optical wave energy in free space, characterized in that the other cross-sectional dimension (t) of the guide strip (10, 20, 42) in a direction ( Fig. 3: yX in which the refractive index ( m; π (1 -Δ)) of the materials (11, 12; 21, 26; 43, 44) on both sides of the guide strip (10, 20, 42) is different, is chosen so that it only has the fundamental waveform of each of leads two orthogonally polarized waveform families, and that the material (12, 26, 44) arranged along a surface (13, 22) of the guide strip (10, 20, 42) lying parallel to the cross-sectional dimension ic is selected so that it is the fundamental waveform of one of the both waveform families suppressed.

2. Dielectric waveguide according to claim 1, characterized in that the material (12, 26, 44) for suppressing the fundamental waveform at the frequency of the optical wave energy has a higher refractive index (n \) than the guide strip (10, 20, 42).

3. Dielectric waveguide according to claim 2, characterized in that the material (12, 26, 44) is a metal.

4. Dielectric waveguide according to claim 2, characterized in that the material (12, 26, 44) is lossy.

The invention relates to a dielectric waveguide for the transmission of optical wave energy of only one waveform with an elongated, low-loss dielectric guide strip with the refractive index η, which has an essentially rectangular cross section, is embedded in a low-loss dielectric base with a smaller refractive index and whose one cross-sectional dimension w in one direction, in which the refractive index of the base on both sides of the guide strip has the same value η (\ - Δ) (Δ = positive number <1), according to the relationship

is chosen, where λ is the wavelength of the optical wave energy in free space.

When transmitting electromagnetic waves via a waveguide or another waveguide It is well known that energy is characterized by one or more waveforms or characteristics Field patterns can spread, depending on the cross-sectional dimension and the Shape of the respective waveguide and the operating frequency. Typically applies to any given Frequency that the larger the cross-sectional dimensions

ίο of the waveguide, the greater the number of waveforms. Normally, it is desirable to limit the propagation to a certain waveform, since its propagation properties are favorable for the specific application, and since propagation with more than one waveform leads to energy loss , conversion-reverse conversion distortion and other disturbing influences.
If the desired waveform just the so-called dominant waveform and the wavelength of the electromagnetic energy are large enough, there are no difficulties in restricting the cross-sectional dimensions of the waveguide so that no other waveforms can be guided besides the dominant waveform. However, this means cannot be used if the desired waveform is not the dominant waveform or if a waveguide with a larger cross section is used to reduce it

jo the attenuation or prescribed for other reasons is. Such oversized waveguides (multimode waveguides) can inherently have more than one Pass on the waveform and therefore lead to disturbances. In such cases one must therefore

j5 pass over more complicated waveguides, for example a helical waveguide.

The development of the optical maser (laser) as a source of coherent radiation at optical wavelengths has greatly increased the problems of conducting electromagnetic wave energy. Because of the exceptionally small wavelengths, none of the methods considered above has so far become practical Aid for a transmission with good efficiency led.

v-, In a known dielectric waveguide of the type mentioned ("Optical Waveguide of Macroscopic Dimensions in Single Mode Operation" by RA Kaplan in the journal "Proceedings of the Institute of Electrical and Electronic Engineers", August

5 (i 1963 and an article »Single-Mode-Guide Laser Components «by E.R. Schineller in the magazine »Microwaves«, January 1968) is said to be through a special By dimensioning the thickness of the waveguide, the propagation can be limited to the fundamental waveform. in the The known arrangement has a transparent dielectric as an embedded guide strip Medium in the form of a liquid between two closely spaced glass plates, whose Refractive index is slightly larger than that of the liquid.

bo The thickness of the liquid layer is measured according to the given relationship for w , but the width is undefined.

Further study of this type of waveguide has shown that the properties of such

b5 Arrangement with regard to the guidance of the waveforms are more complicated than indicated in the above-mentioned articles.

The invention is based on the finding that a

dielectric waveguide can lead pairs of orthogonally polarized waveform families and that discontinuities and other imperfections in the waveguide are coupling and therefore coupling Conversion between the orthogonally polarized waveform families as well as between the Fundamental waveform and the higher waveforms of the same polarization. if So a dielectric waveguide should really only carry a single waveform, must be taken care of be that in addition to the higher order waveforms for the same polarization, the waveforms of the "orthogonal polarization are not guided. The aforementioned known waveguide with a plate-shaped layer of undefined width is therefore at most theoretically, but not in in practice a waveguide for only a single waveform, since the discontinuities and other imperfections are always transformed into the orthogonally polarized waveform families cause.

The invention is therefore based on the object to provide a dielectric waveguide that has a Transmission with only a single waveform in the narrow sense, i.e. not with a pair of Forms of oscillation made possible.

To solve this problem, the invention is based on a dielectric waveguide of the type mentioned and is characterized in that the other cross-sectional dimension of the guide strip in a direction in which the refractive index of the materials is different on both sides of the guide strip is chosen so that it only guides the fundamental waveform of each of two orthogonally polarized waveform families, and that the material arranged along a surface of the guide strip lying parallel to the cross-sectional dimension w is selected so that it suppresses the fundamental waveform of one of the two waveform families

In this way, the guide strip only transmits the fundamental waveform of one polarization direction, even if imperfections in the leader strip per se lead to a transformation into the orthogonal polarized fundamental waveform could take place. As explained in more detail below is, but there is the necessary requirement to dimension the guide strip so that at least the fundamental waveform of both orthogonal polarization directions can be guided, of which then one is suppressed.

The sizing relationships for the other Cross-sectional dimensions are detailed below, taking into account the respective circumstances treated.

The use of a coating of waveguides is known (US-PS 33 50 654). In one case it will a waveguide with a cylindrical core of a cladding made of a material of smaller size Refractive index than that of the core, and on the clad there is a coating of one light-absorbing, opaque material. In another case, instead of the cylindrical Core used a thin plate, which on both sides layers of a material with smaller Index of refraction than that of the plate, followed by a coating of light absorbent material. By suitable choice of the thickness of the core or the thin plate, a waveform selection should be made take place, namely for the core in two mutually perpendicular planes and for the thin plate in one Level in such a way that only one waveform is guided. However, even in the case of the thin plate again a pair of orthogonal waveforms occur. The light-absorbing coating cushions in both cases all unwanted light energy and prevents exit or entry into

in the waveguide, is therefore in a mode selection not involved

If the difference between the refractive indices of the guide strip and the base is very small, the Guide strips according to the invention by many sizes

ij orders greater than the wavelength of the guided Being energy in free space and still only transmits one form of vibration. If desired, the Dimensions of the guide strip but also the wavelength of the guided energy in free space

.'ο be made comparable. The only limitation on the minimum dimensions of the guide strip results from the method used to manufacture the waveguide.
Developments of the invention are the subject of

j) subclaims.

In the drawings shows

F i g. 1 an optical system with a dielectric waveguide,
F i g. 2 a first embodiment of a dielectric

in see waveguide according to the invention,

F i g. 3 and 6 to 11 for explanation dielectric waveguide and the magnetic field distribution along two mutually perpendicular directions across the direction of propagation,

i'i Fig.4 the influence on the field distribution Placing a high admittance material near one side of the waveguide strip,

Fig.5 shows an alternative embodiment of the Invention.

• 4 (1 The following explanation is based on the leadership optical waves including wave energy in the infrared, visible and ultraviolet parts of the Frequency spectrum directed. Accordingly, FIG. 1 shows an optical system with a source 1 for optical

4 ") wave energy and a lens system 2, which consists of of the source 1 emitted wave energy onto one end of a dielectric waveguide 3 as follows focused on the type to be described more precisely.

At the output end of the waveguide 3, a focused

"> (i second lens system 4 from waveguide 3 incoming energy to a consumer 5.

F i g. 2 shows a first embodiment of a dielectric waveguide 3 according to the invention a transparent (low-loss) dielectric

v-, strip 10 with the refractive index π, which is embedded in a second transparent dielectric material 11 with a somewhat smaller refractive index π (1 - Δ).

Here, Δ is a positive number smaller than 1.

Along the free (upper) side of the strip 11 and

bo in contact with this is a layer of a third Material 12 arranged, the properties of which will be explained in more detail below.

To explain and to simplify the mathematical calculations, the strip 10 is with

shown with a rectangular cross-section. The guide strip will only have an essentially rectangular cross-section. In general, the cross-sectional shape of the strip 10 depends on the particular manufacturing process.

proceed from. Typically, the edges of the Strip either be rounded, whereby the cross-section assumes a more elliptical shape, or the edges will be irregular. In addition, the refractive index will typically not change change suddenly, but slowly from one value in one dielectric material to a second value in pass over to an adjacent material. Despite these deviations from the ideal shape, the Operation of the waveguide the principles under consideration, and the actual dimensions of the The strips correspond essentially, if not exactly, to the dimensions defined below.

Before further elucidating the invention, a few general remarks on the field distribution in a dielectric waveguide which contains mutually different dielectric materials should be useful. Accordingly, Figs. 3 and 6 to 11 have been added for explanation. F i g. 3 shows the cross section of a dielectric waveguide which has a guide strip 20 which is embedded in a substrate 21 with a somewhat lower dielectric constant. For the following description, the upper surface of the strip 20 is shown in contact with a material 26 whose refractive index n \ is less than that of the strip 20 and the backing 21. For example, the material 26 can be air for which / Ji = 1.

Quite generally, the waveforms propagating along the strip 20 are characterized by electrical and magnetic field distributions which have components in the direction of propagation and in two mutually perpendicular directions transverse to the direction of propagation. However, if only the main field components are considered, the waveforms can expediently be divided into two families, the electric fields of which are polarized in two mutually perpendicular directions at right angles to the direction of propagation. In Fig. 3, one of these directions, which runs perpendicular to the strip-air interface 22, is denoted by the y-direction, and the other direction, which runs parallel to said interface, is denoted by the x- direction.

6 to 8 show qualitatively the magnetic field distributions of the three lowest order waveforms for both families of waveforms that a strip of width w can carry. F i g. 9 shows the waveform of the next higher order, which is shown for explanation as a vanishing or non-guided waveform.

In principle, each of the waveforms for both families of orthogonally polarized waveforms is characterized by a sinusoidal field distribution within the guide strip 20 for both the x and y directions and by an exponentially decreasing field strength in the substrate 21 and the surrounding air G. 6, the waveform EHoq of the lowest order is characterized by a sinusoidal field profile 30 within the strip 20 in the x-direction with less than half a guide wavelength, a guide wavelength λ _χ for the waveform of the Oth order in the A 'direction being given by

}. _x = 2w Tl
L.

ί2Δ

and by exponentially decreasing field distributions 31 and 32 in the base 21. Because of the symmetry the arrangement to the y-directional axis, the amplitude of the field distribution is symmetrical with respect to the center of the waveguide.

"i The field distribution in the det / direction shown in FIG. 10 (for which q = 0) is similar to the field distribution in the x-direction, since it has a sinusoidally changing region 70 and exponentially regions 71 and 72 the dielectric materia

in lines above and below the guide strip 2C are different, the field distribution in the y-direction is not symmetrical with respect to the center de; Strip 20.

Instead, there is a shift in the direction of the material with the higher dielectric constant, which is shown in FIG. 3, the material of the substrate 21 is This can be seen clearly in Fig. 10, in which the peak amplitude of the sinusoidal portion displaced dei field distribution 70 in the direction toward the boundary surface 22 between the guide strip and the base and correspondingly from the interface 2i between the guide strips and Air is displaced. The exponentially decreasing parts 71 and 7i of the field distribution are accordingly different. A larger part of the electromagnetic wave energy is in the substrate and a smaller part is in the air.

So that each waveform can be guided, the guide strip 20 must have the field distributions dei

jo respective waveform can lead both along the x- ah as well as the y-direction. Assuming materials with the same magnetic permeability, this is realized when both the slope (first derivative) and the amplitude of the sinusoidal

j5 and exponential magnetic fields at the interface between the guide strip 20 and the surrounding materials are the same. This is clearly true for each of the field distributions in FIGS. 6 and 10. As a result, the fundamental waveform EHoo for both families can be guided and passed on in front of orthogonally polarized waveforms in front of strips 20.

A similar case is for the waveforms of the two next higher orders (EH \ _q and Efyq) in FIG . 7 and 8 shown. In both cases one hits

• o 'sinusoidally changing field distribution (40 and 50) within the strip 20 exponential field distributions (41, 42 and 51, 52) with the correct amplitude and slope.
Similarly, the order of the waveforms that can be guided along the y-direction is limited by the thickness f of the guide strip. By way of illustration, it is assumed that the guide strip is too thin to guide any higher order waveform. Consequently, the waveform is of the next higher order (EHp ι) along the y-direction in FIG. 11 at the interface 23 is shown discontinuously and accordingly disappearing. For the purpose of explanation, each of the guided oscillation forms EHoq, EH \ _q and EHi is represented by a field distribution in the x-direction according to FIG. 6, 7 and 8 show a field distribution in the y-direction according to FIG. 10 In this case, 9 = 0.

For the in F i g. 9 waveform EHz ₉ isi

the guide strip 20 is too narrow, and an increasing field distribution 61 and 62 at each boundary surface 22 and 23 makes it impossible to satisfy the condition that a guided waveform has the same slope The result is a coupled waveform

or some higher order waveform is not guided along the strip 20, but spreads over the entire substrate. Such a waveform is called a vanishing waveform

From the above explanation it follows that for a waveform that is to be guided, the guide strip must be large enough to be able to accommodate the required field distribution in two mutually perpendicular transverse directions. This also means that the waveguide carries at least the fundamental waveform for each of the two orthogonally polarized waveform families. Therefore, without any special precautions, a dielectric waveguide cannot be a wave guide for only a single waveform. In contrast, the higher-order waveforms can easily be suppressed by restricting the cross-sectional dimensions of the guide strip. In particular, the width w and the thickness ι of the guide strip for the waveguide described above result for the restriction to the fundamental waveforms

15th

20th

0 <w <

2m 1

(2)

+ tan

- (t) 'ψ

2 \ n ²

2.-7 "

> t

25th

30th

tan

- 1

2.-7 η

\ T \

(3) Equations (2) and (3) given limits so that the wave energy is better held within the guide strip. Then the waveguide can with be bent with a smaller radius of curvature, the manufacturing tolerances can be increased and the handling of the wave energy can be done with greater efficiency.

After the dimensions of the guide strip have been limited so that it can only guide the fundamental waveforms, means are provided to suppress one of the two orthogonally polarized waveforms and prevent propagation to realize only one form of oscillation. To do this, a layer of lossy material is placed in Made contact with a surface of the leader strip. Layer 12 in FIG. 2 consists of one Material that is lossy in the frequency range of interest For the waveform whose electric field primarily perpendicular to the interface 13 between the strip 10 and the Lossy material runs, the energy losses through the layer 12 are relatively low. For however, the waveform which is primarily polarized parallel to the interface 13 is the losses considerable, and this waveform is substantially suppressed

In an alternative embodiment of the invention, instead of an im substantial lossy material made from a material that has a very high characteristic admittance that is relevant to the Frequency is about an order of magnitude above the characteristic admittance of the waveguide

Since the admittance of any material is not given by

Y =

For those cases in which it ² - nf > 2 in ² , equation (3) is reduced to

3 /.

Λη \ ΙΪΛ

4m 12 T

(4)

whereby /. the wavelength of the energy in free space is.

From equation (2) it can be seen that theoretically there is no lower limit for the width of the guide strip This is due to the symmetry of the in F i g. 6 field distribution shown, which always gives the possibility that the slope of the sinusoidal and exponentially changing magnetic fields at the interfaces is the same for each strip width, on the other hand, the thickness of the guide strip is determined by the Fact affects that the field distribution is not symmetrical, and if it is smaller than that by the 55 Equation (3) given width is made, the field conditions at the interface 23 is not satisfied

If the guide strip is completely embedded in the substrate, then π equals ii \ - Δ \ and equation (3) reduces to equation (2), so that

I ω / ι where

g is the conductance

ε is the dielectric constant ω is the angular frequency and μ is the permeability

a high admittance can be achieved either by a high conductance or a high dielectric constant. However, in some materials, such as metals, these parameters become complex and change as a function of frequency. Since there is no convenient way of separating them, the parameter N, which is a complex "index of refraction," is defined for the material as

IU) f

where Co is the dielectric constant of free space

2nf2Ä

>t> 0.

(5)

65

Advantageously, the width and thickness become large made in accordance with the The arrangement of a material of high admittance along the guide strip has the effect of changing the field distributions along the direction for the two differently polarized waveforms so that the undesired waveform disappears while the desired waveform is continued. This is in FIG. 4, where the magnetic field distribution along the ^ direction for the x- and ^ polarized waveforms is shown. If the admittance of layer 12 is significantly greater than that of the guide strip, the magnetic field strength for the x-polarized waveform at interface 13 in essential

Chen zero. It increases sinusoidally and, if the strip thickness is less than '/' of a guide wavelength, a guide wavelength X _y in the y-direction being given by

(8th)

π / 2Vl

so the field strength increases and reaches a maximum at the interface 14. Since the slope of the field strength increases within the strip 10, while the slope in the base 11 decreases, the The condition with regard to the same slope at the interface 14 is not satisfied, and the waveform disappears

For the. For the limit case in which N = oo, the field has a maximum at the interface 13. In all other cases, however, the condition with regard to the same slope at both interfaces can be satisfied, and the y-polarized wave is continued

The attenuation per unit of length for the y-polarized wave results from:

(/ 2l

in

material low loss Refractive index 40 low loss π (1-Δ) 41 low loss π {ί-Δ ') 42 low loss π 43 lossy π (ί-Δ) 44

(9)

where Im means the imaginary part of the term in brackets

Equation (9) shows that the damping of the preferred waveform decreases with increasing N. The material of the layer 12 therefore preferably has a very large admittance at the frequency of interest. As an example, a metal whose admittance at the frequency of interest is an order of magnitude higher than that of the waveguide is preferably used

In the embodiment of Fig.2 the guide strip 10 is partially in a substrate 21 with a uniform refractive index n - embedded However, since the transverse dimensions w and t of the guide strip from the difference in refractive index between the strip and the surrounding medium depend, can (l 4) a larger range of dimensional ratios of the strip can be realized with the aid of the arrangement shown in FIG.

In this embodiment of the invention that is Material 40 and 41 of the pad along the f-dimension of the strip 42 is not the same as the material 43 along the ^ dimensions of the strip 42.

Let us explain a number of different ones Consider arrangements that are described below.

Arrangement 1

IO

Equations (2) and (3) give the maximum aspect ratio for this arrangement

\ * / max

2 tan

2 \ n ²

(10) Arrangement 2

For the case in which πι = n (l - Δ) , d. That is, materials 43 and 44 are the same, both w and t are given by equations in the form of equation (2). In this case, there is no lower limit to the thickness of the strip 42, and the aspect ratio becomes extremely large. However, both w and t are advantageously chosen to be as large as possible. In this case, the dimensional ratio is given by

Arrangement 3

In the case where the material 44 has a high refractive index n n , the thickness t must be less than ¹ Å of a guide wavelength, and the aspect ratio for maximum wound is given by

It is found that for each of the arrangements, the dimensional ratio by changing the ratio nisses ΔΙΔ ' can be changed.

Two more details of the dielectric waveguide were examined. The first property relates to those dimensions of the waveguide that allow a minimum radius of curvature. The second Property concerns those dimensions of the waveguide which for a given transmission power to the highest electric field strength within of the strip. The latter property is always important when nonlinear processes,

4s, for example, modulation, frequency doubling or other parametric operations are to be carried out.

If Wm _1x and im «the maximum permissible strip cross-sectional dimensions of a certain shaft are conductor arrangement for operation with a single waveform, the optimal width ηό _ρ ι and the optimal thickness topi for the minimum radius of curvature result in:

Arrangement 1 / ι ² - η \> 2. Iw ²

(a) for curvatures about the y-axis w _opl «0.68w _times

(b) for curvatures about the x-axis

^L apt

»0.60t"

Arrangement 2 n, = η (1 - / I) (a) for curvatures about the y-axis w _ap , «0.68W ₁₁₁₁₁₁

(13)

(14)

(15)

b) for curvatures around the .x axis

t _opl * 0.68 t _max . order 3 H ₁ » η

[a) for curvatures around the y-axis w _opl * 0.68 w _max

(16)

(17)

(b) Door curvatures about the x-axis

t. "* 0.60 r,""(18)

Consistent with this, the dimensions for maximum field strength are the same as that in each case dimensions given above for minimum curvature. To achieve maximum electric field strength optimal values are therefore obtained for both dimensions of the strip simultaneously for each waveguide type in the manner described.

For this purpose 3 sheets of drawings

Claims (1)

Patent claims: 1.Dielectric waveguide for the transmission of optical wave energy of only one waveform with an elongated, low-loss dielectric guide strip with the refractive index η, which has an essentially rectangular cross-section, is embedded in a low-loss dielectric base with a smaller refractive index and whose one cross-sectional dimension w in a direction in which the refractive index of the base on both sides of the guide strip has the same value π (1 -Δ) {Δ = positive number <1), according to the relationship