[Paper Review] Photonic time crystals: Theory and applications

M. M. Asgari, Puneet Garg+4 more|arXiv (Cornell University)|Apr 7, 2024

Photonic Crystals and Applications4 citations

TL;DR

This paper presents a comprehensive theoretical framework for photonic time crystals (PTCs), artificial materials with time-periodic modulation of electromagnetic properties that create momentum bandgaps instead of energy bandgaps. The work demonstrates that PTCs enable unique phenomena such as exponential wave growth and thresholdless lasing, offering new pathways for optical amplification, enhanced light emission, and advanced imaging beyond classical limits.

ABSTRACT

This tutorial offers a comprehensive overview of photonic time crystals - artificial materials whose electromagnetic properties are periodically modulated in time at scales comparable to the oscillation period of light while remaining spatially uniform. Being the temporal analogs to traditional photonic crystals, photonic time crystals differ in that they exhibit momentum bandgaps instead of energy bandgaps. The energy is not conserved within momentum bandgaps, and eigenmodes with exponentially growing amplitudes exist in the momentum bandgap. Such properties make photonic time crystals a fascinating novel class of artificial materials from a basic science and applied perspective. This tutorial overviews the fundamental electromagnetic equations governing photonic time crystals and explores the groundbreaking physical phenomena they support. Based on these properties, we also oversee a diverse range of applications they unlock. Different material platforms suitable for creating photonic time crystals are discussed and compared. Furthermore, we elaborate on the connections between wave amplification in photonic time crystals and parametric amplification mechanisms in electrical circuits and nonlinear optics. The tutorial will be helpful for readers with physics or engineering backgrounds. It is designed to serve as an introductory guide for beginners and to establish a reference baseline reflecting the current understanding for researchers in the field.

Motivation & Objective

• To establish a theoretical foundation for photonic time crystals (PTCs) as a novel class of artificial materials with time-varying electromagnetic properties.
• To address the fundamental challenge of controlling light propagation through temporal modulation, overcoming limitations of spatially inhomogeneous photonic crystals.
• To explore the physical mechanisms behind momentum bandgaps and exponential eigenmode growth in PTCs, distinguishing them from traditional photonic crystals.
• To identify and analyze realistic implementations of PTCs, including effects of dispersion, finite size, anisotropy, defects, and nonlinearity.
• To demonstrate the potential of PTCs in transformative applications such as thresholdless lasers, enhanced radiation emission, and super-resolution imaging.

Proposed method

• Derives the governing electromagnetic equations for time-varying, spatially uniform media using Maxwell’s equations with time-dependent permittivity.
• Applies plane wave expansion and transfer matrix methods to analyze band structures and identify momentum bandgaps in PTCs.
• Introduces a formalism for eigenmode analysis in PTCs, showing that modes within momentum bandgaps exhibit exponential amplitude growth.
• Models temporal dispersion using time-varying plasma and resonance frequencies to estimate momentum bandgap sizes in realistic dispersive media.
• Investigates finite-sized PTCs, defects, disorder, and anisotropy to assess robustness and practical feasibility.
• Draws analogies between PTCs and parametric amplification in electrical circuits and nonlinear optics, highlighting shared physical principles.

Experimental results

Research questions

• RQ1 How do time-periodic modulations of electromagnetic properties in spatially uniform media lead to momentum bandgaps instead of energy bandgaps?
• RQ2 What are the conditions under which eigenmodes in PTCs exhibit exponential growth, and how does this enable optical amplification?
• RQ3 How do realistic effects—such as temporal dispersion, finite size, defects, and nonlinearity—affect the performance and observability of PTCs?
• RQ4 In what ways do PTCs resemble or differ from parametric amplification in electrical circuits and nonlinear optics?
• RQ5 What are the practical material platforms and design strategies that enable the realization of PTCs across different spectral domains?

Key findings

• Photonic time crystals exhibit momentum bandgaps where energy is not conserved, leading to eigenmodes with exponentially growing amplitudes.
• The size of momentum bandgaps can be estimated using time-varying plasma or resonance frequencies, with analytical expressions derived for dispersive media.
• PTCs enable thresholdless lasing by supporting self-sustained amplification without a population inversion, a key advantage over conventional lasers.
• PTCs enhance the emission rate of radiation from free electrons by engineering the temporal modulation to match the electron's velocity and radiation frequency.
• PTCs allow control of spectral flow and enable optical absorbers that surpass the Rozanov bound, enabling subwavelength absorption beyond classical limits.
• Spatiotemporal photonic crystals with traveling-wave modulation can further enhance momentum bandgap size and support topological edge states, opening new avenues for robust photonic devices.