Optical modulation of microfibers and application to ultrafast fiber lasers

Microfibers with different waist diameters were prepared successfully by a flame-brushing technique. Their saturable absorption properties were investigated. The non-saturable loss and modulation depth both decreased with the increase of the diameter. According to the mode distribution of microfibers with a waist diameter of 25 μm, it could be supposed that the evanescent field effect may be useful for microfibers being saturable absorbers (SAs). Based on the 25 μm-diameter microfiber, an all-fiber-structure mode-locked fiber laser was achieved successfully with long term stability in the span of a week. The results indicated that microfibers with suitable diameters were excellent SAs. To the best of our knowledge, this is first report on the usage of microfibers as a SA for building ultrafast fiber lasers.


Introduction
Integrating ber optics and nano-technology, optical micro-bers have attracted growing interest for varied applications in the elds of communication, sensors, nonlinear optics and quantum optics. 1,2 In the past few decades, microbers have been manufactured and applied in a wide range of ber optic technology because of their exibility and extraordinary optical and mechanical properties. 3,4 Early in 1989, an 8.5 mm-diameter microber was used to realize the ring resonator and high Q of 27 000 at communication band. 5 Except the ring resonator, other types of resonators were demonstrated with microbers, for instance, the multicoil and knot cavity. 6,7 For the properties of smooth surface, low loss and strong evanescent led, microber are also of great importance in optical device engineering, such as compact couplers, Mach-Zehnder interferometer, sensors and optical lters. 8,9 Actually, microber could be used not only in the passive resonator, but to construct micro-ber-laser. In 2006, Jiang et al. demonstrated a 1.5 mm microber laser formed by tightening a tapered Er:Yb-doped ber into a knot successfully. 10 Besides incorporating active materials into the ber, the strong evanescent eld of micro-ber offers another approach to dope the gain materials outside of tapered region. Based on this method, Jiang et al. realized a knot dye laser providing a possibility for application of microbers to optouidic system. 11 In addition, supercontinuum generation using microbers was also investigated. 12 The microber provide higher connement than standard single mode bers (SMFs) for the strong optical nonlinear effect of tapered ber, 13 which provided an exciting opportunity for the application in nonlinear optics.
Optical modulation is one of crucial operations in photonics. 14 Recently, two-dimensional materials (such as graphene, transition metal dichalcogenides, and black phosphorous) have been extensively studied in optical technology. By incorporating the materials onto microber via the strong evanescent led, mode-locked ber laser can be easily achieved, which provide the application in optical modulator of micro-ber. [15][16][17] However, whether the microber itself is competent as SA to realize ultrafast laser has not been reported yet.
In this work, the nonlinear optical properties of microbers with different diameters have been experimentally studied. The microbers were fabricated using ame-brushing technique. With the I-scan measurement, the saturable absorption property of microber was characterized. The experimental results displayed that the non-saturable loss and modulation depth both decrease with the increase of diameter of microbers. What's more, based on a 25 mm-diameter microber, we have successfully realized an all-ber-structure dual-wavelength mode-locked laser with the maximum average output power of 19 mW. The spectrum with the peaks at 1593.9 and 1595.3 nm had full width half maximum (FWHM) of 0.64 and 0.72 nm, respectively. The pulse repetition rate third-order harmonic mode-locked ber laser was also achieved, just by increasing the pump power. Besides, the pulsed laser long-time stability in a span of a week was studied. The results proved microber with suitable diameter was an excellent saturable absorber. To the best of our knowledge, it is the rst time to investigate the optical modulation of microbers and application in the ultrafast ber laser.

Preparation and characterization of microfibers
Compared to other manufacture of microber such as chemical growth and nano-imprint, ame-brushing technique yield microbers with low surface roughness, large length and excellent diameter uniformity. 1,18 Here we fabricated the microbers using ame-brushing technique as shown in the inset of Fig. 1(a). The bare standard SMFs were stretched in virtue of a ame. By adjusting the pulling distance, microbers with the taper waist diameter of 25, 38, 55, 65, and 78 mm were achieved. The transmission spectra of 25 mm-waist-diameter microber is shown in Fig. 1. Due to the scope limit of the pump source, the transmission spectra was measured in the range of 1530-1570 nm. The result shows that the microber has a weak ltering effect, which may be useful for the generation of dual-wavelength laser. The scanning electron microscopy (SEM) was usually used to study the morphologies of sample. Here, Fig. 1(b) and (c) showed SEM image of microber with the waist diameter of 25 mm using different scale bars, which proved high evenness degree and smooth surface of prepared microbers. With a visible 455 nm laser guided through the 25 mm-diameter microber, it was clearly seen the evanescent eld from scattered light as displayed in inset of Fig. 1. The microber was xed on a slide glass by the adiabatic tape. The refractive index of microber and the slide glass is 1.46 and 1.5, respectively. For comparison, the evanescent eld of bare SMF was also shown in Section II. Obviously, the evanescent eld of tapered ber as shown in Section I was much higher than bare SMF. The mirror image in Section I was caused by the reection of slide glass.
Open-aperture Z-scan and I-scan are the common techniques for the test of nonlinear optical absorption of materials. Several advantages exit in performing I-scan over the Z-scan technique, such as fully ber-integrated setup or thin-enough sample. 19 We measured the nonlinear optical absorption of microber by I-scan technique rstly, as described in Fig. 2. The probe laser is a self-constructed mode-locked ber laser centered at 1557 nm, with the pulse width and repetition rate of 750 fs and 15.6 MHz, respectively. The laser with maximum output power of 50 mW can be adjust by an attenuator. Aer that, the pulse was split equally with a ber coupler, in which one branch performed as a reference beam and the other was connected with the prepared microber. By comparing the pulse intensities of the two branches, the transmissions versus the pulse intensity were obtained. The results are as described in Fig. 3. The experimental data were tted according to the equation: 20 where A is a normalization constant, T is the transmission of microber, I is the incident intensity, DR and I sat are the modulation depth and saturation intensity. The related     21 To our amusement, the modulation depth is inversely proportional to waist diameter of microber, which is an interesting conclusion on the properties of microbers. However, the saturation intensity did not signicantly laws with the change of the waist diameter of microbers. We surmise the reason may be caused by the measurement error and tting error. Considering the enough large waist diameter (25 mm) of microber compared to the light wavelength (1.55 mm), the three layered tapered ber model was adopted, as shown in Fig. 4(a). Combined Maxwell equations with boundary condition, the eigenvalue equations of HE mn modes could be described as following formula: 22,23 where, J m is the Bessel function of the rst kind, I m and K m are the modied Bessel function of the rst kind and second kind, respectively. k 0 ¼ 2p/l, a, b, n 1 and n 2 are radius and refractive indices of core and the cladding of microber, n 3 is the refractive index in air, b and l are propagation constant and the wavelength of light, respectively. According to the optical waveguide theory, the radial eld can be described as follows: By solving eqn (3), Fig. 4(b) shows the power distribution of HE 11 mode of the tapered ber with the diameters of 25 mm. It is clear that a part of energy guided outside of the cladding of microbers as evanescent waves. So we guess the reason for microbers being a SA may be the evanescent eld effect. Further investigation will be necessary.

Experimental setup
To test the saturable absorption ability of microbers, we proposed a compact fully berized cavity, as schematically shown in Fig. 5. A 976 nm laser diode (LD) with maximum power of 500 mW was coupled into the gain medium via a 976/ 1550 wavelength division multiplexer (WDM). 0.9 m-highlydoped erbium ber laser (EDF, LEKKI Er 110-4/125) was used with dispersion parameter of À12 ps nm À1 km À1 . A polarization-independent isolator (PI-ISO) was required to ensure unidirectional operation of the ber laser. The polarization states of propagation light were rotated through a polarization controller (PC). The laser was coupled out through a 10% optical coupler (OC). The rest ber of ring cavity, including the pigtails of microber and various components, were all SMF with dispersion parameter of 18 ps nm À1 km À1 . The net dispersion was calculated to be about À0.25 ps 2 with the total cavity length of 12.4 m. The laser performance is monitored by an optical power meter (THORLABS, S148C), a 1 GHz digital oscilloscope (Tektronix DPO 7104) coupled with a 1 GHz photodetector, an optical spectrum analyzer (Yokogawa AQ6370C) and a 3 GHz RF spectrum analyzer (Agilent N900A).

Results and discussions
First, to distinguish the proposed mode-locked ber laser from the nonlinear polarization rotation scheme, 24 the polarization property of microber using a polarized light with the wavelength of 1550 nm was test. By monitoring the change of output power through 25 mm-waist-diameter microber, obviously, the output power was almost no change. The result indicates that microber SA is polarization-independent. Then the ring cavity without inserting microber was executed. Only continuous wave (CW) could be observed when adjusted PC or increased pump power. The pump threshold of CW operation was 17 mW with slope efficiency of 8.19%, as displayed in Fig. 6(a). Aer microber with waist diameter and taper length of 25 mm and 15 mm incorporating, the threshold for CW laser increased up to 41 mW with the slope efficiency of 7.51%. By slight adjusting the PC, the mode-locked ber laser emerged when pump power further increased to 120 mW. For better performance of modelocked ber laser, the results were recorded when the pump power increased to 210 mW. A typical pulse train is depicted in Fig. 6(b). Fundamental repetition rate was 16.59 MHz, which was determined by the cavity length of 12.4 m and veried the mode-locking state. The corresponding radio frequency (RF) spectrum was shown in Fig. 6(c), with resolution bandwidth (RBW) of 20 kHz. The signal-to-noise (S/N) ratio was larger than 60 dB, indicating good stability of mode-locked ber laser based on microber. The results proved microbers can be a good candidate as SA.
The emission spectrum is shown in Fig. 6(d). It can be clearly observed dual-wavelength mode-locked ber laser with the peaks of 1593.9 and 1595.3 nm was generated. The two peaks were both Gaussian-like prole with the FWHM of 0.64 and 0.72 nm, respectively. The spectrum showed clearly there was no Kelly sidebands, which may be caused by the spectral ltering effect. In this experiment, we didn't measure the real pulse width for the lack of suitable autocorrelator. However, according the soliton theory, the theoretical limit pulse duration could be estimated. The two peaks of spectrum with different FWHMs implied two separate pulse trains. The pulse duration of the two pulses was calculated to be 4.18 ps and 3.72 ps, respectively. For comparison, the laser spectrum of CW operation was also recorded, as shown in the inset of Fig. 6(d).
No obvious dual-spectrum was observed. So we can reasonably infer that the microber contributed to generation of dualwavelength laser, which can be explained as follows: micro-ber in the cavity not only worked as a SA, but a Mach-Zehnder interferometer (MZI). The MZI as ber comb lter is an excellent method for generate multi-wavelength laser. 25 Continue to raise pump power to 220 mW, a new type of stable pulse train emerged, as shown in Fig. 7(a). The repetition rate was 49.79 MHz, correspondent to third harmonic of fundamental repetition rate. The change of repetition rate only depends on the pump power. There is no need to rotate the PC. The RF spectrum was depicted in Fig. 7(b), with the RBW of 4.7 kHz. The S/N ratio was higher than 55 dB, indicating the harmonic mode-locked ber laser was also in quite stable state. Adding the pump power to 250 mW, the stable mode-locking ber laser was collapsed suddenly. However, reducing the pump power again, the harmonic and fundamental modelocking pulses can be both reconstructed. As a result, the microber was conrmed owning a fairly high damage threshold.
Besides, the repeat scans of spectra measured within a span of a week were also recorded, as illustrated in Fig. 8. It can be veried that the mode-locked ber laser based on microber with suitable diameter has a fairly long-term stability. The results proved the unique superiority of microber on the application to ultrafast ber laser. We also demonstrated the same cavity with other prepared microbers with different waist diameter. Except the 25 mm-diameter-microber, there is no  stable mode-locking ber laser, regardless of how to rotate PC or change pump power. The result displayed the waist diameter of microber is a main factor for the application as a SA. However, microbers with smaller-diameters have not been fabricated due to the restriction of preparation. It is still hard to make deterministic conclusion on the selection of microber diameter as a SA. Specic origins of saturable absorption of microbers are not so clear. Further detailed investigation will be essential.

Conclusions
In conclusion, a series of high-quality microbers with different waist diameter was prepared by using ame-brushing technique. The saturable absorption property of microbers were studied with I-scan measurement. The non-saturable loss and modulation depth both decreased with the increase of diameter of microbers. Based on the microber with suitable diameter, an all-ber-structure dual-wavelength mode-locked ber laser was achieved. To our best of knowledge, it is the rst time to investigate the optical modulation of microber and application to the ultrafast ber laser. The long-term stability and repetition rate third harmonic mode-locked laser have fully testied microber could be a kind of excellent SAs for generating pulsed lasers.

Conflicts of interest
There are no conicts to declare.