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

Abstract

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...

Free‐electron Optical Nonlinearities in Plasmonic Nanostructures: A Review of the Hydrodynamic Description

“…Kerr‐type nonlinearities, which are predominately determined by heating of the electron gas (its energy redistribution in a conduction band), strongly depend on the energy supplied by the light to the electron plasma and, therefore, are strongly affected by the pulse energy and duration in terms of their values and time‐response, varying over several orders of magnitude . They also may depend on the size of the particles and thickness of a metal layer due to modification of the electron scattering rate in nanostructures …”

“…The nonlinear response described by the two‐temperature model depends on the excitation and probe pulse durations if they are comparable to the characteristic times of the electron relaxation processes . The excitation pulse is absorbed by the metal almost instantaneously so that the mean absorbed power density follows the shape of the incident pulse ( Figure ).…”

“…P and are ultimately directly connected through the electron‐temperature transient response function (inset). Reproduced with permission . Copyright 2016, American Chemical Society.…”

“…[57] They also may depend on the size of the particles and thickness of a metal layer due to modification of the electron scattering rate in nanostructures. [58][59][60] Both coherent and Kerr-type nonlinearities of metals may originate from several families of physical effects. One is related to the nonlinear dynamics of the free carriers plasma and is present in all spectral ranges.…”

“…The nonlinear response described by the two-temperature model depends on the excitation and probe pulse durations if they are comparable to the characteristic times of the electron relaxation processes. [58] The excitation pulse is absorbed by the metal almost instantaneously so that the mean absorbed power density follows the shape of the incident pulse (Figure 3). The rise of the thermalised electron energy density is delayed by 100s of fs as the hot electrons release their energy and thermalise with a characteristic time determined by electron-electron and electronphonon scattering rates.…”