CREOL, The College of Optics & Photonics, UCF. Anomalous Surface Plasmon Dispersion in Metallodielectric Multilayers

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1 Anomalous Surface Plasmon Dispersion in Metalloielectric Multilayers Gray Webb-Woo an Pieter G. Kik CREOL, University of Central Floria, Orlano, FL SPIE San Diego Nanophotonics an Near-fiel Optics slie Introuction Surface plasmons can provie highly confine moes at optical frequencies Short wavelength plasmons have several applications: - Nanolithography - Densely integrate optical circuits - High resolution optical microscopy metal >> > Preiction by Karalis et al. : A. Karalis et al., Phys. Rev. Lett. 9, 9 () A thin high refractive ine film on can give rise to unusual type of strongly confine plasmon with negative group velocity Theoretical stuy by Stockman : M.I. Stockman, Nano Lett., (), -8, () Negative group velocity moes are highly ampe! Question: observable?. Calculate multilayer plasmon ispersion of real materials. Simulate to evaluate feasibility of eperimental emonstration SPIE San Diego Nanophotonics an Near-fiel Optics slie Anomalous Surface Plasmon Dispersion in Metalloielectric Multilayers - SPIE

2 Intuitive picture : origin of anomalous ispersion SP confinement epens on ω - low ω: etene moe ; high ω: confine moe ω Ag air k c + Si Ag Ag air ω ( ra/s)?..... k ( 8 m - ) ω Ag Si k c + Ag Si Ag Si Low ω: etene moe, little overlap with Si: air like ispersion High ω: highly confine moe, large overlap with Si, silicon like ispersion Question: how o these limiting cases connect? SPIE San Diego Nanophotonics an Near-fiel Optics slie Calculation of surface plasmon ispersion relation Eperimentally realizable system: silver substrate, thin silicon cover layer Calculate SP ispersion relation in three layer system Boun surface plasmon moes can eist when: k z k e kz e z ikz ikz k z e kz e ikz ik z e kz e ikz ikz = vacuum silicon silver with i the ielectric function of layer i, an k z the wavevector normal to the film surface: kz i = k ω i c For fie fin zeros of the eterminant using literature ielectric functions Comple k an comple k z SPIE San Diego Nanophotonics an Near-fiel Optics slie Anomalous Surface Plasmon Dispersion in Metalloielectric Multilayers - SPIE

3 Surface plasmon ispersion : nm Si on Ag nm Si Fast moe nm Si Slow moe ω=.8 ra/s nm ω ( ra/s) slow fast SP,ma ~ nm Note: moes to scale 8 Color scale shows H y k (m - ) Dispersion relation in layere system in between an ispersion Observation of fast moe (high v g ) an slow moe (low an negative v g ) Plasmon wavelength of ~nm at visible frequencies! (~/, re light) Single frequency: two moes possible, very ifferent level of confinement SPIE San Diego Nanophotonics an Near-fiel Optics slie Surface plasmon ispersion : nm Si on Ag Determine propagation length from imaginary part of k μm nm nm Si Fast moe nm Si Slow moe nm nm nm μm ω ( ra/s) 8 k (m - ) ω ( ra/s) nm Fast moe nm Slow moe L p (m) Ma. propagation length of slow moe for =nm ~nm Question: is this sufficient to observe oscillatory nature of SP moes? SPIE San Diego Nanophotonics an Near-fiel Optics slie Anomalous Surface Plasmon Dispersion in Metalloielectric Multilayers - SPIE

4 Surface plasmon ispersion : nm Si on Ag Plot propagation length in terms of SP wavelength: L p / SP nm Si Fast moe nm Si Slow moe ω ( ra/s) 8 ω ( ra/s) nm Fast moe nm Slow moe L p /λ SP L p /λ SP k (m - ) L p / λ SP Maimum /e slow moe propagation length for this thickness: one wavelength Net: Fin maimum propagation length of slow moe vs. Si thickness SPIE San Diego Nanophotonics an Near-fiel Optics slie Surface plasmon ispersion : nm Si on Ag Repeat calculation for range of Si thicknesses Angular Frequency (ra/sec)..... = nm 8 9 Real K (/meters) Vacuum Fast Moe Slow Moe Maimum /e Intensity propagation length (meters) Maimum /e Propagation Length vs. Si Film Thickness - Slow Fast Si film thickness in nm Conclusion: maimum propagation length of slow moe ~nm at Si =nm Simulate this system to evaluate feasibility of eperimental emonstration SPIE San Diego Nanophotonics an Near-fiel Optics slie 8 Anomalous Surface Plasmon Dispersion in Metalloielectric Multilayers - SPIE

5 Slow plasmon ecitation through slit Part II: evaluate viability of eperimental observation Eample system: slit in silver film on glass collection moe NSOM To etector (APD) NSOM tip μm Sample illumination Simulate slow plasmon ecitation using illumination through slit SPIE San Diego Nanophotonics an Near-fiel Optics slie 9 Frequency omain simulations Microwave stuio Minimum gri spacing: = nm y = nm z =. nm air Si (nm) Ag Two imensional frequency omain simulation Fine gri neee at sharp corners (ege of slit) an near Si film Bounary conitions simulate array of infinite slits may see staning waves SPIE San Diego Nanophotonics an Near-fiel Optics slie Anomalous Surface Plasmon Dispersion in Metalloielectric Multilayers - SPIE

6 E ω =. ra/s k,s = 8 /m Angular Frequency (ra/sec) Real K (/meters) Both slow an fast moe ecite Determine k, compare with calc. SP wavelength < analytical result Gri nees further refinement SPIE San Diego Nanophotonics an Near-fiel Optics slie E ω =. ra/s k,s =. 8 /m Angular Frequency (ra/sec) Real K (/meters) SP wavelength = analytical result Wavelength of slow plasmon increases Confinement reuce SPIE San Diego Nanophotonics an Near-fiel Optics slie Anomalous Surface Plasmon Dispersion in Metalloielectric Multilayers - SPIE

7 E ω =. ra/s k,s =. /m Angular Frequency (ra/sec) Real K (/meters) SP wavelength = analytical result SP further increase confinement further reuce Fast moe has noticeably shorter SP SPIE San Diego Nanophotonics an Near-fiel Optics slie E ω =. ra/s k,s =. /m Angular Frequency (ra/sec) Real K (/meters) Fast an slow moe ~similar wavelength SPIE San Diego Nanophotonics an Near-fiel Optics slie Anomalous Surface Plasmon Dispersion in Metalloielectric Multilayers - SPIE

8 E ω =. ra/s k,s =. /m Angular Frequency (ra/sec) Real K (/meters) High frequency Ecitation near turning point Fast an slow moe: - Similar k - Group velocity ~ - Localize moe near slit Negative group velocity? SPIE San Diego Nanophotonics an Near-fiel Optics slie Observation of negative phase velocity ω =. ra/s, k,s = 8 /m aa Fast SPP creates staning wave, Slow SPP ehibits negative phase velocity SPIE San Diego Nanophotonics an Near-fiel Optics slie Anomalous Surface Plasmon Dispersion in Metalloielectric Multilayers - SPIE 8

9 Conclusions Analytical calculations - system can lea to anomalous ispersion - Strongly confine slow plasmon preicte at visible frequencies - Maimum propagation length of slow plasmon < nm for Si = nm Numerical simulations - Illumination through slit leas to simultaneous slow an fast plasmon ecitation - Presence of slow plasmons with wavelength ~/ observe - Eperimental observation seems challenging, but feasible Future work - Evaluate slow plasmon ecitation efficiency vs. slit geometry - Attempt eperimental emonstration of slow plasmons on silver SPIE San Diego Nanophotonics an Near-fiel Optics slie Anomalous Surface Plasmon Dispersion in Metalloielectric Multilayers - SPIE 9