Time-Domain Bound States in the Continuum

Area of Science:

• Optics and Photonics
• Wave Phenomena
• Metamaterials

Background:

• Bound states in the continuum (BICs) are typically spatial phenomena where localized states exist within a radiating continuum.
• Wave phenomena are traditionally studied in the spatial domain, limiting exploration in time-varying systems.

Purpose of the Study:

• To introduce and theoretically demonstrate the concept of time-domain bound states in the continuum (TD-BICs).
• To explore the extension of spatial wave phenomena into the temporal domain.
• To investigate novel light-matter interactions in time-varying media.

Main Methods:

• Developing a theoretical framework for TD-BICs based on temporal modulation of refractive index.
• Deriving closed-form solutions to Maxwell's equations in time and one-dimensional space.
• Analyzing the emergence of bound states embedded within a continuum of wave numbers.

Main Results:

• A judiciously designed, rapid temporal modulation of refractive index in a homogeneous medium creates a bound state in time.
• These TD-BICs are mathematically described as exact solutions to the governing wave equations.
• The findings establish a direct analogy between spatial BICs and the proposed temporal counterparts.

Conclusions:

• The concept of TD-BICs is theoretically validated, extending BIC phenomena to the temporal domain.
• This work provides a new paradigm for manipulating wave propagation and light-matter interactions.
• Future research can explore experimental realizations and applications in dynamic optical systems.