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Information on the analysis of phonon dispersion curves in a crystal, specifically in the crystal Nal. the identification of various phonon branches due to the relatively large separation of the frequency dispersion curves. It also mentions that for certain particular values of s, the answer to a question about the absorption vertices for S^ (1) can be seen.
Typology: Lecture notes
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Marshall S. Sparks, et al
Xonics, Incorporated
Prepares for: A d v a n C e d Research Projects Agency Defense Supply Service
6 December 1973
5285 Port Royal Road, Springfield Va. 22151
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Unclassified Sfcunly Clas?\ficalion (^) //A ZZ£ZL2CZL 1 ORIGIN SfrufKy rl«5»ifir«fiun at mit, bujy ol^ DOCUMENT CONTROL DATA »hslrmil and mdrMuie jmu.Kfu.n must^ hr k 4 D antrrrd whrn Ihr wen,!! rrpurl is clasailledl Xonics,^ »T1NC^ Incorporated »CT.VITY^ (Corpur.l.^ mulhor,^ ~^ RJ^ HEPORT^ 5ECUH.T^ I^ C L A 1%, F , c A T I ON 6837 Hayvenhurst Avenue 1 REPORT Van Nuys, T( TLE^ California^91406
lb. GROUP^ Unclassified N/A THEORETICAL STUDIES OF HIGH-POWER INFRARED WINDOW MATERIALS 4 UEJCRlPTive NOTES _(Typ ol report_* and inclusive dalet) » Au TMOR(S) fF(r«t n«in»,^ Second Technical Report, _middl Initial,_*^ la at name) 30 June 1973 through 6 December 1973 Marshall S. Sparks, C. J. Duthler
- REPORT 6 Decemoer 1973 DATE •a CONTRACT OR GRANT NO 6.^ DAHCi5-73-C-0127 PROJEC T NO
7a. TOTALAL 2gf N(^N^ (^) OF PAGES 76. NO OF REFS 184 9a. ORIGINATOR'S REPORT NUMBERISI
»t OTHER this report) REPORT NOISI (Any other number! that may be aealtned ARPA Order No 1969, Amendment No. 1 istribu^ifEy an^hol^J^oRY' wi^^pecific prior approval/asWngton, D, II SUPPLEMENTARY NOTES Sponsored by Advanced Research ProjectsAgency 13 ABSTRACT
12 SPONSORING MILI TARY ACTIVITY Defense Supply Service - Washington Room ID245, The Pentagon Washington, D. C. 20310 Theory indicates that concentrations of less than 0.1 ppm of NO2 , HCO3, SO4', and Cr04 , which are molecular ions that substitute for the halide ion, yield an absorption coefficient ß > 10"^4 cm"^1 at 10. 6(im. Predicted temperature dependences are given. Divalent ions added to strengthen alkali halides should not give rise to measurable (ß^W^crn^1 ) absorption, with two possible exceptions. The known result of no correlation between Pb2+concentration and ß is shown to be the result expected. The U center is the only known impurity in alkali halides with localized vibrational mode -.ufficiently close to 10. ö^m to cause noticeable absorption. Absorp tion in the far high-frequency wings of various impurity-absorption resonances should be im- portant. Molecular and macroscopic surface absorption, electronic states in the band gap in both semiconductor and alkali-halide crystals, and absorption by electrical carriers and electronic absorption are potentially important. Electronic levels with small spacing have already been ob served to give rise to 1R absorption. Material fat'ure from absorption by macroscopic inclu- sions, electrical breakdown of dirty air, stimulated scattering processes, and electron avalanch* breakdown occur at typical breakdown intensities as low as 10", 10^7 , 10^8 , and 10inW/cm^2 , re- spectively. Parametric instabilities of phonons, self focusing, multiphoton absorption, and elec- trostrictive defocusing are shown to have higher breakdown intensities. An explanation of laser damage cone-shaped surface pits in terms of absorption by inclusions is proposed. Parametric instabilities of phonons are predicted to be observable at the Reststrahl resonance and in Ramar scattering. Values of the total power 0 that a window can transmit under specified conditions are calculated for use as figures of merit for window materials. For continuous operation, large-diameter D > Dpp windows should be face cooled, but small-diameter windows may be edge cooled, and & often decreases as the diameter D increases. For pulsed operation, 9
Secunly Classification
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rW ■ l,l^ ' '" '" " •" ■ ■ '" ",l^ ■ " ■ .iii.ii. i IM «V^H THEORETICAL STUDIES OF HIGH-PüWER INFRARED WINl^OW MATERIALS M. Sparks, Principal Investigator, 213/787- C. J. Duthler, Principal Scientist, 213/787- Xonics, Incorporated Van Nuys, California 91406 Second Technical Report 6 December 1973 v ■ Contract No. DAHC15-73-C-Ü Effective Date of Contract: 7 December 1972 Contract Expiration Date: 6 December 1974 Prepared for Defense Supply Service - Washington, D. C, Sponsored by Advanced Research Projects Agency ARPA Order No. 1969, Amendment No. 1; Program Code No.3D This research was supported by the Advanced Research Projects Agency of the Department of Defense and was monitored by the Defense Supply Service-Washington, D.C. under Contract No. DAHC15-73-C-0127. The views and conclusions contained in Ulis document are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of the Advanced Research Projects Agency or the U. S. Government.
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Preface vu Summary 1 A. Introduction B. Extrinsic Absorption 13 I. Introduction 14 II. Classification 15 III. Macroscopic Inclusions 16 IV. Molecules in Anion Sites 16 V. VibraLional Abstrption by Point Imperfections 16 VI. Absorption in the Far Wings of Extrinsic Lines 17 VII. Absorption from Surface Effects 20 VIII. Electrical-Carrier and Electronic Absorption 21 IX. Stress-Induced 10. 6^im Absorption 22 C. Extrinsic Absorption in 10. 6^m Laser Window Materials Due to Molecular-Ion Impurities 26 I. Introduction 27 II. Impurity Spectra 29 III. Temperature Dependence 34 IV. Discussion 36 D. Very High-Intensity Effects 41 E. Explanation of Laser-Damage Cone-Shaped Surface Pits 47 I'. Nonlinear Infrared Absorption from Parametric Instabilities of Phonons ^ I. Introduction 61 II. Two-Phonon Instability 65
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TABLE OF CONTENTS (Cont'd)
III. Application to the Study of Multiphonon Absorption for the Case of a Morse Potential IV. Results and Discussion^208 L, Vertex Corrections for Multiphonon Absorption 229 M. Negligible Intrinsic-Absorption Processes N. Summary of Publications and Results Appendix: Simple Pendulum Instability 2sn•**'
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LIST OF ILLUSTRATIONS Title ££££ Absorption in KC Schematic illustration of the added absorption from U centers in KC1 19 Sketch of inclusion of radius a at a distance d below the plane surface ** Tensile stresses and cone half-angle as function of inclusion depth " Cone-producing fracture for crack nucleaiion at inclusion surface and at plane surface 5S Two-phonon processes 62 Increase of the pair amplitude with increasing nf.... 70 High-order two-phonon output processes 78 Enhanced relaxation frequency of the fund nental mode (nf < ncm )^87 Dependence of fundamental mode amplitude on incident intensity 89 A chain of parametric processes ^ Enhanced relaxation for phonons Q to phonons Q' when nQ -• "n ^^6 Schematic illustration of the time dependence of the amplitude nf of the fundamental mode 99 m-phonon processes » Parametric excitation of m phonons 106 Spectral transmittanct of a thin film schematically illustrating the broadening of the reson-prc at high values of incident intensity **
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This Second Technical Report desciihes the work performed on Contract DAHC15-73-C-0127 on Theoretical Studies of High-Power Infrared Window Materials during the period from June 30, 1^73 through December 6, 1973. The work on the present contract |j a continuation of that of the previous Contract DAHCl!S-72-C-0129. The following investigators contributed to thu leport: Mr. H. C. Chow, research associate Dr. C. J. Duthler, principal research scientist Dr. A. M. Karo, consultant, Lawrence Livermore Laboratory, Livermore, California Dr. A. A. Maradudin, cons tltant. University of California, Irvine, California Dr. D. L. Mills, consultant. University of California, Irvine, California Dr. L. J. Sham, consultant. University of California, San Diego, California Dr. M. Sparks, principal investigator The material in this report constitutes the final results on the subjects covered. Previously reported results are not repeated in the preset report. However, the list of publications and summary of results in Sec. N include all publications and results of this and the prcvicas contract. The brief overviews in the Introduction (Sec. A) and in the general sections B on Extrinsic Absorption Processes and D on Very High-Intensity Effects also mention previous work. As of the present date, the emphasis of the program will be on ultraviolet materials.
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TM. summary covers the material presented in the present report only. An overview of the complete program is given in Sec. A. and the list of publica- tions and outline of results in Sec. N cover the previous investigations as well as those of the present report. Extrinsic Absorption. It is proposed that an important class of impurities limiting infrared transmission in alkali-halide laser-window materials are mole- cular-ion impurities that substitute for the halide ion in these crystals. Evidence is found from a survey of the experimental literature that concentrations of less than 0. ippm of No'. HCO^. So]', and Cro]' will yield an absorption coeffi- cient ß greater than lO^cm"^1 at 10. 6,um. Predicted temperature dependences of impurity-limited ß (10.6Mm) are: T^1 '^6. temperature independent, and de- creasing 9 with increasing temperature depending on the particular ionic im- purity. A theoretical analysis suggests that divalent ions added to alkali halides to strengthen them should not give rise to measurable (ß - lO^cm"^1 ) absorption. Two possible exceptions, which are believed to be unlikely in general, are that a divalent ion could activate another impurity or that the added ions could have elec- tronic levels that are very closely spaced. TUe negative experimental result of no correlation between Pb2+^ concentration and 10.6Mm absorption in alkali halides is shown to be the result expected. The U center is the only known impurity in alkali halides that has a localized vibrational mode sufficiently close to 10.6^ to cause noticeable absorption. Ab- sorption in the f.r high-frequency wing (a« » *ves ) of the impurity-absorption
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An explanation of laser-damage cone-shaped surface pits is proposed. An anisotropic, quasistatic stress distribution is found in the material surround- ing an absorbing inclusion of a radius a centered a distance d below the surface of a transparent host. Maximum tensile stress greater than the pressure at the inclusion-host interface occurs at the angle em = cos" (a/d) from the line join- ing the inclusion center to the surface, resulting in cone-shaped fracture. Nonlinear infrared absorption from parametric instabilities of phonons is con- sidered in detail, and is shown to be negligible in the low-absorption region of expo- nential frequency dependence of the optical absorption coefficient ß. However, it is observable at the Reststrahl resonance and in Raman scattering. At low intensity, the transmission T curve is independent of intensity, as usual, but at high intensity, the T(w) curve broadens and the transmission at resonance increases. The time constant for the approach to the steady state is important since the steady s ce is not attained in short laser pulses in important cases in which long-lived phonons give rise to low steady-state threshold intensities for anomalous absorption. The threshold for the parametric instability is quite sharp when considered as a func- tion of the amplitude of the fundamental phonon, but smooth when considered as a function of the incident laser intensity. In contrast to a previously accepted result, even crystals, such as NaCl, having a center of inversion could have anomalously low thresholds since the threshold is controlled by the phonon (in the pair> having the longer lifetime. Chain instabiuties and enhanced relaxation from mutual inter- action of excited pair phonons are negligible for the phonon instabilities, in contrast to previous results for plasmas and parallel pumping in ferromagnetic resonance, respectively. The method of calculation, using Boson occupation numbers rather
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than mode amplitudes, has the simpUcity and power to allow us to obtain more information about parametric instabilities, including effects above the threshold, than has been possible previously. High-Power 2-6 qm and 10. 6 um Window-Material Figures of Merit with Edge Cooling and Surface Absorption Included. Values of the total power 9 that a window can transmit under specified conditions are calculated for use as figures of merit for window materials. New features of the figures of merit are: consideration of edge as well as face cooling, treatment of surface as well as bulk absorption, use of 9 rather than intensity as the figure of merit, effects of improving materials and calculation for 3. 8 and 5. 25 qm as well as 10. öqm. New results include the following: For continuous operation, large-diameter window i should be face cooled, but small-diameter windows may be edge cooled, and 9 often decreases as the di- ameter D increases. For pulsed operation, 9 increases as D increases, as intui- tively expected. Values of the diameter DEF, abo/e which face cooling should be used, are surprisingly large, ranging between 7 and 100 cm, typically. For pulsed operation and for D > DEF in cw operation, 9 is independent of thermal conduc- tivity K, while for D < Dgj, in cw operation, ^ <x K. For small-diameter win- dows, the high temperature at the center of the window may limit the value of 9 and the theoretical thickness may be I ireasonably small. The alkaline-earth fluorides have the greatest figures of merit for large- diameter windows in the 2-6jim range, with ^ = 76 MW for a one-second pulse on a ten-centimeter-diameter window of BaF 2 at 3.8|/m with a bulk absorption coefficient of 10 cm. For small-diameter windows (1 cm-diameter ), Si, BaF 2 , and GaAs have the greatest values of # « 1.8, 0. H and 0. 76 MW, respectively, for cw or 1 sec pulse duration at 3« B||m. For continuous operation at 10. 6pn
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The Absorption Coefficient of Alkali Halides in the Multiphonon Regime: Effectg of Nonlinear Dipole Moments. The theory of the absorption coefficient for a model of alkali halide crystals in the multiphonon regime developed in the previous report is extended to incorporate the effects of a nonlinear dipolc moment. The resulting expression for the absorption coefficient is evaluated for several different interatomic potential functions and choices for the non- linear dipole moment. We suggest that the relative sign of the contributions to the absotj ion coefficient from crystalline anharmonicity and the nonlinear vari- ation of the electric dipole moment with interatomic separation could be such that these contributions interfere constructively in the alkali halides.
Vertex Corrections for Multiphonon Absorptio i. in the previous technical report, vertex-correction factors A^ were calculated for all processes through n = 6, where n is the nuinber cf final phonons created in the absorption process. In numerical calculations in progress, the value of A was needed. Thus, this seventh-ordei vertex is calculated. Negligible effects. There are many effects in addition to those considered in the present and previous reports that give rise to infrared absorption, but whose strengths are too small to be observable. Simple order-of-magnitude calculations indicate that ultraviolet-induced infrared absorption and low-intensity inelastic scattering including Raman, Brillouin, and ionic Raman and Brillouin scattering, in addition to several processes already mentioned, fell into this category.
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Sec. A
The emphasis to date on the present contract and on a previous contract (DAHCJ5-72-C-012t)) has been on theoretii'al studies of high-power infrared- window materials. Since the remainder of :he program will emphasize studies on ultraviolet materials, a very brief overview of the infrared results is given. A summary of results of the complete program is given in outline form in Sec. N. The motivation for the program on theoretical studi.s of high-power infrared window materials was the availability of high-power infrared lasers for current Department of Defense programs and the realization that lack of transparent ma- terials for windows may limit the usefulness of many laser systems. As higher powers and shorter pulse lengths become available, the problem of obtaining materials with acceptably low absorption will become even more serious. At the beginning of the program, values of the optical absorption coefficient ß of candi- date window materials were needed in order to evaluate the potential performance of the materials. There had been no previous calculations of the numerical values of ß in the highly transparent regions for materials of interest (such as KBr and ZnSe at 10. 6jim), and the available corresponding experimental values were of questionable efficacy since they were believed to be extrinsic (i. e., caused by im- perfections that can be removed in principle). The paucity of experimental and theoretical information on the values of ß was one of the most pressing problems in the Department of Defense high-power window programs. It was especially important to know if the values of ß were in- trinsic or extrinsic and to have reliable estimates of the intrinsic value of ß before undertaking imperfection-identification and sample-purification programs since
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for ß, or, equivalently, the imaginary part of the dielectric constant. Very little conciliation had been given to the calculation of the numerical values of ß, and all such calculations had been for frequencies near the fundamental resonance where ß is large {j3 » 1cm ). There are a number of reasons why there had been no previous calculations for the numerical values of ß in the range of frequencies where ß « 1 cm". First, the need for this information has become pressing only within the last few years as higher-power lasers have become available. Second, previous interest was in obtaining information about the phonon dispersion relations, and this information was obtained without the knowledge of the absolute magnitude of ß. Finally, the calculations are not trivial. Straightforward com- puter calculations of ß in the n-phonon region for large n surely would yield paltry results. n the intervening twenty-four months there has been considerable theoretical and experimental progress. We have explained quantitatively the nearly exponen- tial frequency dependence of the optical absorption frequency j3 observed by Rupprecht^2 and by Deutsch and the substantial deviations from the expected tem- perature dependence observed by Harrington and Hass. The calculations are based on a reasonable model of the lattice with the Born-Mayer interaction potential. They include the dispersion relations of the phonons, and the approximations made were shown to be reasonable. The Raytheon measurements of ß(w) and our theore- tical prediction that there should be no drastic deviations from the extrapolations of the measured ßioc) have settled the question of whether the values of ß mea- sured at l().6)jtm are intrinsic or extrinsic for most materials of interest and have afforded estimates of the intrinsic values. With the exception of KC1, the estimated
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