[Paper Review] Turbulent laser puffs

Svetlana Slepneva, Ben O’Shaughnessy+3 more|arXiv (Cornell University)|Jan 17, 2018

Optical Coherence Tomography Applications13 references3 citations

TL;DR

This paper investigates the laminar-turbulent transition in long-cavity wavelength-swept lasers, demonstrating that turbulence emerges via convectively unstable, localized 'puffs'—analogous to hydrodynamic turbulence—driven by finite-amplitude perturbations. The study combines experimental observations and numerical simulations of delayed differential equations to show that these turbulent puffs propagate and disrupt coherence, limiting laser performance in medical imaging applications.

ABSTRACT

The destabilisation of laminar flows and the development of turbulence has remained a central problem in fluid dynamics since Reynolds' studies in the 19th century. Turbulence is usually associated with complex fluid motions and most of the studies have so far been carried out using liquids or gases. Nevertheless, on a theoretical viewpoint, turbulence may also arise in a wide range of fields such as biology and optics. Here we report the results of experimental and theoretical investigation of the characteristic features of laminar-turbulent transition in a long laser commonly used as a light source in medical imaging and sensing applications. This laminar to turbulence transition in the laser light is characterized by the appearance of turbulent puffs similar to those commonly observed in pipe flows and is accompanied by a loss of coherence and limits the range of applications. We present both experimental results and numerical simulations demonstrating that this transition is mediated by the appearance of a convective instability where localised structures develop into drifting bursts of turbulence, in complete analogy with spots, swirls and other structures in hydrodynamic turbulence

Motivation & Objective

• To understand the laminar-to-turbulent transition in long-cavity wavelength-swept lasers, which limits their use in medical imaging and sensing.
• To investigate whether turbulence in these lasers arises through convective instabilities, similar to those observed in fluid dynamics.
• To characterize the spatiotemporal dynamics of localized turbulent structures—'laser puffs'—and their role in coherence loss.
• To compare experimental results with numerical simulations based on delayed differential equations modeling laser gain and electric field evolution.
• To determine the conditions under which subcritical or supercritical bifurcations lead to turbulent states in the laser system.

Proposed method

• Experimental setup using a 17m cavity wavelength-swept laser with a semiconductor optical amplifier and fast Fabry-Pérot tunable filter.
• Numerical simulations based on a system of delayed differential equations (DDEs) describing the temporal evolution of laser gain $ G(t) $ and electric field envelope $ A(t) $.
• Use of a filter sweep profile $ Δ(t) $ that varies linearly over time, simulating quasi-static tuning to observe bifurcation behavior.
• Transformation to a 'filter frame' where the system is analyzed as if the filter is static, enabling comparison with single-mode solutions.
• Simulation of only the relevant portion of each filter sweep using initial conditions and history data from previous sweeps, with $ T = T_F + \tau $ to model drift.
• Direct numerical integration of the DDEs over $ nT_F < t < nT_F + T_W $, with analytical solutions used for the laminar region before $ t=0 $.

Experimental results

Research questions

• RQ1 Do turbulent puffs emerge in long-cavity lasers through convective instability, similar to those in pipe flow?
• RQ2 How does the direction of filter tuning (increasing vs. decreasing wavelength) affect the bifurcation type and onset of turbulence?
• RQ3 What is the role of finite-amplitude perturbations in triggering the laminar-turbulent transition in these lasers?
• RQ4 How do localized structures such as Nozaki-Bekki holes evolve and contribute to the transition to turbulence?
• RQ5 To what extent do the dynamics of single-mode operation mirror those of chirped FDML lasers in terms of instability mechanisms?

Key findings

• The laminar-turbulent transition in the long-cavity laser is mediated by the appearance of convectively unstable, localized turbulent puffs that drift downstream.
• Experimental and numerical results show a sharp transition from laminar to turbulent states when the filter is tuned through a critical point, with the system exhibiting both subcritical and supercritical Hopf bifurcations depending on tuning direction.
• In the convective regime, noise-induced dropouts—identified as Nozaki-Bekki holes—appear in the cw regime and evolve into turbulent bursts.
• The simulations confirm that the system exhibits drift of turbulent structures relative to the filter profile, with the electric field $ A_n(t) $ shifting forward in time by $ \tau $ per round trip.
• The model accurately reproduces experimental observations, including the appearance of turbulent puffs and coherence loss, validating the DDE-based approach.
• Supplementary movies confirm the experimental and theoretical emergence of turbulent puffs and the dynamics of dropout formation in the convective regime.