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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 9 — Apr. 25, 2011
  • pp: 8367–8378
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Surface plasmon polariton induced optical amplitude and phase modulation in sub-wavelength apertures

Arash Joushaghani, Bo Hou, J. Stewart Aitchison, and Joyce K. S. Poon  »View Author Affiliations


Optics Express, Vol. 19, Issue 9, pp. 8367-8378 (2011)
http://dx.doi.org/10.1364/OE.19.008367


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Abstract

We report on the amplitude and phase modulation of picosecond optical pulses, near λ = 800 nm, transmitted through sub-wavelength rectangular apertures in thin gold films with thicknesses of λ/10 at per-pulse energies of <0.3 nJ or 9 pJ per aperture. Due to the excitation and strong confinement of surface plasmon polaritons in the apertures, the leading edge of a pulse causes a rapid heating of the electrons and lattice to modulate its falling edge. By comparing cross-correlation frequency resolved optical gating measurements with simulations, the thermal effects responsible for the induced pulse dynamics are identified.

© 2011 OSA

1. Introduction

Surface plasmon polaritons (SPPs) are electron density oscillations coupled to electromagnetic waves that are confined to and propagate along metal-dielectric interfaces. They provide a high degree of spatial confinement for optical radiation and hence enhance the physical processes that depend on the optical intensity [1

1. S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics 1, 641–648 (2007). [CrossRef]

]. Although the linear properties of SPPs have been studied extensively in the past few years [2

2. F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82, 729 (2010). [CrossRef]

, 3

3. J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70, 1–87 (2007). [CrossRef]

], their dynamic and nonlinear features have been less explored. Early research on SPP dynamics focused on linear propagation and measured SPP transients [4

4. R. Muller, V. Malyarchuk, and C. Lienau, “Three-dimensional theory on light-induced near-field dynamics in a metal film with a periodic array of nanoholes,” Phys. Rev. B 68, 205415 (2003). [CrossRef]

], group delay, and transit time using interferometry [5

5. A. Dogariu, A. Nahata, R. A. Linke, L. J. Wang, and R. Trebino, “Optical pulse propagation through metallic nano-apertures,” Appl. Phys. B 74, S69–S73 (2002). [CrossRef]

] and near-field optical microscopy [6

6. D. S. Kim, S. C. Hohng, V. Malyarchuk, Y. C. Yoon, Y. H. Ahn, K. J. Yee, J. W. Park, J. Kim, Q. H. Park, and C. Lienau, “Microscopic origin of surface-plasmon radiation in plasmonic band-gap nanostructures,” Phys. Rev. Lett. 91, 143901 (2003). [CrossRef] [PubMed]

]. Recently, researchers have studied optically-induced, reversible changes to SPP properties using pump-probe techniques, with the intent to understand short pulse SPP excitations and create high-speed SPP modulators [7

7. S. Link and M. A. El-Sayed, “Spectral properties and relaxation dynamics of surface plasmon electronic oscillations in gold and silver nanodots and nanorods,” J. Phys. Chem. B 103, 8410–8426 (1999). [CrossRef]

15

15. J. N. Caspers, N. Rotenberg, and H. M. van Driel, “Ultrafast silicon-based active plasmonics at telecom wavelengths,” Opt. Express 18, 19761–19769 (2010). [CrossRef] [PubMed]

]. Central to the modification of the optical transmission in these experiments is the coupling between SPPs and the nonlinear thermal effects of the metal induced by the pump light.

Although these experiments have provided insights into the interactions between light and electrons in metals and have demonstrated a method to modulate SPPs, they have several limitations. First, the measurements relied on SPPs that were delocalized over a periodic structure or a wide waveguide. As a result, the pump pulses were spatially broad, and did not efficiently couple the thermal energy into regions with the highest overlap with the SPPs. The inefficient coupling of the pump pulse required high energies of 0.1–10 μJ per pulse to observe the modulation. Second, the delocalized nature of the SPPs resulted in a low confinement factor of the SPPs in the metal, which necessitated the pump or probe wavelength to be at an interband transition of the metal or the optical excitation of the dielectric to adequately modulate the probe pulses. Finally, these experiments did not measure the optical phase dynamics, which are crucial for a complete characterization of the light-electron interactions.

2. Aperture design and linear properties

We designed and fabricated arrays of rectangular apertures in thin gold films deposited on a glass substrate. The lowest order resonance of the apertures arises from the hybridization of the cut-off resonance of the metallic apertures and the SPPs along the aperture sidewalls [2

2. F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82, 729 (2010). [CrossRef]

, 16

16. B. Hou, X. Q. Liao, and J. K. S. Poon, “Resonant infrared transmission and effective medium response of sub-wavelength h-fractal apertures,” Opt. Express 18, 3946–3951 (2010). [CrossRef] [PubMed]

, 17

17. J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305, 847–848 (2004). [CrossRef] [PubMed]

]. At this resonance, the light is strongly localized in the apertures. The apertures were sufficiently far apart such that the resonance wavelength was independent of the array period. Figure 1(a) shows the geometry of the sample. The width and height of each aperture were 80 nm and 200 nm, respectively. The apertures were arranged on a square lattice with a period of 300 nm in an 80 nm thick gold film. The gold permittivity, as described by the Drude model, is ɛm/ɛ0=ɛb+ωp2/(jωγ0ω2), where ε 0 is the vacuum permittivity, ε b = 9 at room temperature, and is the dielectric constant due to the bound electrons, ω p = 1.32×1016 s−1 is the plasma frequency, and γ 0 = 1.06 × 1014 s−1 is the electron damping rate at room temperature, T 0 = 300 K [18

18. E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1985).

].

Fig. 1 (a) A schematic of the rectangular apertures. (b) The computed electric field and (c) magnetic field amplitudes in the apertures on resonance, where red indicates the highest field intensities. (d) A scanning electron micrograph of the aperture array and (e) the measured (left axis) and calculated (right axis) normalized transmission spectra of x- and y- polarized light.

Accounting for the rounding of the corners, the apertures were designed to support a fundamental resonance at λ ≈ 800 nm. The computed electric and magnetic field amplitudes on resonance are shown in Fig. 1(b) and 1(c) respectively, illustrating the strongly localized nature of the mode. The apertures were fabricated by focused ion beam milling of a 80 nm gold on a 5 nm chromium layer evaporated on a glass substrate. Figure 1(d) shows a scanning electron micrograph of a sample. Following the coordinate convention of Fig. 1(a), x and y-polarized transmission spectra of the array measured with a continuous-wave broadband light source are shown in Fig. 1(e). Since the rectangular slits are anisotropic, x-polarized light exhibited a resonance near λ = 800 nm, which was absent for y-polarized light in the spectral window of interest. The experimental results are in good agreement with the computed spectra shown in Fig. 1(e). The measured spectra were broadened and slightly red-shifted compared to the numerical simulations due to fabrication inhomogeneities of the apertures.

3. Dynamics model and simulations

Over ps time scales, the absorption of an optical pulse leaves the metal in an non-equilibrium state, where the electron temperature, T e, is vastly different from the lattice temperature, T l [19

19. S. I. Anisimov, B. L. Kapeliovich, and T. L. Perelman, “Electron emission from metal surfaces exposed to ultra-short laser pulses,” Sov. Phys. JETP 39, 375–377 (1974).

]. The elevated T e and T l change the metal permittivity which in turn alters the optical pulse transmitted through the apertures.

Fig. 2 A summary of the model used to compute the evolution of light and the properties of the metal. 1. The Helmholtz wave equation was solved at time t. The absorption of light modified the lattice and electron temperatures. 2. The modified temperatures altered the behavior of the electrons to 3. change the metal permittivity. The Helmholtz wave equation was then solved at the next time step, t + Δt, with the new value of metal permittivity assuming the envelope of the light adiabatically followed the changes in permittivity.

3.1. Optical propagation

Due to the sub-ps resolution of the measurements, we simplified the electromagnetic modeling and assumed the electromagnetic fields adiabatically followed the permittivity. We simulated pulse propagation and solved, at each time step, the 3D, spatial Helmholtz wave equation for the magnetic field :
×(1ɛ(r,t)×H)k02H=0,
(1)
where ε(r⃗,t) is the permittivity at position r⃗ and time t. The simulation domain included the metallic apertures, the glass substrate, and the air surrounding the structure. Using symmetry, only one quadrant of the unit cell was modeled.

Since the thermal relaxation time of the metal was much shorter than the repetition period of the laser (a few ns [20

20. Y. Takata, H. Haneda, T. Mitsuhashi, and Y. Wada, “Evaluation of thermal diffusivity for thin gold films using femtosecond laser excitation technique,” Appl. Surf. Sci. 189, 227–233 (2002). [CrossRef]

] vs. 12.5 ns), we model the transmission dynamics with a single incident pulse. The incident pulse was assumed to be Gaussian and x-polarized, with an electric field of E⃗ i = x̂E 0(t) exp( 0 t), where ω 0 is the carrier frequency, and E 0(t) is a slowly-varying envelope of the form
E0(t)exp[2(ln2)t2/τp2+jφ(t)],
(2)
where τp is the full-width at half-maximum (FWHM) temporal width of the pulse intensity, and the phase is φ(t) = 2(ln2)α(t/τp)2, where α is the chirp parameter.

Using the above incident field as the source of electromagnetic radiation in our simulations, Eq. (1) was solved at 0.2 ps time steps with a spatial resolution of 6 nm in three dimensions in the metal to properly account for the thermally induced inhomogeneities in the metal permittivity.

3.2. Metal thermal response

The absorption of the incident field modifies the properties of the metal. The response of the metal to the incident field can be described by two steps. First, the absorption of light elevates both T e and T l. The increased temperatures modify the behavior of free and bound electrons inside the metal which in turn changes the metal permittivity, ε m. For the computations, T e, T l, and ε m were calculated for 10 ps using the same time step and spatial resolution as those for the electromagnetic calculations.

3.2.1. Electron and lattice temperatures

We described the evolution of Te and Tl by the two temperature model [19

19. S. I. Anisimov, B. L. Kapeliovich, and T. L. Perelman, “Electron emission from metal surfaces exposed to ultra-short laser pulses,” Sov. Phys. JETP 39, 375–377 (1974).

]:
CeTet=[KeTe]g(TeTl)+12Re{jωɛmEE*}.,
(3a)
ClTlt=g(TeTl),
(3b)
where Ce ( l ) is the electron (lattice) heat capacity, Ke is the electron thermal conductivity, g is the electron-phonon coupling constant, and E the electric field in the metal. The last term in Eq. (3)(a) results from the ohmic and dielectric dissipation rates in the metal and increases Te by the absorption of light. This term relates the thermal properties of the metal to the magnitude of the electric field.

For the computations, Ce = C 0 Te with C 0 = 71 Jm−3K−2, Cl = 2.48×106 Jm−3K−2 and g = 2.5 × 1016 Wm−1K−1. The electron thermal conductivity was calculated via the free electron gas model with γ(Tl, Te) as the electron scattering rate, such that Ke=K0Te/(Tl+BATe2), where K 0 = 318 Wm−1K−1 and B = 1.2 × 107 s−1K−2. The value of A for thermal conductivity was evaluated at a zero frequency limit from the constant-current electrical resistivity and was A = 1.23 × 1011 s−1K−1 [21

21. N. W. Ashcroft and N. D. Mermin, Solid State Physics (Holt, Rinehart and Winston, 1976).

]. The electron scattering rate was also used to calculate the free electron contribution to the permittivity as discussed in Section 3.2.2.B.

3.2.2. Permittivity

3.2.2.A. Bound electron contribution

The bound electron contribution is due to the optically induced electron interband absorption from the d-band of the gold to its Fermi level, which is at about 2.4 eV (520 nm). Since the wavelengths used in this experiment (λ ≈ 800 nm) were detuned from this transition, the probability of interband transition of bound electrons at room temperature, T 0, was negligible. However, as we shall show, in our experiment, Te could exceed 1000 K, sufficient to promote more conduction electrons to states above the Fermi level. This would increase the number of vacant states below the Fermi level, to which bound electrons in the lower d-band could be optically excited. The interband transition probability could thus be effectively increased even at detuned wavelengths to affect the bound electron permittivity [22

22. R. D. Averitt, S. L. Westcott, and N. J. Halas, “Ultrafast optical properties of gold nanoshells,” J. Opt. Soc. Am. B 16, 1814–1823 (1999). [CrossRef]

].

To evaluate εb, we first calculated the change in the imaginary part of εb, ΔIm{εb}, over a broad range of frequencies by calculating the change in the Fermi distribution of electrons as the temperature rose from T 0 to Te. Then ΔRe{εb} was calculated from ΔIm{εb} using Kramers-Kronig relations. At specific frequencies, ΔRe{εb} and ΔIm{εb} were fitted with polynomials to interpolate their values at an arbitrary temperatures.

Figures 3(a) and 3(b) respectively show –ΔIm{εb} and ΔRe{εb} for several temperatures and frequencies. The total bound electron permittivity is given by εb(Te) = εb(T 0) + ΔRe{εb} + jΔIm{εb}. The wavelengths used for the simulations were slightly different from the experimental values because the calculated and measured resonance peak wavelengths (see Fig. 1(e)) were not identical. The simulation wavelengths were chosen to have the same detuning from the resonance peak as the wavelengths used in the experiments.

Fig. 3 (a) –ΔIm{εb} and (b) ΔRe{εb} calculated at different temperatures for several wavelengths λ = 780 nm, λ = 850 nm, and λ = 750 nm (symbols) and the polynomial fitting for the data at λ = 780 nm (solid lines).

3.2.2.B. Free electron contribution

The elevated temperatures also affect the free electron permittivity. This contribution is primarily due to increases in the electron-electron and electron-lattice scattering rates, which increase the electron damping constant and reduce the thermal conductivity of the metal. Using the Drude model with a modified electron damping rate, γ(Te, Tl), the temperature-dependent permittivity due to free electrons becomes:
ɛf(Tl,Te)ɛ0=ωp2jωγ(Tl,Te)ω2.
(5)

Since we are interested in ps dynamics, we neglected thermal expansion which would make ωp temperature-dependent. We approximated the electron damping rate at optical frequencies as γ=ATl+BTe2, where A = γ 0/T 0 = 3.54 × 1011 s−1K−1 and B = 1.20 × 107 s−1K−2 [23

23. X. Y. Wang, D. M. Riffe, Y. S. Lee, and M. C. Downer, “Time-resolved electron-temperature measurement in a highly excited gold target using femtosecond thermionic emission,” Phys. Rev. B 50, 8016 (1994). [CrossRef]

].

3.3. Simulation results

The coupled equations above were solved in the time domain using a finite-element method software (COMSOL Multiphysics) to compute the temporal evolutions of E⃗, Te, and Tl at all spatial points. Figure 4 shows the results of our model for a 2.7 ps FWHM pulse centered at the SPP resonance wavelength. The evolution of Te and Tl at the spatial point of maximum temperature are shown in Fig. 4(a). The magnitude and rate of the increase in Tl are lower than those of Te because of the larger heat capacity of the lattice compared to the electrons. Figure 4(b) shows the large change in Im{εm} has a similar time-dependence as Te, which implies the Te contribution to the permittivity dominates over Tl.

Fig. 4 The calculated temporal evolution of (a) Te, Tl, and (b) εm for a 2.7 ps FWHM incident pulse with a fluence of 8 mJcm−2 on resonance at the spatial point indicated by the arrows in (e) and (f), which is the point of maximum temperature. The corresponding temporal evolution of (c) the transmission intensity and (d) the transmission phase at various fluences. The spatial distributions of the (e) electron and (f) lattice temperatures at 5 ps.

4. Experimental setup and results

4.1. XFROG measurements

To measure the temporal evolution of the phase and amplitude of ps pulses coupled out of the apertures, we used a sum frequency generation (SFG) XFROG [24

24. S. Linden, H. Giessen, and J. Kuhl, “Xfrog - a new method for amplitude and phase characterization of weak ultrashort pulses,” Phys. Status Solidi B 206, 119–124 (1998). [CrossRef]

]. Figure 5(a) shows the experimental setup. Pulses with a FWHM of 2.7 ps from a wavelength tuneable Ti:Sapphire mode-locked laser (Coherent Mira) were divided into two paths. The pump pulses passed through the sample, while the gating pulses traversed through a delay line. The pump pulses were incident from the glass side to keep the spot area small. Although the optical resonance did not depend on the coupling between the apertures, approximately 30 apertures were excited (spot area of 2.7 μm2) to attain a sufficient signal-to-noise ratio for the measurement. For this spot area, about 57% of the incident light was transmitted and 10% reflected at λ = 800 nm. The time-averaged transmitted power varied almost linearly with the pump fluence. The pump and the gating pulses were combined in a nonlinear β-BaB2O4 (BBO) crystal to generate a SFG signal that was spectrally resolved with an optical spectrum analyzer (OSA) as a function of the delay time between the pump and gating pulses, τ. A typical XFROG trace is shown in Fig. 5(b).

Fig. 5 (a) The XFROG measurement setup. (b) An example of an XFROG trace at λ = 775 nm.

The XFROG traces were analyzed by a commercially available software (FemtoSoft XFROG), which retrieved the amplitude and phase of the transmitted pump pulses given the phase and amplitude of the gating pulses. The amplitude and phase of the gating pulses were measured using the identical setup but with the sample removed. The XFROG data were retrieved with a 512× 512 grid with errors G ≲ 0.0001, where G is the root mean square average of the difference between the measured and retrieved XFROG traces [25

25. K. W. DeLong, D. N. Fittinghoff, and R. Trebino, “Practical issues in ultrashort-laser-pulse measurement using frequency-resolved optical gating,” IEEE J. Quantum Electron . 32, 1253–1264 (1996). [CrossRef]

]. To check the validity of the setup and the retrieval algorithm, we removed the sample, and then compared the frequency marginals, defined as M = ∫ dτI F, where I F(ω, τ) is the resulting FROG trace, with the frequency self-convolution, [I(ω)*I(ω)], of the time-averaged spectrum of the pulse, I(ω), measured by the OSA. The results showed a good agreement between the two, confirming the validity of the retrieval [25

25. K. W. DeLong, D. N. Fittinghoff, and R. Trebino, “Practical issues in ultrashort-laser-pulse measurement using frequency-resolved optical gating,” IEEE J. Quantum Electron . 32, 1253–1264 (1996). [CrossRef]

].

4.2. Optical modulation

Since the spectral bandwidth of ps pulses was much narrower than the transmission bandwidth of the apertures, the linear dispersive effects of the apertures on the pulses were negligible. Any substantial changes to the amplitude and phase of the transmitted pulses were thus dominated by the transient thermal effects. By adjusting the intensity of the incident pump pulses, we observed significant changes to the transmitted pulse shapes.

4.3. Pulse amplitude and phase

Figures 6(a) and 6(b) respectively show the experimentally measured and numerically calculated normalized electric field intensities of the pulses on resonance at several pump fluences. The fronts of the pulses were aligned in time for comparison. The measurements showed that with increasing fluence, the tails of the pulses became more attenuated, consistent with simulations in Fig. 6(b) and Fig. 4(c). The discrepancy between the simulated and measured fluence values was attributed to the difference between the measured and simulated linear transmission as shown in Fig. 1(e). The amplitude change of the falling edge of the pulse exhibited two components: a rapid initial attenuation over about 0.5 ps followed by a more gradual decay. The fast initial decay was due to the Te contribution to εm. As shown in Fig. 4(c), the transmission peaks as Te reaches a maximum and then decays in a time-scale comparable to the Te decay time. The gradual attenuation occurring at a later time was due to the rise in Tl. As a consequence of the different attenuation mechanisms, the transmitted pulses appeared to be narrowed and the peaks appeared to be advanced in time as the fluence increased.

Fig. 6 (Left column) The retrieved normalized electric field intensity, |E|2, and phase on resonance at λ = 800 nm, negatively detuned at λ = 775 nm, and positively detuned at λ = 860 nm from the resonance. (Right column) The numerically calculated normalized electric field intensity, |E|2, and phase on resonance, positively detuned, and negatively detuned from the resonance.

The phase shift was also characterized by a rapid change followed by a more gradual change. However, the relative magnitude of the gradual phase change was much smaller than that of the amplitude. This is because the phase change depends primarily on ΔRe{εm}, but free carrier absorption mainly modifies Im{εm}, and as shown in Fig. 4(b) ΔRe{εm} ≪ ΔIm{εm}, which results in a small phase change. The rapid phase change near the peak of the pulse coincided with the maximum of Te and was dominated by the change in εb(Te), which primarily modified Re{εm}.

The electric field intensity and phase of the transmitted pulses were also simulated and experimentally retrieved at wavelengths detuned from the center of the aperture resonance. These results are shown in Fig. 6(c)–6(f). The net changes in the phase and amplitude of the pulse for the off-resonance wavelengths were smaller than the on-resonance case, because higher fluences were required to couple the same amount of energy into the apertures. The measurements are also in good qualitative agreement with the simulation results.

The discrepancy between the simulated and measured data can be attributed to several factors. Our expressions for Ce, Ke, and g were derived from the free electron gas model. At high electron temperatures (Te ≈ 6000 K), the bound electrons can also be thermally excited, so the free electron gas model we have used is not as accurate. At high incident fluences in our experiments, Te did approach this limit. Also, the measured phase of the incident pulse was not exactly quadratic as modeled in our simulations, and the phase retrieval was most accurate near the center of the pulse, when the amplitude was the highest.

4.4. Pulse width modulation

We have also characterized the effects of the incident pulse fluence on the magnitude of the intensity modulation using the FWHM of transmitted pulse as a metric. Figure 7 shows the percentage change in the FWHM of the retrieved electric field intensity, Δτp, as a function of incident pulse fluence at several wavelengths where Δτp = (τp, pumpτp, gate)p, gate and τp, gate(pump) is the FWHM of the electric field intensity before(after) it propagated through the apertures.

Fig. 7 The percentage change in the FWHM of the retrieved electric field intensity, |E|2, for pump wavelengths centered on resonance at λ = 800 nm and detuned at λ = 775 nm and λ = 860 nm.

The largest change in FWHM was observed for pump wavelengths which were on the aperture resonance at λ = 800 nm. As shown in the linear transmission spectrum in Fig. 1(e), detuning the pump wavelength from the peak of the resonance reduces the amount of optical power coupled into the apertures and the resultant thermal effects in the metal, leading to a smaller change in the FWHM.

Figure 7 also shows that Δτp saturated at high fluences. At these fluences, the electron and lattice temperatures in the metal were raised sufficiently high to reduce the coupling of the incident pump pulse to the aperture, resulting in a saturation of the modulation. Increasing the fluence beyond these values typically resulted in a permanent damage to the apertures.

5. Conclusion

In summary, we have measured and explained the amplitude and phase evolution of ps pulses transmitted through sub-wavelength apertures supporting strongly localized resonances. The observed effects were made possible by the excitation and strong confinement of SPPs in the rectangular apertures, which enhanced the fluence inside the apertures by more than a factor of 5 compared to the pulse fluence in vacuum. The XFROG technique enabled the characterization of the amplitude and phase of the ps pulses with temporal resolution of 100 fs, allowing us to identify the thermal mechanisms responsible for the change in the real and imaginary parts of the metal permittivity.

Even though the incident light was detuned from the metal interband transition and was at modest fluences ≈ 10 mJcm−2, corresponding to an incident energy of 0.275 nJ or 9 pJ per aperture, sub-ps pulse modulation was observed for a propagation length of only 80 nm, 1/10 of the optical wavelength in free-space. Localized resonances circumvent the need for optical pulses at wavelengths determined by the interband transitions of the metal. These apertures can also be used to realize rapid, sub-ps thermally-induced transients in materials incorporated inside the sub-wavelength apertures for applications in low energy, ultra-compact, and ultra-high-speed optical modulators.

Acknowledgments

A. J. and B. H. contributed equally to this work. This work was supported by NSERC. We thank T. Simpson for the sample fabrication at the University of Western Ontario and N. Rotenberg and J. N. Caspers for helpful discussions. A. J. is supported by an NSERC graduate scholarship, and B. H. was supported by an Ontario MRI postdoctoral fellowship.

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S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics 1, 641–648 (2007). [CrossRef]

2.

F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82, 729 (2010). [CrossRef]

3.

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70, 1–87 (2007). [CrossRef]

4.

R. Muller, V. Malyarchuk, and C. Lienau, “Three-dimensional theory on light-induced near-field dynamics in a metal film with a periodic array of nanoholes,” Phys. Rev. B 68, 205415 (2003). [CrossRef]

5.

A. Dogariu, A. Nahata, R. A. Linke, L. J. Wang, and R. Trebino, “Optical pulse propagation through metallic nano-apertures,” Appl. Phys. B 74, S69–S73 (2002). [CrossRef]

6.

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B. Hou, X. Q. Liao, and J. K. S. Poon, “Resonant infrared transmission and effective medium response of sub-wavelength h-fractal apertures,” Opt. Express 18, 3946–3951 (2010). [CrossRef] [PubMed]

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J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305, 847–848 (2004). [CrossRef] [PubMed]

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E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1985).

19.

S. I. Anisimov, B. L. Kapeliovich, and T. L. Perelman, “Electron emission from metal surfaces exposed to ultra-short laser pulses,” Sov. Phys. JETP 39, 375–377 (1974).

20.

Y. Takata, H. Haneda, T. Mitsuhashi, and Y. Wada, “Evaluation of thermal diffusivity for thin gold films using femtosecond laser excitation technique,” Appl. Surf. Sci. 189, 227–233 (2002). [CrossRef]

21.

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Holt, Rinehart and Winston, 1976).

22.

R. D. Averitt, S. L. Westcott, and N. J. Halas, “Ultrafast optical properties of gold nanoshells,” J. Opt. Soc. Am. B 16, 1814–1823 (1999). [CrossRef]

23.

X. Y. Wang, D. M. Riffe, Y. S. Lee, and M. C. Downer, “Time-resolved electron-temperature measurement in a highly excited gold target using femtosecond thermionic emission,” Phys. Rev. B 50, 8016 (1994). [CrossRef]

24.

S. Linden, H. Giessen, and J. Kuhl, “Xfrog - a new method for amplitude and phase characterization of weak ultrashort pulses,” Phys. Status Solidi B 206, 119–124 (1998). [CrossRef]

25.

K. W. DeLong, D. N. Fittinghoff, and R. Trebino, “Practical issues in ultrashort-laser-pulse measurement using frequency-resolved optical gating,” IEEE J. Quantum Electron . 32, 1253–1264 (1996). [CrossRef]

OCIS Codes
(240.6680) Optics at surfaces : Surface plasmons
(300.6430) Spectroscopy : Spectroscopy, photothermal

ToC Category:
Optics at Surfaces

History
Original Manuscript: February 7, 2011
Revised Manuscript: March 29, 2011
Manuscript Accepted: March 31, 2011
Published: April 15, 2011

Citation
Arash Joushaghani, Bo Hou, J. Stewart Aitchison, and Joyce K. S. Poon, "Surface plasmon polariton induced optical amplitude and phase modulation in sub-wavelength apertures," Opt. Express 19, 8367-8378 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-9-8367


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References

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  19. S. I. Anisimov, B. L. Kapeliovich, and T. L. Perelman, “Electron emission from metal surfaces exposed to ultra-short laser pulses,” Sov. Phys. JETP 39, 375–377 (1974).
  20. Y. Takata, H. Haneda, T. Mitsuhashi, and Y. Wada, “Evaluation of thermal diffusivity for thin gold films using femtosecond laser excitation technique,” Appl. Surf. Sci. 189, 227–233 (2002). [CrossRef]
  21. N. W. Ashcroft and N. D. Mermin, Solid State Physics (Holt, Rinehart and Winston, 1976).
  22. R. D. Averitt, S. L. Westcott, and N. J. Halas, “Ultrafast optical properties of gold nanoshells,” J. Opt. Soc. Am. B 16, 1814–1823 (1999). [CrossRef]
  23. X. Y. Wang, D. M. Riffe, Y. S. Lee, and M. C. Downer, “Time-resolved electron-temperature measurement in a highly excited gold target using femtosecond thermionic emission,” Phys. Rev. B 50, 8016 (1994). [CrossRef]
  24. S. Linden, H. Giessen, and J. Kuhl, “Xfrog - a new method for amplitude and phase characterization of weak ultrashort pulses,” Phys. Status Solidi B 206, 119–124 (1998). [CrossRef]
  25. K. W. DeLong, D. N. Fittinghoff, and R. Trebino, “Practical issues in ultrashort-laser-pulse measurement using frequency-resolved optical gating,” IEEE J. Quantum Electron . 32, 1253–1264 (1996). [CrossRef]

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