Localization: Photon Localization in Resonant Media
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LOCALIZATION December 2002 ■ Optics & Photonics News 25 LOCALIZATION Photon Localization in Resonant Media A.A. Chabanov and A. Z. Genack I n analogy with electron localization in insulators, 1 it has been anticipated that photons may be trapped by the construc- tive interference of waves returning to a point within a strongly scattering medi- um. 2 Since the closeness to the transition between diffusive and localized waves de- termines the statistics of multiply scattered waves, charting this transition is of funda- mental interest for both statistical optics and electronic mesoscopic physics. 3 How- ever, the very possibility of observing pho- ton localization in random systems has been called into question by the difficul- ties of achieving strong scattering and of unambiguously detecting electromagnetic localization. Measurements of the exponential scal- ing of transmission have not definitively established photon localization since such scaling may also be due to the presence of absorption. Recently, however, we have shown that the variance of the relative fluctuations of intensity or total transmis- sion provide a decisive test for localization, even in the presence of absorption. These measurements provide a sure guide in the search for photon localization, which can be used to sort out the precise material and structural characteristics that may edge samples towards and potentially across the localization threshold. We have carried out measurements of microwave transmission in an ensemble of random collections of alumina spheres randomly positioned in a copper tube at low density. Scattering from high-index dielectric spheres is strongest when the wavelength is comparable to or smaller than the diameter of the spheres. Strong scattering near the first five Mie reso- nances is evident from the observation of precipitous drops in transmission and sharp peaks in the photon transit time, seen in Figs. 1(a) and 1(b), respectively. 4 However, waves are localized only in a nar- row frequency window above the first res- onance, as indicated by the rise of relative fluctuations above the critical value of 7/3 at the threshold of the localization transi- tion [Fig. 1(c)]. 4 Within this window, the probability distribution for in- tensity becomes extraordinarily broad. 3 At the same time, in contrast to the behavior for dif- fusing waves, the photon tran- sit time becomes correlated with the transmitted intensity [Fig. 1(d)]. 5 This is consistent with the expectation that, for localized waves, the transmit- ted intensity and photon dwell time are each high when the wave is at resonance with a lo- calized state. Localization oc- curs when this correlator is greater than 1.1. When the sample is thinner than the absorption length, we find that the ratio of the field correlation frequency and the mode spacing in a thin sample gives a reliable measure of the extent of localization and is in accord with measurements of conductance and of relative in- tensity fluctuations. 4 The mini- mum of this ratio, known as the Thouless number, occurs above the first Mie resonance as a result of a sharp drop in the density of states due to collec- tive scattering. These results make it possible to track the changing character of static and dynamic wave statistics through the Anderson localiza- tion transition. References 1. P.W.Anderson, Phys. Rev. 109, 1492 (1958). 2. S. John, Localization of Light, Physics Today, 32, May 1991. 3. A.A. Chabanov, M. Stoytchev and A. Z. Genack, Nature 404, 850 (2000). 4. A.A. Chabanov and A. Z. Genack, Phys. Rev. Lett. 87, 153901 (2001). 5. A.A. Chabanov and A. Z. Genack, Phys. Rev. Lett. 87, 233903 (2001). A. A. Chabanov ([email protected]) and A. Z. Genack are with the Physics Department, Queens College of CUNY,Flushing,New York. Figure 1. (a) Average transmitted intensity, <I >, (b) average photon transit time, = <I>/<I >, where is the spectral derivative of the phase ac- cumulated by the field as it propagates through the sample, (c) variance of normalized transmitted in- tensity, var(I/<I>), and (d) dimensionless ratio, = <I>/<I><>, versus frequency in a quasi- 1D alumina sample with length L=80 cm and alu- mina volume filling fraction f=0.068. The dashed lines indicate the localization threshold.
Transcript of Localization: Photon Localization in Resonant Media
LOCALIZATION
December 2002 ■ Optics & Photonics News 25
LOCALIZATIONPhoton Localization in Resonant MediaA.A. Chabanov and A. Z. Genack
In analogy with electron localization ininsulators,1 it has been anticipated that
photons may be trapped by the construc-tive interference of waves returning to apoint within a strongly scattering medi-um.2 Since the closeness to the transitionbetween diffusive and localized waves de-termines the statistics of multiply scatteredwaves, charting this transition is of funda-mental interest for both statistical opticsand electronic mesoscopic physics.3 How-ever, the very possibility of observing pho-ton localization in random systems hasbeen called into question by the difficul-ties of achieving strong scattering and ofunambiguously detecting electromagneticlocalization.
Measurements of the exponential scal-ing of transmission have not definitivelyestablished photon localization since suchscaling may also be due to the presence ofabsorption. Recently, however, we haveshown that the variance of the relativefluctuations of intensity or total transmis-sion provide a decisive test for localization,even in the presence of absorption. Thesemeasurements provide a sure guide in thesearch for photon localization, which canbe used to sort out the precise materialand structural characteristics that mayedge samples towards and potentiallyacross the localization threshold.
We have carried out measurements ofmicrowave transmission in an ensemble ofrandom collections of alumina spheresrandomly positioned in a copper tube atlow density. Scattering from high-indexdielectric spheres is strongest when thewavelength is comparable to or smallerthan the diameter of the spheres. Strongscattering near the first five Mie reso-nances is evident from the observation ofprecipitous drops in transmission andsharp peaks in the photon transit time,seen in Figs. 1(a) and 1(b), respectively.4
However, waves are localized only in a nar-row frequency window above the first res-onance, as indicated by the rise of relativefluctuations above the critical value of 7/3at the threshold of the localization transi-tion [Fig. 1(c)].4 Within this window, the
probability distribution for in-tensity becomes extraordinarilybroad.3 At the same time, incontrast to the behavior for dif-fusing waves, the photon tran-sit time becomes correlatedwith the transmitted intensity [Fig. 1(d)].5 This is consistentwith the expectation that, forlocalized waves, the transmit-ted intensity and photon dwelltime are each high when thewave is at resonance with a lo-calized state. Localization oc-curs when this correlator isgreater than 1.1.
When the sample is thinnerthan the absorption length, wefind that the ratio of the fieldcorrelation frequency and themode spacing in a thin samplegives a reliable measure of theextent of localization and is inaccord with measurements ofconductance and of relative in-tensity fluctuations.4 The mini-mum of this ratio, known asthe Thouless number, occursabove the first Mie resonance asa result of a sharp drop in thedensity of states due to collec-tive scattering. These resultsmake it possible to track thechanging character of staticand dynamic wave statisticsthrough the Anderson localiza-tion transition.
References1. P.W.Anderson, Phys. Rev. 109, 1492
(1958).2. S. John, Localization of Light, Physics
Today, 32, May 1991.3. A.A. Chabanov, M. Stoytchev and A.
Z. Genack, Nature 404, 850 (2000).4. A.A. Chabanov and A. Z. Genack,
Phys. Rev. Lett. 87, 153901 (2001).5. A.A. Chabanov and A. Z. Genack, Phys. Rev. Lett. 87,
233903 (2001).
A. A. Chabanov ([email protected]) and A. Z.Genack are with the Physics Department, QueensCollege of CUNY, Flushing, New York.
Figure 1. (a) Average transmitted intensity, <I>,(b) average photon transit time, � = <I��>/<I>,where �� is the spectral derivative of the phase ac-cumulated by the field as it propagates through thesample, (c) variance of normalized transmitted in-tensity, var(I/<I>), and (d) dimensionless ratio,� = <I��>/<I><��>, versus frequency in a quasi-1D alumina sample with length L=80 cm and alu-mina volume filling fraction f=0.068. The dashedlines indicate the localization threshold.
