# The Theory of Optical Black Hole Lasers

## TL;DR

This paper develops the theoretical framework for optical black hole lasers, demonstrating that amplification of Hawking-like radiation is possible in optical systems through mode propagation and numerical simulations.

## Contribution

It introduces a comprehensive theory for optical black hole lasers, extending the concept from sonic analogues to optical systems and analyzing their amplification mechanisms.

## Key findings

- Amplification of Hawking radiation is theoretically possible in optical analogues.
- Derived an approximation for phase difference governing amplification.
- Numerical simulations confirm pulse propagation and amplification in the system.

## Abstract

The event horizon of black holes and white holes can be achieved in the context of analogue gravity. It was proven for a sonic case that if these two horizons are close to each other their dynamics resemble a laser, a black hole laser, where the analogue of Hawking radiation is trapped and amplified. Optical analogues are also very successful and a similar system can be achieved there. In this work we develop the theory of optical black hole lasers and prove that the amplification is also possible. Then, we study the optical system by determining the forward propagation of modes, obtaining an approximation for the phase difference which governs the amplification, and performing numerical simulations of the pulse propagation of our system.