## 1 Introduction  
Ultrashort optical pulses are now widely applied in many fields of science and engineering. The high peak intensity of ultrashort optical pulses induces nonlinear optical effects, such as two-photon absorption, which enable the imaging of the three-dimensional structures of biological tissue [1]. Ultrashort duration of these optical pulses allows material processing while avoiding the effects of heat dissipation [2]. These applications are mostly based on commercially available mode-locked solid state or fiber lasers. Semiconductor laser diodes (LDs) offer advantages for generating ultrashort optical pulses due to their broad gain bandwidths. The use of direct electrical excitation allows the fabrication of compact and practical ultrashort laser pulse sources [3]. In particular, GaN-based semiconductors have a unique property, to generate photons in the blue-violet region [4, 5]. This is a great advantage of nitride semiconductors since most solid state lasers require wavelength conversion in order to generate ultrashort optical pulses in this wavelength region. We previously developed a blue-violet picosecond pulse laser, based on a GaN-based semiconductor LD [6]. Using a master oscillator power amplifier scheme, we succeeded in generating picosecond optical pluses of 2.2 nJ pulse energy [7]. The peak power was about 630 W, which is the highest so far reported for GaN-based LDs. The pulse energy is comparable to that of blue-violet optical pulses produced by frequency-doubled mode-locked Ti:Sapphire lasers. In addition to developing a high power GaInN semiconductor optical amplifier (SOA), shortening the pulse duration is important for obtaining high-peak-power optical pulses, because the pulse energy available from SOAs is limited by the finite carrier lifetime. However, sub-picosecond optical pulses cannot be routinely generated using mode-locked semiconductor laser diodes (MLLDs). This is due to the strong coupling of the real and imaginary parts of the refractive index in the gain section of semiconductor LDs. In order to avoid this problem, a bisectional laser diode (BS-LD) using a quantum dot active layer was used to generate 390-fs optical pulses [8]. Intracavity dispersion compensation is another technique for reducing chirp in optical pulses from MLLDs. The use of MLLDs with dispersion-compensated external cavities was reported to increase the spectral bandwidth, but not to reduce the pulse duration. In these reports, femtosecond optical pulses were finally obtained only by compressing the optical pulses using dispersion-compensating optics [9]. Previously, we reported the generation of 200-fs optical pulses at 400 nm using a GaInN BS-LD in a dispersion-compensated external cavity, followed by spectral filtering [10, 11]. With a negative intracavity group velocity dispersion (GVD), the output spectrum was broadened and optical pulses with a duration of 200 fs were produced by subsequent spectral filtering. There were three aspects of this situation that differed from previous reports of ultrashort pulse generation using dispersion-compensated MLLDs. First, ultrashort pulses close to the Fourier transform limit were obtained by spectral filtering. Second, the intracavity GVD was negative. Finally, the recovery time for the saturable absorber (SA) was as slow as 15 ps with a reverse bias voltage of 6 V [12]. These experimental conditions were similar to those for soliton mode locking with a slow SA [13]. However, in order to explain the femtosecond pulse generation mechanism in a GaInN MLLD in terms of soliton mode locking, it would be necessary for self-phase modulation to occur in order to balance the intracavity GVD. Furthermore, the theory of soliton mode locking cannot explain the shape of the optical pulses or the spectra of the GaInN MLLD before spectral filtering. In the present study, we examined the temporal and spectral characteristics of optical pulses produced by a dispersion-compensated GaInN MLLD in order to clarify the pulse formation mechanism.