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High-order frequency locking phenomena were recently observed using semiconductor lasers subject to large delayed feedbacks [1,2]. Specifically, the relaxation oscillation (RO) frequency and a harmonic of the feedback-loop round-trip frequency coincided with the ratios 1:5 to 1:11. By analyzing the rate equations for the dynamical degrees of freedom in a laser subject to a delayed optoelectronic feedback, we show that the onset of a two-frequency train of pulses occurs through two successive bifurcations. While the first bifurcation is a primary Hopf bifurcation to the ROs, a secondary Hopf bifurcation leads to a two-frequency regime where a low frequency, proportional to the inverse of the delay, is resonant with the RO frequency. We derive an amplitude equation, valid near the first Hopf bifurcation point, and numerically observe the frequency locking. We mathematically explain this phenomenon by formulating a closed system of ordinary differential equations from our amplitude equation. Our findings motivate new experiments with particular attention to the first two bifurcations. We observe experimentally (1) the frequency locking phenomenon as we pass the secondary bifurcation point, and (2) the nearly constant slow period as the two-frequency oscillations grow in amplitude. Our results analytically confirm previous observations of frequency locking phenomena for lasers subject to a delayed optical feedback.

Using a delay differential equation model we study theoretically the dynamics of a unidirectional class-A ring laser with a nonlinear amplifying loop mirror. We perform linear stability analysis of the CW regimes in the large delay limit and demonstrate that these regimes can be destabilized via modulational and Turing-type instabilities, as well as by an instability leading to the appearance of square-waves. We investigate the formation of square-waves and mode-locked pulses in the system. We show that mode-locked pulses are asymmetric with exponential decay of the trailing edge in positive time and faster-than-exponential (super-exponential) decay of the leading edge in negative time. We discuss asymmetric interaction of these pulses leading to a formation of harmonic modelocked regimes.

A compact Raman laser gas spectrometer is developed. It comprises a high-power green laser at 532.123 nm as an excitation source and a specially designed gas cell with an internal volume of less than 0.6 cm3 that can withstand gas pressures up to 100 atm. The resolution of the spectrometer is ~1 cm−1. The Raman spectra of chemically pure isotopically enriched carbon dioxide (12CO2, 13CO2) and methane (12CH4, 13CH4) gases are studied. The expected limit of detection (LOD) is less than 100 ppm for the isotopologues of CO2 and less than 25 ppm for those of CH4 (at a gas pressure of 50 atm.), making the developed spectrometer promising for studying the sources of emissions of greenhouse gases by resolving their isotopologue composition. We also show the suitability of the spectrometer for Raman spectroscopy of human exhalation.

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