Time domain analysis of a rational harmonic mode locked ring fiber laser

Abstract

In this article, we present a theory of the pulse train generated by a rational harmonic mode locked ring fiber laser. The pulse width is calculated as a function of the rational harmonic order and the optical transfer function of the modulator. The theoretical work is based on a time domain analysis, which predicts that the pulse width decreases when the rational harmonic order goes up. The pulse width as a function of the modulation amplitude and bias level of the modulator was measured, and the experimental results agree with the theory.

Classical coupled oscillators model of the rational harmonic mode locked laser

“…The rational harmonic mode locking mechanism provides a multiplication effect, namely, if the modulation frequency is detuned from the mode interval ⍀ M = ͑k +1/q͒⍀ int , the pulse repetition rate will be as high as ͑k ϫ q +1͒⍀ int . Instead of assuming a Gaussian shape pulse at very beginning, 8 we postulate that the q loops trip photons in Fig. 1 form a set of ghost modes.…”

“…In the device matrix, the round loop phase change for each mode is an integer number multiplied by 2 This approximation has been used in the other models, too, which is valid for the threshold analysis. [6][7][8] It is very easy to change these normalized parameters to the practical ones in the design. It is noted that in the following calculations, the mode number in the cavity is much less than the practical cases.…”

“…Especially, by introducing the concept of ghost mode, the proposed method can be extended to explain the rational harmonic mode locking mechanism. Instead of assuming a Gaussian shape optical pulse, 8 in our approach, the Gaussian pulse shape is a natural conclusion as in the Master equation. 6 It should be noted that the coupled modes concepts have been mentioned in the previous works.…”

“…Zhu et al recently developed an analytical method to simulate the rational harmonic mode locking mechanism based on the assumption of a Gaussianlike shape pulse traveling in the time domain, which agrees well with the experiments. 8 It is the only theoretical model for this important phenomenon. All analytical models present a continuous optical spectrum for the mode locked laser instead of the individual mode amplitude.…”

“…The first one is the analytical approach. [6][7][8] In this category, the most famous model may be the Master equation method, where optical field profile of the locked cavity modes satisfies a governing equation similar to that of the Hamiltonian eigenfunction of a quantum harmonic oscillator. 6 The Master equation predicts a continuous Gaussian function for the mode locked laser spectrum/pulse in both frequency and time domains.…”