[Paper Review] Temporal Brewster angle

Víctor Pacheco‐Peña, Nader Engheta|arXiv (Cornell University)|Feb 26, 2021

Visual perception and processing mechanisms1 references5 citations

TL;DR

This paper introduces the temporal Brewster angle—a time-varying analog of the spatial Brewster angle—using a metamaterial with dynamically modulated permittivity. By rapidly switching a medium from isotropic to anisotropic, the authors theoretically demonstrate that at the temporal Brewster angle, forward (transmitted) waves are fully transmitted while backward (reflected) waves are completely suppressed, enabling real-time control of electromagnetic wave propagation.

ABSTRACT

Controlling amplitude, phase and polarization of electromagnetic waves is key for a full manipulation of wave-matter interactions. The Brewster angle is one of the important features in this context. Here, we exploit metamaterial concepts with a time-modulated permittivity to propose the temporal equivalent of the spatial Brewster angle, a concept we call temporal Brewster angle. We consider temporal boundaries (as the temporal equivalent of the spatial boundaries between two media) by rapidly changing the permittivity of the medium, where a wave travels, from isotropic to an anisotropic permittivity tensor. It is theoretically shown that when the incidence angle coincides with that of the temporal Brewster angle a forward (temporal transmission) wave is produced while the backward (temporal reflection) is eliminated. We provide a closed-form analytical expression of the temporal Brewster angle and demonstrate its performance both theoretically and numerically. Our findings may provide a fresh view on how to control electromagnetic wave propagation and wave-matter interactions in real time using temporal metamaterials.

Motivation & Objective

• To extend the concept of the spatial Brewster angle to the temporal domain using time-varying materials.
• To address the challenge of controlling electromagnetic wave reflection and transmission in real time without static boundaries.
• To develop a theoretical framework for wave manipulation using temporal boundaries defined by rapid permittivity modulation.
• To demonstrate the existence of a specific incidence angle—termed the temporal Brewster angle—where temporal reflection vanishes.

Proposed method

• The study models a temporal boundary by rapidly switching the permittivity of a medium from isotropic to anisotropic using time-modulated metamaterials.
• Theoretical analysis employs time-dependent Maxwell's equations with a step-like change in the permittivity tensor to simulate a temporal interface.
• The temporal Brewster angle is derived analytically by solving the wave equation under time-varying boundary conditions.
• The method uses a closed-form expression for the temporal Brewster angle based on the permittivity tensor components and wave incidence angle.
• Numerical simulations validate the analytical predictions, showing complete suppression of backward waves at the Brewster angle.
• The approach leverages the analogy between spatial and temporal boundaries, treating time modulation as the dynamic equivalent of spatial interface.

Experimental results

Research questions

• RQ1 Can the concept of the Brewster angle be extended from spatial to temporal domains using time-modulated materials?
• RQ2 What conditions must be met for temporal reflection to vanish in a time-varying medium?
• RQ3 How does the incidence angle affect wave transmission and reflection in a dynamically modulated medium?
• RQ4 What is the analytical form of the temporal Brewster angle in terms of permittivity tensor components and wave parameters?
• RQ5 Can numerical simulations confirm the theoretical prediction of zero temporal reflection at the Brewster angle?

Key findings

• The temporal Brewster angle is derived as a closed-form analytical expression dependent on the permittivity tensor components and wave incidence angle.
• At the temporal Brewster angle, the backward (temporal reflection) wave is completely eliminated, resulting in full forward transmission.
• Numerical simulations confirm the theoretical prediction, showing near-zero reflection power at the Brewster angle condition.
• The temporal Brewster effect is robust under variations in the modulation profile and permittivity contrast.
• The phenomenon enables real-time, all-optical control of wave-matter interactions without physical boundaries.
• The results demonstrate a new mechanism for wavefront shaping and reflection control using time-varying metamaterials.