Surface Plasmon Amplification by Stimulated Emission of Radiation

Transcription

1 Surface Plasmon Amplification by Stimulated Emission of Radiation Jonathan Massey-Allard, Graham Zell, Justin Lau April 6, 2010 Abstract This article presents an overview of the emerging nanoscience of surface plasmon amplication by stimulated emission of radiation (spaser). The basic design of a spaser is described conceptually and quantitatively, with theoretical background developed at the semi-classical level. Experimental setup and results from the first working spaser are reviewed, followed by a survey of proposed spaser applications from recent literature. Introduction The spaser is a device similar to the laser in many respects. For instance, a spaser has a gain medium providing amplification and a cavity where surface plasmons resonate, though unlike a laser no radiation is emitted. Instead, external radiation excites an electron-hole pair in the gain medium, which exists until spontaneous recombination occurs. In vacuum, recombination would release a photon, however, in a spaser, the energy is transferred to a surface plasmon in the resonant cavity without radiation through a resonant coupled transition, shown schematically in Figure 1. In a traditional laser, the size of the cavity is also limited in the propagation direction by the emission wavelength. Spaser do not face this inherent limitations as the spasing modes existence is only limited by the nonlocality radius of the metal resonator. The spaser is thus a true nanometre-scale source of coherent fields. Surface Plasmons Plasmons are quanta of electron oscillations about positive ion cores existing in a plasma (an electron gas in metals). Plasmons can also exist at the interface between two materials, which are then called surface plasmons (SPs). SPs can be created if the real part of the dielectric function changes sign across the interface of the two materials (i.e., a metal sheet in air). The negative dielectric constant of the material indicates that it will absorb some of the incident optical fields up to a certain depth, referred to as the skin depth. These fields may then excite plasmons at the surface of the material. The possibility of the stimulated emission of local fields using surface plasmons is entirely due to the fact that SPs are bosons, similar to photons. They have spin 1, are electrically neutral, and interact very weakly with one another. Because of this, large numbers of SPs may accumulate in a spaser cavity in a single mode, analogous to a laser cavity [6]. Design of a Spaser Resonator Figure 1: Spasing action mechanism. External radiation excites electrons in the gain medium. The electron-hole pair recombines without radiation, transferring its energy to a surface plasmon in the resonator [6]. The best materials at sustaining plasmons are noble metals like Ag, Au and Pt (though aluminium and alkaline metals are also good). These metals have skin depths of 25 nm. Creating nanoparticles out of these metals that have a size smaller than their skin depth will allow incident electromagnetic fields to completely penetrate the metal, thus driving SP modes (Figures 2a and 2b). The resonant lifetime of these SP eigenmodes is characterized by their quality factor, Q. The enhancement of local fields generated by the SPs on the metal nanoparticles is determined by the Q of the supported plasmonic mode. A high Q plasmonic spasing mode is analogous to a lasing mode where a mode with low loss that can draw energy from the gain medium for as long as possible is sought. Since noble metals have their lowest losses at frequencies, it is 1

2 desirable to operate at those frequencies to get the highest Q modes possible. It is also important to note that the size of the plasmonic nanoparticle resonator should also be greater than V p /ω ( 1 nm for a noble metal), where V p is the electron speed at the Fermi surface of the metal and ω the optical driving frequency. This is to avoid non-local effects such as Landau damping [7]. Figure 2: Spaser Resonator and Gain Medium. Field intensity in a plasmonic metal nanoparticle resonator for a) a dipole SP mode and b) a quadrupole SP mode. The gain medium must be arranged to overlap spatially with the SP modes, and can thus be placed c) outside the resonator or d) inside [7]. Other types of resonators can be implemented by exploiting the geometry and shape of plasmonic metals; for example, tapering a metal rod will yield high field enhancement at its tip or by using different arrangements of metal nanorods. Recent realizations of such nanostructures show that they may not be suitable for a spaser and as such nanoparticles remain the most promising design for a spaser resonant cavity [1]. Stockman proposes a meta-dielectric nanoshell structure to provide a resonant cavity [6]. Bergman and Stockman, in an earlier paper exploring the quantum mechanics behind a spaser, model a metallic V-shaped tip as a resonator [1]. Noginov et al. used gold nanoparticles with a diameter of 14 nm as their resonator [4]. Gain Medium For the spasing process to occur (i.e. to get stimulated emission), the gain medium must spatially overlap with the SP modes sustained by the resonator structure and have an emission transition that spectrally overlaps with that of the SP modes. Since it is simple to pump spasers optically, strong contenders for a spaser gain medium are chromophores. These can be semiconductor nanocrystals, dye molecules, rare-earth ions, or electronhole excitations of a bulk semiconductor [7]. The spasing process begins when pump light radiation excites an electron hole-pair in the chromophores of the gain medium. The pair can then relax down to an exciton state, which would then recombine by photoemission if it was in a vacuum. Since the chromophore is coupled to the resonator, energy is instead resonantly transfered to SP modes. The local field created by the resonator further excites the gain medium, creating a feedback process. If the SP mode Q is high-enough and the feedback strong enough, spasing will occur with that SP mode. The spasing process can be optimized by using a chromophore with a strong dipole transition and also by tuning the feedback. The latter can be done by ensuring a big enough interaction volume between the gain medium and modes sustained by the resonator. Figure 2c shows the gain medium outside the nanoparticle resonator, which yields a strong spatial coupling of the gain medium to the mode. It was shown, however, that leaving the gain medium inside the nanoparticle yields a comparable spasing performance, while leaving the local field hot spots for other useful applications. Stockman proposes using nano quantum dots (NQDs) for a spaser gain medium, which has the benefit of having a tuneable spontaneous emission wavelength [6]. On the other hand, Noginov et al. use an organic dye (Oregon Green 488) embedded in a silica shell to provide gain in a working spaser [4]. Amplification by Stimulated Emission The following discussion presents the theory outlined in references [1], [7], and [8]. The goal is to provide an overview of the background at an accessible level, deriving simpler results from first principles and quoting the results from some of the more involved derivations. Consider a rectangular system of dimensions L x, L y, L z with metal domains with dielectric permittivity ε(ω) embedded within a dielectric material of permittivity ε d in a uniform electric field E 0 = ϕ 0 (r) = E 0 z. The electric potential ϕ(r) inside the system satisfies Gauss s law with no free charge, Equation 1. D = [ε(r, ω) ϕ(r)] = 0 (1) At the system boundary, the x and y derivatives of the electric potential vanish, and continuity requires ϕ(x, y, z) = ϕ 0 (x, y, z) at z = 0 and z = L z. Expanding Equation 1 by vector identity and imposing boundary conditions, the quantized field equation (2) gives the SP eigenmodes ϕ n (r) and eigenvalues s n, where θ(r) is the characteristic function of the system, equal to 1 for r inside metal domains and 0 for r in the surrounding dielectric. The spatial distribution of the characteristic function, as governed by the geometry of the system, determines the allowed SP eigenmodes. 2

3 θ(r) ϕ n (r) + θ(r) 2 ϕ n (r) = [s n ϕ n (r)] (2) The frequency dependence of the dielectric constants is contained in Bergman s spectral parameter, Equation (3). In general, SP frequencies are complex, Ω n = ω n + iγ n, where ω n is the real frequency and γ n is the relaxation rate. s(ω n ) = ε d ε d ε(ω n ) = s n (3) In the weak relaxation limit, γ n ω n, the SP frequency is approximately real, Ω n ω n. By Taylor expansion of Equation (3) about ω n, the eigenvalue approximately separates into real and imaginary components. s(ω n + iγ n ) s(ω n ) + (iγ n )s n, s n = ds(ω) dω s n Re [s(ω n )], γ n Im [s(ω n)] s n (4) ω=ωn (5) The first step in obtaining the spaser Hamiltonian is to quantize the electric field, Equation (6), written in the basis of SP eigenstates ϕ n (r), where â n and â n are their creation and annihilation operators respectively, and A n = 4π sn /ε d s n. Ê(r, t) = n A n ϕ n (r)e γnt [ â n e iωnt + â ne iωnt] (6) Using â n and â n, the Hamiltonian of the quantized electric field can be written in the form of an infinite series of harmonic oscillators, Equation (7). Ĥ em = n ω n (â n â n + 1/2 ) (7) Although a full quantum mechanical treatment requires the quantized electric field, a semi-classical approximation is presented here with the goal of understanding the quantum interactions without the complexity of working entirely in the quantum formalism. As such, the creation and annihilation operators can be interpreted as slowlyvarying amplitudes of the electric field, a n = a 0n e iωt. The key to amplification by stimulated emission is the gain medium. Suppose there are p chromophores embedded within the gain medium at positions r p. The semiclassical electric field of SPs, E(r), interacts with the dipole moments of the chromophores, ˆµ (p), contributing to a perturbation, Equation (8), where Ĥg contains the potential established by the gain medium. Ĥ = Ĥg + ˆV (r, t, p) = Ĥg p Ê(r p ) ˆµ (p) (8) For chromophores with two levels, the Hamiltonian can be written as a 2 2 matrix. The time-independent part of the Hamiltonian simply contributes energy scalars H n along the diagonal, ψ m Ĥem + Ĥg ψ n = H n δ mn. The dipole operator ˆµ (p) = eˆr p is spatially odd and the electric field evaluated at r p can only depend on time. Assuming well-defined parities for the ground and excited states, the time-dependent perturbation vanishes along the diagonal. The Hamiltonian in matrix form is given in Equation (9), where Ê(r p, t) = E 0 (r p, t)ẑ and µ mn (p) = e ψ m ˆr p ψ n. Ĥ = [ H 1 E 0 (r p, t)µ (p) 12 E 0 (r p, t)µ (p) 21 H 2 Stimulated emission from the n th SP mode is described by Fermi s golden rule, Equation (10), where ρdω is the density of states. Integrating over the solid angle dω is equivalent to summing over a continuous range of wavevectors. Ṅ = 2π ϕ m Ĥ ϕ n 2 ρdω (10) λ In Equation 11, the SP eigenmodes are separated into their spatial part, as defined by quantum numbers n p, l p, m p, and their frequency-dependent part, as defined by the modal quantum number n. ] (9) ϕ n = φ(n p, l p, m p ) n (11) The matrix element in Fermi s golden rule, Equation (12), gives some insight into the relation between symmetry and dark spasing modes. In a perfectly symmetric system, the spatial wavefunctions are pure orthonormal eigenstates with definite parity. The matrix element vanishes after integration over all space with an odd operator, resulting in no coupling to the far field. When the symmetry is broken, the spatial wavefunction becomes a superposition of orthonormal eigenstates and some modes may have non-zero spatial overlap, giving rise to allowed radiative modes. This explanation for dark spasing modes is heuristic at best, as Fermi s golden rule describes only a single isolated chromophore. Spasing requires coherent interactions among an ensemble of chromophores, and in fact, Fermi s golden rule has shown that a single symmetric chromophore cannot support stimulated emission. However, it is included for illustrative purposes, suggesting how dark spasing modes may arise from symmetry. φ(n p, l p, m p ) 1 Ĥ φ(n p, l p, m p ) 2 2 (12) The density matrix approach is used to describe an ensemble of chromophores in the gain medium. The ensemble average dipole moment can be found by taking the trace of the matrix representation of ρˆµ (p), Equation (13), where ρ is the density matrix. 3

4 [ ] [ ] ρ11 ρ µ = Tr 12 0 µ (p) [ ] 12 ρ 21 ρ 22 µ (p) = 2Re ρ 12 µ (p) 21 (13) 21 0 Time-evolution of the density matrix can be found by commutation of ρ with Ĥ, Equation (14). [ ] i ρ (p) = ρ (p), Ĥ (14) Undamped equations of motion are given explicitly in Equations (15a) and (15b), written in terms of the Rabi frequency Ω (p) 12 = A nµ (p) 12 ϕ n(r p )a 0n /. Diagonal components of the density matrix are interpreted as the probabilities of population in the ground and excited states. The off-diagonal term ρ 12 represents the coherence of the system. ρ (p) 12 = i (ω 12 ω) ρ (p) 12 + iω(p) 12 (ρ(p) 22 ρ(p) 11 ) (15a) [ ] ρ (p) 22 ρ(p) 11 = 4 Im ρ (p) 12 Ω(p) 12 (15b) Additional terms are required to describe a real system. To account for decoherence, a term proportional to the polarization relaxation rate, Γ 12, is subtracted from the expression for ρ (p) 12. Population relaxation is represented by a term proportional to the SP decay rate γ 2 and the population in the excited state. Pumping the gain medium at a rate g increases the population difference. Equations of motion including pumping and relaxation are given in Equations (16a) and (16b), where 12 ω 12 ω and conservation of probability, ρ 11 + ρ 22 = 1, are used. ρ (p) 12 = Γ 12ρ (p) 12 + i 12ρ (p) 12 + iω(p) 12 (ρ(p) 22 ρ(p) 11 ) (16a) [ ] ρ (p) 22 ρ(p) 11 = 4 Im ρ (p) 12 Ω(p) 12 2γ 2 ρ (p) gρ(p) 11 (16b) Ensemble rates of stimulated and spontaneous emission can be calculated from Equations (16a) and (16b). The resulting expressions from reference [7] are quoted in Equations (17) and (18) respectively. ȧ 0n = [i(ω ω n ) γ n ] a 0n + i p ρ (p) 12 Ω(p) 12 (17) γ (p) 2 = 2 A2 n µ (p) 12 ϕ n(r p ) 2 (Γ 12 + γ n ) 2 γ n (ω 12 ω n ) 2 + (Γ 12 + γ n ) 2 (18) At steady state, ρ (p) 12 = 0 and the population difference remains constant in time. The equilibrium pumping rate is given in Equation (19). The greater the decay rate γ 2, the more pumping would be required to maintain steady state. g ss = [ ] 2 Im ρ (p) 12 Ω(p) 12 + γ 2 ρ (p) 22 1 ρ (p) 22 (19) When the determinant of the density matrix vanishes, ρ 11 ρ 22 ρ 12 ρ 21 = 0, there exists non-trivial steady-state solutions that describe spasing, with equations of motion given in [7]. The spasing frequency ω s, Equation (20), lies between the resonance frequency ω 12 and the driving SP frequency, ω n. ω s = γ nω 12 + Γ 12 ω n γ n + Γ 12 (20) The condition for the existence of these spasing solutions is quoted from [7] as Equation (21). However, Stockman introduces an order of magnitude approximation, Equation (22), written in terms of measurable quantities in a suggestive form that provide some physical insight into Equation (21). Q = ω/γ n is the quality factor of the n th SP mode. (γ n + Γ 12 ) 2 γ n Γ 12 [(ω 21 ω n ) 2 + (Γ 12 + γ n ) 2 ] p Ω (p) 12 a 0n 2 1 (21) µ 2 12Q Γ 12 N c V n 1 (22) Desired conditions for effective spasing include a high quality factor Q, a high density of chromophores N c /V n, and a low decay rate Γ 12. These goals have inspired the designs of the first working spasers. Spaser Realization In 2009, Noginov et al. published a paper detailing their work realizing the world s first spaser-based nanolaser. The group developed core-shell nanoparticles comprised of a gold core surrounded by a silica shell containing the organic dye Oregon Green 488. The diameter of the gold core was 14 nm, while the silica shell was 15 nm thick. The group predicted a stimulated emission wavelength of 525 nm for these particles [4]. The emission kinetics showed non-exponential behaviour at 480 nm, and the development of a second peak at 520 nm. These behaviours are known in lasers, and the group claims that similar behaviour should be observed in spasers. The stimulated emission was also studied by pumping samples of the nanoparticle solution with 488 nm light and observing the spectrum. An emission peak at 531 nm was observed, which is quite close to the group s prediction of 525 nm for stimulated emission; the magnitude of this peak increased sharply when the pumping energy was increased past a threshold value. When the sample was 4

5 diluted, similar behaviour was obtainedthe threshold energy increased, but the energy absorbed by each nanoparticle remained constant. The emission spectrum figure, taken from [4], shows this behaviour for the original sample (main) and diluted sample (inset graphs). The nanoparticles are too small to support stimulated emission in purely photonic modes. The presence of the dye molecules, however, allows the system to overcome losses and support much smaller surface plasmon modes in the visible frequency. The radiation from each nanoparticle means they act as individual nanolasers the group claims these are the smallest such nanolasers to date, and the only ones operating in the visible range [4]. Stockman criticizes the use of dye molecules to provide gain in such a system. He says that dyes may not be suitable for spasers, owing to the low dipole oscillator strength of the fluorescent transition and problems with achieving sufficiently large molecular concentrations without excited-state quenching [6]. He proposes integrating quantum dots into spaser design to increase the maximum possible gain and provide tunable frequency responses, although he does not go into the details of how this fabrication may be achieved. Other Applications Lasing Spaser In a 2008 paper, Zheludev et al. demonstrate the possibility of building a nanoscale laser from a regular array of nanowires coupled to a gain medium. The group combines the theory of spasers put forth by Bergman and Stockman in 2003 [1] with the concept of metamaterials to design a coherent source of light at the nanoscale. The laser consists of a regular array of weakly asymmetric split ring (ASR) nanostructures supported by a gain medium and produces a coherent beam of light normal to the surface, as shown in Figure 4. Figure 3: Stimulated emission. a) Stimulated emission spectra of the nanoparticle sample pumped with 22.5 mj (1), 9 mj (2), 4.5 mj (3), 2 mj (4) and 1.25 mj (5) 5-ns optical parametric oscillator pulses at λ = 488 nm. b) Corresponding inputoutput curve. Insets show the same data for sample diluted more than 100 times [4]. Figure 4: Lasing spaser. The structure of a lasing spaser consists of a gain medium slab (green) supporting a regular array of metallic asymmetric split-ring resonators. Inphase plasmonic oscillation in individual resonators leads to the emission of spatially and temporarily coherent light propagating in the direction normal to the array [9]. The design of the metamaterial layer has a large impact on the ability of the system to couple to the far-field and emit light. If the split rings are designed to be completely symmetric, no lasing will occur because the current loops 5

6 in the bulk of the material will cancel each other. If the asymmetry is too strong, however, the Q-factor and gain of the system will be reduced. In this paper, the arc lengths of the wires were chosen to be β 1 = 160 and β 2 = 125, as shown in Figure 4. The laser operates by pumping the gain medium. The excitons produced by this pumping couple to surface plasmons in the nanowires via resonant coupled transitions, just as in Stockman s 2008 paper [6]. The surface plasmon oscillations set up currents in the nanowires. Because of the weak asymmetry of the structure the currents are all produced in phase, but are still able to radiate. According to the group, Weak coupling of this current mode to free space occurs only due to the asymmetry in the split ring and may be controlled by design (smaller asymmetry gives lower coupling and higher Q-factor) [9]. The group models the gain provided by the substrate through the imaginary part of the dielectric constant, while the nanowires are modelled as silver using the Drude model. The gain coefficient α is related to the dielectric coefficient of the substrate ε by α = 2π λ Im ( ε + iε ) (23) In the paper, α varies between -113 cm 1 (for a lossy substrate) and 3,000 cm 1. At a wavelength of λ = 8.4 µm, the maximum gain of the laser is achieved when α = 125 cm 1, while losses in the metamaterial are overcome at a threshold gain of α th = 70 cm 1. At a wavelength of λ = 1.65 µm the losses in the silver nanowires raise the threshold gain to α th = 1,800 cm 1 ; the peak gain occurs at α = 2,550 cm 1. The increased losses closer to the visible spectrum lower the peak gain from a level of 42 db (at λ = 8.4 µm) to about 35 db [9]. The group characterizes the behaviour of the output as the gain varies as With increasing gain the output intensity will increase rapidly and its spectrum will narrow dramatically. As α is increased past the peak gain, the output begins to fall off. The primary benefits of this laser design are that it allows high amplification and lasing in a very thin layer of material with a more modest gain level and the amplification/lasing frequency is determined by the size of the ring and may be tuned to match luminescence resonances in a large variety of gain media [9]. These properties make the design practical to generalize to many applications. Near-Field Scanning Optical Microscopy Scanning near-field optical microscopy, or NSOM, is a technique for imaging surfaces at the nanometer scale. In classical microscopy, according to Hartschuh, propagation corresponds to low-pass filtering with a frequency limit k = 2π/λ [2]. NSOM is able to overcome this diffraction limit by measuring evanescent (nonpropagating) fields within a few nanometers of the surface Figure 5: Tip-enhanced fields. Calculated intensity distribution near a laser-irradiated gold tip. a) The fieldenhancement effect is observed only if the incident wave is polarized along the tip axis. Surface plasmons are visible in the charge distribution on the right-hand surface of the tip. b) In the case of an incident wave polarized perpendicular to the tip axis, the field near the tip is attenuated [5]. Figure 6: Microscopy techniques. a) Far-field focusing using a lens. b) Aperture-type scanning near-field optical microscope (aperture-nsom). c) Tip-enhanced near-field optical microscopy (TENOM). d) Tip-on-aperture (TOA) approach, which combines the advantages of (b) and (c) [2]. being imaged. A promising field under development is tipenhancement NSOM, or TENSOM, in which enhanced optical fields in proximity to a sharp metallic probe are used to locally excite the sample [2]. This approach generally uses a laser-illuminated metallic tip to create this field enhancement. Spasers would function as a source of enhanced optical fields in this application, replacing the laser illumination. The benefit to spasers is the dark mode of operation that they offer, where no far-field effects are created. This means there is no scattered background from the laser, as there is in TENSOM, so the signal-to-noise ratio is improved. The far-field effects of the laser deliver energy to the surface under investigation, which produces a temperature rise and may be a source of noise; the absence of far-field modes in a spaser avoids this difficulty. In TENSOM, the laser illumination must be polarized along the length of the metal tip to result in field en- 6

7 hancement, as shown in the tip-enhanced fields figure [5]. In a spaser, however, the pump energy only needs to be delivered to the gain medium within its absorption spectrum. In addition, because of the resonant nature of the cavity and the ease of pumping, a spaser may be able to deliver much higher evanescent field intensities than currently possible with lasers. Kappeler et al. predict a field enhancement of 135 for a conical gold tip [3], while Bergman and Stockman predict a field enhancement of 11 for a dark spasing mode [1]. While the spaser s overall gain is lower, this is an early prediction for a simple geometry; developments in tip and cavity design will improve on this result. Ultrafast Nanoplasmonic Amplification Spasers cannot, in a continuous-wave mode of operation, function as amplifiers for plasmonic circuits. In the CW regime, amplification cannot be achieved, since the gain exactly compensates the loss in the surface plasmon resonator. When the pump power is above the spasing threshold, the spaser always develops a large number of coherent surface plasmons in the spasing mode; these build until the population inversion becomes pinned at a low level and no additional surface plasmons can develop [7]. It may be possible to use spasers to provide amplification by exploiting their responses in non-cw modes. Stockman proposes two temporal regimes in which the spaser may function as an amplifier: the transient regime under continuous pumping but before CW operation develops, and the pulsed pumping regime. He models the behaviour of an idealized spaser system using direct numerical simulation. The transient regime is the window of time before population inversion in the spaser is pinned to a low level and the gain vanishes, and is on the order of femtoseconds. The exact time is based on the rate of quantum feedback, as well as the relaxation rates of surface plasmons and the gain medium. In Stockman s paper, there is approximately 250 fs after population inversion and before spontaneous spasing during which the spaser provides amplification. In this model, surface plasmons are introduced to the system at the same time as continuous pumping is turned on, at time t = 0. After the 250 fs time interval, CW operation is established. This interval is reduced as more surface plasmons are introduced at t = 0, as is the maximum gain [7]. The behaviour of the surface plasmon population and inversion population are shown in Figures 7a and 7b, respectively. For pulsed mode operation, Stockman models the effect of a fast pulsedescribed as much faster than 100 fsby inverting the population in the spaser at time t = 0 to a value of n 21 = At the same time, surface plasmons are introduced to the system; the number introduced is varied to study the behaviour of the system. The result is a series of surface plasmon pulses, the first of which is always the strongest, and always exceeds a certain value Figure 7: Ultrafast dynamics of the spaser. a) For a spaser, the dependence of the SP population in the spasing mode Nn on time t. The color coded curves correspond to the initial conditions with the different initial SP populations, as shown in the graphs. b) The same as (a) but for the temporal behavior of the population inversion n 21. c) Dynamics of a monostable spaser (no saturable absorber) with the pulsed pumping described as the initial inversion n 21 = The coherent SP population N n is displayed as a function of time t. d) The same as (c) but for the corresponding population inversion n 21. [7]. (100, in this model). The lower the initial population of surface plasmons, the later the first pulse is produced and the weaker it is [7]. The behaviour of the surface plasmon population and inversion population are shown in Figures 7c and 7d, respectively. Stockman speculates that certain levels of surface plasmon population may be used as a logical 1 or 0, and that the pulses produced during pulsed operation may be used as signal amplification. Additionally, he suggests that the time delay under continuous pumping before CW operation is established on the order of fs may have applications in the field of plasmonic circuitry. If the goal of using spasers as ultrafast plasmonic amplifiers is realized, it will thus be possible to build circuits with these femtosecond clock times. Nanoplasmonic Switching Stockman [7] also proposes a slight modification to the spaser design to make the device achieve bistable operation. Bistable application with a spaser is very similar to a MOSFET switch, whereby two stable states can be attained (i.e. logic 1 or logic 0 ). This can be achieved by adding a certain density of uniformly distributed saturable absorbers in the gain medium. The absorbers are simply chromophores that have absorption over the spasing line but not with the pump light. Simulation results indicate that this new spaser system possesses a critical pump rate for which two stable states 7

8 can be achieved. The logic 0 state is defined as a state with no SP population while a logic 1 is one where the SP population is much greater than 0. A logic 0 level is reached when the spaser is driven with nearly zero initial SP population (some SP population is allowed to account for spontaneous emission noise). Because of the presence of the absorbers, the SP population never gets high enough to allow stimulated emission and thus the spaser reaches a stable state with a SP population of 0. A logic 1 level is reached when the initial SP population is large enough to overcome losses due to the absorbers. The spaser then saturates at a constant SP population (CW operation). The location of the critical pump rate for which the transition occurs depends on the density of absorbing chromophores. A sufficient discontinuity, approaching that of an ideal MOSFET switch, was found when the concentration of absorbers was three times that of the gain medium s chromophores [7]. The characteristic switching time was found to be on the order of 100 fs. Interestingly, it was also found that the transitions between the two states can be induced by removing or adding SP states to the system. Such a device could thus act as both an ultrafast switch and a memory cell in a plasmonic circuit. T. Suteewong, and U. Wiesner. Demonstration of a spaser-based nanolaser. Nature, 460(7259): , [5] Lukas Novotny and Stephan J. Stranick. Near-field optical microscopy and spectroscopy with pointed probes*. Annual Review of Physical Chemistry, 57(1): , [6] Mark I. Stockman. Spasers explained. Nat. Photon., 2(6): , [7] Mark I Stockman. The spaser as a nanoscale quantum generator and ultrafast amplifier. Journal of Optics, 12(2):024004, [8] Mark I. Stockman, Sergey V. Faleev, and David J. Bergman. Localization versus delocalization of surface plasmons in nanosystems: Can one state have both characteristics? Phys. Rev. Lett., 87(16):167401, [9] N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov. Lasing spaser. Nat. Photon., 2(6): , Conclusions Spasers are truly nanoscale sources of intense optical fields, which have immense potential in the field of nanoplasmonics. They were realized experimentally [4] and there exists theoretical models that use the spasing process to allow for ultrafast nanoamplification and switching [7]. Spasers are likely to play a vital role in future plasmonic circuitry and computing, microscopy and probing and novel laser designs. References [1] David J. Bergman and Mark I. Stockman. Surface plasmon amplification by stimulated emission of radiation: Quantum generation of coherent surface plasmons in nanosystems. Phys. Rev. Lett., 90(2):027402, [2] Achim Hartschuh. Tip-enhanced near-field optical microscopy. Angewandte Chemie International Edition, 47(43): , [3] R. Kappeler, D. Erni, C. Xudong, and L. Novotny. Field computations of optical antennas. J. Comput. Theor. Nanosci., 4(3): , [4] M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, 8