1 2
PERIODIC DIELECTRIC WAVEGUIDE FILTER The invention, and its mode of operation, will be
more fully understood from the following detailed deCROSS-REFERENCE TO RELATED scription, when read in conjunction with the drawing,
in which:
DESCRIPTION OF THE DRAWING
BACKGROUND OF THE INVENTION
This application is a continuation-in-part of our co- 5 pending application Ser. No. 282,205, filed Aug. 21, 1972, and entitled, "Lossless Optical Band-Pass Fil- FIG. 1 is a partially diagramrnatic, partially crosster," which applicatin was a continuation-in-part of ap- sectional view of an optical waveguide, according to plication Ser. No. 236,090, filed Mar. 20, 1972, both the invention;
now abandoned. This application is assigned to the 10 FIG. 2 is a cross-sectional view showing the optical same assignee as the instant invention. waveguide of FIG. 1 in more detail;
FIG. 3 is a graph showing the normalized dispersion curve of the waveguide of FIGS. 1 and 2 for a propagat
1. Field of the Invention • ing mode;
Broadly speaking, this invention relates to optical de- 15 FIG. 4 is a partially diagrammatic, partially crossvices. More particularly, in a preferred embodiment, sectional view of a portion of the optical waveguide of this invention relates to an optical waveguide which ex- FIGS. 1 and 2, used as a band-pass filter and illustrating hibits a continuous filtering action, advantageous for one method of adjusting the band pass thereof; the suppression of unwanted frequencies which may be FIG. S is a partially diagrammatic, partially cross
present in the optical signal propagating through the 20 sectionai view Qf the optical filter of FIG. 4 illustrating guide. another method of adjusting the band pass thereof;
In another embodiment of the invention, a discrete, p\Q 6 is a cross-sectional view of another embodioptical band-pass filter is fabricated from a section of ment of tne invention in which the index of refraction the waveguide which, if desired, may be tuned by the Gf tne waveguide substrate varies periodically, rather application of external energy to the waveguide. 25 {han the optical layer itself.
2. Discussion of the Prior Art FIGS 7 and g are graphs depicting triangular and The recent invention of the laser has led to the devel- square wave index of refraction variations, respec
opment of optical communication systems which are tively;
essentially analogs of established radio-frequency sys- FIGS 9> 10 and n are isometric views of another terns, except that the optical systems are far superior in 30 embodiment of the invention which utilized fiber opterms of system bandwidth. There thus exist optical an- tjcs. and
alogs of such well-known electrical devices as wave- FJG 12 is a partiaily schematic, partially diagramguides, coaxial cables, etc., as well as of discrete de- matic view of an optical communications system, acvices, such as amplifiers, modulators, and band-pass fil- ^ cording to the invention.
As is well known, in radio-frequency communica- DETAILED DESCRIPTION OF THE INVENTION
tions systems, it is frequently necessary to take steps to nG x jllustrates a portion of an optical waveguide
eliminate undesired propagation modes and to filter according to the invention, as well as the typical oper
out unwanted frequency components which are gener- ating environment therefor. As shown, optical waveated as the radio-frequency signal is amplified and "guide 10 comprises a substrate 11, e.g., of glass, having
propagated along the system. a uniform index of refaction n, overlaid with a layer of
Because the power density which is found in a typical optica, material 12, e.g. of glass, having a spatially varylaser communication system may run as high as one ing index of refraction nr. The device is assumed to be million watts per square centimeter, optical wave- located in a medium, such as air, having an index of reguides, and discrete optical band-pass filters, which fraction ^ M .g we„ knQwn for waveguide 10 to func. rely on absorption to provide filtering action, are not tjon as a waveguide; it is necessary that n > „o and n, really practicable. Non-absorptive filters, which filter >
by reflection, are of course known, but such filters are Turning momentarily to FIG. 2, the waveguide 10 is bulk devices and, hence, noncompatible with inte- 5Q depicted in more detail. As previousiy stated, the index
grated optics. of refraction n, of substrate 11 is uniform, but the index
SUMMARY OF THE INVENTION of refraction n, of layer 12 varies periodically. The
, ,, _ index of refraction n of a material can also be expressed
As a solution to this, and other problems, a first em- jn terms of {he jca, dielectric constant e of the mate.
bodiment of the invention comprises an optical device 55 rial> where £ = „2 The Q ica, dielectric constant of including a layer of optical material having a periodic, ,ayer ,2 ... sinusoidal, a, tne principa, axis spatial variation in the index of refraction thereof. In a abQut sQme mean ... accordi tQ the formula; second embodiment of the invention, the optical material is overlaid on a substrate of uniform index of refraction to thereby form an optical waveguide. In a "\ third embodiment of the invention, the index of refrac- < = "i'="', + 2S"2 cos \ d z / (1 > tion of the optical material is uniform, but the index of refraction of the underlying substrate varies in a peri- where,
odic manner. e = the optical dielectric constant at any point in opti
In still further embodiments of the invention, the 65 cal layer 12;
waveguide is a fiber-optic device with either the core, nf= The index of refraction of optical layer 12;
or the surrounding cladding, exhibiting aperiodic index n,2 = the mean value of the optical dielectric con
of refraction variation. stant of optical layer 12;
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25„2 = the amplitude in the sinusoidal variation in the for the p'th mode, and /3p is the wave number for the optical dielectric constant; mode in the guide. The ordinate of the curve, W=d/K,
d = the period of the variation in the optical dielec- is the normalized frequency of the light, where d is the trie constant; and periodicity of the optical dielectric constant variations.
z = the displacement along the direction of propaga- 5 FIG. 3 was plotted for a TE mode, from theoretical caltion. culations, on the assumption that n, = 1.4, n„ — 1.0, and
Now, in accordance with well-known optical theory, w, = 2.5 with an amplitude of optical dielectric constant substrate 11, optical layer 12 and the overlying medium 2Sx„x = 1.28. As can be seen from FIG. 3, for W <0.05 together form an optical waveguide. If the index of re- the curve does not exist. Hence, there will be no propafraction of layer 12 were uniform, light energy which 10 gation at these frequencies. For 0.05 <W —0.23 the was coupled into the waveguide would propagate curve exists, and propagation through the guide will octherealong and could be coupled out at any point along cur. For 0.23 < W < 0.26 the curve again does not exist the guide, typically, the other end thereof, provided, of and there will be no propagation, but for 0.26< W< course, that the frequency of the light source was suffi- 0.29 the curve reappears and propagation will once ciently high so that the wavelength X of the light was 15 more take place. For HO-0.29 the curve again does not less than some predetermined maximum value, above exist and propagation will not take place, which the waveguide is incapable of sustaining propa- The regions of propagation are defined by the exisgation. This upper propagation limit is determined, es- tence of confined space harmonics of all orders. When sentially, by the asymmetric geometry and indices of the transverse decay constant of the first space harthe device. 20 monic becomes imaginary or complex, propagation
On the other hand, if the index of refraction of opti- through the guide is no longer possible. The first order cal layer 12 is not uniform, but varies spatially, accord- space harmonic becomes confined for d > X/(«fp — n,), ing to the relationship set forth in Equation (1), then where nep is the effective index of refraction of the light propagation through the waveguide will not take place of the p'the mode in the guide, and is equal to if the inequality d < X/(«„ + n,) is not satisfied. Ac- 25 X^/2irOther space harmonics, at these periodicities, cordingly, if light is introduced into the waveguide hav- are not confined, but their effect on propagation is less ing a wavelength less than the lower propagation limit, significant than that of first space harmonic scattering, the light will not be transmitted through the waveguide It should be appreciated that by properly adjusting
but will, rather, be deflected out of optical layer 12 into the parameters, for example, Sn, the amplitude of the the atmosphere. In other words, light having a wave- 30 sinusoidal variation in the optical dielectric constant, length which exceeds the upper limit, or which falls the region between the propagating regions of FIG. 3 below the lower limit, will not propagate through the may be made arbitrarily small. Thus, the waveguide acwaveguide, and the waveguide will act, therefore, as a cording to this invention can function equally as well as true band-pass filter. a stop-band filter of arbitrary non-passing filtering re
Returning now to FIG. 1, and an illustrative environ- 35 gion. ment for the invention, light of wavelength X] from a The waveguide shown in FIGS. 1 and 2, or more first optical source 13, for example, a continuous wave practically a band-pass filter comprising a portion of laser, is directed into optical-summing device 14, then- the waveguide, may be tuned by altering the periodicity ce, via a coupling device 15, into filter 10. Coupling de- of the variation in the index of refraction of layer 12. vice 15 may comprise any of several known devices, for 40 This may be accomplished by any of several known example, a prism, optical grating, lens, etc., etc. At the techniques. For example, in FIG. 4 the variation in the same time, light of wavelength Xj from a second optical index of refraction is initially effected by creating an source 17 and light of a wavelength X3 from a third opti- interference pattern on the surface of optical layer 12. cal source 18 are also directed into optical element 14, The interference pattern may be generated by splitting thence, via coupling device 15, into filter 1Q. It is as- 45 the output of a laser 22 by means of a beam splitter 23 sumed, in this example, that the wavelength Xt of and a pair of prisms or mirrors 24 and 25, and then sisource 13 lies above the long-wavelength cut-off point multaneously impinging the optical layer 12 with the that is present in any asymmetric optical waveguide, two beams, as shown. The mutual interference between including the waveguide of this invention. Accordingly, ^ the two laser beams will create an interference pattern this light will not propagate through the filter. It is fur- on the surface of the optical layer and, if the guide mather assumed that X3, the wavelength of light source 18, terial is of the type whose refractive index may be alis shorter than the minimum wavelength which can tered by incident radiant energy, in the places where propagate through filter 10, that is to say, kj(nrp + n,) the light from the two sources is reinforced, the index < d, where d is the periodicity of the variation in the 5J of refraction of the optical layer 12 will be altered. In index of refraction in optical layer 12. Accordingly, the essence, this is a holographic technique and the differlight from source 18 will be deflected out of the optical ence in path length of the two beams must be less than layer 12 to impinge upon some suitable blocking device the coherence length. Correspondingly, where the light 19, for example, a black metal heat sink, which will ab- from the two sources cancels out, the index of refracsorb, or harmlessly dissipate, the radiant energy. Thus, 6Q tion will be unaltered, the net effect being to create a if Xi, the wavelength of light from source 17, lies be- spatial variation in the index of refraction in the directween the upper and lower propagation limits of filter tion of propagation along the waveguide. This spatial 10, this light will be propagated through the filter to uti- variation may be permanent or temporary, depending lization device 21, which may comprise, for example, upon the material of the waveguide. For example, if the an optical detector, or other similar device. 6j material is a dichromated gelatin or a photoresist, the
FIG. 3 depicts the normalized dispersion curve of a variation may be permanently recorded. Some "permawaveguide according to this invention. The abscissa of nent" materials may also be erased, to redefine a new the curve, Bp = fipdl2ir, is the normalized wave number pattern, if desired.
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Accordingly, to the invention, the periodicity of a dif- In this latter regard, it should be noted that the term
fraction pattern produced by this technique, and "substrate," as used in the specification and claims,
hence, the periodicity of the spatial index variation, should not be given its strict literal meaning as it is in
may be altered by changing the angle at which the two tended to encompass, for example, the core or cladding
beams impinge upon the surface of optical layer 12, or 5 of a fiber-optic waveguide, as well as the planar support
by changing the frequency of the laser, or by a combi- of a planar waveguide.
nation of these factors. This will cause the "dark" For example, as shown in FIG. 9, the waveguide acbands in the diffraction pattern to move further apart, cording to this invention may comprise a fiber-optic deor closer together, as the case may be, thereby produc- vice 40 including a central core 41 and a layer of clading a corresponding variation in the periodicity of the '0 ding 42. By analogy to the embodiment of the invention index of refraction variation in the underlying optical shown in FIGS. 1-8, a periodic variation in the index material. of refraction of the cladding 42 (or of the core 41) is FIG. 5 illustrates yet another technique for altering induced and, as a result, the fiber-optic device will exthe periodicity of the variations. This technique com- hibit the same filtering properties as the aboveprises attaching, for example by bonding, an ultrasonic 15 described devices.
transducer 26, to one edge of optical layer 12. The FIG. 10, for example, depicts a periodic variation in
transducer must, of course, be connected to some suit- the index of refraction of the core 41, while the clad
able source of energizing potential, such as a.c. source ding 42 has a uniform index of refraction.
27. The acoustic vibrations from transducer 26 will ere- FIG. 11 illustrates yet another embodiment of the in
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ate a standing wave in optical layer 12 which, in accor- vention in which fiber-optic device 50 comprises a cendance with well-known principles, will selectively alter tral core 51 and a cladding layer 52. As in the example the index of refraction of the layer. The periodicity of of FIG. 9, there is a periodic index of refraction variathe change in the index of refraction may be altered by tion in cladding layer 52, in the direction of propagaaltering the periodicity of the standing wave. This, in 25 tion, but in addition, a radial index of refraction graditurn, may be effected by altering the frequency of ener- ent, which may be either in the cladding or the core, gizing source 27. As shown in FIG. 11, the waveguide, with filtering ac
For those applications where it is less important to tion, may be used, as a normal waveguide might be vary the band-pass of the filter, the variations in the used, in a communications system, rather than a filter index of refraction of optical layer 12 may be perma- 30 per se. In this respect, it is analogous to a helical millinently effected by other techniques, for example, by meter waveguide in that, as the optical energy travels selectively bombarding the optical layer with ions from along the guide, any spurious or unwanted frequency an ion generator, selective metal ion exchange, etc. components present in the optical signal will be sup
It will also be apparent to one skilled in the art that pressed continuously. Further, such a waveguide may periodic variations in the index of refraction of the 35 be used for phase-matching purposes by varying either waveguide comprising the substrate 11, the layer 12, the amplitude or periodicity, or both, of the variation and the overlying medium can comprise periodically in the optical dielectric constant. Phase matching is esindenting or corrugating the surface of the layer 12. sential for the efficiency of certain processes, such as Of course, it is entirely possible to maintain a uniform frequency conversion, modulation, coupling between index of refraction in the material of the waveguide and 40 two or more waveguides, etc. etc. Either the planar to provide a periodic variation in the index of refrac- waveguide of FIGS. 1-8 or the fiber-optic waveguides tion of the substrate. FIG. 6 shows such an arrange- of FIGS. 9-11 may be employed, but for inter-city use, ment. The mathematical analysis is entirely analogous the fiber-optic guides are preferred, to that previously given and the performance of the fil- In the example shown in FIG. 12, light from a laser ter is similar to that of the previous embodiments. It 45 61 is passed through an optical modulator 62, thence, should be noted that, from a practical point of view, to an optical waveguide 63 comprising a central core only the region of the substrate where the evanescent 64 and one (or more) layers of optic cladding 66, or no waves of the field in the optical layer exist need to be cladding. As previously discussed, either central core periodically varied. This region will constitute only the 64 or cladding 66 can have a periodic variation in the uppermost part of the substrate, next to the optical 50 index of refraction. Laser 61 and modulator 62 are layer. connected to some suitable power supply 68, and all
While the embodiments described above contem- are located in a central office at some first location. At plate a periodic variation in the index of refraction that the distant end, the optical waveguide 63 is connected is characterized by a sinusoidal variation in the optical to some suitable optical demodulator 67 which in turn dielectric constant, the invention is not so limited. For 55 is connected to a utilization device 69, for example, a example, as shown in FIGS. 7 and 8, respectively, the telephone carrier channel bank. One or more optical optical dielectric constant could be caused to change amplifiers 71 may be positioned in the optical path of in a triangular wave fashion or in a square wave fash- waveguide 63 to amplify the optical signal which will, ion, but from a practical standpoint, such variations are ^ of course, be attenuated as it travels along the wavemuch more difficult to induce than a sinusoidal varia- guide. Because waveguide 63 acts as a filter, similar to tion. that disclosed above with reference to FIGS. 1-8, spuri
Further, the examples given above deal with planar ous or unwanted frequency components in the optical geometry but one skilled in the art will appreciate that signal will be eliminated, or attenuated to such a low a similar analysis may be performed on nonplanar con- 6J level that from a practical standpoint they can be igfigurations. Thus, the invention may equally well be nored. Such unwanted components may be generated, employed with square, circular rod and fiber-optic ge- for example, by non-linearities in the optical path, such ometries. as the waveguide itself, or the optical amplifiers 71.
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