# Narrowing Linewidth of Wavelength-Swept Active Mode Locking Laser Based on Cross Gain Modulation
## 2 Experiments and Results
To achieve the high modulation depth of the SOA for the mode locking condition, a booster optical amplifier (BOA) (Aeon, Models CL) was inserted to increase the optical power of the intensity-modulated optical pump light at port 2 of the CIR2 up to 11 mW because it is well known that the extinction ratio of an SOA is improved by increasing the power of the pump light [22; 23]. However, the power of the pump light needed to be controlled properly. In the case of the optical pump light being too strong, the gain of the SOA in the ring cavity cannot be fully increased to generate the laser output. The intensity-modulated optical pump light is injected through the circulator port 1 of CIR1 into the SOA in the direction opposite to the lasing signal. This injected pump light leads gain modulation of the SOA by depleting the gain of SOA. Therefore, the modulation depth of the SOA can be controlled via the modulation depth of the injected light. Moreover, the injected pump light reduces the carrier lifetime in the cavity due to stimulated recombination; high modulation frequency can be implemented. In this setup, an ASE of 0.2 mW comes out from the SOA in the cavity and acts as a signal light in the XGM configuration. Figure 1: Experimental setup to measure the modulation depth of the semiconductor optical amplifier (SOA) (M\({}_{\text{SOA}}\)) in (**a**) direct gain modulation (DGM) and (**b**) cross gain modulation (XGM). (**c**) Relative frequency response of the modulation depth of the SOA (M\({}_{\text{SOA}}\)/M\({}_{\text{i}}\)) for both DGM and XGM. E.P. : electrical power; O.P. : optical power; RF-SG: radio frequency signal generator; MZM: Mach-Zehnder modulator; ESA: electric spectrum analyzer; CIR: circulator; PD: photodetector; A\({}_{\text{O}}\): amplitude of output electric signal modulation; A\({}_{\text{P}}\): amplitude of pump electric signal modulation, M\({}_{\text{i}}\): modulation depth of SOA at 0 MHz. The wavelength of the optical pump light is another important parameter for a higher extinction ratio of the XGM. In general, the extinction ratio is maximized when the wavelength of the optical pump light is at the peak of the gain spectrum [21; 22; 23; 24] and the peak of the gain spectrum is red-shifted when strong optical pump light is injected into the SOA due to the depletion of carriers [27; 24]. However, setting the pump light at the center of gain spectrum causes excessive undesired lasing of optical pump light, which decreases the output power at the desired wavelength and the SNR. Therefore, the optical wavelength of the pump light was set to 1590.9 nm at the side of the gain spectrum and the measured extinction ratio was 7.5 dB. A laser output with a short pulse train occurs when the modulation frequency matches the AML condition as follows [9]:  
\[f_{m}=N\cdot FSR \tag{1}\]  
where \(f_{m}\) is the modulation frequency applied to the SOA, \(N\) is the order of harmonic mode locking. The free spectral range of the laser cavity, \(FSR\), is expressed as [9]:  
\[FSR=\frac{c}{n_{eff}L} \tag{2}\]  
where \(L\) is the cavity length, \(n_{eff}\) is the effective refractive index in the fiber ring cavity, and \(c\) is the speed of light in vacuum. The zero-order FSR, \(FSR_{0}\), is driven from the cavity length and the speed of light in the fiber cavity [28; 29]. However, since each wavelength has different AML conditions due to the dispersion medium of the CFBG, the deviation in the lasing wavelength, \(\Delta\lambda_{m}\), is expressed as a function of the modulation frequency,\(f_{m}\)[9];  
\[\Delta\lambda_{m}=-\frac{nL}{cD_{total}f_{m_{0}}}\Delta f_{m} \tag{3}\]  
where \(\Delta f_{m}=f_{m}f_{m0}\),\(f_{m0}\) is the central mode-locking frequency, \(D_{total}\) is the dispersion parameter. Figure 3a,b are examples of the spectral peak shape of static wavelength-swept AML laser at different mode-locking orders under the DGM and XGM configuration, respectively. For the central wavelength of 1574.1 nm and a cavity length of 3.752 m, \(FSR_{0}\) is given as 54.45 MHz.