Flexible pulse-controlled fiber laser

Controlled flexible pulses have widespread applications in the fields of fiber telecommunication, optical sensing, metrology, and microscopy. Here, we report a compact pulse-controlled all-fiber laser by exploiting an intracavity fiber Bragg grating (FBG) system as a flexible filter. The width and wavelength of pulses can be tuned independently by vertically and horizontally translating a cantilever beam, respectively. The pulse width of the laser can be tuned flexibly and accurately from ~7 to ~150 ps by controlling the bandwidth of FBG. The wavelength of pulse can be tuned precisely with the range of >20 nm. The flexible laser is precisely controlled and insensitive to environmental perturbations. This fiber-based laser is a simple, stable, and low-cost source for various applications where the width-tunable and/or wavelength-tunable pulses are necessary.

Controlled flexible pulses have widespread applications in the fields of fiber telecommunication, optical sensing, metrology, and microscopy. Here, we report a compact pulse-controlled all-fiber laser by exploiting an intracavity fiber Bragg grating (FBG) system as a flexible filter. The width and wavelength of pulses can be tuned independently by vertically and horizontally translating a cantilever beam, respectively. The pulse width of the laser can be tuned flexibly and accurately from ,7 to ,150 ps by controlling the bandwidth of FBG. The wavelength of pulse can be tuned precisely with the range of .20 nm. The flexible laser is precisely controlled and insensitive to environmental perturbations. This fiber-based laser is a simple, stable, and low-cost source for various applications where the width-tunable and/or wavelength-tunable pulses are necessary.
To control the laser property, a filter is widely employed into the laser cavity. For instance, a birefringent-platebased filter can stabilize high-energy pulses in the all-normal-dispersion fiber lasers 52 . But its operation wavelength is fixed, as well as its spectral bandwidth is inflexible because it attributes to the thickness of birefringent plate 26,52 . Wavelength tuning can be realized by using an intracavity bandpass filter 46,53 , whereas the spectral bandwidth and the pulse width are still inflexible. Fortunately, fiber Bragg grating (FBG) is an ideal component for fiber lasers because it can provide the changeable dispersion and the tunable transmittance wavelength together with negligible nonlinearity 54,55 . Then, FBG offers the great flexibility for controlling the wavelength of the generated pulses. However, the pulse width of lasers is usually fixed although it can be tuned slightly by changing the pump power or adjusting the components of cavity 45,46 . To address this issue, we have proposed a flexible technique by means of controlling FBG.
In this article, we report a compact pulse-controlled fiber laser for the first time to our best knowledge, in which the pulse width and the pulse wavelength can be controlled precisely by adjusting FBG. The controlled scalable range of pulse width in the proposed fiber laser is accurately tunable from ,7 to ,150 ps. The wavelength of pulse is precisely tunable with the range of .20 nm. This laser is insensitive to environmental perturbations and thus is viable for various practical applications. of the beam, as shown in inset of Fig. 1(b). The angle, h, between the axis of the FBG and the neutral layer of the beam is about 15u.
The integrated CNT-based SA is made by sandwiching a ,2 mm 2 sample between two fiber connectors. The fabrication procedure is shown in our previous report 45 . Figure 1(c) shows the normalized nonlinear absorption of CNT-SA, which is experimentally measured with a homemade ultrafast laser at 1550 nm. The experimental data are fitted as the solid curve of Fig. 1(c) on the basis of a simplified twolevel SA model 45 . Figure 1(c) illustrates that the linear limit of saturable absorption (a 0 ), the nonsaturable absorption (a ns ), and the saturation intensity (I sat ) are about 11.28%, 88.53%, and 27.03 MW/cm 2 , respectively. Figure 1(d) demonstrates the absorption spectra of the pure polyvinyl alcohol (PVA) and the CNT-PVA composite, which are measured by a spectrometer (JASCO V-570 UV-vis-NIR). It is worth noting that the tube diameter of CNTs is ranging from 0.8 to 1.3 nm here, whereas it is less than 2 nm in Ref. 45.
Bandwidth-tunable and wavelength-tunable operations. The beam is bent when the screw G z is translated along z-axis, as shown in Fig. 1(b). The half of the grating is under varying tension, whereas the other half is under varying compression. If the center of the grating is located exactly at the neutral layer of the beam, there will be no strain at the center of the grating 57,58 . In this case, the vertical distance shift at the FBG center is equal to zero and then the central wavelength shift Dl c is also equal to zero according to Eqs.
(1) and (2) (see METHODS). Figure 2(b) shows the induction principle of tension and compression strain along the FBG based on the symmetrical bending. As a result, the bandwidth Dl B of FBG can be flexibly controlled by the tension and compression strain at each side of the FBG without the shift of the central wavelength. Figure 3(a) shows some typically experimental results of reflection spectra of the FBG with the variation of translation. The bandwidth of FBG is changed in the range from about 0.8 to 4 nm. Obviously, the central wavelength approximately remains fixed although the bandwidth-tunable operation is realized.
When the screw G x in Fig. 1(b) is translated horizontally (i.e., along the direction of x-axis), the variation of FBG bandwidth Dl B is slight whereas the central wavelength shifts distinctly.   Experimental results of controlled flexible laser. Self-starting modelocking operation starts at the pump power of ,19 mW. With the appropriate setting of the polarization controller and the pump power, the proposed laser delivers the pulses with different widths by vertically adjusting the FBG (i.e., translating the screw G z along z-axis, as shown in Fig. 1(b)). The typical output spectra are shown in Fig. 4(a) with the central wavelength of ,1535 nm. The corresponding autocorrelation traces of the experimental data and the sech 2shaped fit are shown in Fig. 4 Fig. 4(c) give a signal-to-noise ratio of .60 dB (.10 6 contrast), showing low-amplitude fluctuations and good mode-locking stability 59 . No spectrum modulation is observed over 3 GHz in Fig. 4(d), indicating no Qswitching instability.  Figure 5(b) illustrates that the spectral bandwidth Dl of pulses approximately linearly increases along with Dl B for Dl B , 1 nm, whereas it changes slightly for Dl B . 1.5 nm. The origin of such behavior can be explained as follows. The different parts of FBG reflect the different wavelengths so that the round-trip distances for different frequencies of a pulse are different. When the spectral bandwidth of FBG is large enough, only a part of FBG spectra is employed in the mode-locking operation of fiber lasers and, then, the FBG with larger reflection bandwidth has a slight influence on the laser bandwidth.   Figure 6 demonstrates the typical output spectra by horizontally translating the screw G x along the direction of x-axis. The experimental results show that the spectral bandwidth Dl and pulse width Dt change slightly although the central wavelength of pulses is tuned evidently, indicating the stability of our output pulses. It is seen from Fig. 6 that the tuning range of wavelength is .20 nm with the FWHM spectral bandwidth of ,0.3 nm. The fluctuation of spectral profile originates from the dispersion variation of FBG when the central wavelength of FBG is tuned. The tuning range of wavelength is determined by the FBG. The experimental observations show that our laser can long-termed stably work for both width-tunable and wavelength-tunable operations. It attributes to the intrinsical merit of the CNT-based SA, which is insensitive to the environmental perturbations and the polarization of pulses.

Discussion
In the experiments, the bandwidth of FBGs limits the tuning range of pulse width, as shown in Fig. 5(a). Theoretically, the proposed laser can deliver the pulses with the width of ,1 ps if FBG in Fig. 1 is optimized. It is seen from Fig. 5(a) that the pulse width Dt of laser can be less than 1 ps when the FBG bandwidth Dl B is more than 11 nm. Although it is hard to fabricate a uniform FBG with the bandwidth of .2 nm, the bandwidth of the chirped FBGs can be up to 30 nm easily 54 . We can observe from Fig. 3(a) that the bandwidth Dl B of the uniform FBG can be extended up to 4 nm by vertically translating the screw G z , as shown in Fig. 1(b). However, the reflectivity of FBG decreases along with the increase of Dl B . For instance, the reflectivity of FBG is less than 30% for Dl B < 2.5 nm. As a result, this laser will not operate when Dl B is extended to be more than 2.5 nm.

Methods
Principle of controlled operation. When the beam is bent or elongated (Fig. 2), linearly varying strain along its thickness or length is achieved. The strain response of FBG originates from both the physical elongation of the grating and the change in the refractive index due to photoelastic effects. The central wavelength variation of FBG, Dl c , induced by the strain e along its axial direction is given by 56,57 Dl c~l0 (1{P e )e: Here l 0 is the initial Bragg wavelength of the grating. P e is the effective photoelastic coefficient (approximately equal to 0.22), which is relative to the fiber Poisson ratio and the effective refractive index of the fiber core. 1-P e is the strain tuning coefficient. By vertically translating the screw G z along z-axis in Fig. 1(b), the strain introduced to the beam during bending is transferred to the FBG and induces an axial strain gradient along the grating, i.e., where k is the curvature of the neutral layer of beam, Dz is the vertical distance measured from the neutral layer, and C (0 , C , 1) is a constant introduced to describe the efficiency of strain transfer from the beam to the grating. The variation of Bragg wavelength is proportional to the local axial strain along the grating and the chirp of grating can be achieved when the beam is bent. The strain can be approximately proportional to k and the grating length 57,58 . Then, the reflection bandwidth variation of FBG can be expressed as 57 where l is the length of the grating. By horizontally translating the screw G x along x-axis in Fig. 1(b), the strain introduced to the grating can be approximated by where f is the horizontal displacement at the end of beam. Substituting Eq. (4) into Eq.
(1), we can achieve the central wavelength change of FBG when the translation is along the direction of x-axis, i.e., Dl c~C l 0 (1{P e ) wf L 2 cos (h): In this case, the reflection bandwidth variation of FBG can be approximated to zero, i.e., Dl BV < 0. In fact, when the screw G x in Fig. 1(b) is translated horizontally, the angle between the axis of FBG and the vertical plane of translation is zero, i.e., h 5 0. Thus, Dl BV is equal to zero according to Eq. (3).