Broadband frequency conversion of ultrashort pulses using high-Q metasurface cavities

Frequency conversion of light can be dramatically enhanced using high quality factor (Q-factor) cavities. Unfortunately, the achievable conversion efficiencies and conversion bandwidths are fundamentally limited by the time–bandwidth limit of the cavity, restricting their use in frequency conversion of ultrashort pulses. Here, we propose and numerically demonstrate sum-frequency generation based frequency conversion using a metasurface-based cavity configuration that could overcome this limitation. The proposed experimental configuration takes use of the spatially dispersive responses of periodic metasurfaces supporting collective surface lattice resonances (SLRs), and can be utilized for broadband frequency conversion of ultrashort pulses. We investigate a plasmonic metasurface, supporting a high-Q SLR (Q=500, linewidth of 2 nm) centred near 1000 nm, and demonstrate ~1000-fold enhancements of nonlinear signals. Furthermore, we demonstrate broadband frequency conversion with a pump conversion bandwidth reaching 75 nm, a value that greatly surpasses the linewidth of the studied cavity. Our work opens new avenues to utilize high-Q metasurfaces also for broadband frequency conversion of light.

Part 2: Spatially Dispersive Metasurfaces - IE-GSTC-SD Field Solver with Extended GSTCs

<div>An Integral Equation (IE) based field solver to compute the scattered fields from spatially dispersive metasurfaces is proposed and numerically confirmed using various examples involving physical unit cells. The work is a continuation of Part-</div><div>1 [1], which proposed the basic methodology of representing spatially dispersive metasurface structure in the spatial frequency domain, k. By representing the angular dependence of the surface susceptibilities in k as a ratio of two polynomials, the standard Generalized Sheet Transition Conditions (GSTCs) have been extended to include the spatial derivatives of both the difference and average fields around the metasurface. These extended boundary conditions are successfully integrated here into a standard IE-GSTC solver, which leads to the new IEGSTC-SD simulation framework presented here. The proposed IE-GSTC-SD platform is applied to various uniform metasurfaces, including a practical short conducting wire unit cell, as a representative practical example, for various cases of finite-sized flat and curvilinear surfaces. In all cases, computed field distributions are successfully validated, either against the semi-analytical Fourier decomposition method or the brute-force full-wave simulation of volumetric metasurfaces in the commercial Ansys FEM-HFSS simulator.</div>

Part 2: Spatially Dispersive Metasurfaces - IE-GSTC-SD Field Solver with Extended GSTCs

<div>An Integral Equation (IE) based field solver to compute the scattered fields from spatially dispersive metasurfaces is proposed and numerically confirmed using various examples involving physical unit cells. The work is a continuation of Part-</div><div>1 [1], which proposed the basic methodology of representing spatially dispersive metasurface structure in the spatial frequency domain, k. By representing the angular dependence of the surface susceptibilities in k as a ratio of two polynomials, the standard Generalized Sheet Transition Conditions (GSTCs) have been extended to include the spatial derivatives of both the difference and average fields around the metasurface. These extended boundary conditions are successfully integrated here into a standard IE-GSTC solver, which leads to the new IEGSTC-SD simulation framework presented here. The proposed IE-GSTC-SD platform is applied to various uniform metasurfaces, including a practical short conducting wire unit cell, as a representative practical example, for various cases of finite-sized flat and curvilinear surfaces. In all cases, computed field distributions are successfully validated, either against the semi-analytical Fourier decomposition method or the brute-force full-wave simulation of volumetric metasurfaces in the commercial Ansys FEM-HFSS simulator.</div>

Part 1: Spatially Dispersive Metasurfaces: Zero Thickness Surface Susceptibilities & Extended GSTCs

<div>A simple method to describe spatially dispersive metasurfaces is proposed where the angle-dependent surface susceptibilities are explicitly used to formulate the zero thickness sheet model of practical metasurface structures. It is shown that if the surface susceptibilities of a given metasurface are expressed as a ratio of two polynomials of tangential spatial frequencies, k_||, with complex coefficients, they can be conveniently expressed as spatial derivatives of the difference and average fields around the metasurface in the space domain, leading to extended forms of the standard Generalized Sheet Transition Conditions (GSTCs) accounting for the spatial dispersion. Using two simple examples of a short electric dipole and an all-dielectric cylindrical puck unit cells, which exhibit purely tangential surface susceptibilities and reciprocal/symmetric transmission and reflection characteristics, the proposed concept is numerically confirmed in 2D. A single Lorentzian has been found to describe the spatio-temporal frequency behavior of a short dipole unit cell, while a multi-Lorentzian description is developed to capture the complex multiple angular resonances of the dielectric puck. For both cases, the appropriate spatial boundary conditions are derived.</div>

Part 1: Spatially Dispersive Metasurfaces: Zero Thickness Surface Susceptibilities & Extended GSTCs

<div>A simple method to describe spatially dispersive metasurfaces is proposed where the angle-dependent surface susceptibilities are explicitly used to formulate the zero thickness sheet model of practical metasurface structures. It is shown that if the surface susceptibilities of a given metasurface are expressed as a ratio of two polynomials of tangential spatial frequencies, k_||, with complex coefficients, they can be conveniently expressed as spatial derivatives of the difference and average fields around the metasurface in the space domain, leading to extended forms of the standard Generalized Sheet Transition Conditions (GSTCs) accounting for the spatial dispersion. Using two simple examples of a short electric dipole and an all-dielectric cylindrical puck unit cells, which exhibit purely tangential surface susceptibilities and reciprocal/symmetric transmission and reflection characteristics, the proposed concept is numerically confirmed in 2D. A single Lorentzian has been found to describe the spatio-temporal frequency behavior of a short dipole unit cell, while a multi-Lorentzian description is developed to capture the complex multiple angular resonances of the dielectric puck. For both cases, the appropriate spatial boundary conditions are derived.</div>

A Fiber Bundle Space Theory of Nonlocal Metamaterials

It is proposed that spacetime is not the most proper space to describe metamaterials with nonlocality. Instead, we show that the most general and suitable configuration space for doing electromagnetic theory in nonlocal domains is a proper function-space infinite-dimensional (Sobolev) vector bundle, a special case of the general topological structure known as fiber bundles. It appears that this generalized space explains why nonlocal metamaterials cannot have unique EM boundary conditions at interfaces involving spatially dispersive media.

A Fiber Bundle Space Theory of Nonlocal Metamaterials

It is proposed that spacetime is not the most proper space to describe metamaterials with nonlocality. Instead, we show that the most general and suitable configuration space for doing electromagnetic theory in nonlocal domains is a proper function-space infinite-dimensional (Sobolev) vector bundle, a special case of the general topological structure known as fiber bundles. It appears that this generalized space explains why nonlocal metamaterials cannot have unique EM boundary conditions at interfaces involving spatially dispersive media.