A design method of spatiotemporal optical pulse using level‐set based time domain topology optimization

Abstract

Recently, two emerging areas of photonics research, ultrafast photonics, and nanophotonics have started to come together. One of the main problems in this field is the precise control of spatial and temporal profiles of the optical pulses.In this paper, we propose a design method for user-specified spatiotemporal optical pulses using a level set-based time-domain topology optimization method.In the proposed method, the optimization problem is formulated based on time domain Maxwell equations so that the spatiotemporal optical pulses can be treated directly. The objective function is defined using the envelope information of the pulses, and an efficient way to calculate this information, based on calculations of the complex electromagnetic field, is introduced. A level set-based topology optimization method is applied to obtain optimized configurations.Using the proposed method, the spatiotemporal user-specified pulse profiles can be designed by modifying the structural details of the nanostructures through which the pulses propagate. As a simple example, we demonstrate that the optimized structures focus optical pulses into a single or multiple focal points with a user-specified pulse-width. The results show that the proposed method is able to design highly controlled spatiotemporal optical pulses by engineering the nanophotonic structure. KEYWORDSfinite difference methods, level sets, topology design INTRODUCTIONNanophotonics and ultrafast photonics are main subjects of research in the current photonics research field. Nanophotonics is the study of the behavior of light on the nanometer scale and of the interaction of nanometer-scale objects with light. Nanophotonics is an emerging technology with many applications 1-4 such as surface-enhanced Raman scattering, near field optical microscopy, and metamaterials. On the other hand, ultrafast photonics is the study of light and its interaction with matter on short timescales of less than a picosecond. 5,6 The main interest in this field is to investigate the processes that occur in atoms, molecules, and solids, such as the dynamics of and correlations between electrons.Nanophotonics and ultrafast photonics, which developed independently, have recently started to merge. [7][8][9] In the vicinity of a nanostructure, ultrafast pulses drastically change their spatial and temporal profiles. In other words, the spatiotemporal optical pulse profile can be arbitrarily changed by adjusting the surrounding nanostructure. Spatially and temporally controlled ultrafast pulses potentially offer an efficient way to enhance light-matter interactions at the nanoscale and provide a promising platform for information processing.Int J Numer Methods Eng. 2019;117:605-622.wileyonlinelibrary.com/journal/nme

Time Reversal Differentiation of FDTD for Photonic Inverse Design

“…In FDTD, R E and R H are operators that must be derived manually for each specific system geometry, boundary condition, and tunable parameter. ∂ R E , H /∂ p i can be well approximated for photonic shape optimization. − However, for arbitrary optimizations, R E and R H may not have an analytic form and require careful mapping onto the FDTD results (see refs , , and and the Supporting Information).…”

“…The integrand g [ E ( x , t ), H ( x , t )] is differentiated analytically to obtain ∂ g /∂ E ( x , t ),∂ g /∂ H ( x , t ), which are time-dependent vector-valued functions evaluated using the time-varying stored field values from the forward simulation. These derivatives are then used as current sources for the adjoint simulation over the same geometry to get the adjoint electric and magnetic fields E A ( x , t ), H A ( x , t ) with the modified Maxwell equations in eqs and , with the initial conditions being E A ( x ,τ = 0) = 0, H A ( x ,τ = 0) = 0 in terms of the reverse time τ = T – t . normal∇ × E A ( x , T − t ) = − μ ∂ H A ( x , T − t ) ∂ italict + ∂ italicg ∂ bold-italicH ( x , T − t ) normal∇ × H A ( x , T − t ) = ϵ ∂ E A ( x , T − t ) ∂ t + ∂ g ∂ bold-italicE ( x , T − t ) …”