2011 - Opt Lett - Accepted - Revised

8/19/2019 2011 - Opt Lett - Accepted - Revised

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Anomalous retroreflection from strongly absorbing

nanoporous semiconductors

S. Ya. Prislopski1, E.K.Naumenko

1, I. M. Tiginyanu

2,3, L. Ghimpu

2, E. Monaico

3, L. Sirbu

2, and S.V.Gaponenko

1*

1 B. I. Stepanov Institute of Physics, National Academy of Sciences of Belarus, Minsk 220072, Belarus2 Institute of Electronic Engineering and Nanotechnologies“D.Ghitu”, Academy of Sciences of Moldova, Chisinau MD-2028, Moldova

3 National Centre for Materials Study and Testing, Technical University of Moldova,Chisinau MD-2004, Moldova* Corresponding author. Tel: (375 17) 284 04 48, e-mail: [email protected]

Pronounced retroreflection behavior is reported for a fishnet nanoporous strongly absorbing semiconductor material.

Retroreflection features a half-cone about 0,3 rad along with diffusive specular reflection for all angles of incidence.

Retroreflection is apparent by the naked eye with day light illumination and exhibits no selectivity with respect to

wavelength and polarization of incident light featuring minor depolarization of retroreflected light. The reflectance in

backward direction measures 12% with respect to a white scattering etalon. The phenomenon can be classified neither as

coherent backscattering nor as Anderson localization of light. The primary model includes light scattering from strongly

absorptive and refractive super-wavelength clusters existing within the porous fishnet structure. A reasonable qualitativeexplanation is based on the fact that strict retroreflection obeys shorter paths inside absorbing medium whereas all

alternative paths will lead to stronger absorption of light.

Light propagation in complex nanostructured media,in spite of being old and well established field ofoptics, demonstrates definite “renaissance” duringthe last decades owing to wealth of predicted andobserved phenomena for random and aperiodicmedia. These include coherent backscattering[1], Anderson localization[2,3], photonic glass concept[4],

propagation of waves in quasiperiodic[5] andfractal[6] structures, anisotropic scattering inaligned nanoporous dielectrics[7], Letokhov’s (random) lasers[8]. A review on these issues can befound, e.g. in Ref.[9]. All above phenomenanecessarily imply non-absorptive material formingdesirable nanostructured medium since multiple

scattering and interference of scattered light wavesare of principal importance. In this letter, we reporton non-trivial scattering behavior of fishnetnanoporous semiconductor InP in the spectral rangeof interband optical transitions where multiplescattering is inhibited by strong absorption. Lightscattering appears as persisting retroreflectioncoexisting with diffusive specular reflection.

Nanoporous InP samples were fabricated byelectrochemical etching from (100)-oriented n -typeInP:Si wafers with free carrier concentration 3×1018 cm-3. The etching was carried out in a double cellusing four Pt electrodes: reference electrode in theelectrolyte, reference electrode on the sample,

counter electrode, and working electrode, all of themconnected to a Keithley 236 source measure unit[10]. A 5% HCl aqueous solution at different galvanostaticconditions was used as the electrolyte. Itstemperature was kept constant at T = 23°C by meansof a Julabo F25 thermostat on one side of the doublecell. The electrolyte was continuously pumpedthrough both cells with peristaltic pumps. The areaof the sample exposed to the electrolyte was 0.12 cm2.The experiments were performed in the dark, andthe holes necessary for the dissolution of thematerial were created by the breakdown of the

depletion layer. A total of eight samples werefabricated using different potential variation withtime for the period of a few minutes.

The morphology of the etched samples wasexamined using a VEGA TESCAN TS 5130MMscanning electron microscope (SEM) equipped withan Oxford Instruments INCA energy dispersive x-raysystem. Porous structures with a high degree ofdisorder and variable porosity can be seen in Fig. 1for the four representative samples.

Scattering/reflectance indicatrices were measuredat wavelength 531 nm where real n and imaginary parts of the complex refraction index are n =3.8 and = 0.5[11]. The latter corresponds to the absorptioncoefficient 1.3105 cm-1. A cw Nd:LSB microchip solidstate laser (LEMT, Belarus) was directed at incidentangle α , the spot size from the beam at the samplewas ~2 mm. The scattered light was collected atvarying angle β and guided to a detector (LN/CCD-1152-E 16-bit CCD array, Princeton Instruments).Eight samples obtained for various etchingconditions have been examined. Six of them showpersisting retroreflection behavior.

Figs. 2a to 2d show a set of scattering angulardiagrams (intensity vs. scanning angle β ) for the foursamples imaged in Figs. 1a to 1d, respectively.Sample presented in Fig. 1a and Fig. 2a is one of thetwo samples showing negligible retroreflection whilespecular diffuse reflection is pronounced. Thissample has sub-wavelength structure and moreover,pronounced islands on the surface nearlyhomogeneous with respect to wavelength scale. Figs.1b,c,d and Figs. 2b,c,d demonstrate pronouncedretroreflection dominating over specular reflection.

In Figs. 2e,f scattering diagrams for the tworeference structures are given, namely nanoporousnon-absorbing dielectric with cylindric verticallyaligned sub-wavelength pores (Fig. 2e, anodicalumina similar to that studied in our paper[7]) and


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a white diffusive etalon (Fig. 2f, the spectralreflectance standard BN-R98-S5C, Gigahertz-OptikGmbH, Germany). Nanoporous alumina showsdominating specular reflectance with weakretroreflection contribution. The spectral reflectancestandard features typical diagram indicative ofmultiple diffusive scattering. Two of eight examinedsamples showed specular behavior like that inFig. 2a whereas 6 of 8 examined samples showedretroreflection like that presented in Figs. 2b,c,d.

The specular reflection (Fig. 2a) is wellunderstood in terms of effective medium approachsince microstructure of this sample has definitelysub-wavelength scale (Fig. 1a). Similar behavior isinherent in a nanoporous alumina as arepresentative sub-wavelength porous non-absorbingdielectric. Remarkable is pronounced retroreflectionin Figs. 2b,c,d for the samples which have fishnetcells comparable to or less than the wavelengths forthe visible light. We consider this behavior as non-trivial and unexpected. The absolute value ofretroreflectance is 12% with respect to the spectral

reflectance standard. Data for different angles ofincidence and polarizations of incident light aregiven in Fig. 3 for sample #6 presented in Fig. 1b andFig. 2b. At angle of incidence close to normal( = 60…80o) retroreflection dominates over specularreflection. At grazing angle of incidence = 15…30o retroreflection remains, specular reflectance for s-polarized light rises up while falling down for p-polarized light. The latter is expected from thestandard theory of light reflection. Notably,retroreflection is persistent in every case showingneither noticeable dependence on angle of incidencenor on s/p-type polarization of incident light.

The retroreflected light is characterized by a60…65% degree of polarization which coincides withthe polarization of the incident light for s-, p-, andmixed ps-polarizations. Strong polarization ofretrorelflected light reproducing incident lightpolarization is indicative of inhibited multiplescattering. That is not surprising based on stronginterband optical absorption of InP.

Searching for explanation of the observedphenomenon, a number of known retroreflectiveeffects are to be analyzed.

(i) Coherent backscattering[1] is not the casesince it occurs in narrow angle contrary to our datawhich shows retroreflection half-cone of 0.35 rad.

(ii) Anderson localization[2,3] can be supposedbased on high refraction index of InP and can lead toretroreflection. However, high InP absorption makes Anderson localization less probable.

(iii) We exclude Bragg reflection since there isneither angle nor wavelength dependence. Moreover,Bragg reflection is expected to occur not only in thebackward but in other selected directions as well.

(iv) Retroreflection is known for space dust (the socalled opposition effect[12]) from multiple scatteringby clusters of non-absorbing spherical particles. Itcannot explain our observations since the minor

depolarization of retroreflected light contradicts withpronounced polarization rotation observed andpredicted for space dust.

(v) Enhanced retroreflection has been described forrandom metal gratings[13,14]. However for metals,contrary to semiconductors, negative value ofdielectric function can be of principle importance.

(vi) Retroreflection in case of random dielectricgratings occurs but by no means dominates,scattering along direction normal to the samplesurface being dominative[14].

(vii) Retroreflection mechanisms for roughsurfaces[15] seem not to be the case.

Among disordered absorbing materials, porous Sishould be mentioned. But neither of tens of porousSi samples with brush-like structure examined by usin 1990-ies[16] has shown retroreflective behavior.Thus we suppose both specific fishnet or foam-likestructure and strong absorption are meaningful inretroreflection understanding.

To check this assumption we developed a primarymodel of light scattering by an ensemble of spheres

possessing optical constants inherent in InP. Wefound that, indeed, strong absorbance does promoteretroreflective features of scattering, and, moreover,properties of retroreflected light fit rather reasonablethe experimental data (Fig. 4). Howeverretroreflection develops in the theory only for particlediameter d > 1 μm, i.e. well exceeding lightwavelength. Smaller particles feature no pronouncedretreflection as compared to scattering in otherdirections. To achieve certain conformity of theobserved data with this simple theory one shouldsuppose that multiple cluster-like arrangementspresent within fishnet structure offering scatteringconditions similar to large monolithic particles. This

effective-medium-like cluster approach makes theproposed explanation at least partly plausible.Smaller particles in this model do contribute as wellsince these promote inhibition of multiple reflection.

Otherwise we can pose a problem thatretroreflection observed in strongly absorbing porousmaterial needs further theoretical and experimentalstudies for deeper insight into the underlyingprocesses. We cannot exclude that readily observableand persisting retroreflection may result fromcertain conservation rules[17]. A reasonablequalitative explanation may also rely upon the factthat strict retroreflection obeys shorter paths insideabsorbing medium whereas all alternative paths will

lead to stronger absorption of light. This can explainwhy retroreflection is dominating in the scatteringdiagram. Light waves scattered into other directionshave lower chance to survive.

In conclusion, retroreflection has beensystematically observed for nanoporous stronglyabsorbing InP plates with fishnet topology. Thephenomenon is insensitive to incident lightwavelength and polarization being readily observableby the naked eye with day light. The results arebelieved to stimulate further studies of lightpropagation in complex media.


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Helpful discussions with S. V. Zhukovsky, A. N. Ponyavina, S. F. Mingaleev, and M. V.Korolkov are acknowledged. The work has beensupported by the Belarus-Moldova BRFFI project.

References

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Fig.1. SEM images of four InP samples

Fig. 2. Scattering angular diagrams: (a,b,c,d) for the foursamples previously imaged in Figs. 1a,b,c,d, respectively;(e) for a nanoporous alumina plate with vertically alignedsub-wavelength pores; (f) for the spectral reflectancestandard. Lines with arrow indicate the incidence direction( = 45o and 40o)

Fig. 3. Scattering diagrams for s-, p-, and mixed ps-

polarization of incident light for the sample #6 for threevalues of incidence angle . Incidence direction is shown bythe arrow. The inset shows naked-eye observation ofretroreflection in day light with a staple indicatingincidence direction and a bulk GaAs sample shown forcomparison

Fig. 4. Measured and calculated light intensity versusangle of detection. Experimental data are taken for thesample #6 presented in Fig. 3 ( p- polarization of incidentlight, angle of incidence α = 20º). Calculations arepresented for a random ensemble of spherical particleswith average diameter 0,3 and 1.4 μm, n = 3.8, κ = 0.5


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three dimensions. J. Opt. Soc. Amer. A24

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2011 - Opt Lett - Accepted - Revised