40:
519:
2305:
529:
196:
mode" or an "evanescent mode"; while a different author will just state that no such mode exists. Since the evanescent field corresponding to the mode was computed as a solution to the wave equation, it is often discussed as being an "evanescent wave" even though its properties (such as carrying no energy) are inconsistent with the definition of
492:) or (2) those in which the evanescent wave couples two media in which traveling waves are allowed, and hence permits the transfer of energy or a particle between the media (depending on the wave equation in use), even though no traveling-wave solutions are allowed in the region of space between the two media. An example of this is
2362:). The evanescent wave coupling takes place in the non-radiative field near each medium and as such is always associated with matter; i.e., with the induced currents and charges within a partially reflecting surface. In quantum mechanics the wave function interaction may be discussed in terms of particles and described as
600:
components, however, superimpose constructively, so there can be no solution without a non-vanishing transmitted wave. The transmitted wave cannot, however, be a sinusoidal wave, since it would then transport energy away from the boundary, but since the incident and reflected waves have equal energy,
124:
Everyday electronic devices and electrical appliances are surrounded by large fields which are evanescent; their operation involves alternating voltages (producing an electric field between them) and alternating currents (producing a magnetic field around them) which are expected to only carry power
2357:
interaction in electromagnetic field theory. Depending on the nature of the source element, the evanescent field involved is either predominantly electric (capacitive) or magnetic (inductive), unlike (propagating) waves in the far field where these components are connected (identical phase, in the
106:
For instance, in the illustration at the top of the article, energy is indeed carried in the horizontal direction. However, in the vertical direction, the field strength drops off exponentially with increasing distance above the surface. This leaves most of the field concentrated in a thin boundary
195:
The formal solution to the wave equation can describe modes having an identical form, but the change of the propagation constant from real to imaginary as the frequency drops below the cut-off frequency totally changes the physical nature of the result. The solution may be described as a "cut-off
144:
arise in various contexts where a propagating electromagnetic wave is involved (even if confined). The term then differentiates electromagnetic field components that accompany the propagating wave, but which do not themselves propagate. In other, similar cases, where a propagating electromagnetic
102:
In many cases one cannot simply say that a field is or is not "evanescent" – having the
Poynting vector average to zero in some direction (or all directions). In most cases where they exist, evanescent fields are simply thought of and referred to the same as all other electric or magnetic fields
487:
More generally, practical applications of evanescent waves can be classified as (1) those in which the energy associated with the wave is used to excite some other phenomenon within the region of space where the original traveling wave becomes evanescent (for example, as in the
1801:
219:
arises from the physics involved. In these cases, solutions to the wave equation resulting in imaginary propagation constants are likewise called "evanescent", and have the essential property that no net energy is transferred, even though there is a non-zero field.
1395:
308:
within one third of a wavelength of any radio antenna. During normal operation, an antenna emits electromagnetic fields into the surrounding nearfield region, and a portion of the field energy is reabsorbed, while the remainder is radiated as EM waves.
1670:
2109:
605:. We therefore conclude that the transmitted wave must be a non-vanishing solution to Maxwell's equations that is not a traveling wave, and the only such solutions in a dielectric are those that decay exponentially: evanescent waves.
807:
2223:
103:
involved, without any special recognition of those fields' evanescence. The term's use is mostly limited to distinguishing a part of a field or solution in those cases where one might only expect the fields of a propagating wave.
552:
along z. One might expect that for angles leading to total internal reflection, the solution would consist of an incident wave and a reflected wave, with no transmitted wave at all, but there is no such solution that obeys
149:
at the interface between glass and air), the term is invoked to describe that part of the field where the wave is suppressed (such as light traveling through glass, impinging on a glass-to-air interface but beyond the
1930:
2556:
411:
1243:
are the refractive index of the medium where the incident wave and the reflected wave exist, the refractive index of the medium where the transmitted wave exists, and the angle of incidence respectively,
83:), one can still identify as an evanescent field the component of the electric or magnetic field that cannot be attributed to the propagating wave observed at a distance of many wavelengths (such as the
1531:
1160:
192:
propagate as a wave but falls off exponentially, so the field excited at that lower frequency is considered evanescent. It can also be simply said that propagation is "disallowed" for that frequency.
79:
but whose energy is spatially concentrated in the vicinity of the source (oscillating charges and currents). Even when there is a propagating electromagnetic wave produced (e.g., by a transmitting
1706:
2927:
Fan, Zhiyuan; Zhan, Li; Hu, Xiao; Xia, Yuxing (2008). "Critical process of extraordinary optical transmission through periodic subwavelength hole array: Hole-assisted evanescent-field coupling".
358:, can overcome the diffraction limit; however these systems are then limited by the system's ability to accurately capture the evanescent waves. The limitation on their resolution is given by
125:
along internal wires, but not to the outsides of the devices. Even though the term "evanescent" is not mentioned in this ordinary context, the appliances' designers still may be concerned with
1250:
922:
866:
1456:
346:. Matter radiates both propagating and evanescent electromagnetic waves. Conventional optical systems capture only the information in the propagating waves and hence are subject to the
121:
from (or toward) the surface, so that one could properly describe the field as being "evanescent in the vertical direction". This is one example of the context dependence of the term.
1042:
1011:
1833:
1539:
1959:
593:
are satisfied if the reflected wave has the same amplitude as the incident one, because these components of the incident and reflected waves superimpose destructively. Their
2338:
may be effected by placing the fiber cores close together so that the evanescent field generated by one element excites a wave in the other fiber. This is used to produce
2260:
1981:
1241:
980:
2290:
2320:
refers to the coupling between two waves due to physical overlap of what would otherwise be described as the evanescent fields corresponding to the propagating waves.
478:
1214:
1187:
949:
51:) propagating along a metal-dielectric interface. The fields away from the surface die off exponentially (right hand graph) and those fields are thus described as
715:
666:
1989:
689:
640:
1857:
1698:
1082:
1062:
723:
458:
434:
2117:
2633:
90:
A hallmark of an evanescent field is that there is no net energy flow in that region. Since the net flow of electromagnetic energy is given by the average
2347:
2471:
2409:
489:
282:
2324:
161:, different technologies or problems have certain types of expected solutions, and when the primary solutions involve wave propagation the term
1865:
2711:
2331:
overlaps another dense medium in the vicinity. This disrupts the totality of the reflection, diverting some power into the second medium.
250:, in the case of acoustical waves) cannot be discontinuous at a boundary, as would be the case if there was no evanescent wave field. In
2308:
Plot of 1/e-penetration depth of the evanescent wave against angle of incidence in units of wavelength for different refraction indices.
316:) has been fabricated and demonstrated its competence for excitation of surface electromagnetic waves in the periodic structure using a
3014:
2962:
Karalis, Aristeidis; J.D. Joannopoulos; Marin Soljačić (February 2007). "Efficient wireless non-radiative mid-range energy transfer".
2516:
364:
1468:
1093:
130:
355:
1796:{\displaystyle \mathbf {E} (\mathbf {r} ,t)=\operatorname {Re} \left\{E(\mathbf {r} )e^{i\omega t}\right\}\mathbf {\hat {z}} }
2821:
2802:
Neice, A., "Methods and
Limitations of Subwavelength Imaging", Advances in Imaging and Electron Physics, Vol. 163, July 2010.
2641:
2416:
to excite fluorophores close to a surface. This is useful when surface properties of biological samples need to be studied.
2374:
Evanescent wave coupling is commonly used in photonic and nanophotonic devices as waveguide sensors or couplers (see e.g.,
2451:
2481:
2327:
in which the evanescent field very close (see graph) to the surface of a dense medium at which a wave normally undergoes
305:
557:. Maxwell's equations in a dielectric medium impose a boundary condition of continuity for the components of the fields
2399:
2837:
Zeng, Shuwen; Yu, Xia; Law, Wing-Cheung; Zhang, Yating; Hu, Rui; Dinh, Xuan-Quyen; Ho, Ho-Pui; Yong, Ken-Tye (2013).
513:
1390:{\displaystyle k_{y}=k_{t}\cos \theta _{t}=\pm k_{t}\left(1-{\frac {\sin ^{2}\theta _{i}}{n_{ti}^{2}}}\right)^{1/2}}
616:
value. Because the vector has imaginary components, it may have a magnitude that is less than its real components.
1700:
direction), then the electric field of any of the waves (incident, reflected, or transmitted) can be expressed as
246:. The physical explanation for the existence of the evanescent wave is that the electric and magnetic fields (or
871:
815:
17:
2226:
129:
evanescence, in order to prevent or limit production of a propagating electromagnetic wave, which would lead to
94:, this means that the Poynting vector in these regions, as averaged over a complete oscillation cycle, is zero.
2666:
1404:
2385:
2578:
Takayama, O.; Bogdanov, A.A.; Lavrinenko, A.V. (2017). "Photonic surface waves on metamaterial interfaces".
1665:{\displaystyle k_{y}=\pm ik_{t}\left({\frac {\sin ^{2}\theta _{i}}{n_{ti}^{2}}}-1\right)^{1/2}=\pm i\alpha }
1016:
985:
294:
1809:
343:
3143:
3133:
347:
274:
1935:
3118:
2839:"Size dependence of Au NP-enhanced surface plasmon resonance based on differential phase measurement"
2466:
2413:
2328:
1462:
541:
522:
237:
48:
2350:
The device is usually called a power divider in the case of microwave transmission and modulation.
500:
2746:
Sreekanth, Kandammathe
Valiyaveedu; Zeng, Shuwen; Shang, Jingzhi; Yong, Ken-Tye; Yu, Ting (2012).
2232:
1964:
3138:
3097:
2441:
2359:
1219:
958:
242:
151:
328:
3128:
2426:
2269:
602:
554:
301:
158:
39:
463:
290:
258:
representing particle motion normal to the boundary cannot be discontinuous at the boundary.
2381:
Evanescent wave coupling is used to excite, for example, dielectric microsphere resonators.
2981:
2936:
2850:
2759:
2720:
2587:
2431:
2339:
2104:{\displaystyle E(\mathbf {r} )=E_{o}e^{-i(-i\alpha y+\beta x)}=E_{o}e^{-\alpha y-i\beta x}}
1677:
1192:
1165:
927:
549:
342:, systems that capture the information contained in evanescent waves can be used to create
169:
76:
802:{\displaystyle \mathbf {k_{t}} \ =\ k_{y}{\hat {\mathbf {y} }}+k_{x}{\hat {\mathbf {x} }}}
8:
2218:{\textstyle \alpha =k_{t}\left({\frac {\sin ^{2}\theta _{i}}{n_{ti}^{2}}}-1\right)^{1/2}}
694:
645:
177:
165:
is frequently applied to field components or solutions which do not share that property.
2985:
2940:
2854:
2763:
2724:
2709:
Marston, Philip L.; Matula, T.J. (May 2002). "Scattering of acoustic evanescent waves".
2591:
671:
622:
3072:
3047:
2997:
2971:
2780:
2747:
2611:
2354:
1842:
1683:
1067:
1047:
494:
443:
419:
332:
262:
247:
134:
3077:
2909:
2838:
2817:
2785:
2662:
2637:
2603:
2446:
2363:
2335:
324:
251:
212:
133:, since a propagating wave "steals" its power from the circuitry or donates unwanted
3067:
3059:
3029:
3001:
2989:
2944:
2899:
2889:
2858:
2775:
2767:
2728:
2691:
2615:
2595:
613:
313:
181:
64:
31:
350:. Systems that capture the information contained in evanescent waves, such as the
75:, is an oscillating electric and/or magnetic field that does not propagate as an
3123:
2948:
2292:
is ignored since it does not physically make sense (the wave amplification along
544:
in two dimensions, with the interface between the media lying on the x axis, the
270:
91:
80:
3048:"Cell-substrate contacts illuminated by total internal reflection fluorescence"
2748:"Excitation of surface electromagnetic waves in a graphene-based Bragg grating"
2599:
2456:
2436:
2263:
1088:
545:
3103:
2993:
2862:
2398:
Evanescent wave coupling plays a major role in the theoretical explanation of
536:
and (bottom) evanescent wave at an interface in red (reflected waves omitted).
3112:
2913:
2392:
2375:
2343:
317:
286:
266:
255:
216:
185:
518:
269:
them to very low temperatures, and to illuminate very small objects such as
113:. However, despite energy flowing horizontally, along the vertical there is
2894:
2877:
2789:
2607:
109:
107:
layer very close to the interface; for that reason, it is referred to as a
44:
3081:
2577:
2384:
Evanescent coupling, as near field interaction, is one of the concerns in
184:) the propagation constant becomes an imaginary number. A solution to the
157:
Although all electromagnetic fields are classically governed according to
3063:
2304:
1925:{\displaystyle E(\mathbf {r} )=E_{0}e^{-i\mathbf {k} \cdot \mathbf {r} }}
1836:
609:
437:
3015:"'Evanescent coupling' could power gadgets wirelessly", Celeste Biever,
2976:
2904:
2878:"Advances in Functional Solution Processed Planar 1D Photonic Crystals"
2682:
Tineke Thio (2006). "A Bright Future for
Subwavelength Light Sources".
952:
533:
339:
278:
236:, evanescent waves are formed when waves traveling in a medium undergo
2961:
2771:
2732:
2695:
2476:
2461:
2346:. At radio (and even optical) frequencies, such a device is called a
579:. For the polarization considered in this example, the conditions on
351:
233:
208:
173:
146:
84:
951:
is the magnitude of the wave vector of the transmitted wave (so the
240:
at its boundary because they strike it at an angle greater than the
30:"Evanesce" redirects here. For the album by Anatomy of a Ghost, see
481:
528:
27:
Type of field where the net flow of electromagnetic energy is zero
2405:
Evanescent wave coupling is used in powering devices wirelessly.
261:
Electromagnetic evanescent waves have been used to exert optical
203:
Although this article concentrates on electromagnetics, the term
2551:{\displaystyle \mathbf {S} =\mathbf {E} \times \mathbf {H} ^{*}}
406:{\displaystyle k\propto {\frac {1}{d}}\ln {\frac {1}{\delta }},}
289:
can be used in a gas sensor, and evanescent waves figure in the
2510:
2313:
229:
3030:
Wireless energy could power consumer, industrial electronics
2630:
IEEE Standard
Dictionary of Electrical and Electronics Terms
2876:
Lova, Paola; Manfredi, Giovanni; Comoretto, Davide (2018).
1526:{\displaystyle \sin \theta _{i}>\sin \theta _{c}=n_{ti}}
1155:{\displaystyle n_{i}\sin \theta _{i}=n_{t}\sin \theta _{t}}
608:
Mathematically, evanescent waves can be characterized by a
265:
on small particles to trap them for experimentation, or to
197:
312:
Recently, a graphene-based Bragg grating (one-dimensional
3104:
Evanescent and propagating waves animation on
Youtube.com
3033:
717:, the wave vector of the transmitted wave has the form
460:
is the distance between the object and the sensor, and
2745:
2120:
1680:
is perpendicular to the plane of incidence (along the
1407:
2875:
2634:
The
Institute of Electrical and Electronics Engineers
2519:
2272:
2235:
1992:
1967:
1938:
1868:
1845:
1812:
1709:
1686:
1542:
1471:
1253:
1222:
1195:
1168:
1096:
1070:
1050:
1019:
988:
961:
930:
874:
818:
726:
697:
674:
648:
625:
507:
466:
446:
422:
367:
612:
where one or more of the vector's components has an
254:, the physical explanation is exactly analogous—the
2708:
2816:(5th Global ed.). Pearson. pp. 135–137.
2550:
2284:
2254:
2217:
2103:
1975:
1953:
1924:
1851:
1827:
1795:
1692:
1664:
1525:
1450:
1389:
1235:
1208:
1181:
1154:
1076:
1056:
1036:
1005:
974:
943:
916:
860:
801:
709:
683:
660:
634:
472:
452:
428:
405:
2472:Total internal reflection fluorescence microscope
2410:total internal reflection fluorescence microscope
1819:
1787:
490:total internal reflection fluorescence microscope
283:total internal reflection fluorescence microscope
3110:
514:Total internal reflection § Evanescent wave
2702:
1932:, and substituting the transmitted wave vector
223:
145:wave would normally be expected (such as light
2836:
2926:
2712:Journal of the Acoustical Society of America
2622:
2391:Coupling of optical fibers without loss for
2353:Evanescent-wave coupling is synonymous with
668:and the interface of the two mediums as the
2681:
2325:frustrated total internal reflection (FTIR)
2299:
917:{\displaystyle k_{y}=k_{t}\cos \theta _{t}}
861:{\displaystyle k_{x}=k_{t}\sin \theta _{t}}
2650:
1451:{\textstyle n_{ti}={\frac {n_{t}}{n_{i}}}}
3071:
2975:
2903:
2893:
2779:
2303:
527:
517:
38:
3045:
2656:
327:, the evanescent-wave solutions of the
14:
3111:
356:near field scanning optical microscopy
2811:
2675:
2412:uses the evanescent wave produced by
1037:{\displaystyle {\hat {\mathbf {y} }}}
1006:{\displaystyle {\hat {\mathbf {x} }}}
176:is a strong function of frequency (a
2580:Journal of Physics: Condensed Matter
1983:, we find for the transmitted wave:
304:, evanescent waves are found in the
207:is used similarly in fields such as
188:having an imaginary wavenumber does
1828:{\displaystyle \mathbf {\hat {z}} }
24:
2400:extraordinary optical transmission
1461:If a part of the condition of the
619:For the plane of incidence as the
508:Total internal reflection of light
180:). Below a certain frequency (the
97:
25:
3155:
3091:
2843:Sensors and Actuators B: Chemical
2538:
2529:
2521:
2000:
1969:
1954:{\displaystyle \mathbf {k_{t}} }
1945:
1941:
1916:
1908:
1876:
1816:
1784:
1753:
1719:
1711:
1024:
993:
982:is the angle of refraction, and
789:
762:
733:
729:
275:single protein and DNA molecules
3039:
3023:
3008:
2955:
2920:
2869:
2830:
2482:Wheeler–Feynman absorber theory
2369:
1044:are the unit vectors along the
331:give rise to the phenomenon of
285:). The evanescent wave from an
2805:
2796:
2739:
2571:
2513:, the complex Poynting vector
2495:
2055:
2031:
2004:
1996:
1880:
1872:
1757:
1749:
1729:
1715:
1028:
997:
793:
766:
43:Schematic representation of a
13:
1:
2565:
2386:electromagnetic compatibility
2296:the direction in this case).
1084:axis direction respectively.
3046:Axelrod, D. (1 April 1981).
2949:10.1016/j.optcom.2008.07.077
2661:(3rd ed.). John-Wiley.
2657:Jackson, John David (1999).
2255:{\displaystyle \beta =k_{x}}
1976:{\displaystyle \mathbf {k} }
498:, and is known generally as
295:attenuated total reflectance
224:Evanescent wave applications
140:The term "evanescent field"
87:of a transmitting antenna).
7:
3052:The Journal of Cell Biology
2419:
1862:By assuming plane waves as
1236:{\displaystyle \theta _{i}}
975:{\displaystyle \theta _{t}}
10:
3160:
2882:Advanced Optical Materials
2501:Or, expressing the fields
532:Representation of a (top)
511:
495:wave-mechanical tunnelling
117:net propagation of energy
29:
2994:10.1016/j.aop.2007.04.017
2863:10.1016/j.snb.2012.09.073
2659:Classical Electrodynamics
2467:Total internal reflection
2414:total internal reflection
2329:total internal reflection
2323:One classical example is
2285:{\displaystyle +i\alpha }
1463:total internal reflection
542:total internal reflection
523:Total internal reflection
333:wave-mechanical tunneling
256:Schrödinger wave-function
238:total internal reflection
49:surface plasmon polariton
2600:10.1088/1361-648X/aa8bdd
2488:
2452:Resonant energy transfer
2318:evanescent-wave coupling
2300:Evanescent-wave coupling
501:evanescent wave coupling
318:prism coupling technique
2442:Plasmonic metamaterials
2360:impedance of free space
1064:axis direction and the
534:refracted incident wave
473:{\displaystyle \delta }
344:super-resolution images
2895:10.1002/adom.201800730
2812:Hecht, Eugene (2017).
2552:
2427:Coupling (electronics)
2309:
2286:
2256:
2219:
2105:
1977:
1955:
1926:
1853:
1829:
1797:
1694:
1666:
1527:
1452:
1391:
1237:
1210:
1183:
1156:
1078:
1058:
1038:
1007:
976:
945:
918:
862:
803:
711:
685:
662:
636:
603:conservation of energy
540:For example, consider
537:
525:
474:
454:
440:that can be resolved,
430:
407:
302:electrical engineering
60:
2929:Optics Communications
2636:. 1992. p. 458.
2558:has a zero real part.
2553:
2340:fiber-optic splitters
2334:Coupling between two
2307:
2287:
2257:
2220:
2106:
1978:
1956:
1927:
1854:
1830:
1798:
1695:
1667:
1533:, is satisfied, then
1528:
1453:
1392:
1238:
1211:
1209:{\displaystyle n_{t}}
1184:
1182:{\displaystyle n_{i}}
1157:
1079:
1059:
1039:
1008:
977:
946:
944:{\displaystyle k_{t}}
919:
863:
804:
712:
686:
663:
637:
531:
521:
512:Further information:
475:
455:
431:
408:
291:infrared spectroscopy
42:
3064:10.1083/jcb.89.1.141
2646:. IEEE STD 100-1992.
2517:
2432:Electromagnetic wave
2348:directional coupler.
2270:
2233:
2227:attenuation constant
2118:
1990:
1965:
1936:
1866:
1843:
1810:
1707:
1684:
1540:
1469:
1405:
1251:
1220:
1193:
1166:
1094:
1068:
1048:
1017:
986:
959:
928:
872:
816:
724:
695:
672:
646:
623:
480:is a measure of the
464:
444:
420:
365:
329:Schrödinger equation
170:propagation constant
77:electromagnetic wave
2986:2008AnPhy.323...34K
2941:2008OptCo.281.5467F
2855:2013SeAcB.176.1128Z
2764:2012NatSR...2E.737S
2725:2002ASAJ..111.2378M
2592:2017JPCM...29T3001T
2187:
1622:
1365:
710:{\displaystyle y=0}
661:{\displaystyle z=0}
601:this would violate
555:Maxwell's equations
293:technique known as
178:dispersion relation
159:Maxwell's equations
3019:, 15 November 2006
2752:Scientific Reports
2684:American Scientist
2548:
2336:optical waveguides
2310:
2282:
2252:
2215:
2170:
2101:
1973:
1951:
1922:
1849:
1825:
1793:
1690:
1662:
1605:
1523:
1448:
1387:
1348:
1233:
1206:
1179:
1152:
1074:
1054:
1034:
1003:
972:
941:
914:
858:
799:
707:
684:{\displaystyle xz}
681:
658:
635:{\displaystyle xy}
632:
538:
526:
470:
450:
426:
403:
263:radiation pressure
248:pressure gradients
172:of a hollow metal
168:For instance, the
61:
3144:Quantum mechanics
3134:Materials science
2964:Annals of Physics
2823:978-1-292-09693-3
2772:10.1038/srep00737
2733:10.1121/1.4778056
2696:10.1511/2006.1.40
2643:978-1-55937-240-4
2447:Quantum tunneling
2364:quantum tunneling
2188:
1852:{\displaystyle z}
1822:
1790:
1693:{\displaystyle z}
1623:
1446:
1366:
1077:{\displaystyle y}
1057:{\displaystyle x}
1031:
1000:
796:
769:
747:
741:
548:along y, and the
453:{\displaystyle d}
429:{\displaystyle k}
398:
382:
348:diffraction limit
325:quantum mechanics
306:near-field region
252:quantum mechanics
213:quantum mechanics
182:cut-off frequency
16:(Redirected from
3151:
3119:Electromagnetism
3086:
3085:
3075:
3043:
3037:
3027:
3021:
3017:NewScientist.com
3012:
3006:
3005:
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2907:
2897:
2873:
2867:
2866:
2834:
2828:
2827:
2809:
2803:
2800:
2794:
2793:
2783:
2743:
2737:
2736:
2706:
2700:
2699:
2679:
2673:
2672:
2654:
2648:
2647:
2632:. New York, NY:
2626:
2620:
2619:
2575:
2559:
2557:
2555:
2554:
2549:
2547:
2546:
2541:
2532:
2524:
2499:
2291:
2289:
2288:
2283:
2261:
2259:
2258:
2253:
2251:
2250:
2224:
2222:
2221:
2216:
2214:
2213:
2209:
2200:
2196:
2189:
2186:
2181:
2169:
2168:
2167:
2155:
2154:
2144:
2136:
2135:
2110:
2108:
2107:
2102:
2100:
2099:
2072:
2071:
2059:
2058:
2019:
2018:
2003:
1982:
1980:
1979:
1974:
1972:
1960:
1958:
1957:
1952:
1950:
1949:
1948:
1931:
1929:
1928:
1923:
1921:
1920:
1919:
1911:
1895:
1894:
1879:
1859:axis direction.
1858:
1856:
1855:
1850:
1834:
1832:
1831:
1826:
1824:
1823:
1815:
1802:
1800:
1799:
1794:
1792:
1791:
1783:
1780:
1776:
1775:
1774:
1756:
1722:
1714:
1699:
1697:
1696:
1691:
1671:
1669:
1668:
1663:
1649:
1648:
1644:
1635:
1631:
1624:
1621:
1616:
1604:
1603:
1602:
1590:
1589:
1579:
1571:
1570:
1552:
1551:
1532:
1530:
1529:
1524:
1522:
1521:
1506:
1505:
1487:
1486:
1457:
1455:
1454:
1449:
1447:
1445:
1444:
1435:
1434:
1425:
1420:
1419:
1396:
1394:
1393:
1388:
1386:
1385:
1381:
1372:
1368:
1367:
1364:
1359:
1347:
1346:
1345:
1333:
1332:
1322:
1308:
1307:
1292:
1291:
1276:
1275:
1263:
1262:
1242:
1240:
1239:
1234:
1232:
1231:
1215:
1213:
1212:
1207:
1205:
1204:
1188:
1186:
1185:
1180:
1178:
1177:
1161:
1159:
1158:
1153:
1151:
1150:
1135:
1134:
1122:
1121:
1106:
1105:
1083:
1081:
1080:
1075:
1063:
1061:
1060:
1055:
1043:
1041:
1040:
1035:
1033:
1032:
1027:
1022:
1012:
1010:
1009:
1004:
1002:
1001:
996:
991:
981:
979:
978:
973:
971:
970:
950:
948:
947:
942:
940:
939:
923:
921:
920:
915:
913:
912:
897:
896:
884:
883:
867:
865:
864:
859:
857:
856:
841:
840:
828:
827:
808:
806:
805:
800:
798:
797:
792:
787:
784:
783:
771:
770:
765:
760:
757:
756:
745:
739:
738:
737:
736:
716:
714:
713:
708:
690:
688:
687:
682:
667:
665:
664:
659:
641:
639:
638:
633:
479:
477:
476:
471:
459:
457:
456:
451:
435:
433:
432:
427:
412:
410:
409:
404:
399:
391:
383:
375:
314:photonic crystal
271:biological cells
69:evanescent field
65:electromagnetics
32:Evanesce (album)
21:
3159:
3158:
3154:
3153:
3152:
3150:
3149:
3148:
3109:
3108:
3098:Evanescent wave
3094:
3089:
3044:
3040:
3028:
3024:
3013:
3009:
2977:physics/0611063
2960:
2956:
2925:
2921:
2888:(24): 1800730.
2874:
2870:
2835:
2831:
2824:
2810:
2806:
2801:
2797:
2744:
2740:
2707:
2703:
2680:
2676:
2669:
2655:
2651:
2644:
2628:
2627:
2623:
2576:
2572:
2568:
2563:
2562:
2542:
2537:
2536:
2528:
2520:
2518:
2515:
2514:
2500:
2496:
2491:
2486:
2422:
2372:
2302:
2271:
2268:
2267:
2246:
2242:
2234:
2231:
2230:
2205:
2201:
2182:
2174:
2163:
2159:
2150:
2146:
2145:
2143:
2142:
2138:
2137:
2131:
2127:
2119:
2116:
2115:
2077:
2073:
2067:
2063:
2024:
2020:
2014:
2010:
1999:
1991:
1988:
1987:
1968:
1966:
1963:
1962:
1944:
1940:
1939:
1937:
1934:
1933:
1915:
1907:
1900:
1896:
1890:
1886:
1875:
1867:
1864:
1863:
1844:
1841:
1840:
1814:
1813:
1811:
1808:
1807:
1782:
1781:
1764:
1760:
1752:
1745:
1741:
1718:
1710:
1708:
1705:
1704:
1685:
1682:
1681:
1640:
1636:
1617:
1609:
1598:
1594:
1585:
1581:
1580:
1578:
1577:
1573:
1572:
1566:
1562:
1547:
1543:
1541:
1538:
1537:
1514:
1510:
1501:
1497:
1482:
1478:
1470:
1467:
1466:
1440:
1436:
1430:
1426:
1424:
1412:
1408:
1406:
1403:
1402:
1377:
1373:
1360:
1352:
1341:
1337:
1328:
1324:
1323:
1321:
1314:
1310:
1309:
1303:
1299:
1287:
1283:
1271:
1267:
1258:
1254:
1252:
1249:
1248:
1227:
1223:
1221:
1218:
1217:
1200:
1196:
1194:
1191:
1190:
1173:
1169:
1167:
1164:
1163:
1146:
1142:
1130:
1126:
1117:
1113:
1101:
1097:
1095:
1092:
1091:
1069:
1066:
1065:
1049:
1046:
1045:
1023:
1021:
1020:
1018:
1015:
1014:
992:
990:
989:
987:
984:
983:
966:
962:
960:
957:
956:
935:
931:
929:
926:
925:
908:
904:
892:
888:
879:
875:
873:
870:
869:
852:
848:
836:
832:
823:
819:
817:
814:
813:
788:
786:
785:
779:
775:
761:
759:
758:
752:
748:
732:
728:
727:
725:
722:
721:
696:
693:
692:
673:
670:
669:
647:
644:
643:
624:
621:
620:
598:
591:
584:
577:
570:
566:
562:
516:
510:
484:of the sensor.
465:
462:
461:
445:
442:
441:
436:is the maximal
421:
418:
417:
390:
374:
366:
363:
362:
226:
100:
98:Use of the term
92:Poynting vector
73:evanescent wave
35:
28:
23:
22:
18:Evanescent wave
15:
12:
11:
5:
3157:
3147:
3146:
3141:
3139:Nanotechnology
3136:
3131:
3126:
3121:
3107:
3106:
3101:
3093:
3092:External links
3090:
3088:
3087:
3058:(1): 141–145.
3038:
3022:
3007:
2954:
2919:
2868:
2829:
2822:
2804:
2795:
2738:
2701:
2674:
2667:
2649:
2642:
2621:
2586:(46): 463001.
2569:
2567:
2564:
2561:
2560:
2545:
2540:
2535:
2531:
2527:
2523:
2493:
2492:
2490:
2487:
2485:
2484:
2479:
2474:
2469:
2464:
2459:
2454:
2449:
2444:
2439:
2437:Plasmonic lens
2434:
2429:
2423:
2421:
2418:
2371:
2368:
2312:Especially in
2301:
2298:
2281:
2278:
2275:
2264:phase constant
2249:
2245:
2241:
2238:
2212:
2208:
2204:
2199:
2195:
2192:
2185:
2180:
2177:
2173:
2166:
2162:
2158:
2153:
2149:
2141:
2134:
2130:
2126:
2123:
2112:
2111:
2098:
2095:
2092:
2089:
2086:
2083:
2080:
2076:
2070:
2066:
2062:
2057:
2054:
2051:
2048:
2045:
2042:
2039:
2036:
2033:
2030:
2027:
2023:
2017:
2013:
2009:
2006:
2002:
1998:
1995:
1971:
1947:
1943:
1918:
1914:
1910:
1906:
1903:
1899:
1893:
1889:
1885:
1882:
1878:
1874:
1871:
1848:
1821:
1818:
1804:
1803:
1789:
1786:
1779:
1773:
1770:
1767:
1763:
1759:
1755:
1751:
1748:
1744:
1740:
1737:
1734:
1731:
1728:
1725:
1721:
1717:
1713:
1689:
1674:
1673:
1661:
1658:
1655:
1652:
1647:
1643:
1639:
1634:
1630:
1627:
1620:
1615:
1612:
1608:
1601:
1597:
1593:
1588:
1584:
1576:
1569:
1565:
1561:
1558:
1555:
1550:
1546:
1520:
1517:
1513:
1509:
1504:
1500:
1496:
1493:
1490:
1485:
1481:
1477:
1474:
1443:
1439:
1433:
1429:
1423:
1418:
1415:
1411:
1399:
1398:
1384:
1380:
1376:
1371:
1363:
1358:
1355:
1351:
1344:
1340:
1336:
1331:
1327:
1320:
1317:
1313:
1306:
1302:
1298:
1295:
1290:
1286:
1282:
1279:
1274:
1270:
1266:
1261:
1257:
1230:
1226:
1203:
1199:
1176:
1172:
1149:
1145:
1141:
1138:
1133:
1129:
1125:
1120:
1116:
1112:
1109:
1104:
1100:
1073:
1053:
1030:
1026:
999:
995:
969:
965:
938:
934:
911:
907:
903:
900:
895:
891:
887:
882:
878:
855:
851:
847:
844:
839:
835:
831:
826:
822:
810:
809:
795:
791:
782:
778:
774:
768:
764:
755:
751:
744:
735:
731:
706:
703:
700:
680:
677:
657:
654:
651:
631:
628:
596:
589:
582:
575:
568:
564:
560:
509:
506:
469:
449:
425:
414:
413:
402:
397:
394:
389:
386:
381:
378:
373:
370:
243:critical angle
225:
222:
152:critical angle
131:radiation loss
99:
96:
26:
9:
6:
4:
3:
2:
3156:
3145:
3142:
3140:
3137:
3135:
3132:
3130:
3129:Metamaterials
3127:
3125:
3122:
3120:
3117:
3116:
3114:
3105:
3102:
3099:
3096:
3095:
3083:
3079:
3074:
3069:
3065:
3061:
3057:
3053:
3049:
3042:
3036:press release
3035:
3031:
3026:
3020:
3018:
3011:
3003:
2999:
2995:
2991:
2987:
2983:
2978:
2973:
2969:
2965:
2958:
2950:
2946:
2942:
2938:
2934:
2930:
2923:
2915:
2911:
2906:
2901:
2896:
2891:
2887:
2883:
2879:
2872:
2864:
2860:
2856:
2852:
2849:: 1128–1133.
2848:
2844:
2840:
2833:
2825:
2819:
2815:
2808:
2799:
2791:
2787:
2782:
2777:
2773:
2769:
2765:
2761:
2757:
2753:
2749:
2742:
2734:
2730:
2726:
2722:
2718:
2714:
2713:
2705:
2697:
2693:
2689:
2685:
2678:
2670:
2664:
2660:
2653:
2645:
2639:
2635:
2631:
2625:
2617:
2613:
2609:
2605:
2601:
2597:
2593:
2589:
2585:
2581:
2574:
2570:
2543:
2533:
2525:
2512:
2508:
2504:
2498:
2494:
2483:
2480:
2478:
2475:
2473:
2470:
2468:
2465:
2463:
2460:
2458:
2455:
2453:
2450:
2448:
2445:
2443:
2440:
2438:
2435:
2433:
2430:
2428:
2425:
2424:
2417:
2415:
2411:
2406:
2403:
2401:
2396:
2394:
2393:fiber tapping
2389:
2387:
2382:
2379:
2377:
2376:prism coupler
2367:
2365:
2361:
2358:ratio of the
2356:
2351:
2349:
2345:
2344:fiber tapping
2341:
2337:
2332:
2330:
2326:
2321:
2319:
2315:
2306:
2297:
2295:
2279:
2276:
2273:
2265:
2247:
2243:
2239:
2236:
2228:
2210:
2206:
2202:
2197:
2193:
2190:
2183:
2178:
2175:
2171:
2164:
2160:
2156:
2151:
2147:
2139:
2132:
2128:
2124:
2121:
2096:
2093:
2090:
2087:
2084:
2081:
2078:
2074:
2068:
2064:
2060:
2052:
2049:
2046:
2043:
2040:
2037:
2034:
2028:
2025:
2021:
2015:
2011:
2007:
1993:
1986:
1985:
1984:
1912:
1904:
1901:
1897:
1891:
1887:
1883:
1869:
1860:
1846:
1838:
1777:
1771:
1768:
1765:
1761:
1746:
1742:
1738:
1735:
1732:
1726:
1723:
1703:
1702:
1701:
1687:
1679:
1659:
1656:
1653:
1650:
1645:
1641:
1637:
1632:
1628:
1625:
1618:
1613:
1610:
1606:
1599:
1595:
1591:
1586:
1582:
1574:
1567:
1563:
1559:
1556:
1553:
1548:
1544:
1536:
1535:
1534:
1518:
1515:
1511:
1507:
1502:
1498:
1494:
1491:
1488:
1483:
1479:
1475:
1472:
1464:
1459:
1441:
1437:
1431:
1427:
1421:
1416:
1413:
1409:
1382:
1378:
1374:
1369:
1361:
1356:
1353:
1349:
1342:
1338:
1334:
1329:
1325:
1318:
1315:
1311:
1304:
1300:
1296:
1293:
1288:
1284:
1280:
1277:
1272:
1268:
1264:
1259:
1255:
1247:
1246:
1245:
1228:
1224:
1201:
1197:
1174:
1170:
1147:
1143:
1139:
1136:
1131:
1127:
1123:
1118:
1114:
1110:
1107:
1102:
1098:
1090:
1087:By using the
1085:
1071:
1051:
967:
963:
954:
936:
932:
909:
905:
901:
898:
893:
889:
885:
880:
876:
853:
849:
845:
842:
837:
833:
829:
824:
820:
780:
776:
772:
753:
749:
742:
720:
719:
718:
704:
701:
698:
678:
675:
655:
652:
649:
629:
626:
617:
615:
611:
606:
604:
599:
592:
585:
578:
571:
556:
551:
547:
543:
535:
530:
524:
520:
515:
505:
503:
502:
497:
496:
491:
485:
483:
467:
447:
439:
423:
400:
395:
392:
387:
384:
379:
376:
371:
368:
361:
360:
359:
357:
353:
349:
345:
341:
336:
334:
330:
326:
321:
319:
315:
310:
307:
303:
298:
296:
292:
288:
287:optical fiber
284:
280:
276:
272:
268:
264:
259:
257:
253:
249:
245:
244:
239:
235:
231:
221:
218:
217:wave equation
214:
210:
206:
201:
199:
193:
191:
187:
186:wave equation
183:
179:
175:
171:
166:
164:
160:
155:
153:
148:
143:
138:
136:
132:
128:
122:
120:
116:
112:
111:
104:
95:
93:
88:
86:
82:
78:
74:
70:
66:
58:
54:
50:
46:
41:
37:
33:
19:
3055:
3051:
3041:
3025:
3016:
3010:
2967:
2963:
2957:
2935:(21): 5467.
2932:
2928:
2922:
2905:11567/928329
2885:
2881:
2871:
2846:
2842:
2832:
2813:
2807:
2798:
2755:
2751:
2741:
2716:
2710:
2704:
2690:(1): 40–47.
2687:
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2333:
2322:
2317:
2311:
2293:
2113:
1861:
1805:
1678:polarization
1675:
1460:
1400:
1086:
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618:
607:
594:
587:
580:
573:
558:
550:polarization
539:
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299:
260:
241:
227:
215:, where the
204:
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139:
135:interference
126:
123:
118:
114:
110:surface wave
108:
105:
101:
89:
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68:
62:
56:
52:
45:surface wave
36:
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2457:Snell's law
1837:unit vector
1089:Snell's law
610:wave vector
438:wave vector
281:(as in the
127:maintaining
3113:Categories
2668:047130932X
2566:References
2355:near field
953:wavenumber
340:microscopy
279:microscopy
205:evanescent
163:evanescent
53:evanescent
2970:(1): 34.
2914:2195-1071
2544:∗
2534:×
2477:Waveguide
2462:Superlens
2280:α
2237:β
2191:−
2161:θ
2157:
2122:α
2094:β
2088:−
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2079:−
2050:β
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1820:^
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998:^
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902:
850:θ
846:
794:^
767:^
691:plane at
642:plane at
614:imaginary
468:δ
396:δ
388:
372:∝
352:superlens
234:acoustics
209:acoustics
174:waveguide
147:refracted
85:far field
59:direction
2790:23071901
2608:29053474
2420:See also
924:, where
3082:7014571
3073:2111781
3002:1887505
2982:Bibcode
2937:Bibcode
2851:Bibcode
2781:3471096
2760:Bibcode
2758:: 737.
2721:Bibcode
2616:1528860
2588:Bibcode
2511:phasors
2342:and in
2262:is the
2225:is the
1839:in the
1835:is the
1676:If the
482:quality
81:antenna
55:in the
3124:Optics
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2912:
2820:
2814:Optics
2788:
2778:
2665:
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2114:where
1806:where
1216:, and
1162:where
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572:, and
546:normal
416:where
230:optics
2998:S2CID
2972:arXiv
2612:S2CID
2489:Notes
1961:into
1401:with
812:with
71:, or
67:, an
3078:PMID
2910:ISSN
2818:ISBN
2786:PMID
2663:ISBN
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2604:PMID
2505:and
1489:>
1013:and
868:and
586:and
354:and
277:for
267:cool
232:and
211:and
198:wave
142:does
119:away
3068:PMC
3060:doi
3034:MIT
2990:doi
2968:323
2945:doi
2933:281
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2859:doi
2847:176
2776:PMC
2768:doi
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843:sin
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563:, H
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300:In
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