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Optical control of photon tunneling through an array of nanometer-scale cylindrical channels

Optical control of photon tunneling through an array of nanometer-scale cylindrical channels
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    a  r   X   i  v  :  c  o  n   d  -  m  a   t   /   0   2   0   7   4   5   0  v   1   [  c  o  n   d  -  m  a   t .  s   t  r  -  e   l   ]   1   8   J  u   l   2   0   0   2 Optical control of photon tunneling through an array of nanometer scale cylindricalchannels I. I. Smolyaninov, A. V. Zayats (1) , A. Stanishevsky, and C. C. Davis Electrical and Computer Engineering Department, University of Maryland, College Park, MD 20742  (1) Department of Pure and Applied Physics, Queen’s University of Belfast, Belfast BT7 1NN,UK  (February 1, 2008)We report first observation of photon tunneling gated by light at a different wavelength in anartificially created array of nanometer scale cylindrical channels in a thick gold film. Polarizationproperties of gated light provide strong proof of the enhanced nonlinear optical mixing in nanometricchannels involved in the process. This suggests the possibility of building a new class of ”gated”photon tunneling devices for massive parallel all-optical signal and image processing.PACS no.: 78.67.-n, 42.50.-p, 42.65.-k In our recent work [1,2] some of the unusual proper-ties of naturally occurring extremely small pinholes inthick gold films covered with highly optically nonlinearpolydiacetylene layers have been studied. Measurementsof photon tunneling through individual nanometer scalepinholes has provided strong indication of ”photon block-ade” effect similar to Coulomb blockade phenomena ob-served in single-electron tunneling experiments [1]. Wehave also reported observation of photon tunneling be-ing gated by light at a different wavelength in similar butsomewhat larger pinholes [2]. These observations suggestpossibility of building a new class of ”gated” photon tun-neling devices for all-optical signal and image processingin classical and quantum communications and comput-ing. A big step forward would be to artificially fabricatesuch devices in controllable and reproducible manner.Moreover, massive parallel all-optical signal processingcan be achieved if large arrays of such pinholes with en-hanced nonlinear properties can be created. However,transition from individual pinholes to a periodic arrayof them leads to new physics involved in the nonlinearoptical processes.Linear optical properties of metallic films perforatedwith an array of periodic subwavelength holes and ex-hibiting the so-called extraordinary enhanced opticaltransmission have been intensively studied recently (see[3–5] and Refs. therein). Although the exact natureof the enhanced transmission in two-dimensional case(which is significantly different from a better understoodone-dimensional case of subwavelength slits) is still notfully established, the role of surface plasmon polaritons(SPPs) in this process is commonly accepted. SPP Blochwaves can be excited by incident light on the interfaces of a periodically nanostructured film, which may be treatedas a surface polaritonic crystal [5–7]. Resonant light tun-neling via states of surface polariton Bloch waves is one of the mechanisms involved in the enhanced transmission.A fundamental difference between conventional pho-tonic crystals and surface polaritonic crystals is a differ-ent electromagnetic field distribution close to the surface.Surface polariton is an intrinsically two-dimensional ex-citation whose electromagnetic field is concentrated at ametal interface. Thus, in contrast to photonic crystals,strong electromagnetic field enhancement takes place ata SPP crystal interface related to the surface polaritonfield localization [8]. Such enhancement effects are absentin photonic crystals. Field enhancement results in muchstronger nonlinear response achieved with surface polari-tonic crystals as it is related to the local field strength.This can significantly facilitate nonlinear optical mixingin such structures.As a logical step forward, we can ask what would hap-pen if a periodically nanostructured metal film would beembedded in a nonlinear optical material. In this Letterwe report first experimental studies of nonlinear opticalproperties of arrays of artificial nanometer-scale cylin-drical pinholes in free standing thick gold films, whichexhibit strong nonlinear optical mixing due to the pres-ence of nonlinear material inside the pinholes and on theinterfaces of the film. In addition to the SPP effectson the film interfaces, due to pronounced cylindricalityof the holes, the shape-resonances (cylindrical surfaceplasmons) can be excited in the holes [9]. At a giventransmitted optical power, for a small cylinder diametersoptical field of a cylindrical surface plasmon grows in-versely proportional to the diameter. Thus, sufficientlythin cylindrical pinholes filled with nonlinear optical ma-terial should start to exhibit enhanced nonlinear opticalmixing.In our experiments rectangular arrays of nanometriccylindrical holes have been patterned into a freestanding400 nm thick gold membrane using focused gallium ionbeam (FIB) milling. To avoid stress in the gold mem-brane, the gold film is supported by 50 nm thick  Si 3 N  4 membrane with 5 nm intermediate Cr layer. Since thereis no glass/metal interface, milling artifacts such as re-deposited material can be avoided leading to a better-defined structure geometry. We have been successful inpatterning relatively large areas (500  µ m x 500  µ m) of the gold membranes, creating nanosized holes with di-mensions down to 20 nm. The diameter of the hole canbe controlled by using a controlled endpoint terminationtechnique. In this technique a Faraday cup is placed un-derneath the membrane and the transmitted ion currentis measured  in-situ   during FIB milling. The milling canthen be terminated, by blanking the ion beam, once a1  defined ion current is passing through the emerging holein the membrane. The images of the cylindrical pinholearrays fabricated in a 400 nm thick free standing goldfilm are shown in Fig. 1. Similar to the sample prepara-tion described in [1], a drop of poly-3-butoxy-carbonyl-methyl-urethane (3BCMU) polydiacetylene solution inchloroform was deposited onto the gold film surface. Af-ter solvent evaporation films of polydiacetylene were lefton both the top and the bottom surfaces of the perfo-rated gold film. Such 3BCMU polydiacetylene films holdthe current record for the largest fast nonresonant optical χ (3) nonlinearity [10].   FIG. 1. Focused ion beam milled arrays of cylindrical pin-holes in a 400 nm thick free standing gold film. The scale baris 500 nm. Our experimental setup is shown in Fig.2. A bentoptical fiber tip similar to the bent tips often used innear-field optical microscopes [11] was used to collect thetransmitted light. The fiber tip was positioned abovethe individual pinhole array in contact with the thickpolymer coating using a far-field optical microscope andthe shear-force distance control system commonly used innear-field optical setups. [12] Since pinhole arrays weretypically separated by at least 10  µ m distances, prop-erties of individual arrays were studied in the absenceof any background scattered light. Under far-field micro-scope control, ∼ 30 × 30 µm 2 areaof the sample containingthe pinhole array of interest has been illuminated with488 nm light of a CW argon ion laser and the 633 nmlight of a CW He-Ne laser. The latter was used as signallight and the former was used as control light in the opti-cal gating experiments. The samples were illuminated atthe angle of incidence of approximately 45 o so that theprojection of the illuminating light wavevector onto thesurface is in the direction approximately correspondingto the direction along the hole rows (Γ − X   direction of the Brillouin zone).   bent fiber tip3BCMUgold filmpinhole array633 nm    H  e  -   N  e    l  a  s  e  r  A  r    i  o  n    l  a  s  e  r lens 488 nm chopperlock-inreferencePMTred filter 633 nmsignal outin FIG. 2. Schematic view of the experimental setup. First we have studied how transmission of the arrays atthe signal light wavelength ( λ  = 633 nm) is affected by si-multaneous illumination with control light ( λ  = 488 nm).In order to observe light controlled tunneling directly, wemodulated the incident 488 nm light with a chopper ata frequency of 1.2 kHz. Light transmitted through thepinhole array was collected with the fiber and detectedwith a photomultiplier (PMT) through an optical filterwhich completely cuts off the blue light. Modulation of the transmission of the array with 20 nm holes at the633 nm wavelength induced by modulation of P-polarizedcontrol light illuminating the same area was observed us-ing a lock-in amplifier , which was synchronized with thechopper (Fig. 2). Thus, the intensity variations of thesignal light tunneling through the pinhole array inducedby 488 nm light have been measured directly (Fig. 3).The time behavior of the observed switching is deter-mined by the time constant of the lock-in-amplifier ( ∼  3s) needed for the signal integration. At the same time,for the arrays with larger holes ( ∼  100 nm diameter) nosignificant variations of the transmission was observedfor the given wavelengths and intensities of signal andcontrol light.   01020304050607080050010001500 shutteropened shutteropened shutteropened shutterclosedshutterclosedshutterclosed     T   r   a   n   s   m    i   s   s    i   o   n   o    f    6    3    2   n   m    l    i   g    h    t   m   o    d   u    l   a    t   e    d    b   y    4    8    8   n   m    l    i   g    h    t  Time (sec) 2  FIG. 3. Modulation of the 20 nm pinholes array transmis-sion at 633 nm induced by modulation of control light. Theshutter of control light was closed and opened three timesduring the experiment. Polarization properties of the signal light passingthrough the array of smallest pinholes are strikingly dif-ferent from the polarization properties of the transmittedred light measured in the absence of blue light illumina-tion. These polarization properties provide a very strongproof of nonlinear optical mixing in the polydiacetylene-filled pinholes. In the absence of modulating blue light,transmission of P-polarized red light is higher than thetransmission of S-polarized red light by approximatelya factor of 3. This observation is consistent with thetheoretical model of the enhanced transmission of sub-wavelength pinhole arrays relying on the excitation of surface polaritons on both film interfaces, since at theoblique incidence the light of different polarizations in-teracts with different SPP resonances. This ratio of P-to S-polarized light transmission has been observed tobe rather insensitive to the pinhole diameter in a stud-ied range of the pinhole sizes as is expected since thespectrum of the SPP excitations depends mainly on theperiodicity of the structure.However, under the modulation with P-polarized bluelight, the P to S ratio in the modulated red light transmis-sion jumps to approximately a factor of 20. Polarizationmeasurements offer the best distinction between nonlin-ear optical mixing effects of interest and possible thermaleffects such as thermal expansion of the pinholes, heat-ing of the filling material etc. which could interfere withthe nonlinear optical effects. Thermal modulation of sub-wavelength aperture transmission has been observed pre-viously under intense aperture illumination [13]. We wereable to observe similar effects in the pinhole arrays trans-mission at much larger than usual illumination intensi-ties achieved by much tighter focusing (to within a-few-micrometers spots) of the modulating blue light. How-ever, polarization dependence of the modulated red lightobtained under such conditions is very weak (Fig.4(c)):the P to S ratio in the thermally modulated red lighttransmission falls to approximately a factor of 1.5.   -500501001502002503000246810121416182022 PS (c)(b)(a)reference transmission of 633 nm through same holesthermal effect observed on large holes at large power     T   r   a   n   s   m    i   s   s    i   o   n   o    f    6    3    3   n   m     l    i   g    h    t   m   o    d   u    l   a    t   e    d    b   y    4    8    8   n   m     l    i   g    h    t    (   a .   u .    )  Polarization Angle (degrees) FIG. 4. (a) Polarization dependence of the modulationof the 20 nm pinholes array transmission at 633 nm inducedby modulation of P-polarized 488 nm light. (b) Polarizationdependence of the same array transmission at 633 nm withoutillumination with blue light. (c) Polarization dependence of the thermal modulation of the red light transmission. Extremely strong polarization dependence of the mod-ulated transmission of the signal light can be explainedtaking into account the properties of surface polaritonBloch waves on the periodically perforated gold surfaces,the properties of surface plasmons in cylindrical chan-nels, and the properties of a  χ (3) nonlinear susceptibilitytensor of 3BCMU polydiacetylene.To understand the observed transmission behavior, letus consider the spectrum of electromagnetic excitationsin our system. At certain combinations of incidence an-gles and wavelengths, the electromagnetic wave incidenton the periodic structure excites the surface polaritonBloch waves. Diffraction of light on a periodic structureprovides the wave vector conservation needed for the cou-pling to SPP [8]: k SP   =  ωc sinθ u xy δ  s −  p ±  p 2 πD  u x ± q  2 πD  u y ,  (1)where  δ  s −  p  = 1 for P-polarized incident light (definedwith respect to the film interface) and 0 for S-polarizedlight,  k SP  is the surface polariton wave vector on a pe-riodic interface,  u xy  is the unit vector in the direction of the in-plane component of the incident light wave vector, u x  and  u y  are the unit reciprocal lattice vectors of a pe-riodic structure, D is its periodicity (assumed to be thesame in both x- and y-directions), and p and q are theinteger numbers corresponding to the different propaga-tion directions of the excited SPP modes. Since SPP is ingeneral a longitudinal excitation, the electric field of theexcitation light should have an electric field componentperpendicular to the surface or parallel to the SPP prop-agation direction. Therefore, according to Eq.(1) surfacepolaritons excited with S-polarised light correspond tothe Bloch waves at the edge of the even Brillouin zones(standing modes), while for P-polarized excitation theyare propagating Bloch waves.3  In our case, the metal film is sufficiently thick toneglect the interaction between surface polaritons ex-cited on different interfaces, therefore two independentsets of resonances can be considered [8]. Since oneside of the metal film is covered with a polymer ( ǫ  ≈ 1.7) while another is in contact with Cr/Si 3 N 4  ( ǫ  ≈ 2.0), the SPP resonant conditions will be slightly dif-ferent on different interfaces of the film. (The disper-sion of surface polaritons on a smooth surface is given by k SP   =  ω/c ( ǫǫ m / ( ǫ + ǫ m )) 1 / 2 , where  ǫ m  and  ǫ  are the di-electric functions of metal and adjacent medium, respec-tively.) Since the filling factor of the structures underconsideration is small enough ( f   = ( d/D ) 2 ) the modifi-cations of the SPP dispersion on a smooth interface isexpected to be also small, and it can be used to esti-mate the resonant frequencies of the SPP Bloch wavesexcitation. Considering Γ − X   direction of the Brillouinzone (  p  =  ± 1 , ± 2 ,... ; q   = 0), for P-polarised incidentlight and the angle of incidence of 45 o used in the exper-iment, the SPP Bloch waves corresponding to 3rd and4th Brillouin zone are excited at the wavelengths close to λ  = 633 nm on the polymer-metal interface. The SPPstates related to the illuminated (Si 3 N 4 ) interface will bered-shifted with respect to this frequency. At the sametime for S-polarised light, the resonant SPP frequencieson the metal-polymer interface are far away from the sig-nal light frequency while SPP Bloch waves from the 4thBrillouin zone of the illuminated interface are relativelyclose to it. This SPP is about twice weaker than theSPP on a pure gold surface due to presence of a Cr layerwhich has strong losses at this wavelength ( Imǫ  ≈  30).Analogous picture can be constructed in the Γ − M   direc-tion of the SPP Brillouin zone, but the related resonantfrequencies (  p,q  ) = ( ± 1 , ± 1) will lie between the frequen-cies determined by (  p,q  ) = ( ± 1 , 0) and (  p,q  ) = ( ± 2 , 0),and therefore, far from the signal wavelength. However,these resonances can become important for other anglesof incidence.To complete the picture, the resonances associatedwith cylindrical channels in a metal film should be con-sidered [9]. For thick films with well defined cylindri-cality of the channels ( d << h ), the spectrum of sur-face electromagnetic excitations in channels has a rathercomplicated structure with both radiative and nonradia-tive modes present. Individual cylindrical channels willhave a discrete spectrum of resonances asymptoticallyapproaching surface plasmon frequency ( ǫ m  =  − ǫ ) fromthe high frequency side. For polymer-filled channels thesemodes overlap the frequency of the control blue light forlarge quantum numbers s >>  1. The interaction betweenchannels in an array can additionally broaden these reso-nances leading to minibands [14]. Thus, quasi-continuousspectrum of the states related to the cylindrical surfaceplasmons can be expected in the spectral range of thecontrol light. For infinitely long cylindrical channels thespectrum of wave vectors along the cylinder axis  h z  iscontinuous. Physically one can imagine these excitationsas surface modes of a spiral trajectory on a cylinder chan-nel surface. Real (nonradiative) surface modes can notbe excited directly by light, but at the frequency cor-responding to the control light the very long wave vec-tor SPP can be excited on the periodically perforatedpolymer-metal interface, which then can be coupled tocylindrical surface plasmons.In the absence of control light, the transmission of red light takes place via resonant tunneling through thestates of SPP Bloch waves on the polymer-metal inter-face. The changes of the incident light polarization resultin the shift of the SPP resonances and, hence, variation of the transmission. Being confined to the polymer-coatedinterface, the SPP modes responsible for this transmis-sion are very sensitive to the dielectric constant of thepolymer, since changes of the dielectric constant modifythe SPP resonant conditions and the transmission coeffi-cient. Control(blue) light coupled into cylindrical surfaceplasmons either via their radiative part or via surfacepolaritons results in the local changes of the dielectricconstant of the polymer due to third-order Kerr nonlin-earity. Local electromagnetic field is strongly enhancedin and around the channel due to cylindrical surface plas-mons excitation because of small volume of these surfacemodes ( E  L  ∼ 1 /d ).The polarization properties of the polymer moleculesthemselves may play significant role in the observed in-creaseof the P to S ratioin the modulated transmissionof red light. The third-order nonlinearity of 3BCMU poly-diacetylene is contributed mainly by the  π -electrons inthe backbone of the polymer [10]. Each straight segmentof polymer backbone could be treated as identical one-dimensional rod-like chromophore. At the microscopiclevel the  χ (3) tensor of 3BCMU is dominated by only onecomponent:  χ (3) ssss , where  s  is the direction of the poly-mer chain. This fact has been verified in measurementsof different components of the macroscopic  χ (3) tensorof spin-coated thin polymer 3BCMU films, where poly-mer backbones have random in-plane orientations, deter-mined by a flat substrate. [10] In our case, the preferentialdirection for the long polymer backbones inside narrowcylindrical channels ought to be the direction along thechannel. The nonlinear optical mixing of interest is de-termined by the components  D l ( ω 2 ) of the optical fieldinside the channels at  λ 2  = 633 nm: D l ( ω 2 ) =  χ (3) ijkl E  i ( ω 1 ) E  j ( ω 1 ) E  k ( ω 2 ) ,  (2)where  ω 1  and  ω 2  are the frequencies of blue and red light,respectively. If the zzzz-components (along the channeldirection) of  χ (3) ijkl  dominate the third-ordersusceptibility,the modulated red light must be strongly P-polarized.At the same time, at the frequency of the blue light  ω 1 the electromagnetic field in the cylindrical channels isdominated by the plasmon modes with large wave vectorsalong the channel, for which optical field oscillations havesignificant longitudinal component, which is along thechannel direction. Thus, one should expect the enhancednonlinear optical mixing to occur while electromagnetic4  field is traveling through small cylindrical holes.In conclusion, we have reported first observation of photon tunneling gated by light at a different wavelengthin an artificially created array of nanometer scale cylin-drical channels in a thick gold film. Polarization proper-ties of gated light provide strong proof of the enhancednonlinear optical mixing in nanometric channels involvedin the process. [1] I.I. Smolyaninov  et al. , Phys. Rev. Lett. 88, 187402(2002).[2] I.I. Smolyaninov  et al. , cond-mat/0205160.[3] T.W. Ebbesen  et al. , Nature (London) 391, 667 (1998).[4] A. Krishnan  et al. , Optics Comm. 200, 1 (2001).[5] L. Salomon  et al. , Phys. Rev. Lett. 86, 1110 (2001).[6] N. E. Glass and A. A. Maradudin, Phys. Rev. B 29, 1840(1984).[7] W. L. Barnes  et al. , Phys. Rev. B 54, 6227 (1996).[8] H. Raether,  Surface Plasmons  , Springer, Berlin, 1988.[9]  Electromagnetic Surface Modes  , A.D. Boardman, Ed.,John Willey, New York, 1982.[10] K. Yang  et al. , Optics Comm. 164, 203 (1999).[11] A. Lewis  et al. , Ultramicroscopy, 61, 215 (1995).[12] E. Betzig  et al. , Appl. Phys. Lett. 60, 2484 (1992).[13] D.I. Kavaldjiev  et al. , Appl. Phys. Lett. 67, 2771 (1995).[14] V. Kuzmiak  et al. , Phys. Rev. B 50, 16835 (1994). 5
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