Superposition- and interference-induced optical spectrum distortion in the figure-9 fiber laser

TL;DR

This work tackles the puzzling spectral distortion observed in figure-9 fiber lasers by isolating intracavity beams with a low-filter TCWDM beam splitter and applying interference-superposition theory. The authors demonstrate two all-PM figure-9 lasers at $f=190.6\text{ MHz}$ and $f=92.4\text{ MHz}$, and show that the distorted spectra at the interference and superposition ports can be accurately reproduced by simple spectral superposition and interference models, rather than invoking nonlinear effects. A key finding is that the $p$-component intensities at the beam splitter differ, while the $s$-component intensities are nearly equal, accounting for a stable spectral offset between intracavity and output pulses; pump-power variations further modulate this offset and can generate a central peak. These insights provide a new framework for simulating spectra and deepen the understanding of spectral evolution and pulse dynamics in figure-9 lasers, with implications for measuring configurations and port-based diagnostics.

Abstract

The output pulse spectra of the figure-8 and figure-9 lasers typically exhibit more pronounced distortion than those from mode-locked lasers based on other saturable absorbers, as well as the spectra of their own intracavity pulses. Here, we demonstrate two figure-9 lasers with repetition rates of 190.6 MHz and 92.4 MHz and introduce a self-designed beam splitter that exhibits minimal spectral filtering into the fiber loop to output two interference-free pulses. By applying superposition and interference calculations to the experimental spectra of these two pulses, we obtained calculated spectra and found that their characteristics agree with the distortion features observed in the experimental spectra from the other two ports where superposition and interference occur. Therefore, we conclude that the severe spectral distortion is caused by spectral superposition and interference, rather than the commonly believed nonlinear effects. Furthermore, analysis based on the interference theory of the figure-9 laser reveals that the $p$-components of the two intracavity light beams usually interfere with non-equal intensity at the beam splitter where interference occurs, while the $s$-components always interferes with almost equal intensity. This mechanism results in a significant yet stable spectral difference between the intracavity and output pulses. Moreover, a change in the pump power can amplify the difference between the two $s$-components, thereby leading to the emergence of a minor peak at the optical spectrum center. These findings provide new perspectives for simulating spectra that closely resemble experimental results and deepen our understanding of spectral evolution and pulse dynamics of the figure-9 lasers.

Figures (5)

• Figure 1: Experimental setup of the mode-locked fiber laser. Col1, Col2, Col4, Col5, Col6: collimators; Col3: WDM collimator; EDF: erbium-doped fiber; TCWDM: tap coupler hybrid with WDM; PBS1, PBS2, PBS3, PBS4: polarization beam splitters; QWP: quarter-wave plate; HWP: half-wave plate; FR: Faraday rotator. The four output ports are Tap1 port, Tap2 port, superposition port and interference port.
• Figure 2: (a) Stable pulse train from the laser with 190.6 MHz repetition rate. (b) RF spectrum of the laser with 190.6 MHz repetition rate. Inset: the broad-span RF spectrum. (c) Stable pulse train from the laser with 92.4 MHz repetition rate. (d) RF spectrum of the laser with 92.4 MHz repetition rate. Inset: the broad-span RF spectrum.
• Figure 3: Optical spectra of the four output ports of the figure-9 lasers with repetition rates of (a) 190.6 MHz and (b) 92.4 MHz. The corresponding calculated spectra, based on the data from (a) and (b), are shown in (a1)–(a4) and (b1)–(b4), respectively. The spectral bases of the measured spectra are 1.35 dB apart.
• Figure 4: (a) Schematic diagram of beam splitting on PBS1. (b) Schematic diagram of beam splitting on PBS2. (c) The optical intensity of each component varies with nonreciprocal phase bias $\theta$.
• Figure 5: Changes in normalized output power of four output ports of the mode-locked laser as pump power gradually decreases.