## 2 Experimental Method and Results  
Figure 1 shows the configuration of the developed Tm-Ho co-doped ultrashort pulse fiber laser. A 1.4 m piece of Tm-Ho co-doped fiber (THDF) (TH-1100, Neufern, East Granby, CT, USA) was used as the gain fiber. The output of a single mode laser diode (TH1550, Thorlabs, Newton, MA, USA) was amplified with a double clad Erbium (Er)-Ytterbium (Yb) co-doped fiber amplifier (FA-33, PriTel, Naperville, IL, USA), and introduced into the THDF through a wavelength division multiplexed (WDM) coupler. As a mode-locker, we used polyimide film dispersed with SWNT [15]. SWNTs with an almost constant diameter of around 1.6 nm were selectively synthesized by the e-DIPS method [16]. The thicknesses of the films were 35-45 \(\upmu\)m. They showed a strong absorption peak around 1.9 \(\upmu\)m. In this work, we used two kinds of polyimide films, film A and film B, with different magnitudes of absorption. The modulation depths were 12.3% and 20.5% for films A and B, respectively [15]. The characteristics of the two films are summarized in Table 1.  
The fiber laser cavity consisted of single mode fiber devices. Two optical isolators were used to realize the one way operation and to protect the SWNT polyimide film. A 75:25 coupler was used as the output coupler. An additional WDM coupler was used to remove the residual pump beam. In order to realize the oscillation wavelength control without any spatial device, we developed an in-line wavelength tunable spectral filter. Figure 2 shows the configuration of the wavelength tunable spectral filter. It consisted of two polarizers, polarization maintaining fibers (PMFs), and single mode fiber (SMF) with a polarization controller (PC). The configuration is similar to that developed for a Yb-doped fiber laser in [21]. In this work, we applied a stress-applying type PC to realize the tunable operation. The FC/APC connectors were spliced at the ends of the filter, and easily inserted into the fiber laser cavity. An additional PC was used to control the optical loss at the first polarizer in the spectral filter. Polarizer 1 was spliced with PMF1, which was inclined by 45 degrees. For the output port, polarizer 2 was spliced with PMF2 which was also inclined by 45 degrees. A SMF with PC was inserted in between the PMF1 and PMF2. By the operation of the PC, we can demonstrate the bandwidth and wavelength tunable operation [21]. Figure 3 shows the wavelength dependence of the developed spectral filter. In this work, the lengths of PMF1, SMF, and PMF2 were 10 cm, 14.5 cm, and 7 cm, respectively. A wideband supercontinuum and optical spectrum analyzer were used for this measurement [22]. The transmission spectra were obtained by dividing the observed output spectra by the observed input spectra. The numerical results were analyzed using the [PERSON] matrix. As shown in Figure 3a, the numerically obtained transmission spectra showed similar periodical behavior to the experimentally observed ones. The numerical and experimental transmission bandwidths were 29.5 nm and 23 nm, respectively. It was considered that the discrepancy between experimental and numerical spectra was mainly caused by the variation of parameters in the fiber devices. In the experiment, when the magnitude of applied stress was controlled in the PC, the transmission spectra were shifted continuously by the combination of polarization change and birefringence in PMFs, and the wavelength tunable operation was achieved, as shown in Figure 3b. A continuous wavelength tuning of 15 nm was observed. During the wavelength tuning operation, the peak-peak contrast changes as well, owing to the effect of birefringence and polarization control. The sharp dips were caused by the effect of water absorption in air. In this work, in order to examine the dependence on net cavity dispersion, an ultrahigh numerical aperture fiber (UHNA4) which has strong normal dispersion property was used to vary the net cavity dispersion.