Capturing Arbitrary Waveform without Absorption with Synthesis of Complex Frequencies

Abstract

An arbitrary optical waveform can be synthesized by complex-frequency waves as well as by realfrequency harmonic waves. While single complex-frequency wave with exponentially rising waveform can be perfectly absorbed in lossless structures. Here, we propose that arbitrary waveforms can be captured without any absorption through the synthesis of complex frequencies in a lossless system. The scattering matrix zeros of the system correspond to a set of complex frequencies with exponentially rising waveforms, each of which can be virtually and perfectly absorbed. Thus, an arbitrary waveform, decomposed into these complex frequencies automatically, can be captured without any absorption. Then, in a well-designed coupled cavity system, various waveforms such as exponentially decaying, Gaussian, rectangular, and triangular profiles, are captured with high efficiency. The proposed mechanism has potential applications in enhancing light-matter interactions, optical energy storage, and photonic quantum memory.

Figures (4)

• Figure 1: CAW through synthesis of complex frequencies. (a) Schematic of CAW by a lossless system whose scattering matrix zeros correspond to a series of complex frequencies. An arbitrary waveform can be synthesized from a series of (b) harmonic real-frequency waves and (c) exponentially rising complex-frequency waves. (d) Eigenvalues of scattering matrix with multiple zeros and poles.
• Figure 2: (a) Schematic of a lossless system with $N$ modes and $M$ channels. (b) The distribution of scattering matrix zeros $\omega_n + i \gamma_{n}$ on the complex plane. The orange region represents the spectral distribution of arbitrary waveform with the width $\Gamma_0$.
• Figure 3: Demonstration of CAW. (a) Schematic of the periodic cavity chain with uniform coupling strength $J$ between adjacent cavities. (b) Distribution of the scattering matrix zeros for the cavity number $N=10, 30, 50$ and $70$. (c) The capture efficiency as a function of $N$ for five input waveforms. (d) Captured energy versus time for five input waveforms with $N=30$. Energy is stored by turning off the coupling between the waveguide and cavities at the moment of maximum efficiency (solid curves); otherwise, it is re-emitted into the waveguide (dashed curves). Here $\kappa_{N}=2J$, $J=0.2\Gamma_{0}N$.
• Figure 4: Capture of ED waveform. (a) Schematic of non-uniform cavity chain. (b) The coupling strength $J_{n,n+1}$ between adjacent cavities with $\kappa_{N}=20\Gamma_{0}$. (c) The distribution of scattering matrix zeros for a uniform chain (blue circles) and a non-uniform chain (red squares). (d) Capturing process of an ED waveform in a uniform chain (blue curves) and non-uniform chain (red curves).