1497:
1524:
beam gives a limitation on the switching speed, and hence limits the modulation bandwidth. The finite velocity of the acoustic wave means the light cannot be fully switched on or off until the acoustic wave has traveled across the light beam. So to increase the bandwidth the light must be focused to a small diameter at the location of the acousto-optic interaction. This minimum focused size of the beam represents the limit for the bandwidth.
1520:
the intensity at the Bragg angle increases. So the acousto-optic device is modulating the output along the Bragg diffraction angle, switching it on and off. The device is operated as a modulator by keeping the acoustic wavelength (frequency) fixed and varying the drive power to vary the amount of light in the deflected beam.
2566:
Input light need not be polarized for a non-collinear design. Unpolarized input light is scattered into orthogonally polarized beams separated by the scattering angle for the particular design and wavelength. If the optical design provides an appropriate beam block for the unscattered light, then two
1519:
A simple method of modulating the optical beam travelling through the acousto-optic device is done by switching the acoustic field on and off. When off the light beam is undiverted, the intensity of light directed at the Bragg diffraction angle is zero. When switched on and Bragg diffraction occurs,
1001:
In contrast, Bragg diffraction occurs at higher acoustic frequencies, usually exceeding 100 MHz. The observed diffraction pattern generally consists of two diffraction maxima; these are the zeroth and the first orders. However, even these two maxima only appear at definite incidence angles close
69:
of a medium due to the presence of sound waves in that medium. Sound waves produce a refractive index grating in the material, and it is this grating that is "seen" by the light wave. These variations in the refractive index, due to the pressure fluctuations, may be detected optically by refraction,
1335:
takes over from Raman–Nath diffraction. It is simply a fact that as the acoustic frequency increases, the number of observed maxima is gradually reduced due to the angular selectivity of the acousto-optic interaction. Traditionally, the type of diffraction, Bragg or Raman–Nath, is determined by the
1523:
There are several limitations associated with the design and performance of acousto-optic modulators. The acousto-optic medium must be designed carefully to provide maximum light intensity in a single diffracted beam. The time taken for the acoustic wave to travel across the diameter of the light
2575:
An acousto-optic deflector spatially controls the optical beam. In the operation of an acousto-optic deflector the power driving the acoustic transducer is kept on, at a constant level, while the acoustic frequency is varied to deflect the beam to different angular positions. The acousto-optic
1532:
The principle behind the operation of acousto-optic tunable filters is based on the wavelength of the diffracted light being dependent on the acoustic frequency. By tuning the frequency of the acoustic wave, the desired wavelength of the optical wave can be diffracted acousto-optically.
2258:
970:
Raman–Nath diffraction is observed with relatively low acoustic frequencies, typically less than 10 MHz, and with a small acousto-optic interaction length, ℓ, which is typically less than 1 cm. This type of diffraction occurs at an arbitrary angle of incidence,
2567:
beams (images) are formed in an optical passband that is nearly equivalent in both orthogonally linearly polarized output beams (differing by the Stokes and Anti-Stokes scattering parameter). Because of dispersion, these beams move slightly with scanning rf frequency.
2754:(AOMs). In an AOM, only the amplitude of the sound wave is modulated (to modulate the intensity of the diffracted laser beam), whereas in an AOD, both the amplitude and frequency are adjusted, making the engineering requirements tighter for an AOD than an AOM.
1861:
2561:
53:
1209:
771:
2691:
1470:
2043:
2131:
565:
883:
161:
and Nath (1937) have designed a general ideal model of interaction taking into account several orders. This model was developed by
Phariseau (1956) for diffraction including only one diffraction order.
2435:
73:
The acousto-optic effect is extensively used in the measurement and study of ultrasonic waves. However, the growing principal area of interest is in acousto-optical devices for the deflection,
351:
1587:: the wedge angle between the input and output faces of the filter cell (the wedge angle is necessary for eliminating the angular shift of the diffracted beam caused by frequency changing);
1029:. The first order maximum or the Bragg maximum is formed due to a selective reflection of the light from the wave fronts of ultrasonic wave. The Bragg angle is given by the expression,
784:
given by the speed of the sound wave in the medium. Light which then passes through the transparent material, is diffracted due to this generated refraction index, forming a prominent
464:
medium. This then gives rise to the variation of the refractive index. For a plane acoustic wave propagating along the z axis, the change in the refractive index can be expressed as
1738:
2604:
1539:
The polarization of the incident light can be either ordinary or extraordinary. For the definition, we assume ordinary polarization. Here the following list of symbols is used,
2466:
1636:
1516:, properties of the optical wave may be modulated. The acousto-optic interaction also makes it possible to modulate the optical beam by both temporal and spatial modulation.
196:
2341:
1027:
996:
813:
2714:
2627:
2361:
1703:
1607:
1232:
930:
906:
666:
2381:
2314:
2287:
1585:
1559:
615:
2458:
1658:
1386:
1360:
384:
134:
has a history of similar duration, again starting with the ancient Greeks. In contrast, the acousto-optic effect has had a relatively short history, beginning with
2100:
2073:
1730:
1680:
1326:
1299:
595:
458:
276:
249:
2734:
2747:
was awarded to Eric A. Cornell, Wolfgang
Ketterle and Carl E. Wieman. Another application of acoustic-optical deflection is optical trapping of small molecules.
1536:
There are two types of the acousto-optic filters, the collinear and non-collinear filters. The type of filter depends on geometry of acousto-optic interaction.
2766:
is used as a standard to compare when measuring photoelastic coefficients. Lithium niobate is often used in high frequency devices. Softer materials, such as
2123:
1272:
1252:
950:
639:
428:
408:
222:
3098:
2927:
1035:
674:
2635:
2881:
1483:
limit the frequency range of acousto-optic interaction. As a consequence, the speed of operation of acousto-optic devices is also limited.
1475:
which is known as the Klein–Cook parameter. Since, in general, only the first order diffraction maximum is used in acousto-optic devices,
1394:
2253:{\displaystyle (9)\ \nu (\alpha )=\nu _{110}{\sqrt {\cos ^{2}\alpha +\left({\frac {\nu _{001}}{\nu _{110}}}\right)^{2}\sin ^{2}\alpha }}}
1869:
2834:
470:
142:
by an acoustic wave, being propagated in a medium of interaction, in 1922. This was then confirmed with experimentation in 1932 by
821:
3172:
2740:
2460:
between the diffracted and non-diffracted beams defines the view field of the filter; it can be calculated from the formula,
2389:
2854:
Gal, M. (2005). "Modulation and switching of light" (Lecture Notes on
Optoelectronics). The University of New South Wales.
3035:
2898:
104:
284:
154:
111:
applications, where optically generated and optical measurements of ultrasound gives a non-contact method of imaging.
202:
3217:
1856:{\displaystyle (7)\ n_{\varphi }={\frac {n_{0}n_{e}}{\sqrt {n_{0}^{2}\cos \varphi +n_{e}^{2}\sin ^{2}\varphi }}}}
99:
Along with the current applications, acousto-optics presents interesting possible application. It can be used in
2783:
3102:
2819:
2814:
2751:
960:
2744:
100:
2923:
2556:{\displaystyle (11)\ \beta =\arcsin \left({\frac {\lambda f_{0}}{n_{0}\nu }}\sin \alpha +\varphi \right)}
2805:, with slow acoustic waves make high efficiency devices at lower frequencies, and give high resolution.
2579:
461:
2576:
deflector makes use of the acoustic frequency dependent diffraction angle, where a change in the angle
668:
is the amplitude of variation in the refractive index generated by the acoustic wave, and is given as,
3202:
2988:
1614:
1513:
139:
85:, which have made the acousto-optic effect easier to observe and measure. Technical progress in both
81:
and frequency shifting of light beams. This is due to the increasing availability and performance of
3152:
2873:
2798:
2779:
785:
777:
181:
3212:
3132:
2767:
2319:
1005:
974:
791:
46:
3077:
3036:"Optical properties of solid and liquid medias subjected to high-frequency elastic vibrations"
3016:
2877:
2771:
2699:
2609:
2346:
1688:
1592:
1480:
1476:
1332:
1217:
964:
915:
891:
648:
618:
135:
78:
2366:
2292:
2265:
1570:
1544:
600:
3050:
3006:
2996:
2957:
2829:
2824:
2802:
2443:
1643:
1496:
1365:
1339:
359:
90:
66:
2078:
2051:
1708:
1665:
1479:
is preferable due to the lower optical losses. However, the acousto-optic requirements for
1304:
1277:
573:
436:
254:
227:
2719:
788:. This diffraction pattern corresponds with a conventional diffraction grating at angles
171:
3054:
2948:
Brillouin, L. (1922). "Diffusion of Light and X-rays by a
Transparent Homogeneous Body".
2992:
3222:
3207:
3011:
2976:
2108:
1257:
1237:
935:
624:
413:
393:
207:
123:
86:
3196:
2102:) polarized beams are determined by taking into account their dispersive dependence.
1509:
147:
2763:
175:
2961:
26:
that studies the interactions between sound waves and light waves, especially the
1660:: the angle between deflected and non-deflected light at the central frequency;
158:
143:
127:
27:
909:
642:
108:
93:
74:
38:
2902:
1609:: the angle between the incident light wave vector and axis of the crystal;
2775:
1505:
1204:{\displaystyle (5)\ \sin \theta _{B}=-{\frac {\lambda f}{2n_{i}\nu }}\left,}
956:
199:
131:
3020:
2316:
are the sound velocities along the axes and , consecutively. The value of
1561:: the angle between the acoustic wave vector and the crystallographic axis
766:{\displaystyle (3)\ \Delta n=-{\frac {1}{2}}\sum _{j}n_{0}^{3}p_{zj}a_{j},}
3001:
224:. Photoelasticity is the variation of the optical indicatrix coefficients
52:
2686:{\displaystyle (12)\ \Delta \theta _{d}={\frac {\lambda }{\nu }}\Delta f}
1638:: the angle between the input face of the cell and acoustic wave vector;
781:
96:
has brought valuable benefits to acousto-optic components' improvements.
153:
The particular case of diffraction on the first order, under a certain
23:
387:
157:, (also predicted by Brillouin), has been observed by Rytow in 1935.
119:
1465:{\displaystyle (6)\ Q={\frac {2\pi \lambda \ell f^{2}}{n\nu ^{2}}},}
70:
diffraction, and interference effects; reflection may also be used.
2038:{\displaystyle (8)\ f_{i}(\varphi )={\frac {\nu }{\lambda }}\left}
1495:
460:
are a result of the acoustic wave which has been excited within a
82:
51:
42:
34:
31:
65:
In general, acousto-optic effects are based on the change of the
1504:
By varying the parameters of the acoustic wave, including the
560:{\displaystyle (2)\ n(z,t)=n_{0}+\Delta n\cos(\Omega t-Kz),\,}
1732:
of the filter are defined by the following set of equations,
1234:
is the wavelength of the incident light wave (in a vacuum),
1301:
is the refractive index for the incident optical wave, and
878:{\displaystyle (4)\ \Lambda \sin(\theta _{m})=m\lambda ,\,}
1328:
is the refractive index for the diffracted optical waves.
3072:
3070:
3068:
3066:
3064:
2430:{\displaystyle (10)\ \alpha _{\ell }=\varphi +\alpha }
433:
Specifically in the acousto-optic effect, the strains
2722:
2702:
2638:
2612:
2582:
2469:
2446:
2392:
2369:
2349:
2322:
2295:
2268:
2134:
2111:
2081:
2054:
1872:
1741:
1711:
1691:
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1617:
1595:
1573:
1547:
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1368:
1342:
1307:
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1038:
1008:
977:
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627:
603:
576:
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439:
416:
396:
362:
287:
257:
230:
210:
184:
56:
A diffraction image showing the acousto-optic effect.
959:produces two distinct diffraction types. These are
2728:
2708:
2685:
2621:
2598:
2555:
2452:
2429:
2375:
2355:
2335:
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1601:
1579:
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1021:
990:
944:
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765:
660:
633:
609:
589:
559:
452:
422:
402:
378:
345:
270:
243:
216:
190:
2762:All materials display the acousto-optic effect.
955:Light diffracted by an acoustic wave of a single
2977:"On the scattering of light by supersonic waves"
346:{\displaystyle (1)\ \Delta B_{i}=p_{ij}a_{j},\,}
170:The acousto-optic effect is a specific case of
2870:Laser Ultrasonics: Techniques and Applications
815:from the original direction, and is given by,
2868:Scruby, C.B.; Drain, L.E. (January 1, 1990).
776:The generated refractive index, (2), gives a
8:
932:is the wavelength of the acoustic wave and
122:has had a very long and full history, from
2716:is the optical wavelength of the beam and
174:, where there is a change of a material's
3127:
3125:
3123:
3121:
3119:
3099:"ELECTRO-OPTIC AND ACOUSTO-OPTIC DEVICES"
3010:
3000:
2721:
2701:
2667:
2658:
2637:
2611:
2606:as a function of the change in frequency
2590:
2581:
2521:
2509:
2499:
2468:
2445:
2409:
2391:
2368:
2348:
2327:
2321:
2300:
2294:
2273:
2267:
2236:
2226:
2214:
2204:
2198:
2178:
2172:
2166:
2133:
2110:
2086:
2080:
2059:
2053:
2004:
1985:
1980:
1967:
1962:
1956:
1926:
1907:
1889:
1871:
1838:
1828:
1823:
1801:
1796:
1784:
1774:
1767:
1758:
1740:
1716:
1710:
1690:
1667:
1645:
1622:
1616:
1594:
1572:
1546:
1450:
1435:
1416:
1396:
1367:
1341:
1312:
1306:
1285:
1279:
1259:
1239:
1219:
1182:
1177:
1164:
1159:
1141:
1131:
1120:
1114:
1091:
1073:
1061:
1037:
1013:
1007:
982:
976:
937:
917:
893:
874:
853:
823:
799:
793:
754:
741:
731:
726:
716:
702:
676:
650:
626:
602:
581:
575:
556:
511:
472:
444:
438:
415:
395:
367:
361:
342:
333:
320:
307:
286:
262:
256:
235:
229:
209:
183:
2863:
2861:
16:The study of sound and light interaction
2899:"Optics Highlights: 1. Ancient History"
2846:
1331:In general, there is no point at which
2739:AOD technology has made practical the
2736:is the velocity of the acoustic wave.
1274:is the velocity of the acoustic wave,
2125:, depends on the angle α, such that,
597:is the undisturbed refractive index,
7:
2048:Refractive indices of the ordinary (
1388:respectively, where Q is given by,
130:and modern times. As with optics,
3055:10.1051/jphysrad:01932003010046400
2677:
2651:
2613:
2599:{\displaystyle \Delta \theta _{d}}
2583:
919:
837:
690:
652:
604:
535:
520:
300:
14:
3173:"The Nobel Prize in Physics 2001"
3153:"Acousto-optic effect: Deflector"
2750:AODs are essentially the same as
150:, and also by Lucas and Biquard.
2930:from the original on 3 July 2007
3133:"Acousto-optic effect: Filters"
3034:Lucas, R.; Biquard, P. (1932).
2975:Debye, P.; Sears, F.W. (1932).
1631:{\displaystyle \alpha _{\ell }}
2645:
2639:
2476:
2470:
2399:
2393:
2156:
2150:
2141:
2135:
2025:
2013:
1997:
1991:
1950:
1938:
1901:
1895:
1879:
1873:
1748:
1742:
1404:
1398:
1045:
1039:
952:is the integer order maximum.
859:
846:
831:
825:
684:
678:
550:
532:
501:
489:
480:
474:
294:
288:
1:
2835:Schaefer–Bergmann diffraction
2343:is determined by the angles
1528:Acousto-optic tunable filter
191:{\displaystyle \varepsilon }
105:structural health monitoring
2962:10.1051/anphys/192209170088
2336:{\displaystyle \alpha _{1}}
1254:is the acoustic frequency,
1022:{\displaystyle \theta _{B}}
991:{\displaystyle \theta _{0}}
808:{\displaystyle \theta _{n}}
3239:
2924:"The History of Acoustics"
2741:Bose–Einstein condensation
1705:and the central frequency
1682:: the transducer length.
1500:An acousto-optic modulator
645:of the acoustic wave, and
2752:acousto-optic modulators
2709:{\displaystyle \lambda }
2622:{\displaystyle \Delta f}
2571:Acousto-optic deflectors
2356:{\displaystyle \varphi }
1698:{\displaystyle \varphi }
1602:{\displaystyle \varphi }
1227:{\displaystyle \lambda }
925:{\displaystyle \Lambda }
901:{\displaystyle \lambda }
661:{\displaystyle \Delta n}
2820:Acousto-optic deflector
2815:Acousto-optic modulator
2376:{\displaystyle \alpha }
2309:{\displaystyle v_{001}}
2282:{\displaystyle v_{110}}
1580:{\displaystyle \gamma }
1554:{\displaystyle \alpha }
1492:Acousto-optic modulator
610:{\displaystyle \Omega }
45:in general) through an
3078:"Acousto-optic effect"
2745:Nobel Prize in Physics
2730:
2710:
2687:
2623:
2600:
2557:
2454:
2453:{\displaystyle \beta }
2431:
2377:
2357:
2337:
2310:
2283:
2254:
2119:
2096:
2069:
2039:
1857:
1726:
1699:
1676:
1654:
1653:{\displaystyle \beta }
1632:
1603:
1581:
1555:
1501:
1466:
1382:
1381:{\displaystyle Q\ll 1}
1356:
1355:{\displaystyle Q\gg 1}
1322:
1295:
1268:
1248:
1228:
1205:
1023:
992:
961:Raman–Nath diffraction
946:
926:
902:
879:
809:
767:
662:
635:
611:
591:
561:
454:
424:
404:
380:
379:{\displaystyle p_{ij}}
347:
272:
245:
218:
192:
101:nondestructive testing
57:
3002:10.1073/pnas.18.6.409
2731:
2711:
2688:
2624:
2601:
2558:
2455:
2432:
2378:
2358:
2338:
2311:
2284:
2255:
2120:
2097:
2095:{\displaystyle n_{e}}
2075:) and extraordinary (
2070:
2068:{\displaystyle n_{0}}
2040:
1858:
1727:
1725:{\displaystyle f_{i}}
1700:
1677:
1675:{\displaystyle \ell }
1655:
1633:
1604:
1582:
1556:
1499:
1487:Acousto-optic devices
1467:
1383:
1357:
1323:
1321:{\displaystyle n_{d}}
1296:
1294:{\displaystyle n_{i}}
1269:
1249:
1229:
1206:
1024:
993:
947:
927:
912:of the optical wave,
903:
880:
810:
768:
663:
636:
612:
592:
590:{\displaystyle n_{0}}
562:
455:
453:{\displaystyle a_{j}}
425:
405:
381:
348:
273:
271:{\displaystyle a_{j}}
251:caused by the strain
246:
244:{\displaystyle B_{i}}
219:
193:
55:
2874:Taylor & Francis
2729:{\displaystyle \nu }
2720:
2700:
2636:
2610:
2580:
2467:
2444:
2390:
2367:
2347:
2320:
2293:
2266:
2132:
2109:
2105:The sound velocity,
2079:
2052:
1870:
1739:
1709:
1689:
1685:The incidence angle
1666:
1644:
1615:
1593:
1571:
1545:
1395:
1366:
1340:
1305:
1278:
1258:
1238:
1218:
1036:
1006:
1002:to the Bragg angle,
975:
936:
916:
892:
822:
792:
675:
649:
625:
601:
574:
471:
437:
414:
394:
386:is the photoelastic
360:
285:
255:
228:
208:
182:
166:Acousto-optic effect
140:diffraction of light
3043:Journal de Physique
2993:1932PNAS...18..409D
2950:Annales de Physique
2799:mercury(I) chloride
2743:for which the 2001
1990:
1972:
1833:
1806:
1187:
1169:
786:diffraction pattern
778:diffraction grating
736:
89:and high frequency
2768:arsenic trisulfide
2726:
2706:
2683:
2619:
2596:
2553:
2450:
2427:
2373:
2353:
2333:
2306:
2279:
2250:
2115:
2092:
2065:
2035:
1976:
1958:
1853:
1819:
1792:
1722:
1695:
1672:
1650:
1628:
1599:
1577:
1551:
1502:
1462:
1378:
1352:
1318:
1291:
1264:
1244:
1224:
1201:
1173:
1155:
1019:
988:
942:
922:
898:
875:
805:
763:
722:
721:
658:
631:
607:
587:
557:
450:
420:
400:
376:
343:
268:
241:
214:
188:
155:angle of incidence
58:
47:ultrasonic grating
2883:978-0-7503-0050-6
2772:tellurium dioxide
2675:
2650:
2531:
2481:
2404:
2248:
2220:
2146:
2118:{\displaystyle v}
2028:
1915:
1884:
1851:
1850:
1753:
1481:Bragg diffraction
1477:Bragg diffraction
1457:
1409:
1333:Bragg diffraction
1267:{\displaystyle v}
1247:{\displaystyle f}
1148:
1101:
1050:
965:Bragg diffraction
945:{\displaystyle m}
836:
712:
710:
689:
634:{\displaystyle K}
619:angular frequency
485:
423:{\displaystyle j}
403:{\displaystyle i}
390:with components,
299:
217:{\displaystyle a}
79:signal processing
3230:
3218:Nonlinear optics
3187:
3186:
3184:
3183:
3169:
3163:
3162:
3160:
3159:
3149:
3143:
3142:
3140:
3139:
3129:
3114:
3113:
3111:
3110:
3101:. Archived from
3094:
3088:
3087:
3085:
3084:
3074:
3059:
3058:
3040:
3031:
3025:
3024:
3014:
3004:
2972:
2966:
2965:
2945:
2939:
2938:
2936:
2935:
2920:
2914:
2913:
2911:
2910:
2901:. Archived from
2894:
2888:
2887:
2865:
2856:
2855:
2851:
2830:Sonoluminescence
2825:Nonlinear optics
2803:lead(II) bromide
2735:
2733:
2732:
2727:
2715:
2713:
2712:
2707:
2692:
2690:
2689:
2684:
2676:
2668:
2663:
2662:
2648:
2628:
2626:
2625:
2620:
2605:
2603:
2602:
2597:
2595:
2594:
2562:
2560:
2559:
2554:
2552:
2548:
2532:
2530:
2526:
2525:
2515:
2514:
2513:
2500:
2479:
2459:
2457:
2456:
2451:
2436:
2434:
2433:
2428:
2414:
2413:
2402:
2382:
2380:
2379:
2374:
2362:
2360:
2359:
2354:
2342:
2340:
2339:
2334:
2332:
2331:
2315:
2313:
2312:
2307:
2305:
2304:
2288:
2286:
2285:
2280:
2278:
2277:
2259:
2257:
2256:
2251:
2249:
2241:
2240:
2231:
2230:
2225:
2221:
2219:
2218:
2209:
2208:
2199:
2183:
2182:
2173:
2171:
2170:
2144:
2124:
2122:
2121:
2116:
2101:
2099:
2098:
2093:
2091:
2090:
2074:
2072:
2071:
2066:
2064:
2063:
2044:
2042:
2041:
2036:
2034:
2030:
2029:
2009:
2008:
1989:
1984:
1971:
1966:
1957:
1931:
1930:
1916:
1908:
1894:
1893:
1882:
1862:
1860:
1859:
1854:
1852:
1843:
1842:
1832:
1827:
1805:
1800:
1791:
1790:
1789:
1788:
1779:
1778:
1768:
1763:
1762:
1751:
1731:
1729:
1728:
1723:
1721:
1720:
1704:
1702:
1701:
1696:
1681:
1679:
1678:
1673:
1659:
1657:
1656:
1651:
1637:
1635:
1634:
1629:
1627:
1626:
1608:
1606:
1605:
1600:
1586:
1584:
1583:
1578:
1565:of the crystal;
1560:
1558:
1557:
1552:
1512:, frequency and
1471:
1469:
1468:
1463:
1458:
1456:
1455:
1454:
1441:
1440:
1439:
1417:
1407:
1387:
1385:
1384:
1379:
1361:
1359:
1358:
1353:
1327:
1325:
1324:
1319:
1317:
1316:
1300:
1298:
1297:
1292:
1290:
1289:
1273:
1271:
1270:
1265:
1253:
1251:
1250:
1245:
1233:
1231:
1230:
1225:
1210:
1208:
1207:
1202:
1197:
1193:
1192:
1188:
1186:
1181:
1168:
1163:
1149:
1147:
1146:
1145:
1136:
1135:
1125:
1124:
1115:
1102:
1100:
1096:
1095:
1082:
1074:
1066:
1065:
1048:
1028:
1026:
1025:
1020:
1018:
1017:
997:
995:
994:
989:
987:
986:
951:
949:
948:
943:
931:
929:
928:
923:
907:
905:
904:
899:
884:
882:
881:
876:
858:
857:
834:
814:
812:
811:
806:
804:
803:
780:moving with the
772:
770:
769:
764:
759:
758:
749:
748:
735:
730:
720:
711:
703:
687:
667:
665:
664:
659:
640:
638:
637:
632:
616:
614:
613:
608:
596:
594:
593:
588:
586:
585:
566:
564:
563:
558:
516:
515:
483:
459:
457:
456:
451:
449:
448:
429:
427:
426:
421:
409:
407:
406:
401:
385:
383:
382:
377:
375:
374:
352:
350:
349:
344:
338:
337:
328:
327:
312:
311:
297:
277:
275:
274:
269:
267:
266:
250:
248:
247:
242:
240:
239:
223:
221:
220:
215:
197:
195:
194:
189:
67:refractive index
3238:
3237:
3233:
3232:
3231:
3229:
3228:
3227:
3193:
3192:
3191:
3190:
3181:
3179:
3171:
3170:
3166:
3157:
3155:
3151:
3150:
3146:
3137:
3135:
3131:
3130:
3117:
3108:
3106:
3096:
3095:
3091:
3082:
3080:
3076:
3075:
3062:
3038:
3033:
3032:
3028:
2974:
2973:
2969:
2947:
2946:
2942:
2933:
2931:
2922:
2921:
2917:
2908:
2906:
2896:
2895:
2891:
2884:
2867:
2866:
2859:
2853:
2852:
2848:
2843:
2811:
2795:
2791:
2787:
2760:
2718:
2717:
2698:
2697:
2654:
2634:
2633:
2608:
2607:
2586:
2578:
2577:
2573:
2517:
2516:
2505:
2501:
2498:
2494:
2465:
2464:
2442:
2441:
2405:
2388:
2387:
2365:
2364:
2345:
2344:
2323:
2318:
2317:
2296:
2291:
2290:
2269:
2264:
2263:
2232:
2210:
2200:
2194:
2193:
2174:
2162:
2130:
2129:
2107:
2106:
2082:
2077:
2076:
2055:
2050:
2049:
2000:
1922:
1921:
1917:
1885:
1868:
1867:
1834:
1780:
1770:
1769:
1754:
1737:
1736:
1712:
1707:
1706:
1687:
1686:
1664:
1663:
1642:
1641:
1618:
1613:
1612:
1591:
1590:
1569:
1568:
1543:
1542:
1530:
1494:
1489:
1446:
1442:
1431:
1418:
1393:
1392:
1364:
1363:
1338:
1337:
1308:
1303:
1302:
1281:
1276:
1275:
1256:
1255:
1236:
1235:
1216:
1215:
1154:
1150:
1137:
1127:
1126:
1116:
1107:
1103:
1087:
1083:
1075:
1057:
1034:
1033:
1009:
1004:
1003:
978:
973:
972:
934:
933:
914:
913:
890:
889:
849:
820:
819:
795:
790:
789:
750:
737:
673:
672:
647:
646:
623:
622:
599:
598:
577:
572:
571:
507:
469:
468:
440:
435:
434:
412:
411:
392:
391:
363:
358:
357:
329:
316:
303:
283:
282:
258:
253:
252:
231:
226:
225:
206:
205:
180:
179:
172:photoelasticity
168:
138:predicting the
117:
63:
22:is a branch of
17:
12:
11:
5:
3236:
3234:
3226:
3225:
3220:
3215:
3210:
3205:
3195:
3194:
3189:
3188:
3177:NobelPrize.org
3164:
3144:
3115:
3089:
3060:
3026:
2987:(6): 409–414.
2967:
2940:
2915:
2889:
2882:
2857:
2845:
2844:
2842:
2839:
2838:
2837:
2832:
2827:
2822:
2817:
2810:
2807:
2793:
2789:
2785:
2759:
2756:
2725:
2705:
2694:
2693:
2682:
2679:
2674:
2671:
2666:
2661:
2657:
2653:
2647:
2644:
2641:
2618:
2615:
2593:
2589:
2585:
2572:
2569:
2564:
2563:
2551:
2547:
2544:
2541:
2538:
2535:
2529:
2524:
2520:
2512:
2508:
2504:
2497:
2493:
2490:
2487:
2484:
2478:
2475:
2472:
2449:
2438:
2437:
2426:
2423:
2420:
2417:
2412:
2408:
2401:
2398:
2395:
2372:
2352:
2330:
2326:
2303:
2299:
2276:
2272:
2261:
2260:
2247:
2244:
2239:
2235:
2229:
2224:
2217:
2213:
2207:
2203:
2197:
2192:
2189:
2186:
2181:
2177:
2169:
2165:
2161:
2158:
2155:
2152:
2149:
2143:
2140:
2137:
2114:
2089:
2085:
2062:
2058:
2046:
2045:
2033:
2027:
2024:
2021:
2018:
2015:
2012:
2007:
2003:
1999:
1996:
1993:
1988:
1983:
1979:
1975:
1970:
1965:
1961:
1955:
1952:
1949:
1946:
1943:
1940:
1937:
1934:
1929:
1925:
1920:
1914:
1911:
1906:
1903:
1900:
1897:
1892:
1888:
1881:
1878:
1875:
1864:
1863:
1849:
1846:
1841:
1837:
1831:
1826:
1822:
1818:
1815:
1812:
1809:
1804:
1799:
1795:
1787:
1783:
1777:
1773:
1766:
1761:
1757:
1750:
1747:
1744:
1719:
1715:
1694:
1671:
1649:
1625:
1621:
1598:
1576:
1550:
1529:
1526:
1493:
1490:
1488:
1485:
1473:
1472:
1461:
1453:
1449:
1445:
1438:
1434:
1430:
1427:
1424:
1421:
1415:
1412:
1406:
1403:
1400:
1377:
1374:
1371:
1351:
1348:
1345:
1315:
1311:
1288:
1284:
1263:
1243:
1223:
1212:
1211:
1200:
1196:
1191:
1185:
1180:
1176:
1172:
1167:
1162:
1158:
1153:
1144:
1140:
1134:
1130:
1123:
1119:
1113:
1110:
1106:
1099:
1094:
1090:
1086:
1081:
1078:
1072:
1069:
1064:
1060:
1056:
1053:
1047:
1044:
1041:
1016:
1012:
985:
981:
941:
921:
897:
886:
885:
873:
870:
867:
864:
861:
856:
852:
848:
845:
842:
839:
833:
830:
827:
802:
798:
774:
773:
762:
757:
753:
747:
744:
740:
734:
729:
725:
719:
715:
709:
706:
701:
698:
695:
692:
686:
683:
680:
657:
654:
630:
606:
584:
580:
568:
567:
555:
552:
549:
546:
543:
540:
537:
534:
531:
528:
525:
522:
519:
514:
510:
506:
503:
500:
497:
494:
491:
488:
482:
479:
476:
447:
443:
419:
399:
373:
370:
366:
354:
353:
341:
336:
332:
326:
323:
319:
315:
310:
306:
302:
296:
293:
290:
265:
261:
238:
234:
213:
187:
167:
164:
126:, through the
124:ancient Greece
116:
113:
87:crystal growth
62:
59:
20:Acousto-optics
15:
13:
10:
9:
6:
4:
3:
2:
3235:
3224:
3221:
3219:
3216:
3214:
3211:
3209:
3206:
3204:
3201:
3200:
3198:
3178:
3174:
3168:
3165:
3154:
3148:
3145:
3134:
3128:
3126:
3124:
3122:
3120:
3116:
3105:on 2004-10-18
3104:
3100:
3093:
3090:
3079:
3073:
3071:
3069:
3067:
3065:
3061:
3056:
3052:
3048:
3044:
3037:
3030:
3027:
3022:
3018:
3013:
3008:
3003:
2998:
2994:
2990:
2986:
2982:
2978:
2971:
2968:
2963:
2959:
2955:
2951:
2944:
2941:
2929:
2925:
2919:
2916:
2905:on 2007-05-12
2904:
2900:
2897:Taylor, L.S.
2893:
2890:
2885:
2879:
2875:
2871:
2864:
2862:
2858:
2850:
2847:
2840:
2836:
2833:
2831:
2828:
2826:
2823:
2821:
2818:
2816:
2813:
2812:
2808:
2806:
2804:
2800:
2796:
2781:
2780:lead silicate
2777:
2773:
2769:
2765:
2757:
2755:
2753:
2748:
2746:
2742:
2737:
2723:
2703:
2680:
2672:
2669:
2664:
2659:
2655:
2642:
2632:
2631:
2630:
2629:is given as,
2616:
2591:
2587:
2570:
2568:
2549:
2545:
2542:
2539:
2536:
2533:
2527:
2522:
2518:
2510:
2506:
2502:
2495:
2491:
2488:
2485:
2482:
2473:
2463:
2462:
2461:
2447:
2424:
2421:
2418:
2415:
2410:
2406:
2396:
2386:
2385:
2384:
2370:
2350:
2328:
2324:
2301:
2297:
2274:
2270:
2245:
2242:
2237:
2233:
2227:
2222:
2215:
2211:
2205:
2201:
2195:
2190:
2187:
2184:
2179:
2175:
2167:
2163:
2159:
2153:
2147:
2138:
2128:
2127:
2126:
2112:
2103:
2087:
2083:
2060:
2056:
2031:
2022:
2019:
2016:
2010:
2005:
2001:
1994:
1986:
1981:
1977:
1973:
1968:
1963:
1959:
1953:
1947:
1944:
1941:
1935:
1932:
1927:
1923:
1918:
1912:
1909:
1904:
1898:
1890:
1886:
1876:
1866:
1865:
1847:
1844:
1839:
1835:
1829:
1824:
1820:
1816:
1813:
1810:
1807:
1802:
1797:
1793:
1785:
1781:
1775:
1771:
1764:
1759:
1755:
1745:
1735:
1734:
1733:
1717:
1713:
1692:
1683:
1669:
1661:
1647:
1639:
1623:
1619:
1610:
1596:
1588:
1574:
1566:
1564:
1548:
1540:
1537:
1534:
1527:
1525:
1521:
1517:
1515:
1511:
1507:
1498:
1491:
1486:
1484:
1482:
1478:
1459:
1451:
1447:
1443:
1436:
1432:
1428:
1425:
1422:
1419:
1413:
1410:
1401:
1391:
1390:
1389:
1375:
1372:
1369:
1349:
1346:
1343:
1334:
1329:
1313:
1309:
1286:
1282:
1261:
1241:
1221:
1198:
1194:
1189:
1183:
1178:
1174:
1170:
1165:
1160:
1156:
1151:
1142:
1138:
1132:
1128:
1121:
1117:
1111:
1108:
1104:
1097:
1092:
1088:
1084:
1079:
1076:
1070:
1067:
1062:
1058:
1054:
1051:
1042:
1032:
1031:
1030:
1014:
1010:
999:
983:
979:
968:
966:
962:
958:
953:
939:
911:
895:
871:
868:
865:
862:
854:
850:
843:
840:
828:
818:
817:
816:
800:
796:
787:
783:
779:
760:
755:
751:
745:
742:
738:
732:
727:
723:
717:
713:
707:
704:
699:
696:
693:
681:
671:
670:
669:
655:
644:
628:
620:
582:
578:
553:
547:
544:
541:
538:
529:
526:
523:
517:
512:
508:
504:
498:
495:
492:
486:
477:
467:
466:
465:
463:
445:
441:
431:
430:= 1,2,...,6.
417:
397:
389:
371:
368:
364:
339:
334:
330:
324:
321:
317:
313:
308:
304:
291:
281:
280:
279:
263:
259:
236:
232:
211:
204:
201:
185:
177:
173:
165:
163:
160:
156:
151:
149:
145:
141:
137:
133:
129:
125:
121:
114:
112:
110:
106:
102:
97:
95:
92:
91:piezoelectric
88:
84:
80:
76:
71:
68:
60:
54:
50:
48:
44:
40:
36:
33:
29:
25:
21:
3180:. Retrieved
3176:
3167:
3156:. Retrieved
3147:
3136:. Retrieved
3107:. Retrieved
3103:the original
3092:
3081:. Retrieved
3046:
3042:
3029:
2984:
2980:
2970:
2953:
2949:
2943:
2932:. Retrieved
2918:
2907:. Retrieved
2903:the original
2892:
2869:
2849:
2764:Fused silica
2761:
2749:
2738:
2695:
2574:
2565:
2439:
2262:
2104:
2047:
1684:
1662:
1640:
1611:
1589:
1567:
1562:
1541:
1538:
1535:
1531:
1522:
1518:
1514:polarization
1503:
1474:
1330:
1213:
1000:
969:
954:
887:
775:
569:
432:
355:
176:permittivity
169:
152:
118:
98:
72:
64:
61:Introduction
19:
18:
3203:Diffraction
3097:Simcik, J.
3049:: 464–477.
1336:conditions
462:transparent
198:, due to a
128:renaissance
94:transducers
28:diffraction
3197:Categories
3182:2020-12-14
3158:2007-08-07
3138:2007-08-07
3109:2004-10-28
3083:2007-08-07
2956:: 88–122.
2934:2007-08-07
2909:2007-08-07
2841:References
2440:The angle
910:wavelength
643:wavenumber
278:given by,
200:mechanical
109:biomedical
75:modulation
39:ultrasound
3213:Acoustics
2778:glasses,
2776:tellurite
2758:Materials
2724:ν
2704:λ
2678:Δ
2673:ν
2670:λ
2656:θ
2652:Δ
2614:Δ
2588:θ
2584:Δ
2546:φ
2540:α
2537:
2528:ν
2503:λ
2492:
2483:β
2448:β
2425:α
2419:φ
2411:ℓ
2407:α
2371:α
2351:φ
2325:α
2246:α
2243:
2212:ν
2202:ν
2188:α
2185:
2164:ν
2154:α
2148:ν
2023:α
2017:φ
2011:
1995:φ
1982:φ
1974:−
1954:±
1948:α
1942:φ
1936:
1928:φ
1913:λ
1910:ν
1899:φ
1848:φ
1845:
1814:φ
1811:
1760:φ
1693:φ
1670:ℓ
1648:β
1624:ℓ
1620:α
1597:φ
1575:γ
1549:α
1506:amplitude
1448:ν
1429:ℓ
1426:λ
1423:π
1373:≪
1347:≫
1222:λ
1171:−
1129:λ
1118:ν
1098:ν
1077:λ
1071:−
1059:θ
1055:
1011:θ
980:θ
957:frequency
920:Λ
896:λ
869:λ
851:θ
844:
838:Λ
797:θ
714:∑
700:−
691:Δ
653:Δ
605:Ω
542:−
536:Ω
530:
521:Δ
301:Δ
186:ε
136:Brillouin
132:acoustics
3021:16587705
2928:Archived
2809:See also
782:velocity
3012:1076242
2989:Bibcode
908:is the
641:is the
617:is the
115:History
24:physics
3019:
3009:
2880:
2696:where
2649:
2489:arcsin
2480:
2403:
2145:
1883:
1752:
1408:
1214:where
1049:
888:where
835:
688:
570:where
484:
388:tensor
356:where
298:
203:strain
120:Optics
83:lasers
3223:Waves
3208:Light
3039:(PDF)
1510:phase
159:Raman
148:Sears
144:Debye
43:sound
35:light
32:laser
3017:PMID
2981:PNAS
2878:ISBN
2774:and
2363:and
2289:and
1362:and
963:and
146:and
107:and
41:(or
3051:doi
3007:PMC
2997:doi
2958:doi
2534:sin
2302:001
2275:110
2234:sin
2216:110
2206:001
2176:cos
2168:110
2002:sin
1933:cos
1836:sin
1808:cos
1052:sin
841:sin
527:cos
37:by
30:of
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3175:.
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3063:^
3047:71
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3041:.
3015:.
3005:.
2995:.
2985:18
2983:.
2979:.
2954:17
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2926:.
2876:.
2872:.
2860:^
2801:,
2797:,
2794:33
2790:12
2788:As
2786:55
2784:Ge
2782:,
2770:,
2643:12
2474:11
2397:10
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1508:,
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967:.
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178:,
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3185:.
3161:.
3141:.
3112:.
3086:.
3057:.
3053::
3023:.
2999::
2991::
2964:.
2960::
2937:.
2912:.
2886:.
2792:S
2681:f
2665:=
2660:d
2646:)
2640:(
2617:f
2592:d
2550:)
2543:+
2523:0
2519:n
2511:0
2507:f
2496:(
2486:=
2477:)
2471:(
2422:+
2416:=
2400:)
2394:(
2329:1
2298:v
2271:v
2238:2
2228:2
2223:)
2196:(
2191:+
2180:2
2160:=
2157:)
2151:(
2142:)
2139:9
2136:(
2113:v
2088:e
2084:n
2061:0
2057:n
2032:]
2026:)
2020:+
2014:(
2006:2
1998:)
1992:(
1987:2
1978:n
1969:2
1964:0
1960:n
1951:)
1945:+
1939:(
1924:n
1919:[
1905:=
1902:)
1896:(
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1887:f
1880:)
1877:8
1874:(
1840:2
1830:2
1825:e
1821:n
1817:+
1803:2
1798:0
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1786:e
1782:n
1776:0
1772:n
1765:=
1756:n
1749:)
1746:7
1743:(
1718:i
1714:f
1563:z
1460:,
1452:2
1444:n
1437:2
1433:f
1420:2
1414:=
1411:Q
1405:)
1402:6
1399:(
1376:1
1370:Q
1350:1
1344:Q
1314:d
1310:n
1287:i
1283:n
1262:v
1242:f
1199:,
1195:]
1190:)
1184:2
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1175:n
1166:2
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1157:n
1152:(
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1139:f
1133:2
1122:2
1112:+
1109:1
1105:[
1093:i
1089:n
1085:2
1080:f
1068:=
1063:B
1046:)
1043:5
1040:(
1015:B
984:0
940:m
872:,
866:m
863:=
860:)
855:m
847:(
832:)
829:4
826:(
801:n
761:,
756:j
752:a
746:j
743:z
739:p
733:3
728:0
724:n
718:j
708:2
705:1
697:=
694:n
685:)
682:3
679:(
656:n
629:K
583:0
579:n
554:,
551:)
548:z
545:K
539:t
533:(
524:n
518:+
513:0
509:n
505:=
502:)
499:t
496:,
493:z
490:(
487:n
481:)
478:2
475:(
446:j
442:a
418:j
410:,
398:i
372:j
369:i
365:p
340:,
335:j
331:a
325:j
322:i
318:p
314:=
309:i
305:B
295:)
292:1
289:(
264:j
260:a
237:i
233:B
212:a
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