Perturbation Theory Limits Multimode Light Propagation in Dispersive Optical Cavities

The precise control of light pulses, utilising their inherent temporal modes, underpins advances in computing and communication technologies, yet remains a significant challenge when nonlinear effects and dispersion interact within optical systems. K. S. Tikhonov, D. M. Malyshev, and V. A. Averchenko investigate the role of group velocity dispersion, often considered a hindrance, as a potential tool for manipulating light within optical cavities. Their work presents a novel approach, employing perturbation theory to analyse dispersive effects in a synchronously pumped cavity, and crucially, establishes the boundaries of this technique’s validity in complex multimode systems. By comparing theoretical predictions with rigorous calculations, the researchers identify the critical parameters that determine when perturbation theory breaks down, offering valuable insights for the design and optimisation of future optical devices.

This work focuses on the role of group velocity dispersion within optical cavities, a phenomenon traditionally viewed as detrimental but increasingly recognised as a versatile tool for quantum light manipulation. Researchers developed a perturbation-theory-based approach to analyse how group velocity dispersion affects light within a synchronously pumped dispersive cavity, establishing the limits of its accuracy in complex systems.

Perturbation Theory Models Dispersive Optical Cavities

Scientists are investigating the use of simplified mathematical approximations, known as perturbation theory, to model the behaviour of pulsed light within dispersive optical cavities. These cavities, highly reflective chambers used in lasers and for enhancing light-matter interactions, alter the shape of light pulses due to a phenomenon called dispersion, where different colours of light travel at slightly different speeds. The research asks whether perturbation theory can accurately predict how these light pulses change as they bounce back and forth inside the cavity. Perturbation theory works by starting with a simple solution and then adding small corrections to account for more complex effects.

However, its accuracy depends on how small these corrections are. The team considered temporal modes, which describe the shape of light pulses in time, and Hermite-Gaussian modes, specific shapes light pulses can take. They accounted for the Sellmeier equation, which describes how a material bends light, and considered group velocity dispersion (GVD) and third-order dispersion (TOD), measures of how dispersion affects the shape of a light pulse. The research demonstrates that while perturbation theory is a useful tool, it has limitations. Higher-order modes, representing more complex pulse shapes, are particularly problematic because the dispersive effects increase with their complexity, making the approximations less accurate.

However, the rate at which light loses energy within the cavity, known as the decay rate, can mitigate these effects. If the decay rate is high enough, it can suppress the growth of dispersive effects, improving the accuracy of the approximations. The team identified a critical threshold for the mode order beyond which perturbation theory breaks down, dependent on the ratio of the decay rate to the dispersion. This work has significant implications for quantum optics and quantum information, where precise control of light pulses is essential. Understanding the limitations of the models used to describe these pulses is crucial for achieving accurate results in experiments and for building quantum technologies.

The research also informs the design of lasers and other optical devices, highlighting the importance of carefully validating the models used in physics and engineering. By providing a rigorous analysis of the conditions under which simplified models can be used, this work contributes to a deeper understanding of light manipulation within optical cavities. To illustrate this concept, consider predicting the path of a ball rolling down a hill. A simple approximation works well on a gently sloping hill, but becomes inaccurate on a steep and bumpy one, requiring a more complex model. Similarly, this research determines when simplified approximations are sufficient for describing light pulses in a dispersive cavity and when a more complex model is necessary.

Coherent Pulse Amplification via Dispersion Control

Scientists are achieving unprecedented control over light pulses by meticulously studying the role of group velocity dispersion within optical cavities. Researchers developed a perturbation-theory-based approach to analyse how group velocity dispersion affects light within a synchronously pumped dispersive cavity, establishing the limits of its accuracy in complex systems. The team modelled the propagation of light pulses within a ring cavity containing a nonlinear medium, coherently pumping it with a periodic train of pulses. By precisely matching the pulse period to the cavity’s round-trip time, scientists ensured coherent amplification of the light.

The analysis demonstrates that when the temporal duration of each pulse is significantly shorter than both the inter-pulse separation and the round-trip time, the system’s dynamics can be accurately tracked by monitoring a single representative pulse over multiple cavity traversals. Experiments reveal the relationship between the electric field amplitude of the pulse after each round-trip and its corresponding spectral amplitude is governed by the Fourier transform. Measurements confirm that by comparing exact solutions with those obtained through perturbation theory, scientists can delineate the validity range of the perturbative approach. This breakthrough delivers a deeper understanding of light manipulation within optical cavities, paving the way for advancements in quantum computing, communication, and metrology.

Perturbation Theory Limits in Dispersive Cavities

This work investigates the validity of perturbative solutions used to model the dynamics of light pulses within optical cavities, specifically addressing the impact of group velocity dispersion. By comparing these approximate solutions with rigorous steady-state calculations, researchers established a clear understanding of when perturbation theory accurately predicts system behaviour. The analysis reveals that the accuracy of the perturbative approach depends critically on the interplay between dispersion strength, the order of the optical mode, and the rate at which the cavity loses energy. Notably, the study demonstrates that higher-order modes are more susceptible to inaccuracies when using perturbation theory, due to their stronger interaction with dispersive effects.

However, the team found that increasing the decay rate of these modes can mitigate these effects, improving the reliability of the perturbative solution. This research provides valuable insight into the limitations of commonly used modelling techniques and offers guidance for selecting appropriate parameters to ensure accurate predictions in complex optical systems. The authors acknowledge that the analysis focuses on an empty cavity and that extending these findings to more complex scenarios, such as those involving nonlinear media, will require further investigation. Future work could explore the influence of different cavity designs and materials on the validity of perturbation theory, potentially leading to improved modelling techniques for a wider range of optical applications.