# Narrowing Linewidth of Wavelength-Swept Active Mode Locking Laser Based on Cross Gain Modulation
## 1 Introduction  
Over the last decade, the wavelength-swept laser has been used as a powerful tool in biomedical imaging and various sensing application areas [1; 2; 3; 4; 5; 6]. In general, wavelength-swept lasers use wavelength-tunable filters with mechanical movements, such as Fabry-Perot tunable filters [1; 2; 3] and angle-scanning filters with diffraction gratings [4]. Recently, a few advanced designs of wavelength-swept lasers, such as Fourier-domain mode-locking lasers [5] and micro-electro-mechanical system (MEMS) tunable vertical-cavity surface-emitting lasers (VCSELs) [6], have shown high performances with fast sweep rates of over a few hundred kHz, wide bandwidths of over 100 nm, and narrow linewidths of under 0.1 nm, which are commonly required for optical coherence tomography (OCT) [7]. However, owing to the mechanical movement of their conventional wavelength tunable filters, such lasers inherently suffer from thermal and mechanical instabilities and nonlinear tuning problems [7; 8; 9; 10]. Nowadays, wavelength-swept active mode locking (AML) lasers have been developed by exploiting a radio frequency (RF) signal generator to modulate the gain of a semiconductor optical amplifier (SOA) using an electric current pump directly, which can implement an output wavelength tuning from the AML condition matching in a chromatic dispersion cavity [8; 9; 10]. Wavelength-swept AML lasers have not only demonstrated sweep rates of over 100 kHz [8; 9; 10] and bandwidths of 100 nm [11] but have also shown a few particular advantages, such as higher duty ratios (\(>\) 90%), linear sweeping (\(>\)0.9999), and phase stability, due to their unique kinetic wavelength sweeping mechanism that eliminates conventional mechanical and sinusoidal movement [10; 12]. However, wavelength-swept AML lasers have a critical drawback: a thick linewidth (larger than 0.25-0.61 nm) [8; 9; 10; 13; 14] compared to conventionalwavelength-swept lasers based on mechanical movement filters [1; 2; 3; 4; 5; 6]. This means that one of the most critical challenges currently to use wavelength-swept AML lasers as a light source for practical applications is to reduce the linewidth [8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19].  
It has been experimentally investigated that there is a tendency for reducing linewidth of the wavelength-swept AML lasers at higher modulation frequencies [15; 16]. As a theoretical approach to this issue, a discrete model of wavelength-swept AML laser has been proposed recently to show that the AML matching conditions with both higher modulation frequency and higher dispersion cavity are helpful to induce a narrower spectral linewidth [17; 18]. However, under the direct gain modulation (DGM) configuration used for most wavelength-swept AML laser schemes, this linewidth narrowing approach by increasing the modulation frequency is mostly limited below the region of a few hundred MHz. It has been experimentally shown that the lasing output cannot be built from the amplified spontaneous emission (ASE) spectra due to the modulation response degradation in a higher modulation frequency region. Because the carrier lifetime of an SOA is several hundreds of picoseconds, the modulation response of SOA is dramatically decreased at high frequencies around GHz range in a conventional DGM method wavelength-swept AML laser [20; 21].  
Meanwhile, it has been studied that the cross gain modulation (XGM) method can be used to modulate the optical gain by injecting intensity-modulated optical pump light into the SOA, instead of the conventional current-modulated electric pump injection into the SOA under the DGM configuration [22; 23; 24; 25; 26]. It is also known that the XGM can improve the frequency response of the modulation depth of the SOA by reducing the lifetime in the cavity [22; 23]. In this study, we investigate the static and dynamic characteristics of the novel wavelength-swept laser by adapting the XGM method into the AML condition for the first time, as far as we know.