Introduction

Fiber-based lasers attract extensive attention due to their various advantages such as compactness, reliability and high stability1,2,3,4,5,6,7,8,9,10,11,12. A variety of mode-locking techniques have been developed to make pulse lasers as versatile tools for many applications in fiber telecommunication, optical frequency comb generation, metrology and microscopy13,14,15,16,17,18,19,20,21,22,23. So far, a number of saturable absorbers (e.g. the nonlinear polarization rotation24,25,26,27,28,29,30, nonlinear optical loop mirror31,32,33, semiconductor saturable absorber mirror34,35,36,37,38, graphene39,40,41,42,43 and carbon nanotube (CNT)44,45,46,47) have been proposed to implement the mode-locking operation. Among them, CNTs are particularly interesting for pulse generation because of highly environmental stability and being insensitive to the polarization of pulses evolving in the laser cavity45,46,47,48,49,50,51.

To control the laser property, a filter is widely employed into the laser cavity. For instance, a birefringent-plate-based filter can stabilize high-energy pulses in the all-normal-dispersion fiber lasers52. But its operation wavelength is fixed, as well as its spectral bandwidth is inflexible because it attributes to the thickness of birefringent plate26,52. Wavelength tuning can be realized by using an intracavity bandpass filter46,53, 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 nonlinearity54,55. 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 cavity45,46. 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.

Results

Experimental setup of controlled flexible laser

The schematic diagram of controlled flexible fiber laser is shown in Fig. 1(a). The proposed laser consists of a FBG system, a circulator (CIR), a CNT saturable absorber (SA), a polarization controller (PC), a wavelength-division multiplexer (WDM), an 8-m-long erbium-doped fiber (EDF) with 6 dB/m absorption at 980 nm, a fused coupler with 10% output ratio and a piece of single-mode fiber (SMF). The dispersion parameters of EDF and SMF are about 11.6 and −22 ps2/km at 1550 nm, respectively. The total cavity length is ~21.5 m.

Figure 1
figure 1

(a) Laser setup. EDF, erbium-doped fiber; WDM, wavelength-division multiplexer; PC, polarization controller; LD, laser diode; CIR, circulator; FBG, fiber Bragg grating; CNT, carbon nanotube. (b) FBG system. A uniform FBG is glued in a slanted direction onto the lateral side of a right-angled triangle cantilever beam. The flexible cantilever beam is made of polyurethane. (c) Nonlinear absorption characterization of the CNT-SA. The solid curve is fitted from the experimental data (circle symbols). (d) Absorption spectra of the pure polyvinyl alcohol (PVA) and the CNT-PVA composite. The red stripe illustrates the spectral gain region of the Er3+-doped fiber.

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The key component of this laser, shown in Fig. 1(b), is a FBG system that introduces the accurately width-tunable and wavelength-tunable operations for pulse generation. A uniform FBG is glued in a slanted direction onto the lateral side of a right-angled triangle cantilever beam with length L = 18 cm, width w = 3 cm and thickness h = 1.2 cm. The flexible cantilever beam is made of polyurethane with the high resistance against fatigue. The FBG is carefully attached by using the UV curable epoxy. The center of FBG lies on the neutral plane of the beam, as shown in inset of Fig. 1(b). The angle, θ, between the axis of the FBG and the neutral layer of the beam is about 15°.

The integrated CNT-based SA is made by sandwiching a ~2 mm2 sample between two fiber connectors. The fabrication procedure is shown in our previous report45. 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 two-level SA model45. Figure 1(c) illustrates that the linear limit of saturable absorption (α0), the nonsaturable absorption (αns) and the saturation intensity (Isat) are about 11.28%, 88.53% and 27.03 MW/cm2, 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 Gz 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 grating57,58. In this case, the vertical distance shift at the FBG center is equal to zero and then the central wavelength shift Δλc 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 ΔλB 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.

Figure 2
figure 2

Schematic diagram of bandwidth-tunable and wavelength-tunable operations by flexibly controlling FBG.

(a) Without the translation in the free state, (b) vertically translating the screw Gz along the direction of z-axis and (c) horizontally translating the screw Gx along the direction of x-axis.

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Figure 3
figure 3

Typically reflection spectra of FBG.

(a) Vertically translating the screw Gz along z-axis. The FBG bandwidth ΔλB is changed whereas the central wavelength approximately is fixed. ΔλB is about 0.8, 1, 1.4, 1.8, 2.2, 3, 3.4 and 4 nm from inner to outer, respectively. (b) Horizontally translating the screw Gx along x-axis. The central wavelength of FBG is tuned with the range of >20 nm, whereas the spectral profile changes slightly.

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When the screw Gx in Fig. 1(b) is translated horizontally (i.e., along the direction of x-axis), the variation of FBG bandwidth ΔλB is slight whereas the central wavelength shifts distinctly. Figure 2(c) demonstrates the induction principle of strain along the uniform FBG. The experimental results are shown in Fig. 3(b), where the central wavelength of FBG is tuned with the range of >20 nm but the spectral profile changes slightly. The theoretical explanation can be achieved from Eqs. (3) and (5) (see METHODS). Obviously, the bandwidth- and wavelength-tunable operations can be realized independently by the vertical and horizontal translations, respectively.

Experimental results of controlled flexible laser

Self-starting mode-locking 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 Gz 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 sech2–shaped fit are shown in Fig. 4(b). The full width at half maximum (FWHM) spectral bandwidths are about 0.035, 0.07, 0.216 and 0.386 nm at the FBG bandwidths of 0.17, 0.35, 0.71 and 1.48 nm, respectively. The corresponding pulse widths (Δτ) are about 73.5, 35, 14.6 and 9.2 ps, respectively. Then, the calculated time-bandwidth products (TBPs) are about 0.33, 0.31, 0.40 and 0.45, respectively, which are close to the value of the transform-limited sech2-shaped pulses. The fluctuation of TBPs originates from the variations of the FBG bandwidth, the optical spectrum and the total dispersion of laser cavity. The radio frequency (RF) spectra in Fig. 4(c) give a signal-to-noise ratio of >60 dB (>106 contrast), showing low-amplitude fluctuations and good mode-locking stability59. No spectrum modulation is observed over 3 GHz in Fig. 4(d), indicating no Q-switching instability.

Figure 4
figure 4

Typical laser characteristics.

(a) Optical spectra at the FBG bandwidths (ΔλB) of 0.17, 0.35, 0.71 and 1.48 nm (from inner to outer) by vertically translating the screw Gz in Fig. 1(b). (b) Autocorrelation traces of the experimental data (circle symbols) and sech2–shaped fit (solid curves). The FWHM spectral bandwidths (Δλ) and the corresponding pulse widths (Δτ) are about 0.035 nm and 73.5 ps, 0.07 nm and 35 ps, 0.216 nm and 14.6 ps and 0.386 nm and 9.2 ps, respectively. (c) Fundamental RF spectrum with the resolution of 2 Hz and the span of 200 Hz. Inset in the top left corner: RF spectrum with the resolution of 10 Hz and the span of 80 kHz. Inset in the top right corner: oscilloscope traces with the separation of ~104.13 ns, corresponding to 9.60376 MHz of the fundamental harmonic frequency that is independent of the pump power. (d) Wideband RF spectrum up to 3 GHz.

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Figures 5(a) and 5(b) show the relationships of the pulse width Δτ and the spectral bandwidth Δλ with respect to the FBG bandwidth ΔλB, respectively. The corresponding TBPs are ranging from ~0.31 to ~0.47 for the experimental data. The symbols and solid curves denote the typically experimental data and the fit curves, respectively. In the experiments, the maximum of pulse width Δτ can be up to ~152 ps and the minimum of Δτ can be down to ~7 ps. Note that the tuning range of Δτ is limited by the FBGs. We can observe from Fig. 5(a) that the pulse width Δτ approximately decreases with a rational function according to the FBG bandwidth ΔλB. The rational equation that produces the best fit is as . It is seen from Fig. 5(b) that the spectral bandwidth Δλ approximately increases with a polynomial function of degree 5 with respect to ΔλB. The polynomial equation that produces the best fit is as . Figure 5(b) illustrates that the spectral bandwidth Δλ of pulses approximately linearly increases along with ΔλB for ΔλB < 1 nm, whereas it changes slightly for ΔλB > 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 5
figure 5

(a) Pulse width Δτ and (b) spectral bandwidth Δλ with respect to the FBG bandwidth ΔλB.

The beam is translated vertically, i.e., translating the screw Gz along the direction of z-axis.

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Figure 6 demonstrates the typical output spectra by horizontally translating the screw Gx along the direction of x-axis. The experimental results show that the spectral bandwidth Δλ and pulse width Δτ 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.

Figure 6
figure 6

Output spectra of laser by horizontally translating the screw Gx along the direction of x-axis.

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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 Δτ of laser can be less than 1 ps when the FBG bandwidth ΔλB 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 easily54. We can observe from Fig. 3(a) that the bandwidth ΔλB of the uniform FBG can be extended up to 4 nm by vertically translating the screw Gz, as shown in Fig. 1(b). However, the reflectivity of FBG decreases along with the increase of ΔλB. For instance, the reflectivity of FBG is less than 30% for ΔλB ≈ 2.5 nm. As a result, this laser will not operate when ΔλB 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, Δλc, induced by the strain ε along its axial direction is given by56,57

Here λ0 is the initial Bragg wavelength of the grating. Pe 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-Pe is the strain tuning coefficient. By vertically translating the screw Gz 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 κ is the curvature of the neutral layer of beam, Δz 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 κ and the grating length57,58. Then, the reflection bandwidth variation of FBG can be expressed as57

where l is the length of the grating.

By horizontally translating the screw Gx 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.,

In this case, the reflection bandwidth variation of FBG can be approximated to zero, i.e., ΔλBV ≈ 0. In fact, when the screw Gx in Fig. 1(b) is translated horizontally, the angle between the axis of FBG and the vertical plane of translation is zero, i.e., θ = 0. Thus, ΔλBV is equal to zero according to Eq. (3).

Measurement method

An optical spectrum analyzer (Yokogawa AQ-6370), an autocorrelator (APE PulseCheck SM1600), a 6-GHz oscilloscope (LeCroy WaveMaster 8600A), a radio-frequency (RF) analyzer (Agilent E4447A) and a 10-GHz photodetector are used to measure the laser output performances.