Analytical description of an imperfect Fabry-Perot etalon
Ivan Prikryl
A new approach using the diffraction method of linear superposition is used for the analytical description
of an imperfect Fabry-Perot etalon. Derived simple relations for the transfer coefficients of a corrugated
thin-film system may find a broader field of application.
1. Introduction
The Fabry-Perot etalon is being used as an extremelypowerful tool in different spectroscopic applicationsrequiring a combination of high resolution and highthroughput.1-12 The higher the requirements forspectral resolution and the fainter the intensity of inputsignal, the more stringent are the requirements on theinstrument performance.13 14
Etalons used to measure fractional shifts in spectrallines or their fractional broadening require very accuratespecification of their transmission functions which areaffected by various defects. Despite recent progress inthe fabrication of high-resolution etalons, there has notbeen evident similar progress in the analytical de-scription of the optical properties. In fact, the mostrecent analytical approach was by Hernandez 15 in1966.
The purpose of this paper is to present a new ana-lytical approach based on application of the diffractionmethod of linear superposition. Preparatory remarksand a discussion of the working assumptions aresubjects of Sec. II. In Sec. III we solve first the problemof diffraction on one corrugated boundary of a finiteaperture thin-film system, and later we extend the in-vestigation to the whole stratified medium. The resultsderived in this section are then used to find the etalontransmission function. Finally, two different alterna-tives for the specification of the instrumental profilefunction associated with two different ways of etalonscanning are presented.
The author is with University of Michigan, Space Physics ResearchLaboratory, Ann Arbor, Michigan 48109.
The input signal illuminating the Fabry-Perot etaloncan be decomposed into its monochromatic compo-nents. In our description we will mostly follow only oneof these components. We will consider this componentto be represented by a spectrum of plane waves with theamplitudes of the plane waves being nonzero onlywithin a small angle (no more than a couple of degrees).To obtain the instrumental profile, we shall supposethat there is the same perturbation function (definedlater) for any wavelength of a narrow frequency spec-trum processed by the etalon.
Further, we will suppose that the effective broadeningof the angular spectrum of plane waves due to diffrac-tion on imperfect and finite surfaces of the Fabry-Perotetalon remains within an angle no larger than a fewdegrees. Strictly speaking, because we have a finiteaperture of the etalon, the resulting angular spectrumcannot be limited. However, the amplitudes of planewaves which propagate outside the above specified anglemay be so small that they can be suppressed. This isclearly justified for any practicable etalon dimension.The surface profile of a Fabry-Perot etalon which ischaracterized by bowing and by surface microstructuresand also by the departure from parallelism can be givenby a functional description of the surface relief. For awell-constructed Fabry-Perot etalon, the scales of thesedefects are mostly of the order of very small fractionsof the wavelength of light, keeping the meaningfulscattering within the angle specified in our assump-tion.
From diffraction grating theory it is a well-known factthat the method of linear superposition (which hasmany parallels in other branches of physics) is adequatefor finding the diffracted field if the grating profile issmooth and shallow.16-19 A more general criterion onthe acceptable ratio between the groove depth andgrating period can be found in Ref. 19. Since all sig-nificant harmonics of the Fourier decomposition of asurface function of the Fabry-Perot etalon clearly ex-ceed the requirements derived for the sinusoidal grating
profile, we can intuitively deduce that the diffractionmethod of linear superposition is suitable for the in-vestigation of our nonperiodical surface profile as well.The Fourier harmonics with smaller periods which arerelated to microstructure, pits, and crests so small thatthey cannot be distinguished by incident light can besuppressed.
Finally, in our approach we will assume that all thelayers of a thin- film reflection coating of the etalon mapthe smooth-and-shallow surface of the substrate. Thismeans that any coating will be supposed to be an equi-distant stratified medium.
Ill. Transfer Coefficients of a Corrugated Thin-FilmSystem
First, let us consider one boundary of a thin-filmsystem where its lateral size is given by the aperturefunction { 1 within the aperture domain
l0 otherwise, (1)
and its profile satisfies the equation
z = g(x,y), (2)
where g(x,y) is the corrugation function. The corru-gation function g(x,y) is defined only over the aperturedomain. It describes any departures of the realboundary from the plane z = 0, which is supposed to bethe plane perpendicular to the optical axis of theFabry-Perot etalon. All the surface defects of theetalon, i.e., surface irregularities, bowing, and depar-tures from parallelism, are included in the corrugationfunction.
A monochromatic field component interacting withthe boundary generally consists of four subfields-theright- and left-going fields on each side of the boundary.In agreement with our working assumption that thecorrugation of the boundary is sufficiently smooth andshallow, we can represent each of the above specifiedsubfields by a spectrum of plane waves. Further, sup-posing the axes of the beams lie at the plane x = 0, wedecompose each plane wave of any spectrum into twowaves: one wave with the electric and one with themagnetic field vector parallel to the real vector x(1,0,0).We will call the former and latter waves the x and ywaves, respectively. Strictly speaking, this decompo-sition can be realized only when the wave normals of theplane waves, real or complex, are parallel with the planex = 0. In such a case, the X and Y waves are in the sand p polarizations with respect to the fictitious planesurface z = 0, respectively. If the wave normal is notparallel with the plane x = 0, our decomposition can bea good approximation only if both real vectors generallydefining the complex wave vector subtend small angleswith the plane x = 0. This requirement is assumed tobe satisfied for all the plane waves whose amplitudes arenot negligibly small.
In practice, the axis of the illuminating beam is usu-ally parallel to the z axis. In this case, our approach willsmear differences between two possible polarizationsif, in addition, small directional variations of the surface
FL
1'
FR
FR
z
FL
Fig. 1. Electromagnetic field on a boundary of the corrugatedthin-film system.
normal can be suppressed. Then it is satisfactory toinvestigate only x or y waves. We will follow bothgroups of waves, extending our approach to the case ofoblique incidence. By using common symbols we willbe able to describe the behavior of both these groupssimultaneously.
Now, let the subscripts R and L denote the charac-teristic parameters of the right- and left-going waves,respectively, and let the quantities belonging behind theoptical surface be provided with a prime as illustratedin Fig. 1. Then, introducing the common symbol F forthe complex amplitude of the electric field of any xplane wave and for the complex amplitude of the mag-netic field of any y plane wave, the eight fields incidenton and reflected from the boundary can be approxi-mated as follows:
x 2ff FR(aR,R) exp[-ikR(aR,R) *r]daRdR,
(3)x (2)2 IfT FL(aL,3 L) exp[-ikL(aL,L) * rdojdL,
(2)2 ff Fi(Cau,3') exp[-ik'R(aR,R) * r]da'rdfl,
x (2 )2 J F(a{LOL) exp[-ik(aL,fl~) r]daY~doL,(4)
where the time-dependent factor expiwt has beensuppressed, r = r(x,y,z) is the position vector, and kR= kR(CaR,3R,YR), kL = kL(aL,L,YL), k -kR(a4,O/,-y), and k = k(a,,y) are the wavevectors. The third component of the wave vector iscomplex if the medium is conducting.
Putting r = r(xy,O) into Eq. (4), the integrals (4) giveus field distributions
xfR(x,y), XL(X,y), R(x,y), xf'L(x,y) (5)
in the plane z = 0. All these distributions have to bespace-limited functions being zero everywhere outsidethe aperture domain. Depending on whether it is the
x or y waves under investigation the functions (5) arethe electric or magnetic fields. All the pairs f(x,y),F(a,3) are the Fourier pairs.
Assuming that the significantly nonzero right-goingplane waves propagate only within a small solid anglearound the wave normals ko(OOoyo) and ko(0,/3,yo),the field distributions on boundary (2) can be approx-imated by the expressions
When the x or y waves are under investigation, all theamplitudes f (x ,y) are the amplitudes of the electric ormagnetic field, Eq. (11) represents the boundary con-dition for the tangential components of the electric ormagnetic fields, and Eq. (12) represents those for thetangential component of the magnetic or electric fields,respectively.
Boundary conditions (11) and (12) have to be satisfiedfor any x ,y. Outside the aperture domain this is auto-matically obeyed because all the functions f (x,y) areequal to zero there. To solve the boundary conditions,let us introduce the modified amplitudes
ORL(XY) = OOY ± YOg(X,Y) [= 7 A g(xy)
0RL(XY) = /OY 7g(XY) [= 2 n'g(x,y)]*
and where the expressions in the brackets are valid oif the axis of the illuminating beam is perpendicularthe plane z = 0. n and n' are the indices of refractiwhich can generally be complex, and X is the wavelentof light in vacuum. Since boundary (2) is supposedhave only very small and smooth surface variations, Isurface normal can be approximated by the unit vecz(0,0,1). This means that expressions (6) can be c:sidered to represent directly the tangential compomnof the electric or magnetic fields depending on whetlthe x or y waves are studied. Further, the tangentcomponents of the magnetic fields for the x wavesthose of the electric fields for the y waves can be w
where 0 signifies convolution, the functions F(a,o) arethe Fourier transforms of f (x,y), i.e.,
her FR(aR,flR) = Jj fR(x,y) expi(aRx + 3Ry)dxdy,tial -
or FL (aL,L) = JJ fL(x,y) expi(aLx + 13Ly)dxdy,
FR(aOR,R) = r fR(x2y) expi(a'Rx + 0'y)dxdy,
(8) Fi(ai,fli) = fi(x,y) expi(a'Lx + O3y)dxdy,
(14)
and the functions G (a4o) are the Fourier transformdefined as follows:
(9)
or the optical impedances
X =- z- ko [ jn2 n l
X'= 2@Z k [no|L (10)
respectively, y = y(0,1,0), c is the velocity of light invacuum, A and ,u' are permeabilities, and the functionskR,L(x,y) and q5R,L(X,y) are defined by Eqs. (7). Theexpressions in the brackets again are valid only for theperpendicular illumination of the etalon. Using Eqs.(6) and (8) we can write the boundary conditions asfollows:
where the unit vectors x and y have been removecSince the functions B(a,3) have to be the FoL
transforms of space-limited functions being zeroerywhere outside the aperture domain, we can sultute the integrations by the summations without loany information if we select the sampling points foisummation separated not more than
(Aa) = 2r/L, and (AO3) = 2r/Ly,
where L. and Ly are the linear dimensions of the a]ture domain. From the knowledge of the functB(a,3) at the sampling points, we can recoverfunctions B(a,/) at any point by using the samptheorem.
Further, to satisfy boundary conditions (16) andfor any x,y, we have to satisfy
aR = L = aR = aL,
3R = L = 3R = L, I
and for convenience we will write a and ,B without sscripts and primes. Conditions (19) can be interprEas the phase boundary conditions. Applying (19conditions (16) and (17), these conditions can be sstituted by the system of two linear equations,
BR(a,) + BL(aq3l) = B(a,O) + B(a,3)
X[BR(a,fl) - BL(aOj) = X'[B(a,fl) - B(aO)J,
which has to be satisfied for each sampling point cThis system can be interpreted as the amplitiboundary condition.
The phase and amplitude boundary conditi(19)-(21) have to be obeyed on each boundary ofthin-film system. The sets of the complex amplituF(a,3) on individual ideally flat boundaries areindependent. If we suppress the angular dependeof the phase shift angles for the plane waves in any tfilm, the obvious phase transformation between Ineighboring boundaries can be written as
FI?,(a,3) = exp(iyohv) FRV+I(a,O),
FL,,(a,O) = exp(-iyoh,) FL,+i (a,O), Jwhere h, is the mechanical thickness of the th t]layer located between vth and (v + 1) boundaries.is yo in the vth thin layer. The relationship of Icomplex amplitudes to the individual boundariesdenoted by the second subscript. Assuming that Icorrugated thin-film system is equidistant, i.e.,
G,?,(a,) = GR,+I(a,O),
GL,(Osa~) = GL.,+l(af), Jthen also
1.trierev-
)sti-singthe
B,(a,f) = exp(iyoh,BR,+l(a,1, |I
BL(aI) = exp(-iTyO,h,)BL,,+l(a,f), |(24)
because the exponential expressions in Eqs. (22) are(18) supposed to be constants.
We can see that the transfer relations (20), (21), andper- (24) for the modified amplitudes B(a,o) are formallyons identical with those for the amplitudes of plane wavesthe going through the ideally plane thin-film system (see,lng for example, Ref. 20). From here we can draw a very(17) useful conclusion: The well-known transfer coeffi-
cients derived in the classical thin-film theory alsodetermine the relations between the modified ampli-
9) tudes of a corrugated equidistant thin-film system.Obviously, if the modified amplitudes represent the
ub- ratios of the electric or magnetic fields, we have to usesub- the transfer coefficients defined as the ratios of the)ted electric or magnetic fields, respectively.to From now on we will be interested only in the outer
3ub- fields of the thin-film system and only in the case whenthe axis of the beam is perpendicular to the system, i.e.,
(20) when ao = 0o, = 0 and yo, = 2rn,/-y. Let us considerthat the corrugated thin-film system is illuminated by
(21) a right-going spectrum of plane waves of known am-TA plitudes FR (a,o) being significant only within a narrow;de angle around axis z, and let FR(a,o) and FL (a,3) be the
unknown amplitudes of the transmitted and reflectedons spectra of plane waves, respectively. Further, let n andthe n' be the indices of refraction of the input and outputdes media, respectively. The corresponding modifiednot amplitudes BR (a,3), BR (a,O), and BL (a,O) are given bynce convolutions (13). Then, in agreement with the pre-
hin viously derived results, we havetwo
(22)
hin
701'Lhe
isthe
(23)
BR(aOI) = tRBR(a2,),
BL (a,) = rRBR (a,),
(25)
(26)
where the coefficients tR and rR are the well-knowntransmission and reflection amplitude coefficients ofthe ideal thin-film system normally illuminated by theright-going plane wave. For our narrow effective spacespectrum, we have suppressed the dependence of tR andrR on a and fl. Applying Eqs. (13), (14), and (15) toEqs. (25) and (26), we can easily find that
Fj (a4,) = tR FR(a,) 0 P{ (aI),
FL(a,3) = rR-(FR(a,O) 0 P% (a,),
(27)
(28)
where the perturbation functions P) (aA) and P) (a,O)are defined by
If the same thin-film system is illuminated by a left-going beam with the known amplitude distributionF(L)(a,o3) instead of FR (,$), we can similarly derive forthe transmitted F(L)(a,O) and reflected F(R)(a,0) am-plitudes
F(L)(a,) = tL * F(L)(a,0) 0 P(L(afi), (31)
F'(R)(a,f) = rL F(L)(a,O) 0 P(L(afi), (32)
where Pt) (a,3) = pt) (a,0, and P) (a,o) is defined byEq. (30), where n is substituted by -n'.
IV. Transmission Function of the Fabry-Perot Etalon
The well-known formula for the transmission coef-ficient tR of an ideal Fabry-Perot sandwich is
tRI * tRii exp -id (33)1 - rLirRIi exp - i24'd
where the transfer coefficients t = t(a,) and r = r(a,o)are furnished with the subscript R or L if they arecomputed for a right- or left-going incident plane wave,and they are furnished with the second subscript I orII if they are related to the reflective coating of the firstor second surface of the thick distance layer. The phaseshift angle lId = 41d(a,o,hd) equals
Id(a,0,hd) = E(a,O) * hd, (34)
where
e= [(2) _ a2 - i2] (35)
and hd is the optical thickness of the distance layer atnormal incidence.
Formula (33) may easily be developed in the infinitegeometric series
allowing for an interpretation in terms of multiple re-flections in the separation layer. In fact, setting upseries (36) by following individual zigzags in the layerand then summing to the closed form (33) is a techniqueoften used. This will also be our way to obtain an ex-pression for the transmission function of an imperfectetalon. Following the individual zigzags of the wholespace spectra, we get for the transmission function tR
= tR(coY,hd) of an imperfect etalon the infinite series
'd = I'd(a,,hd) is given by Eq. (34), and the coeffi-cients tRI, tRI, rRII, and rLI of the ideal thin-film re-flectors are supposed to be constants taken for thenormal incidence. To obtain Eq. (38), we have re-peatedly used Eqs. (27)-(32) denoting nj, n2 nd, andn 3 , the refractive indices of the input medium, distancelayer, and output medium, respectively.
Note that the choice of the number of terms used inEq. (38) depends on the reflectivity of the etalon coatingand on the specific characterization of etalon imper-fections. This choice can be made during a numericalevaluation.
V. Instrumental Profile of the Fabry-Perot Etalon
The instrumental profile function I(X,X') mediatesthe transform between the etalon input (X scale) andoutput (X' scale). We will seek the instrumental profilefunction I(X,X') given by the intensity output for amonochromatic input reevaluated in the X scale throughthe resonance condition for phase angle hId. We will dothis despite the fact that the transmission function (38)and consequently the instrumental profile I(X,X') con-tain a complex dependence on the variables hd, X, a, and/ which affect these functions not only through thephase angle 'd, as would be the case for an ideal etalon.Even if it is quite adequate to consider that the per-turbation functions (39)-(42) remain constant duringan etalon scan, the functional dependence on hd, A, a,and X is more complicated because of the convolutionsin Eq. (38).
Two different definitions of the instrumental profilefunction I(X,X') should be considered in practice. Eachis related to a different kind of etalon scan. One scanvaries the optical thickness hd, and the other varies theviewing angle y/k. Note that, only in in the formercase, the input amplitude distribution FR (a,3) may berepresented by the delta function.
If tR(c,f,hd) is transmission function (38), for themonochromatic input the resulting intensity at a singlepoint (av,/,hd) is
J(a,O,hd) = 2 I tR(a,1,hd) 12, (43)
where the multiplicative factor 2 is due to the two pos-sible polarizations. This intensity distribution (43) is
most often detected by an annular, or in the limitingcase by a circular, detector in the focal plane of a lens.Let p be the inner radius of the annular detector, S bethe constant area of its surface, and f be the focal lengthof the lens. Then the detected intensity as a functionof hd and p is
and k is the wave number in air. To obtain the in-strumental profile function I(X,X'), the evaluated in-tensity function (44) has only to be reevaluated in theX scale. If the optical thickness scan is applied, fol-lowing the current approach we can write for the in-strumental profile
I(AA'= ) = I[hd(X),p = const], (48)
where
hd(X) = hdma 2- e (hdmax 2- hdmax 1), (49)
and if the image-plane scan is used, the instrumentalprofile function can be described by
I(X,X' = ) = I[hd = const,p(X)J, (50)
where
P = Pmax 1 + e(Pmax 2 -Pax ) (51)
In the scale-transform equations (49) and (51), hdmaxiand Pmax , i = 1,2 are the values of hd and p for whichthe functions I(hd, p = const) and I(hd = const, p)evaluated for = reach two sequential maxima. Thevalue e, which is less than unity, is a fractional part ofthe interference order for the wavelength X and hd =hdmax 2 or p = Pmax 1 when thickness or angular scanningis applied, respectively.
Now, it is common procedure to convolve the in-strumental profile I(X,X') with an input intensity dis-tribution L (X) to get the instrumental response L'V) .This is quite justified when all the variable a, , hd, andX appear only in the phase angle 'd. This is not ourcase anymore. In our case the input-output operationhas to be expressed by the general superposition inte-gral
L'(X') = f I(X,X')L(X)dX (52)
rather than by a simple convolution. An imperfectsystem is not -invariant, it is -variant, i.e., differentwavelengths are affected differently by the etalon. Tomodify the computed function I(hd,p) into the instru-mental profile function I(N,X'), we have to also gener-alize relations (48) and (50). We write
I(X,X') = I[hd(X),p(A')] (53)
I(X,X') = I[hd(X'),P(X) (54)
when the optical thickness scanning and angular scan-ning are used, respectively. The function dependencehd (X) and p(X) remains to be approximated by Eqs. (49)and (51).
Finally, note that the function I(hd,p) can be mea-sured experimentally if an etalon is equipped with thepossibility of both kinds of scan. Using a frequency-stabilized laser for illuminating the etalon, we can di-rectly measure the function I(hd,p). The illuminatingbeam should have the same spatial distribution as thedistribution of light intended to be analyzed by theetalon.
VI. Conclusion
A new analytical approach for the investigation ofdifferent defects of the Fabry-Perot etalon has beenpresented. The effects of microsurface imperfections,bowing, and departure from parallelism as well as theeffect of finite aperture of the etalon are incorporatedinto the perturbation function. The detector aperturedoes not affect the transmission function but does affectthe instrumental profile [see Eq. (44)]. Tolerance im-perfections of reflective layers can be incorporated intothe transfer coefficients of a noncorrugated thin-filmsystem. Any defect can be investigated separately orin combination with others by using a proper analyticor numerical simulation of the corrugated function. Inconnection with numerical computation, the proposedmethod enables one to simulate and evaluate differentspecific situations of practical interest.
The derived expressions for the transfer coefficientsof a corrugated equidistant thin-film system may alsobe useful in other branches of applied optics.
The author thanks P. Hays and T. Killeen for theirconcern and for reading the manuscript. This work wascarried out under NASA grant UARS/HRDI 018716 tothe University of Michigan.
References1. J. E. Mack, D. P. McNutt, F. L. Roesler, and R. J. Chabbal, Appl.
Opt. 2, 873 (1963).2. E. B. Armstrong, Planet. Space Sci. 16, 211 (1968).3. M. A. Biondi and W. A. Feibelman, Planet. Space Sci. 16, 431
(1968).4. G. Hernandez, Appl. Opt. 9, 1225 (1970).5. A. Title, Fabry-Perot Interferometers as Narrow Band Optical
13. D. Rees, T. J. Fuller-Rowell, A. Lyons, T. L. Killeen, and P. B.Hays, Appl. Opt. 21, 3896 (1982).
14. T. L. Killeen, P. B. Hays, B. C. Kennedy, and D. Rees, Appl. Opt.21, 3903 (1982).
15. G. Hernandez, Appl. Opt. 5, 1745 (1966).16. R. Petit and M. Cadilhae, C. R. Acad. Sci. 262, 468 (1966).17. R. F. Millar, Proc. Cambridge Philos. Soc. 65, 773 (1969).18. R. F. Millar, Proc. Cambridge Philos. Soc. 69, 175 (1971).19. P. M. van den Berg and J. T. Fokemer, J. Opt. Soc. Am. 69, 27
(1979).20. Z. Knittl, Optics of Thin Films (Wiley, New York, 1976).
proceedings is not subject to all the constraints of refereed journalarticles. In SURFACE STUDIES WITH LASERS, the authors allpreach from tiny pulpits; several times I wished for someone to strideabout on a stage large enough for the topic, waving his arms and in-fecting me with the enthusiasm which I am confident must haveabounded in Mauterndorf's medieval castle.
RICHARD F. HAGLUND
Books continued from page 620
bulk materials. There are also several papers devoted to the principalphysics issue in SERS, namely, the relative roles of electromagneticand charge-transfer mechanisms in SER scattering.
The remaining non-SERS papers are an intriguing miscellany,notably the work on surface-enhanced luminescence and on surfacesecond-harmonic generation, a sensitive technique for detecting ad-sorbed monolayers.
The section on laser surface spectroscopy is a fascinating com-pendium of classical laser spectroscopic techniques applied to sur-faces. These include IR photoacoustic spectroscopy, laser-inducedfluorescence, laser photochemistry, spectral hole-burning in absorbingdyes, lateral (evanescent) wave detection, surface-electric-field-induced Raman scattering, rotational molecular spectroscopy, andBrillouin scattering. A brief catalog of the systems discussed herehints at the many interesting problems of basic and applied researchwhich can be treated by adapting standard spectroscopic tools:catalytic oxidation of NH3 on Pt; water oxidation on semiconductors;Fermi-level pinning on GaAs; surface magnons in epitaxially grownferromagnetic films; and molecular interaction kinetics on surfaces.The physical systems studied are relatively simple and controllable,however, and compared to the problems of the fourth section of thebook, even amenable to simple physical modeling. Hence this sectionreally also merits the title laser surface science.
In contrast, the last group of papers is a mixed bag of topics whichfalls under the general rubric of materials processing using lasers or,say, laser surface technology. These range from photoionization ofboth substrate and adsorbate through photochemistry on surfacesto laser-induced surface damage and laser-catalyzed chemical vapordeposition. The general theme is the use of lasers to mediate or, insome cases, to catalyze processes such as oxidation, annealing, im-plantation, and restructuring; in short, in Boyd's phrase, to do lasermicrochemistry. From the point of view of the nonspecialist, this isin some respects both the most interesting section of the book and theone leaving the most unanswered questions. It is clear that the pro-cesses covered are very complicated, lend themselves poorly tomodeling, and are mostly in the black-art stage. On the other hand,the careful reader will be able to pinpoint areas where further workon surface physics and chemistry may have important ramificationsin technocology.
On the whole, I found the book to be an interesting and informativevolume. It conveys nicely the flavor of a research conference in a newand rapidly expanding field of surface science. The rapidity of itspublication enhances the value of the book and indeed compensatesfor its few shortcomings. The book is certainly to be recommended,both as a souvenir for those who attended the conference and as asummary for those who did not get to Mauterndorf last March.
The only real disappointment I felt in reading the book was the lackof any overview of the topic-a piece or two which would have placedthe necessarily fragmented vignettes of individual research papersinto a broader perspective. Such a comprehensive introduction orconclusion could even have served as a vehicle for speculative or vi-sionary comments on the field, given that publication of conference
Infrared and Millimeter Waves. Edited by KENNETH J.BUTTON. Academic Press, New York. Vol. 8, ElectromagneticWaves in Matter, Part 1, 1983. 435 pp. $65.00. Vol.9, MillimeterComponents and Techniques, Part 1, 1983. 346 pp. $61.00.
Since each chapter in a book of this nature is a survey by an experton a specialized topic, it is impossible to write a composite review ina few words. However, the titles listed below will serve as a guide tothe usefulness of the material for a particular researcher.
Volume 8 contains:Properties of dielectric materials, by G. W. Chantry;Far-infrared spectroscopy on high polymers, by W. F. X. Frank andU. Leute;Submillimeter solid-state physics, by S. Perkowitz;Review of the theory of infrared and far-infrared free-carrier behaviorin semiconductors, by B. Jensen;Review of recent improvements in pyroelectric detectors, by A.Hadni;Cyclotron and Zeeman transitions in photoexcited semiconductorsat far infrared, by T. Ohyama and E. Otsuka;High-temperature infrared reflectivity spectroscopy by scanninginterferometry, by F. Gervais;Millimeter and submillimeter waves interacting with giant atoms(Rydberg states), by P. Goy; andFar-infrared spectroscopy in InAs-GaSb layered structures, by J. C.Maan.
Volume 9 contains:Millimeter-wave communications, by K. Miyauchi;A comparative study of millimeter-wave transmission lines, by TatsuoItoh and Juan Rivera;Dielectric waveguide electrooptic devices, by Marvin B. Klein;Millimeter-wave propagation and remote sensing of the atmosphere;by Edward E. Altshuler;Technology of large radio telescopes for millimeter and submillimeterwavelengths, by J. W. M. Baars;A gyrotron study program, by G. Boucher, P. Boulanger, P.Charbit, G. Faillon, A. Herscovici, E. Kammerer, and G.Mourier;Multimode analysis of quasi-optical gyrotrons and gyroklystrons, byAnders Bondeson, Wallace M. Manheimer, and Edward Ott.
Some earlier volumes of this series have been reviewed in AppliedOptics: Vol. 2: 19, 2821 (1980) Vols. 3-6: 22, 2398 (1983); and Vol.7: 23, 15 Jan. in press (1984).
