Optical properties of C-shaped subwavelength waveguides in metallic (silver) films on silicon substrates are studied in the range of 0.6-6 mu m. Power throughput and resonant wavelengths of several transmission modes are studied by varying the waveguide length (or metal thickness). Among three types of transmission modes, the fundamental order of the Fabry-Perot-type mode was shown to attain remarkably high power throughputs (as high as 12). With optimized design of the aperture, the resonant wavelength of this mode occurs in the 1-2 mu m wavelength range, suggesting that such apertures can be utilized to achieve plasmonic-enhanced silicon photonic devices at telecommunication wavelengths

Fathpour, S.

Lopatiuk-Tirpak, O.

Ma, J.

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University of Central Florida STARS Faculty Bibliography 2010s Faculty Bibliography 1-1-2010 Optical transmission properties of C-shaped subwavelength waveguides on silicon O. Lopatiuk-Tirpak University of Central Florida J. Ma University of Central Florida S. Fathpour University of Central Florida Find similar works at: https://stars.library.ucf.edu/facultybib2010 University of Central Florida Libraries http://library.ucf.edu This Article is brought to you for free and open access by the Faculty Bibliography at STARS. It has been accepted for inclusion in Faculty Bibliography 2010s by an authorized administrator of STARS. For more information, please contact STARS@ucf.edu. Recommended Citation Lopatiuk-Tirpak, O.; Ma, J.; and Fathpour, S., "Optical transmission properties of C-shaped subwavelength waveguides on silicon" (2010). Faculty Bibliography 2010s. 460. https://stars.library.ucf.edu/facultybib2010/460 Appl. Phys. Lett. 96, 241109 (2010); https://doi.org/10.1063/1.3455839 96, 241109© 2010 American Institute of Physics.Optical transmission properties of C-shapedsubwavelength waveguides on siliconCite as: Appl. Phys. Lett. 96, 241109 (2010); https://doi.org/10.1063/1.3455839Submitted: 02 March 2010 . Accepted: 27 May 2010 . Published Online: 16 June 2010O. Lopatiuk-Tirpak, J. Ma, and S. FathpourARTICLES YOU MAY BE INTERESTED INEffects of hole depth on enhanced light transmission through subwavelength hole arraysApplied Physics Letters 81, 4327 (2002); https://doi.org/10.1063/1.1526162Optical transmission properties of C-shaped subwavelength waveguideson siliconO. Lopatiuk-Tirpak,1 J. Ma,1 and S. Fathpour1,2,a1CREOL, The College of Optics and Photonics, University of Central Florida, Orlando,Florida 32816, USA2School of Electrical Engineering and Computer Science, University of Central Florida, Orlando,Florida 32816, USAReceived 2 March 2010; accepted 27 May 2010; published online 16 June 2010Optical properties of C-shaped subwavelength waveguides in metallic silver films on siliconsubstrates are studied in the range of 0.6–6 m. Power throughput and resonant wavelengths ofseveral transmission modes are studied by varying the waveguide length or metal thickness.Among three types of transmission modes, the fundamental order of the Fabry–Perot-type mode wasshown to attain remarkably high power throughputs as high as 12. With optimized design of theaperture, the resonant wavelength of this mode occurs in the 1–2 m wavelength range, suggestingthat such apertures can be utilized to achieve plasmonic-enhanced silicon photonic devices attelecommunication wavelengths. © 2010 American Institute of Physics. doi:10.1063/1.3455839Subwavelength apertures are promising candidates formany nanophotonics applications where a combination ofhigh transmittance and subwavelength spot size isnecessary.1,2 Among the possible configurations, C-shapedsingle apertures have certain advantages due to their compactstructure, which does not require the presence of arrays1,3or extensive corrugation.4 C-shaped apertures have beenutilized in photodetectors,5,6 waveguides,7,8 and surface-emitting lasers.9 There have been a number of numericalstudies addressing the transmission properties of C-shapedapertures.7,10 Most of them, however, studied free-standingapertures in metallic films. As we have shown in our earlierwork,11 the properties of the C-apertures are altered quitedramatically by the refractive index of its surrounding media.This means that while numerical simulations in vacuum sug-gest impressive intensity enhancements and extraordinarytransmission, these findings cannot necessarily be expectedto be realized experimentally when the aperture is fabricatedon a substrate.In this paper, we report the results of a numerical studyof the transmission properties of a C-shaped aperture-waveguide in silver Ag metallic films on a silicon sub-strate. Particularly, it is intended to study the power through-put PT of various involved transmission modes in order topredict their impact on the performance of silicon nanopho-tonic devices ultracompact photodetectors, nanoantennas,etc. at telecommunication wavelengths.The dimensions of the aperture used in this study areshown in the inset of Fig. 1. The choice of the lateral dimen-sions of the aperture was motivated by the ultimate goal ofachieving highest possible PT at wavelengths relevant totelecommunication applications. The calculations were per-formed using the finite-integration method within the CSTMICROWAVE SUITE. Optical properties of the Ag film weresimulated by fitting the experimentally obtained dielectricconstant values12 to the Drude model.11 The undoped siliconsubstrate is simply modeled as a dielectric with refractiveindex of 3.45 to facilitate interpreting the results. This as-sumption is justified considering that silicon’s optical lossand dispersion are small compared to that of silver in thewavelength range of interest. The remainder of the space,including the aperture cavity, is set to vacuum. The excita-tion source was a plane wave with the amplitude of 1 V/m,polarized along the y-axis in the inset of Fig. 1. It was as-sumed that the excitation impinges from vacuum onto themetallic aperture +z direction.PT is defined as the ratio of total power at the exit sur-face to that impinging upon the physical area of theaperture.13 Total power at the exit was calculated by integrat-ing half the real part of the normal component of the com-plex Poynting vector, S, over the entire x-y plane immedi-ately adjacent to the metal-semiconductor interface 2 nminto silicon. This choice of the plane is only to facilitate thenumerical calculation of PT, since only Sz is needed. In gen-eral, any arbitrary surface that encompasses the whole trans-mitting area in silicon gives the same result. It was indeedconfirmed that the error due to neglecting the lateral energyaElectronic mail: fathpour@creol.ucf.edu.FIG. 1. Color online Spectral distribution of electric field magnitude as afunction of the thickness of silver layer. The dashed lines indicate the evo-lution of the ESCP mode A and of the three orders of the FP mode B, C,and D. The arrow indicates the spectral position of the SP mode E. Inset:geometry and dimensions of the C-shaped aperture studied in this work.APPLIED PHYSICS LETTERS 96, 241109 20100003-6951/2010/9624/241109/3/$30.00 © 2010 American Institute of Physics96, 241109-1flow—related to Sx and Sy in the very thin 2 nm siliconlayer adjacent to the metal—is negligible. This necessaryclarification also applies to the same method of calculatingPT in our earlier publication.11The evolution of spectral response with metal film thick-ness is shown in Fig. 1. The response is measured at point P1in the inset of Fig. 1. The spectrum shows three differenttypes of modes. They include: one evanescently coupled sur-face plasmon ESCP mode denoted as A; one thickness-invariant surface plasmon SP mode associated with thesubstrate-metal interface at the wavelength of approximately1 m denoted as E; and a Fabry–Perot FP-type cavitymode, showing an increasing number of orders with in-creased thickness denoted as B, C, and D.11It is apparent from Fig. 1 that the change in the reso-nance wavelengths of the FP mode orders, FP, is not linearwith d the FP cavity length, as might be expected for a trueFP mode under ideal conditions. It must be pointed out thatthe wavelength of the FP resonances is determined not onlyby the thickness of the cavity but also by the phase change,, upon reflection from the front and back surfacesFP = 2d/N − / , 1where N is an integer.14 Therefore, the spectral position ofthe FP peaks can and does in this case differ considerablyfrom 2d /N.The PT for each mode at its peak wavelength as a func-tion of d was computed Fig. 2. The ESCP mode is clearlyevanescent in nature, since its PT decays exponentially withd. Although the transmittance via this mode may be some-what high and extraordinary, PT4 for small metal filmthicknesses, it is not suitable for telecom applications, sincethe peak wavelength occurs in the 3.5–4 m wavelengthrange Fig. 1. The wavelength peak for this mode is indeedin the 1–2 m range of interest and the PT can be evenhigher PT6 if the substrate refractive index is close to 1,i.e., a free-standing apertures.11 These observations on trans-mission properties of the ESCP mode in C-shaped aperturesmay explain the discrepancy between prediction of high PTin free-standing apertures10 and low performance of fabri-cated nanophotonic devices based on them apertures onsemiconductors.5Another interesting finding of Fig. 2 is that the PT forthe SP mode oscillates versus d with a nearly constant period400 nm. Closer inspection and comparison of Figs. 1 and 2reveals that the peaks in PT occur at the wavelengths ofspectral overlap of SP and FP modes. As each successiveorder of the FP mode crosses the wavelength of the SP peak,both local intensity and PT of the SP mode increase sharply.Note that this same phenomenon has the opposite effect onthe PT of the FP modes, i.e., it causes a sudden drop in thePT, particularly apparent at d=600 nm for FP2 secondorder of the FP mode, open triangles in Fig. 2 and d=1000 nm for FP3 open diamonds. The Poynting vectordistribution at the wavelength of the FP mode acquires thesymmetry characteristics of the SP, and a large fraction ofpower is scattered back toward the entrance surface.11 Thefact that PT of the SP mode peaks during such couplingindicates that the energy flow at these crossover wavelengthsmay have a hybrid character.The most noteworthy result of this study is the behaviorof the PT of the first order of the FP mode FP1 of theaperture-waveguide. As shown in Fig. 2, by manipulating thethickness of the metal layer i.e., waveguide length, PT val-ues of nearly 12 can be achieved. Thus, it is important tofocus on this fundamental FP mode for nanophotonic appli-cations on real substrates rather than the tempting ESCPmode which appears to have modestly high PT but only infree-standing apertures. A high extraordinary PT of 12 forFP1 is due to the light-gathering ability of the subwavelengthmetal structure, where the energy incident onto the metalsurface is captured in the form of surface plasmon waves and“funneled” via the waveguide FP-type mode.The origin of the peak in the PT occurring at d=1000 nm in Fig. 2 may be related to the phase difference inEq. 1. That is, the PT is maximal when the incident andreflected waves in the aperture cavity are in phase with eachother. As mentioned before, varying the thickness of themetal layer affects both FP and  and therefore it is plau-sible that for a certain value of d this optimal condition canbe achieved. Assuming N=1, for the fundamental FP mode,we calculated  for every FP at each value of d using Eq.1 and found that PT indeed peaks when  is close to zeroFIG. 3. Spatial distribution of the first derivative of the z-component of thePoynting vector along the direction of propagation, along the line containingpoint P1 in the inset of Fig. 1. Inset: PT as a function of phase see Eq. 1.FIG. 2. PT vs metal layer thickness for the five transmission modes consid-ered in this study.241109-2 Lopatiuk-Tirpak, Ma, and Fathpour Appl. Phys. Lett. 96, 241109 2010inset of Fig. 3. This finding is further supported by thespatial distribution of the PT for this mode. Figure 3 showsthe normalized z-derivatives through point P1 of thez-component of the Poynting vector, dSZ /dz, for five differ-ent values of d. This figure is intended to illustrate that ford=1000 nm the thickness at which the peak in PT occurs,the spatial distribution is most uniform, i.e., dSZ /dz0. Thisis consistent with the minimal phase change upon reflectionfrom the cavity surfaces. Furthermore, it is interesting to notethat for all d1000 nm, the SZ slopes toward the entrancesurface, while the opposite is true for d1000.The two higher orders of the FP mode FP2 and FP3show similar tendencies and may peak as d is increased be-yond 2500 nm. Figure 4 presents the PTs of the three FPmodes as a function of peak wavelength, FP. It is evidentthat although the PTs of different FP modes are different forthe same waveguide lengths see Fig. 2, the PTs show simi-lar trends when plotted versus FP. It is well-known that thereflectance of a FP cavity with fixed length is a periodicfunction of wavelength with the peaks corresponding to eachsuccessive order of the FP mode. In other words, the value ofthe reflectance at the peak wavelength of each FP order is thesame. By increasing the cavity length i.e., the metal filmthickness in the present case, higher FP orders can result inresonant wavelengths and hence reflectivities identical tothose of the lower orders in thinner metal thicknessesor shorter waveguides. Therefore, it is not surprising thatthe variation in the reflectance and hence the PT is almostthe same for all three FP orders when plotted versus FP.A PT of 7 is predicted for FP1 at FP=1.55 m wave-length of telecommunication at d=400 nm. Similar PTs canbe achieved at the higher FP2 and FP3 orders at the samewavelength, however at the expense of 1100 nm and2000 nm metal thicknesses, respectively. Clearly, for thisaperture geometry, only the FP1 mode renders itself to nano-photonic devices when practical thicknesses related to devicefabrication issues are considered. Finally, it is noted that thehighest PT of 12 is predicted in Fig. 4 for the FP1 mode atthe peak wavelength of FP1.92 m. Further optimizationof the lateral geometry of the C-shaped nanoaperture canblueshift the PT in Fig. 4, in order to attain a maximal valuein the telecommunication range of 1.3–1.55 m.In summary, this study shows that even under the con-ditions of refractive index mismatch between the aperturecavity and the substrate, high PT values can be achieved inC-shaped subwavelength aperture-waveguides in near-infrared wavelengths. For this purpose it is not only neces-sary to optimize the design of the aperture both shape andthickness but to also emphasize the FP-type modes.This work was partially supported by the NASA FloridaSpace Grant Consortium under Award No. 16296041-Y5.1T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, NatureLondon 391, 667 1998.2C. Genet and T. W. Ebbesen, Nature London 445, 39 2007.3P. B. Catrysse and S. H. Fan, J. Nanophotonics 2, 021790 2008.4F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martin-Moreno,Phys. Rev. Lett. 90, 213901 2003; T. Thio, K. M. Pellerin, R. A. Linke,H. J. Lezec, and T. W. Ebbesen, Opt. Lett. 26, 1972 2001.5L. Tang, D. A. B. Miller, A. K. Okyay, J. A. Matteo, Y. Yuen, K. C.Saraswat, and L. Hesselink, Opt. Lett. 31, 1519 2006.6S.-X. Liu, P. An, Z.-Y. Zhang, Q. Zhang, L.-Q. Shen, and G.-Y. Jiang,Electron. Lett. 45, 30 2009.7P. Hansen, L. Hesselink, and B. Leen, Opt. Lett. 32, 1737 2007.8L. Y. Sun and L. Hesselink, Opt. Lett. 31, 3606 2006.9Z. L. Rao, J. A. Matteo, L. Hesselink, and J. S. Harris, Appl. Phys. Lett.90, 191110 2007.10X. L. Shi and L. Hesselink, J. Opt. Soc. Am. B 21, 1305 2004; X. L. Shi,L. Hesselink, and R. L. Thornton, Opt. Lett. 28, 1320 2003.11O. Lopatiuk-Tirpak and S. Fathpour, Opt. Express 17, 23861 2009.12M. A. Ordal, L. L. Long, R. J. Bell, S. E. Bell, R. R. Bell, R. W. Alex-ander, Jr., and C. A. Ward, Appl. Opt. 22, 1099 1983.13J. Matteo and L. Hesselink, Opt. Express 13, 636 2005.14Y. Pang, C. Genet, and T. W. Ebbesen, Opt. Commun. 280, 10 2007.FIG. 4. Variation in PT with resonant wavelength for three orders of the FPmode.241109-3 Lopatiuk-Tirpak, Ma, and Fathpour Appl. Phys. Lett. 96, 241109 2010

Optical transmission properties of C-shaped subwavelength waveguides on silicon

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Optical transmission properties of C-shaped subwavelength waveguides on silicon

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