Ideal Optical Antimatter using Passive Lossy Materials under Complex Frequency Excitation

TL;DR

The paper addresses the loss barrier in realizing optical antimatter and complementary media by introducing complex-frequency excitation applied to passive lossy Lorentz–Drude materials. It proves a constructive framework whereby arbitrary complex permittivity and permeability can be accessible, enabling a complementary pair with lossless propagation and unity transmission for all wavevectors. The authors demonstrate, via numerical simulations, optical antimatter, an ideal negative-index lens with perfect focusing, and superscattering, all realized with passive materials at a complex frequency. This temporally structured-light approach broadens the practical realization of transformation-optics concepts and offers a pathway to experiments that circumvent material losses in optical metamaterials.

Abstract

The original concept of left-handed material has inspired the possibility of optical antimatter, where the effect of light propagation through a medium can be completely cancelled by its complementary medium. Despite recent progress in the development of negative-index metamaterials, losses continue to be a significant barrier to realizing optical antimatter. In this work, we show that passive, lossy materials can be used to realize optical antimatter when illuminated by light at a complex frequency. We further establish that one can engineer arbitrary complex-valued permittivity and permeability in such materials. Strikingly, we show that materials with a positive index at real frequencies can act as negative-index materials under complex frequency excitation. Using our approach, we numerically demonstrate the optical antimatter functionality, as well as double focusing by an ideal perfect lens and superscattering. Our work demonstrates the power of temporally structured light in unlocking the promising opportunities of complementary media, which have until now been inhibited by material loss.

Figures (3)

• Figure 1: Optical antimatter at complex frequency. In panels (a)--(c), the colors blue, teal, yellow and orange correspond to Media 1, 2, 3, 4, as described in Table \ref{['lorentz_param_table']}, respectively. Black denotes vacuum. (a) Schematic of initial structure with circular scatterer of radius 150 nm embedded in slab of thickness 0.6 $\mu$m. Dashed white line indicates location of TM-polarized plane wave source. (b) Schematic of structure placed adjacent to its complementary counterpart. (c) Free space configuration with plane wave source. (d)--(f) TM-polarized Re[$H_z$] field patterns at the complex frequency $\omega = \omega_c$ for the configurations in (a), (b), and (c), respectively. (g)--(i) TM-polarized Re[$H_z$] field patterns at the real frequency $\omega = \omega_r$ for the configurations in (a), (b), and (c), respectively. In (f) and (i), the red and yellow dashed lines mark the effective location of the optically cancelled complementary media pair, respectively. For each $\omega$, field plots are normalized to the same maximum and minimum values. All field plots were generated using FDFD ceviche_ref_2019, with Bloch boundary conditions in the transverse ($y$) direction and PML boundary conditions in the propagation ($x$) direction. Plots show 0th diffraction order in free space.
• Figure 2: Double focusing effect of an ideal perfect lens enabled by optical antimatter under complex frequency excitation. (a) Schematic of three layers comprised of Medium 1, Medium 2, Medium 1 depicted using color scheme of Fig. \ref{['optical_antimatter']}. Layer thicknesses from left to right: $d_0 = 0.5\lambda_0$, $d_1 = \lambda_0$, $d_2 = 0.5\lambda_0$ where $\lambda_0$ is the wavelength in Medium 1 at $\omega=\omega_c$. (b) Magnitude of Poynting vector for a Gaussian point source originating in leftmost layer at complex frequency $\omega = \omega_c$ and at (d) real frequency $\omega = \omega_r$ normalized to their respective maximum values. Dashed white lines indicate interfaces between Medium 1 and Medium 2. For clarity, only propagating waves are plotted in the complex frequency case. (c) Transmission coefficient through setup shown in panel (a) at $\omega=\omega_c$ and at (e) $\omega=\omega_r$. In both plots, $k_0$ refers to the wavevector defined in Medium 1 at $\omega=\omega_c$. Red dashed lines mark the boundary between evanescent and propagating waves. All plots shown are for TM polarization.
• Figure 3: Superscattering using optical antimatter at complex frequency. (a) Schematic of air scatterer with radius $r=18.75$ nm embedded in Medium 1 and surrounded by an annulus of complementary Medium 2 with thickness $18.75$ nm. (b) Field distribution of Re[$H_z$] in panel (a) under plane wave excitation at complex frequency from left. The yellow circle indicates the boundary between the annulus and the surrounding medium. The magenta circle indicates the boundary of the inner air scatterer. (c) Schematic of air scatterer with radius $R=66.6$ nm embedded in Medium 1. (d) Field distribution of Re[$H_z$] in panel (c) under plane wave excitation at complex frequency from left. The black circle indicates the boundary of the air scatterer.

Theorems & Definitions (1)

• Theorem 1