Comb optical interference filter

High total transmission, tunable comb filter structures are described which comprise moderately thick layers of optical material having periodic or multiply periodic refractive index modulation features comprising a multiplicity of coherently-coupled, weakly-resonant optical cavities, resulting in and characterized by spectra of high order (5 or higher) relative to a fundamental (lowest order) cavity resonance, consisting of narrow, moderate to high density reflection lines occurring in one or more sets, each set being characterized by lines equally spaced by wave number if optical dispersion is neglected. Filters of the invention can be structured to be tuned, electro-optically or mechanically such that the peaks within a spectral band of interest shift by one harmonic order and/or from one peak position to the next, to reflect or transmit light of any specific wavelength within a band. The individual features defining optical cavities may be thin compared to a wavelength of interest as, for example, when metal films are used as part of a singly periodic comb filter, or may consist of a section whose thickness is equal to several wavelengths, but which is short compared to a cavity length.

BACKGROUND OF THE INVENTION 
The present invention relates generally to optical comb filters, and more 
particularly to high total transmission, tunable comb filter structures 
comprising moderately thick layers of optical material having periodic or 
multiply periodic refractive index modulation features resulting in a 
multiplicity of coupled, weakly-resonant optical cavities, characterized 
by spectra of high order relative to a fundamental resonance, consisting 
of narrow, moderate to high density reflection lines occurring in one or 
more sets, each set being characterized by lines equally spaced by wave 
number. Filters can be designed to be tuned, electrically or mechanically, 
such that the line peaks within a spectral band of interest shift by one 
harmonic order and/or from one peak position to the next. Thus a filter 
may be tuned to reflect or transmit light of any specific wavelength 
within a band. The individual features defining optical cavities may be 
thin compared to a wavelength of interest as, for example, when metal 
films are used as part of a singly periodic comb filter, or may consist of 
a section whose thickness is equal to several wavelengths. 
For the purposes of describing the invention and defining the scope 
thereof, the term "optical" shall, in accordance with customary usage, be 
defined herein to include only vacuum ultraviolet, ultraviolet, visible, 
near infrared, mid-infrared and far infrared regions of the 
electromagnetic spectrum lying between about 0.01 and 1000 microns. 
An optical comb filter may be defined as a filter whose spectra consists of 
a series of narrow reflection or transmission lines. In structures 
embodied by the present invention, the reflection spectra lines of a set 
are narrower than the spacing between neighboring lines; the spacing 
between line peaks of a set, in wave number units, is determined by the 
optical length of recurring optical cavities of equal optical length; 
cavities of equal length may be adjoining or separated and/or may 
physically overlap cavities of the same or of a different length. 
The comb filter structures according to the present invention may yield 
sets of comb reflection lines whose peak amplitudes are uniform or 
modulated by one or more identifiable envelope functions relating to the 
detailed refractive index modulation of the material within the boundaries 
of the recurring optical cavities. The filters can be structured to 
produce envelope functions in accordance with application requirements. 
There are numerous examples of prior art that are included under the above 
definition of a comb or tunable comb filter which are distinct from the 
present invention in design specifications and spectral characteristics. 
The best known example is a simple Fabry-Perot (F-P) filter, which 
consists of a single optical cavity with highly reflecting boundary 
features which may be metal films or index modulated dielectric films. The 
F-P filter transmits narrow spectral lines and reflects most light 
incident from a spectrally broad collimated source (see Atherton et al, 
"Tunable Fabry-Perot Filters", Opt Eng 20N:6, 806 (1981); Jenkens et al 
"Fundamentals of Optrics, 4th Edition, McGraw Hill, inc. NY, N.Y. (1976); 
Born et al, "Principles of Optics", 3rd Revised Edition, Pergamon Press, 
NY, N.Y. (1965)). Interference filters based on thin film stacks and 
multiple F-P cavities have been described (Dobrowolski in Chapter 8 of the 
Optical Society of America, "Handbook of Optics) Multiple F-P cavity 
filters where the reflectors are moderate to highly reflecting metal films 
are discussed in Dobrowolski, but these are different in structure and 
function than the filters under consideration here. In those cases, 
cavities are F-P type and the spectra of interest are narrow transmission 
lines. This invention pertains to multiple cavity filters in which cavity 
resonances are relatively weak and which filters provide high order 
reflection comb lines and moderate to high total transmission of a broad 
spectral band. 
When a broad band of collimated light is incident on a F-P cavity having 
low absorption, those frequencies which resonate within the cavity, the 
comb spectra, will be transmitted as narrow lines, while the majority of 
the light is reflected. Thus the total transmission of a F-P type comb 
filter is relatively low and the total reflectivity is relatively high, so 
long as the band of incident light is broad compared to the F-P filter 
spectral lines. 
If an optical system requires high throughput of a broad of optical 
frequencies, then a F-P type comb filter may be included only if used in 
reflection; Also, if high transmission of a narrow line source is of 
interest then the F-P filter may be suitable for providing high total 
transmission of such a source. If low total throughput is allowed for a 
band of frequencies then the F-P can be used to block light from most of a 
band while passing one or more narrow lines within the band (that, is F-P 
type filters can be used as moderate to low density reflection filters for 
bands of light between narrow ranges of transmission); however, if a high 
degree of rejection is required, as may the case when using a tunable 
filter to reject a laser line, then the F-P is not a suitable tunable 
filter except when used in reflection. 
The tunable comb filters which are the subject of this invention are 
distinctive in design and construction from the F-P type and capable of 
providing a function that is the opposite of that of the simple F-P type 
and those which are closely related. The filters consist of single or 
multiply periodic index modulation features forming cavities each of which 
is terminated by features presenting low to moderate reflectance of a more 
or less broad range of frequencies. Such a filter may highly reflect one 
or more sets of narrow lines, each line set being equally spaced in 
frequency or wave number (neglecting dispersion, i.e. n.sub.a =constant), 
while transmitting most of a relatively broad band of incident light. Such 
a filter can be used as a transmitting element in systems requiring high 
total throughout of a broad band of collimated light while providing a 
high degree of rejection of any specific in-band spectral line by tuning. 
Another filter type conforming to the above definition of a comb filter, 
which is also distinct from the present design criteria, is a multiline, 
stack, rugate or Bragg type filter. These are not based on moderate to 
high harmonics of optical cavities in that the only significant 
reflections for a particular modulation are the first order (FIG. 4a, 
infra) and occasionally the second order. These filters are most typically 
constructed by stepwise or continuous modulation of the refractive index 
of a film in accordance with a profile resulting from superposing a number 
of individual periodic stepwise or sinusoidal modulations, each of which 
contributes to a specific spectral reflection line (see Gunning, U.S. Pat. 
No. 4,952,025). An alternative approach is to construct the multiline 
filter by laying down a single series of periodically modulated layers 
each having a different modulation period, such that each layer generates 
a specific reflection line (FIG. 4a, infra). These two types may be 
classified as parallel and series constructions, respectively. In at least 
one case it has been recognized that it may be advantageous to construct 
what might be called a parallel-series filter consisting of a 
superposition of two or more short periods with a long period of 
modulation extending through the entire structure wherein different parts 
of the total thickness contain different shorter periods of modulation, 
these parts occurring in series, as in Gunning. The presumed advantage is 
that the reflection lines will have a more nearly common optical density, 
since the optical density of each line of a filter is proportional to the 
number of periods of the corresponding part of the index modulation. The 
widths of the spectral lines for filters of this type are inherently 
broader than those of the cavity filters (see FIGS. 1, 4b and 5, infra) 
according to the invention, so that high total transmission of a broad 
band source cannot be maintained when lines are spaced close enough for 
practical electro-optical tuning from line to line. 
A review of literature on tunable filters has not revealed any filters 
which are alike in design and function to those described herein. Yeh et 
al, "Electrooptic tunable filter structures," in Proceedings SPIE Vol 202 
Active Optical Devices, p-1 (1979), Chang, "Electronically tunable optical 
spectral filters", Optical Engineering, Vol. 20, No. 6, p 805 (1981), and 
Gunning, "Electro-Optically tuned spectral filters: a review," Optical 
Eng. Vol. 20, No. 6, p 837 (1981) review a number of types of tunable or 
cavity filters. Most are not designed to produce comb spectra, and when 
they are it is a line spectra in transmission separated by relatively 
broad regions of reflection. Some of the tunable filters deal with 
producing and or tuning one spectral line; for example, by deforming a 
thin film stack under high pressure to tune the fundamental (lowest order) 
reflection line (Kimura, et al. "Tunable multilayerfilm 
distributed-Bragg-reflector filter", J. Appl. Phys., Vol. 50, No. 3, 
p-1222 (1979)), or inducing index modulation acoustically, (Chang, 
"Acousto-optic tunable filters, Optical Engineering, 20, No. 6, p-824 
(1981); ), Yariv et al, "Optical Waves in Crystals", John Wiley & Sons, 
NY, N.Y. (1984); or by rotating polarization between plane polarizers as 
with the electrical tuning of a stack of birefringent material (Henderson 
et al, "Programmable electro-optic tunable filters", SPIE Vol 202, Active 
Optical Devices, p 16 (1979); Title et al, "Tunable birefringent 
networks", Ibid, p-47)). The filters that involve optical cavities 
exclusively deal with F-P type where cavities are bounded by moderate to 
highly reflecting structures which may be a metal film or a transparent 
dielectric film having a periodic refractive index modulation (Gunning et 
al, "Multiple-cavity infrared electro-optic tunable filter, Ibid p-21; van 
de Stade et al, "Multimirror Fabry-Perot Interferometers, Opt. Soc. Am." 
Vol. 2, No. 8, p 1363 (1985); Jain et al, "Dual tunable Fabry-Perot 
spectrally agile filter", Optical Engineering, Vol. 23, No. 2, p 159 
(1984); and Maeda et al, "Electronically Tunable Liquid-Crystal-Etalon 
Filter for High-Density WDM Systems, IEEE Photonics Tech. Lett. 2, No. 11, 
p-820 (1990)). Some of the filters provide lines that are narrow in 
transmission which occur within a relatively broad reflection band 
associated with the optical period of the cavity boundary index modulation 
(Lytel et al, "Narrowband electrooptic tunable notch filter", Applied 
Optics, Vol. 25, No. 21, p-3889 (1986)). Some of the multiple cavity F-P 
type structures are concerned with the suppression of comb lines and/or 
increasing the free spectral range between transmission lines associated 
with a single F-P cavity, (Gunning et al, van de Stadt et al, and Jain et 
al) while others are concerned with providing interference among cavities 
of slightly different length to broaden a transmission line while 
providing a sharp cutoff in transmission. (Dobrowolski, and van de Stadt) 
Others are concerned with controlling the strength of interference fields 
within a multiple cavity F-P structure in order to increase the 
transmission of a single narrow line by reducing absorption by defects at 
modulation steps. (Southwell et al, U.S. Pat. No. 4,790,634). Still others 
are concerned with employing nonlinear optical material in an F-P optical 
cavity to produce optical bistability. (Miller et al, U.S. Pat. No. 
4,790,634) The construction of singly and multiply periodic cavity filters 
having narrow, moderate to high optical density reflection lines that 
provide moderate to high total transmission of a broad band and provide 
for rapid tuning of reflection lines over a free spectral range according 
to the invention is lacking in the prior art. 
In accordance with a principal feature of the invention, no individual 
feature of a filter of the invention reflects more than 70% at any optical 
wavelength in a band of interest. The peak reflectance R(u,v) and the peak 
reflectance R and optical density D for the comb filters, respectively, 
corresponding to each individual element f(u,v) and group of like elements 
can be derived from the following set of relations, where absorption is 
assumed to be zero (Becker, "Design and Analysis of Optical Comb Filters", 
Tech. Rpt. WRDC-TR-90-4012., AD Number B142749 (1990) at pp 35, 40 and 59, 
and Yariv et al at page 197: 
EQU R(v)=1-T(v)=tanh.sup.2 .PSI.(v) 
EQU D(v)=-log.sub.10 (T(v)) 
EQU D(v)=2 log.sub.10 cos h.PSI.(v) 
EQU .PSI.(v)=U.PSI.(u,v).ident.bm(u,v).DELTA..epsilon./.epsilon..sub.a 
EQU D(v).apprxeq.0.868.PSI.(V)-0.6, .PSI.(v)&gt;&gt;1 
EQU D(v).apprxeq.0.434.PSI..sup.2 (v), .PSI.(v)&lt;&lt;1, 
where b is a constant of order unity and equal to .pi./4 for sinusoidal 
modulation, T is the percent transmission, and D is the optical density, 
the other terms being defined below. 
It is therefore a principal object of the invention to provide an improved 
tunable comb type interference filter. 
It is a further object of the invention to provide a tunable comb filter 
such that reflection lines may be spaced at intervals that permit 
electro-optic tuning by at least one harmonic order, in order to reflect 
(prevent the transmission of) light of any specific frequency within a 
band of interest. 
It is another object of the invention to provide a tunable comb filter 
providing multiple reflection lines such that each neighboring line pair 
associated with an optical cavity of length L.sub.R are separated by a 
spectral difference substantially larger (2 times or more) than the line 
half-widths in order that the total transmission of a broad light band may 
be moderate to high. 
It is another object of the invention to provide a comb filter where the 
peak amplitude of individual or groups of reflection lines is weighted by 
control of the refractive index profile in addition to the refractive 
index excursion. In general such a filter may be described by a series of 
adjacent features each having a distinctive index modulation which is 
repeated at selected intervals, resulting in a series of optical cavities, 
which may overlap spatially and which provide for moderately to strong 
reflection lines as a result of the feature spacings being designed to 
provide constructive (in phase) reflections from a series of identical or 
similar features or cavities. 
These and other objects of the invention will become apparent as a detailed 
description of representative embodiments proceeds. 
SUMMARY OF THE INVENTION 
In accordance with the foregoing principles and objects of the invention, 
high total transmission, tunable comb filter structures are described 
which comprise moderately thick layers of optical material having periodic 
or multiply periodic refractive index modulation comprising a multiplicity 
of coherently coupled, weakly-resonant optical cavities, resulting in and 
characterized by spectra of high order (5 or higher) relative to a 
fundamental (lowest order) cavity resonance, consisting of narrow, 
moderate to high density reflection lines occurring in one or more sets, 
each set being characterized by lines equally spaced by wave number if 
optical dispersion is neglected. Filters can be designed to be tuned, 
electro-optically or mechanically, such that the peaks within a spectral 
band of interest shift by one harmonic order and/or from one peak position 
to the next. Thus a filter may be tuned to reflect or transmit light of 
any specific wavelength within a band. The individual features defining 
optical cavities may be thin compared to a wavelength of interest as, for 
example, when metal films are used as part of a singly periodic comb 
filter, or may consist of a section whose thickness is equal to several 
wavelengths, but which is short compared to a cavity length.

DETAILED DESCRIPTION 
Referring now to the drawings, FIG. 1 shows reflection versus wave number 
for a representative comb filter of the invention showing lines a-g 
equally spaced as a function of wave number. FIGS. 2 and 3 illustrate two 
embodiments of the filter structure according to the teachings of the 
invention, viz, asymmetric simple periodic and multiply periodic cavity 
filters. In FIG. 2, use of higher harmonic resonances of a singly periodic 
modulation of the refractive index of a transparent medium, wherein the 
index modulation period comprises a series of long and short sections, 
which enhance the magnitude of the high harmonics in comparison to equal 
length sections, yields a high total transmission comb filter that may 
have high optical density reflection lines whose amplitudes tend toward a 
constant value, i.e., a spectrum generally similar to that of FIG. 1. Each 
period of this structure may be considered to be an optical cavity capable 
of producing a series of weak resonances determined by the cavity length 
L.sub.R. In FIG. 3, a series of optical cavities each comprise a series of 
short periodic subsections, wherein the modulation and cavity lengths are 
selected to provide interference conditions that result in desired filter 
properties including the position, spacing, width and amplitude of the 
reflection lines; in the simplest case, a series of short periodic 
sections are repeated exactly to form weakly resonant optical cavities of 
equal length wherein each cavity may contain internal modulation which is 
fairly transparent to the stronger resonances of that specific type 
optical cavity. 
Referring now specifically to FIG. 2, shown schematically therein is a 
singly periodic stepwise modulated comb filter 20 of the invention 
providing high total transmission. The value n.sub.i represents the 
refractive index of the substrate or another medium 26 adjacent to the 
filter 20 through which an incident light wave 28 of spatial frequency 
k.sub.o impinges at angle .theta.. Filter 20 comprises layers 22 of 
thickness d.sub.1, and 24 of thickness d.sub.2, in regularly repeated 
layer pairs, represented in FIG. 2 by regions labeled for the different 
respective refractive indices n.sub.1 and n.sub.2 of the layers, and 
defining periodic subsections 25 of length L.sub.R each including a layer 
pair 22,24. The optical length of the cavity (n.sub.1 d.sub.1 +n.sub.2 
d.sub.2) is in this case approximately equal to n.sub.2 d.sub.2 
.congruent.n.sub.2 L.sub.R. The thinner of the layers 22 may have a 
thickness d.sub.1 of the order of a wavelength in the range of interest if 
the material is a dielectric but may need be much thinner if the material 
is a metallic film in order for the film to be moderately transparent. In 
accordance with a principal teaching of the invention, the length n.sub.2 
d.sub.2 is equal to or greater than 5 times longer than n.sub.1 d.sub.1 in 
order to enhance the higher order harmonics of cavity 25. 
Layers 22 may comprise a thin layer of any conducting material such as 
silver, gold, aluminum or indium tin oxide where the layer thickness 
permits no more than about 70% reflection and no more than about 5% 
absorption of wavelengths of interest, or any transparent dielectric 
material such as SiO.sub.2, TiO.sub.2, germanium, silicon or BaTiO.sub.3 
where the thickness is of the order of a wavelength of interest. Layers 24 
may comprise any transparent dielectric material of different index than 
layer 22 including, for example, those just mentioned and LiNbO.sub.3, 
ZnO, 2-methyl-4-nitroaniline (MNA), liquid crystal composite (LCC, liquid 
crystal droplets in a polymer matrix), or elastic material such as 
polystyrene/collodion, applied to or deposited upon a suitable substrate 
or otherwise sandwiched between supporting layers as necessary to provide 
structural support to the filter. The fabrication technique selected for 
depositing filter layers in any disclosed embodiment of the invention 
depends on the wavelength range for which the filter is intended and 
nature of the materials used. From X-ray wavelengths to the mid-infrared, 
vacuum deposition techniques such as MBE, MOCVD, thermal evaporation, 
laser pulse and particle sputtering, spin coating or combinations thereof 
may be used. For mid-infrared and beyond, solid wafers of optical material 
may be polished or otherwise formed to consistent thickness and coated, 
joined or otherwise combined with another material to produce the desired 
layered configuration. If it is required to provide that the resulting 
filter be directly electro-optically tunable, the thicker layers 24 must 
be electro-optically active. Tuning of filters that do not include 
electro-optical materials may be accomplished by mechanical deformation of 
the structure or by angle tuning (tilting). 
Layers 22,24 may be individually homogeneous, with each having a 
characteristic uniform index of refraction, n.sub.1, n.sub.2, 
respectively, or the respective refractive indices may be internally 
modulated as required in order to tailor the comb peak amplitude envelope 
in the spectral range of interest. 
The spectral characteristics of filter 20 shown in FIG. 2 change if the 
filter, shown as regions of refractive index n.sub.1,n.sub.2, is permitted 
to evolve from having equal lengths to highly unequal lengths. If the 
total length of a period 25 remains constant while the length of one of 
the two segments (layer 22) tends toward zero from a condition of equal 
optical lengths (n.sub.1 d.sub.1 =n.sub.2 d.sub.2), the spectral 
characteristic of filter 20 changes from one having a single dominant 
fundamental resonant frequency and subdued harmonics, to a well-define 
uniformly spaced series of resonant frequencies having nearly equal 
strength in the spectral range of interest, provided that the individual 
layers 22 and 24 are not internally modulated. Thus the result of a 
moderate to small amplitude index modulation and several to a large number 
of periods of modulation may be a uniform amplitude comb filter or with 
selected modulation of the shorter layer 22, on the scale of a 
half-wavelength in the wavelength range of interest, the envelope of the 
reflection line peak amplitudes may be caused to peak in the range of 
interest. 
The position and spacing (free spectral range, FSR) of the comb peaks of a 
cavity filter such as those shown in FIGS. 2 and 3 in terms of wavelength, 
wave vector and frequency, respectively, are given by, 
##EQU1## 
where m is an integer, and .lambda..sub.m, k.sub.m and F.sub.m are the 
respective wavelength, wave vector and frequency of the mth harmonic 
referenced to vacuum, n.sub.a is the average refractive index (which 
usually increases with decreasing wavelength in transparent dielectric 
materials), L.sub.R =d.sub.1 +d.sub.2 is the length of one period (one 
cavity), .theta.is the angle of incidence of a light ray to the filter 
normal, and c is the velocity of light. The magnitude of harmonics of the 
fundamental increases as the shape of the periodic modulation departs from 
that which can be fitted by a simple sinusoidal wave form. In the extreme 
case, L.sub.R .congruent.d.sub.2 in FIG. 2, the index modulation consists 
of a series of sharp peaks (delta functions) which results in a reflection 
spectrum (e.g. FIG. 1) comprising a series of sharp lines. 
By selecting L.sub.R and the filter material and/or by manipulating the 
refractive index by alloying materials one can cause comb peaks of the 
order of 100 or less to fall near (within about 0.2% or 0.3% of) the 
wavelength of several selected laser lines in the visible and near 
infrared. For example, by using the wavelength dependent ordinary index 
n.sub.o of LiNbO.sub.3, a polarization independent electro-optically 
tunable filter for angles near .theta.=0 results, where the difference 
between 7 major laser lines and comb lines is less than 0.3% when the free 
spectral range is of the order of 1% and more of the comb line 
wavelengths. Such an arrangement may be beneficial by shortening the 
tuning response time of a filter. Thus the tuning voltage and tuning angle 
may be reduced from a set value, but the maximum voltage or off normal 
angle to be applied to reach any of a set of lines may not be 
substantially reduced unless the nearest comb lines occur to one side of 
the selected lines. (The comb lines shift unidirectionally with electric 
field or angle.) 
FIGS. 4b and 5a and 5b show examples where L.sub.R is selected, with 
n.sub.a independent of wavelength, to cause comb peaks to fall near 
selected spectral lines and to be enhanced in magnitude near those lines. 
In FIG. 5a the envelopes associated with the d(v) show little effect of 
overlap and the strongest comb lines are adjacent to the selected line, 
while in FIGS. 4b and 5b the envelopes associated with the d(v) overlap 
causing comb peaks between the selected lines to be stronger than those 
adjacent to the selected lines. Note that the comb lines of FIG. 4b 
nearest the selected lines have the same optical density as the 
corresponding lines in the series Bragg filter of FIG. 4a. 
Comb line broadening will occur in filters structured according to the 
invention because of imperfect modulation. Some broadening may be 
desirable in cases such as for a comb line to reflect a less restrictive 
range of wavelengths or a less restrictive range of angles at a given 
wavelength. This situation is similar to the case of multiple F-P type 
cavities where cavity spacing is purposely varied from a common value to 
broaden a comb peak while providing a sharp cutoff in transmission, 
(Dobrowolski, and van de Stadt et al). Also, as in the case of multiple 
F-P type cavities, cavities with slightly different L.sub.R values may be 
produced in order to intentionally broaden comb peaks by forming 
overlapping comb sets in the spectral band of interest. 
Referring now to FIG. 3, illustrated schematically therein is a multiple 
cavity, multiply periodic comb filter 30 of the invention. Filter 30 can 
be best described as having a plurality of internally modulated features 
associated with the parameter v, where the modulation is designed to 
provide a desired structure for the amplitude envelope of the comb peaks. 
In some of the simpler cases, the optical cavities C(u,v), which in 
general have individual lengths L(u,v), are all of equal length L.sub.R 
producing a single set of reflecting comb lines, characterized by a peak 
spacing k.sub.n -k.sub.n-1 =.pi./n.sub.a L.sub.R cos .theta. where n.sub.a 
is the average index of the cavities (In this case the cavities differ 
only in the order of the elements f(u,v).) and further characterized by 
comb peak amplitudes as determined by the specific modulation provided the 
filter elements f(u,v) and the spacing between like elements, L.sub.R. A 
general condition of the invention is that L(u,v)=m(v).lambda..sub.m 
(v)/2n.sub.a cos .theta. where m(v) is an integer and .lambda..sub.m (v) 
is the corresponding wavelength, referenced to vacuum, and which if near 
.lambda..sub.o (v), where .lambda..sub.o (v) is the fundamental for the 
modulation unit of length d(v), will be strongly reflected by the filter 
elements associated with the parameter v; this condition ensures that the 
reflections from like filter elements will be in phase. 
In FIG. 3 filter elements f(u,v) are composed of sinusoidal modulation 
producing a reflectance R(u,v) at a characteristic wavelength 
.lambda..sub.o (v), to be defined below, and like subfilter elements have 
equal number of periods M(u,v)=M(v). This need not be the case in general 
but is likely to be the case in most applications. In general each cavity 
of length L(u,v) of filter 30 comprises a series of subfilter elements 
f(u,v) which in turn comprise a small integer number M(u,v) of whole 
modulation periods of length d(v). (These periods may have any form of 
modulation but are most likely to be stepwise or sinusoidally modulated.) 
Each subfilter element f(u,v) has a length s(u,v) given by 
EQU s(u,v)=M(u,v)d(v). 
In special cases, as noted above, s(u,v) may be independent of u. For 
normally incident light, the fundamental (denoted here by the subscript o) 
reflection line frequency F.sub.o and wavelength .lambda..sub.o, F.sub.o 
(v)=c/.lambda..sub.o (v), associated with the subfilter elements f(u,v) 
for all values of u, of filter 30 are derived from, 
EQU .lambda..sub.o (v)=2n.sub.a d(v) cos .theta., 
where n.sub.a is the average refractive index within filter 30, 
d(v)=d.sub.v is the period of modulation of a filter element, .theta. is 
the angle of incidence relative to the normal to filter 30 and c and 
.lambda..sub.o are the wave velocity and wavelength, respectively, in 
vacuum. The filter elements f(u,v) are repeated two or more times, and in 
order that like filter elements contribute most effectively in reflecting 
.lambda..sub.o (v) and its harmonics, it is required that the phase 
spacing between similar elements be a multiple of .pi., or equivalently 
that the physical spacing L(u,v) between similar elements be 
EQU L(u,v)=m(u,v).lambda..sub.o (v)/2n.sub.a 
where m(u,v) is an integer and n.sub.a is the average index, appropriate to 
the wavelength, within the cavity corresponding to the length L(u,v) as 
indicated in FIG. 3. Such a compound filter may consist of a series of 
filter elements: 
EQU f(1,1),f(1,2) . . . f(1,v) . . . f(1,V),f(2,1),f(2,2) . . . f(2,v) . . . 
f(2,V) . . . f(u,1) . . . f(U,V). 
where the f(u,v), v=1 to V, represent short sinusoidal or otherwise simply 
modulated filter elements of length s(u,v)=m(u,v)d(v) consisting of 
periods of length d(v) situated in series. This is illustrated with V=3 in 
FIG. 3. The filter elements having a common v, e.g. v=1, may be identical 
or may have a common subperiod of length d(v) but a different length 
s(u,v) and number of cycles M(u,v). In general, the cavities are taken as 
the space between the origins, and the ends of like filter elements f(u,v) 
and f(u+1,v), which have a common d(v), so that the lengths of these 
cavities L(u,v) are given by the following sequence of sums: 
##EQU2## 
In the special case where s(u,v) is independent of u, s(u,v)=s(v), a 
multiply periodic structure results having a major period of length 
L(u,v)=L.sub.R providing a single set of comb peaks. More generally, if a 
series of cavities formed from subfilter sets is to act cooperatively to 
enhance the reflection amplitude of a set of chosen wave-lengths and 
require a minimum amount of tuning from a set situation, one may select 
wavelength approximately and determine by iterating which periods d(v) and 
wavelengths .lambda..sub.o (v)=2n.sub.a d(v) near the desired wavelengths 
satisfy the condition that all cavities of length: 
EQU L(u,v)=m(u,v)d(v)=m(u,v).lambda..sub.o (v)/2n.sub.a (.lambda..sub.o 
(v)),v=1 to V (2) 
where the m(u,v) are integers. In Eq (2) the fact that n.sub.a is a 
function of .lambda..sub.o is explicitly indicated. 
A special case of interest is where all subfilter elements s(u,v) are equal 
in length or have lengths divisible by a common length, but contain 
different lengths d(v). In this case the filter comb sets have some common 
harmonic frequencies and the fundamental of one set may be a harmonic of 
another. If the product m(u,v)d(v) is the same for all u and v, the filter 
will produce one set of comb lines associated with the length L.sub.R 
=m(u,v)d(v) as is the case for the filters of FIGS. 4b and 5a and 5b. 
The condition imposed by Eq (2) and the requirement that reflections R(u,v) 
from individual subfilter elements f(u,v) be moderate to small, (less than 
70%) results in a filter with moderate to quite narrow reflection lines 
spaced in accordance with Eq (1). A set of comb lines will generally 
result for each distinct cavity length. The relative amplitudes and 
half-widths of the reflection lines are determined by the lengths of 
s(u,v)=M(u,v)d(v), and the magnitude of the modulation 
.epsilon.(u,v,z)=n.sup.2 (u,v,z) along the normal direction z of the 
subperiod elements d(v), and the number of cavities U of each type that 
contribute to the amplitude of a comb peak. When Eq (2) is satisfied, 
connecting the comb peaks may yield an envelope with a maximum occurring 
at or near a characteristic frequency, wave number, or wavelength 
(fundamental or harmonic) of each subfilter element d(v), v=1, V, or 
between when the envelope structure associated with individual subfilter 
elements d(v) overlap (FIGS. 4b, 5a, 5b). The half-width of an envelope 
when uniquely associated with a series of elements containing periods of 
length d(v), depends ideally on the total number and modulation depth of 
these periods. 
In the event that a filter of the invention comprises layers having 
refractive index which is modulated, and if the modulation depths 
.DELTA..epsilon.(z) of the dielectric constant are small compared to the 
average value of the dielectric constant .epsilon..sub.a =n.sub.a.sup.2, 
then the resulting reflection spectrum will approximate the Fourier 
transform of the dielectric profile .epsilon.(z) where z is the normalized 
physical position in the filter. To achieve a given spectrum, the 
dielectric profile is made as close as possible to this Fourier transform. 
In the simplest case, FIGS. 1 and 2, the Fourier transform of a comb 
spectrum is a comb profile. 
A series of filter elements f(u,v), u=1 to U and v=1 to V, according to the 
invention include U not less than 2, no elements f(u,v) having a 
reflection greater than 70% and further meeting the conditions of Eq (2) 
whereby the filters act cooperatively in reflection to provide relatively 
narrow reflection lines separated by relatively broader ranges of 
transmission. Taken in a more general form such a series can be reduced to 
numerous special cavity filter cases found in the literature, which 
include a few f(u,v) at least two of which produce a large reflectance 
(greater than 70%) and by the condition causing destructive interaction 
between selected reflections, that is 
EQU L(u,v)=[m(u,v)+1/2].lambda.(v)/2n.sub.a, 
which yields narrow transmission lines separated by relatively broad 
regions of reflection. By letting U=1 the series f(u,v) may also represent 
an adjacent series of Bragg structures which may be sinusoidally modulated 
as in FIG. 4a or stepwise modulated, or a superimposed set of simple 
modulations referred to earlier as parallel modulation, both of which 
result in relatively broad reflection lines compared to the invention and 
which do not form cavities in the usual sense. 
The foregoing discussion has considered only filters comprising the 
described periodic or multiply periodic layered structure. Ordinarily, 
however, the layered structure is sandwiched between thick supporting 
layers, which may add significant undesired interference effects. These 
interferences are characterized by harmonic resonances conforming to Eq 
(1) with L.sub.R replaced by L, the length of the total filter structure, 
and are affected by the magnitude and abruptness of the transition from 
the average filter index to that of the substrate of other bounding 
medium. The resulting interference effects may be minimized by grading the 
index or adding an intermediate index layer to minimize undesired 
reflections. 
Filters constructed according to the teachings of the invention may be made 
electro-optically tunable by constructing from layers comprising an 
electro-optically active material to which a suitable electric field may 
be imposed, the parameters of which depend upon filter layer material 
selection, and the degree to which peaks in the interference spectrum of 
the filter need be shifted. The degree of tuning is proportional to the 
change in the index n.sub.a (.lambda..sub.m) induced by the applied 
voltage. TABLE 1 provides examples of the material parameters and tuning 
conditions for two uniaxial optical crystalline materials and one 
isotropic liquid crystal composite which might be used to make a tunable 
filter that is polarization independent for normally incident light by 
requiring that the optic axis of the film be normal to the film. These 
specific examples show the field and voltage required to shift a line at 
633 nm by one percent. That is, .DELTA..lambda..sub.m /.lambda..sub.m 
=.DELTA.n.sub.o /n.sub.o =0.01. (Here n.sub.o is equivalent of n.sub.a in 
the general development and is used to denote the ordinary index of the 
uniaxial material.) The filter thickness and distance between electrodes 
is assumed to be 100 microns which might include 5 to 20 typical cavities 
of the invention. The appropriate linear electro-optic (Pockels) formula, 
.DELTA.n.sub.o =-n.sub.o.sup.3 r.sub.13 E/2 and quadratic electro-optical 
(Kerr) formula, (n.sub.e -n.sub.o)=K.lambda.E.sup.2 and data are from 
Yariv et al, supra, and from Sansone et al. ("Large Kerr effects in 
transparent encapsulated liquid crystals", J. Appl. Phys. 67, No. 9 4253 
(1990)). Also used is the relation that n-n.sub.o =(n.sub.e -n.sub.o)/3 
where n is the index for the unpoled encapsulated isotropic liquid crystal 
material. The K value for the encapsulated liquid crystal composite (LCC) 
material is assumed to be 5000 times that of CS.sub.2, which corresponds 
to a suitably transparent (nonscattering) material. The symbols used here 
are n.sub.o the ordinary refractive index where the material is uniaxial 
or becomes uniaxial under the applied external field, E=V.sub.a /L, where 
V.sub.a is the applied voltage and L is the total length of the filter and 
also the distance between electrodes; r.sub.13 is a linear electro-optic 
coefficient, and K is the quadratic electro-optic coefficient for an 
isotropic Kerr material with index n at the wavelength .lambda.=633 nm. 
Here n.sub.o and n correspond to n.sub.a, the average index for the 
modulated structure used in earlier discussion. The point of Table I is to 
show that direct tuning of electro-optic materials with high voltages 
provides only small shifts in comb filter lines, so that comb lines need 
to be narrow and closely spaced or positioned close to laser source lines 
in order to tune electro-optically to and reflect the line. Even if 
voltages were made higher than indicated in TABLE I, one may find that the 
electro-optic effect saturates as in an example case of the LCC where 
n.sub.e -n.sub.o saturates at 0.055 (see Sansone et al). 
TABLE I 
______________________________________ 
r.sub.13 E V.sub.a 
Material N.sub.o (pm/v) (Mv/cm) 
(kv) 
______________________________________ 
LiNBO3 2.286 9.6 3.98 39.8 
Ba.sub..25 Sr.sub..75 Nb.sub.2 O.sub.6 
2.3117 67 0.594 5.94 
______________________________________ 
K E V.sub.a 
Material n (pm/v.sup.2) 
(Mv/cm) 
(kv) 
______________________________________ 
LCC 1.597 159 0.173 1.73 
______________________________________ 
A filter of the invention may also be tuned electro-optically by using an 
elastically deformable material and a means of applying pressure such as a 
piezoelectric crystal. Still another method which permits larger shifts in 
comb peaks is angle tuning. The relative change can be determined by 
simply noting from Eq (1) that (.lambda..sub.2 
-.lambda..sub.1)/.lambda..sub.1 =(cos .theta..sub.2 -cos 
.theta..sub.1)/cos .theta..sub.1 ; the shift d.lambda./d.theta. goes as 
sin .theta. so is smallest near .theta.=0. 
The invention therefore provides an improved tunable comb type optical 
interference filter. It is understood that modifications to the invention 
may be made as might occur to one skilled in the field of the invention 
within the scope of the appended claims. All embodiments contemplated 
hereunder which achieve the objects of the invention have therefore not 
been shown in complete detail. Other embodiments may be developed without 
departing from the spirit of the invention or from the scope of the 
appended claims.