Nonlinear optical model for strip plasmonic waveguides

Lysenko, Oleg; Bache, Morten; Lavrinenko, Andrei V.

doi:10.1364/josab.33.001341

Cited by 8 publications

(48 citation statements)

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“…27 However, even when these dependences are taken into account, the observed intrinsic nonlinearity (3) of gold additionally increases with the reduction of the film thickness (Figure 2). Using the experimental values on the imaginary part of the third-order susceptibility of gold, The third-order susceptibility of bulk gold for different pulse durations was calculated using the two-temperature model (TTM) of the free electron temporal dynamics 18,19 (see Supporting…”

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“…In the formula for the field localization parameter Au  , the initial two-dimensional integrals over the plasmonic mode area were reduced to one-dimensional integrals over the z-coordinate due to the waveguide symmetry. 27 The only contribution to the effective nonlinear loss parameter of the LRSPP waveguide mode comes from gold because the photon energy at 1030 nm is less than half the bandgap energies for the adhesion and cladding materials of the waveguide.Gold layer thickness t Au affects the effective nonlinear absorption coefficient of the LRSPP mode via the field localization parameter Au  (which increases with t Au ) and mode effective area A eff (which decreases with t Au ). 27 However, even when these dependences are taken into account, the observed intrinsic nonlinearity (3) of gold additionally increases with the reduction of the film thickness (Figure 2).…”

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“…27 The only contribution to the effective nonlinear loss parameter of the LRSPP waveguide mode comes from gold because the photon energy at 1030 nm is less than half the bandgap energies for the adhesion and cladding materials of the waveguide.…”

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“…The collision frequency of electrons in thin gold layers increases comparing to bulk gold, and it leads to enhancement of the effective third-order nonlinear susceptibility. 26,27 The developed theoretical approach can be used to determine the third-order nonlinear susceptibility of free-electron gas in metals for any wavelength, pulse duration and metal layer thickness, once the nonlinear susceptibility of bulk metal for cw excitation are known and the electron-confinement enhancement factor is determined experimentally for a particular type of nanostructure.In future it will be important to investigate the linear and nonlinear optical properties of the waveguides with even thinner gold layers (up to ~10 nm). The standard Drude model breaks down at the metal layer thicknesses below 10 nm due to possible nonlocal 37,38 and quantum effects.…”

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confidence: 99%

“…26,27 The third-order susceptibility of a gold film, which affects transmission (reflection) of light through (from) a film as well as propagation of plasmonic modes on the film interfaces is known to depend on both the pulse duration and thickness of the film. 20 The goal of this paper is to quantify such dependences in experiment and theory on nonlinear propagation of the LRSPP modes in Au strip waveguides.…”

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Nonlinear Dynamics of Ultrashort Long-Range Surface Plasmon Polariton Pulses in Gold Strip Waveguides

et al. 2016

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We study experimentally and theoretically nonlinear propagation of ultrashort long-range surface plasmon polaritons in gold strip waveguides. The nonlinear absorption of the plasmonic modes in the waveguides is measured with femtosecond pulses revealing a strong dependence of the third-order nonlinear susceptibility of the gold core on the pulse duration and layer thickness. A comprehensive model for the pulse duration dependence of the third-order nonlinear susceptibility is developed on the basis of the nonlinear Schrödinger equation for plasmonic mode propagation in the waveguides. The model accounts for the intrinsic delayed (noninstantaneous) nonlinearity of free electrons of gold as well as the thickness of the gold film, and is experimentally verified. The obtained results are important for the development of active plasmonic and nanophotonic components. 2Plasmonic nanostructures represent a unique platform for many linear and nonlinear optical applications. 1 A great variety of plasmonic waveguides for integrated optics, 2,3 nanofocusing, 4,5 sensing, 6,7 lasing and amplification of light 8,9 has been proposed. In particular, special attention has recently been paid to the nonlinear optical properties of plasmonic waveguides, hybrid plasmonic waveguides, and other elements important for future nanophotonic communication approaches. [10][11][12] Bulk metals, thin metal layers, and plasmonic metamaterials have been investigated in the nonlinear regime. [13][14][15] The nonlinear propagation of surface plasmon polaritons (SPPs) in plasmonic waveguides can be studied in terms of either the second-order nonlinearity, 16,17 or the third-order nonlinearity. 18,19 The latter is particularly important because it is present in all materials. In metals, it mainly arises due to hot-electron contributions from changes of the intrinsic electronic temperature after absorption of the incident light. Typically, the electron relaxation time in noble metals is on the few-picosecond scale, 18,19 implying that their nonlinear susceptibility can depend on the laser pulse duration if it is shorter than or comparable with the electron relaxation time. 20 The majority of the experimental data on the third-order nonlinear susceptibility of gold were collected near the interband transitions in a wavelength range of 532-630 nm for pulse durations between 100 fs and 1 ns. 20 Most results were obtained with the z-scan method, reporting very high values of the third-order susceptibility in the range of 10 -16 -10 -15 m 2 /V 2 . [21][22][23][24] However, the linear propagation losses of SPPs in Au-based waveguides, which are also related to the same interband transitions, are very high (~30-40 dB/mm) in this wavelength range. 25 On the other hand, nanophotonic and plasmonic devices are extensively exploited in the infrared (IR) wavelength range. 2,3 The propagation losses of long-range SPPs (LRSPPs) in Au-based waveguides can be ~2-5 dB/mm at the telecommunication wavelengths. 25 Meanwhile, the third-3 order susceptibility of...

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Nonlinear Dynamics of Ultrashort Long-Range Surface Plasmon Polariton Pulses in Gold Strip Waveguides

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Nonlinear plasmonics of three-dimensional Dirac semimetals

et al. 2018

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The three-dimensional Dirac semimetal (3D DSM) is a new class of material with a slew of electronic and optical properties in common with graphene, while structurally having a bulk form like real metals. In particular, the Dirac band structure of 3D DSM conferred very high optical nonlinearities much like the case for graphene. Consequently, we found that 3D DSM has respectable nonlinear plasmonic performance in comparison with graphene, while retaining the structural benefits of bulk metals, having reduced passive plasmonic losses, and is much easier to handle in fabrication facilities. 3D DSM is expected to play a strong role in providing strong optical nonlinearities for all-optical switching and at the same time offering a superior platform for nanophotonic device integration.

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Ultrafast nonlinear dynamics of thin gold films due to an intrinsic delayed nonlinearity

Bache

Lavrinenko

2017

J. Opt.

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Abstract. Using long-range surface plasmon polaritons light can propagate in metal nano-scale waveguides for ultracompact opto-electronic devices. Gold is an important material for plasmonic waveguides, but although its linear optical properties are fairly well understood, the nonlinear response is still under investigation. We consider propagation of pulses in ultrathin gold strip waveguides, modeled by the nonlinear Schrödinger equation. The nonlinear response of gold is accounted for by the two-temperature model, revealing it as a delayed nonlinearity intrinsic in gold. The consequence is that the measured nonlinearities are strongly dependent on pulse duration. This issue has so far only been addressed phenomenologically, but we provide an accurate estimate of the quantitative connection as well as a phenomenological theory to understand the enhanced nonlinear response as the gold thickness is reduced. In comparison with the previous works, the analytical model for the power-loss equation has been improved, and can be applied now to cases with a high laser peak power. We show new fits to experimental data from literature and provide updated values for the real and imaginary part of the nonlinear susceptibility of gold for various pulse durations and gold layer thicknesses. Our simulations show that the nonlinear loss is inhibiting efficient nonlinear interaction with low-power laser pulses. We therefore propose to design waveguides suitable for the mid-IR, where the ponderomotive instantaneous nonlinearity can dominate over the delayed hot-electron nonlinearity and provide a suitable plasmonics platform for efficient ultrafast nonlinear optics.

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Nonlinear optical model for strip plasmonic waveguides

Cited by 8 publications

References 30 publications

Nonlinear Dynamics of Ultrashort Long-Range Surface Plasmon Polariton Pulses in Gold Strip Waveguides

Nonlinear Dynamics of Ultrashort Long-Range Surface Plasmon Polariton Pulses in Gold Strip Waveguides

Nonlinear plasmonics of three-dimensional Dirac semimetals

Ultrafast nonlinear dynamics of thin gold films due to an intrinsic delayed nonlinearity

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