Universal relationships for the parameters of fiber laser generation have been established.

The article has been published in the journal Optics and Laser Technology. An erbium laser is a solid-state laser whose active medium can consist of crystals or glasses doped with erbium ions (Er³⁺). These lasers are widely utilized in medicine, telecommunications, materials science, and industry. Classic fiber lasers are characterized by a low level of doping in the active medium and a long resonator. Such laser resonators generate a broad spectrum of radiation, comprising numerous longitudinal modes. Reducing the length of the resonator leads to spectral narrowing of the laser emission down to a single-mode output. Besides the resonator length, the concentration of erbium ions in the active medium also influences the emission characteristics.

The effective miniaturization of erbium fiber lasers is a critical challenge in modern optics. One solution is to increase the degree of doping in the laser's active medium. An increase in the concentration of erbium ions leads to their interaction, which, in turn, alters the configuration of the quantum levels in the medium. As a result, the laser begins to emit in a pulsed mode.

A team of physicists from the V. A. Kotelnikov Institute of Radioengineering and Electronics of the Russian Academy of Sciences and MIPT, along with colleagues, created two sets of erbium-doped active fibers: fibers with a relatively high concentration of erbium in the core (≈ 0.03 percent) and those with an extremely high concentration of erbium in the core (≈ 0.3 percent). Lasers with such active media exhibit two generation thresholds: the first threshold marks the onset of generation in the pulsed mode, while the second indicates the transition to continuous wave operation.

“Understanding the formation of pulses has still lacked knowledge about the general fundamental features of the pulsed mode depending on the control parameters. In this study, we experimentally revealed such dependencies. We also demonstrated the power-law behavior of the system parameters (average output power, pulse frequency, and duration) over a broad range of pump intensity above the critical point. Our group thoroughly examined the relationships between parameters and operating modes, specifically the transition from pulsed mode to continuous generation mode, as well as the effects of resonator length, doping level, and pump power,” explained Alexander Smirnov, associate professor at Lomonosov Moscow State University and leading researcher at MIPT.

The scientists obtained the dependencies of pulse duration and frequency for various generation wavelengths (1539–1557 nm) and resonator lengths. In the experiments conducted, they demonstrated a universal dependence of frequency, duration, and amplitude of pulses on the output power of erbium lasers. The physicists also determined the critical indices for the created fiber lasers. Their values differ from standard integer and half-integer values, indicating the non-trivial nature of the obtained dependencies. However, the significant difference in the doping levels of the fibers and the lengths of the laser resonators has a minimal effect on the deviation of the critical indices.

“We have been studying and developing erbium fiber lasers for quite some time. Previously, we conducted a comparative analysis of the pulsed mode operation of the erbium laser pumped at wavelengths of 1490 nm and 976 nm. At first glance, resonant excitation at a wavelength of 1490 nm resulted in a sharp increase in pulse frequency and a decrease in duration compared to excitation at a wavelength of 976 nm.

However, considering the model we presented in our 2018 study, we hypothesized that since the occurrence of pulses is determined by the generation process itself, the pulse repetition frequency and duration should primarily depend on the generation power rather than the pump power, acquiring a certain universal character. The experimental data from this work fully confirmed this hypothesis. We showed that the frequency and duration of pulses are determined by the output power,” stated Oleg Butov, deputy director for science at the Kotelnikov Institute of Radioengineering and Electronics of the Russian Academy of Sciences, and leading researcher at MIPT.

The scientists plan to continue their work on creating and studying the properties of linearly polarized erbium fiber lasers that operate stably in a single-mode regime with an extremely narrow generation line.

This work was done in collaboration with researchers from the V. A. Kotelnikov Institute of Radioengineering and Electronics of the Russian Academy of Sciences, MIPT, HSE, Lomonosov Moscow State University, the Prokhorov General Physics Institute of the Russian Academy of Sciences, the Dukhova Institute of Automation, and the Institute of Theoretical and Applied Electrodynamics of the Russian Academy of Sciences.

This research was supported by a grant from the Russian Science Foundation.