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We have demonstrated broad supercontinuum (SC) generation by using a highly nonlinear tapered tellurite microstructured fiber pumped by a 15-ps-pulsed laser with the peak power of 375 W. The fiber is characterized with a short section with a large diameter followed by a long section with a small diameter. The SC was mainly generated in the last 30-cm-long section which had a core diameter of 0.9 μm and a zero dispersion wavelength around the pump wavelength. Such a core size and a dispersion profile were chosen to ensure the SC was mainly broadened by phase matched four-wave mixing. The SC spans from UV to mid IR. The 10 dB spectrum is from 780 to 1890 nm. The input peak power is much lower than conventionally adopted in the picosecond regime. The constructed SC light source is cost-effective, since neither femtosecond pulsed laser nor high power picosecond pulsed laser is adopted.
©2012 Optical Society of America
1. Introduction
In the latest ten years, research on fiber based supercontinuum (SC) generation is very active. Various nonlinear fiber based SC light sources have already found numerous technological applications so far, which involve optical frequency metrology, multi-wavelength optical source, and pulse compression, etc [1]. Typical SC light source comprises mainly a nonlinear fiber with engineered dispersion, and a femtosecond or picosecond pulsed pump laser. The pump wavelength is in the anomalous dispersion region and close to the zero dispersion wavelength (ZDW). Compared with picosecond pump pulse, femtosecond pump pulse can induce a broader SC spectrum in the same fiber pumped with a similar pulse-energy. Additionally, when femtosecond pulse is short enough to ensure a low soliton order, the SC generation can have a good coherence [2]. However, for many applications where coherence is not indispensable, more consideration is given to characteristics such as economy, power scalability, and performance stability. In those cases picosecond-pulse-pumped SC source is advantageous. In the picosecond regime, the output spectral shape and bandwidth of SC are less sensitive to the fiber lengths and the chirp parameter of pump pulse than in the femtosecond regime [3,4]. In particular, pump pulse with temporal width broader than 10 ps is preferable because it can avoid the complications and inconveniences of complex femtosecond oscillators [5]. Actually SC sources with picosecond or even longer pump pulses have been utilized widely in many biophotonics applications [6–9].
In the picosecond regime, since the pulse is wide temporally, to ensure a flat and broadband SC generation, a high pump-pulse-energy was required to provide a high pump peak power. The mode-locked picosecond pulsed laser always has a repetition rate of at least several tens of kHz. Therefore the pump laser is necessary to have a comparatively high average power. Consequently, if the flatness and bandwidth of SC are highly demanded, the power density must be high simultaneously. However, for some applications the SC power density is not necessary to be high. In these cases the SC light source pumped by picosecond pulse is not really economical.
In this work, we try to develop a broadband and flat SC light source by a low pump power. To be cost-effective, in the scheme neither femtosecond pulsed laser nor high power picosecond pulsed laser is indispensable. We have adopted a microstructured fiber with an extremely high nonlinearity as well as tailored dispersion. The fiber is made of tellurite glass, which has the nonlinear refractive index higher than silica glass by more than one order of magnitude. Compared with other highly nonlinear soft glass fibers, for example, chalcogenide or fluoride fiber, tellurite fiber has a high chemical stability at fiber drawing temperature, and therefore can be fabricated without special protective atmosphere which is complicated and expensive. In our scheme the tellurite fiber is tapered to have a 30-cm-long section which has a core diameter of 0.9 μm and a zero dispersion wavelength around the pump wavelength. Such a core size and a dispersion profile were chosen to ensure the SC was mainly broadened by phase matched four-wave mixing (FWM).
The tapered fiber has some important advantages. Firstly, the nonlinearity is improved, and the dispersion is tailored. Secondly, the fiber is convenient for coupling at the enlarged fiber end. It is very helpful, since most of the highly nonlinear fibers are not convenient for coupling due to their ultra small core diameters. Thirdly, the damage threshold is increased. Generally at the tip of coupling, the fiber exhibits the highest temperature. The temperature decreases approximately exponentially along the fiber length [10]. The damage always firstly occurs at the tip of coupling. The damage threshold of whole fiber is mainly determined at the tip. An enlarged core can have a high damage threshold, so a high pump power can be adopted. In our work, by using a short tapered tellurite fiber pumped by a 15-ps-pulsed laser, we obtained SC light source which spans from UV to mid IR (10 dB bandwidth: 780-1890 nm).
2. Experiment
The composition of tellurite glass and detailed fabrication process of fiber can be found elsewhere [11]. The longitudinally varying diameter was realized by changing the speed of fiber drawing. A 75-cm-long fiber was used to generate SC. The dependence of core diameter on the fiber length is shown in Fig. 1(a) . The fiber is characterized with a short section with a large diameter followed by a long section with a small diameter. It is different from previous fibers reported in [12] and [13] where most section has a large constant diameter and only a small portion around center is tapered. The original core diameter was 2.8 μm. The smallest core diameter was 0.9 μm. It is predicted from the outside diameter. A cross section of the fiber with the core diameter of 0.9 μm is shown in inset of Fig. 1(a).
Fig. 1 (a) The core diameter along the fiber length. Inset shows the cross section of the fiber with the core diameter of 0.9 μm. (b) Chromatic dispersion of the tellurite microstructured fiber with different core diameters, and dependence of the nonlinear coefficient on the core diameter.
The pump source was a commercially available 1064 nm picosecond pulsed fiber laser. The pulse width was 15 ps and the repetition rate was 80 MHz. The laser was connected to a single-mode fiber (SMF) by a connector. The beam from the SMF was collimated into parallel by a lens with a NA of 0.25. The parallel beam was focused and coupled into the tellurite microstructured fiber by a lens with a NA of 0.40. The coupling efficiency, defined as the launched power divided by the power incident on the lens, was about 30%. The fiber was pumped at the facet with the large diameter. The output end of the microstructured fiber was mechanically spliced with a silica large-mode-area-fiber by using the butt-joint method. The other end of the large-mode-area-fiber was connected to an optical spectrum analyzer (OSA).
3. Results and discussions
The fully vectorial finite difference method was used to calculate the wavelength dependent propagation constants from which the chromatic dispersion was calculated. Figure 1(b) shows the calculated dispersion. With the decreasing core diameter, the dispersion decreases, and therefore the ZDW shifts to short wavelengths. For the core diameters of 2.8 μm, 1.8 μm, 1.1 μm, and 0.9 μm, the ZDWs are 1465 nm, 1240 nm, 1110 nm, and 1070 nm, respectively.
The nonlinear coefficient was calculated by:
where λ is the wavelength, F(x,y) is the profile of the field, and n2 is the nonlinear refractive index. n2 of tellurite glass is 5.9 × 10−19 m2/W and λ is 1064 nm. The calculated dependence of nonlinear coefficient on the core diameter is also shown in Fig. 1(b). For the largest core diameter it is 0.80 m−1W−1, and for the smallest core diameter it is 5.5 m−1W−1. The nonlinearity is improved around 6 times by reducing the core size.
The measured peak-power-dependent SC spectra in the tapered microstructured fiber are shown in Fig. 2(a) . In [14] we have demonstrated the SC generation of a suspended nanowire with a core diameter of about 480 nm pumped by a 1557 nm laser with the same method of coupling. The coupling efficiency is only 2%. In this work, the coupling efficiency is much higher. The bandwidth increases with the increase in peak power of the launched pulse. With the highest peak power of 375 W (corresponding to an average power of 450 mW), the SC spectrum covers 350-2000 nm, which spans from UV to mid IR. The 10 dB bandwidth of SC spectrum, covering 780-1890 nm, is more than one octave, if the strong pump peak is excluded. Figure 2(b) shows the fiber glows blue under the maximum pump power. The visible light is obvious only at the end segment of the fiber, around 20 cm long. For the ultra small core fiber, one of the main losses is the scattering loss originated from the roughness of the inner surface of the holes [15]. The scattering loss is inversely proportional to the fourth power of wavelength. So the fiber glows blue because the blue light suffers a high scattering loss.
Fig. 2 (a) Measured peak-power-dependent SC spectra in the tapered microstructured fiber. The curve is displaced by 15 dB. (b) The fiber glows blue with the input peak power of 375 W. (c) Simulated SC spectrum in a 30-cm-long fiber with the core dimeter of 0.9 μm.
We also measured a 50-cm-long tellurite microstructured fiber with a constant core diameter of 2.8 μm in the same way. The results (not shown) are very similar to that in [16]. Under the maximum pump power we could only observe the emission peaks of three orders of stimulated Raman scattering (SRS). Since the pump wavelength of 1064 nm locates in the normal dispersion region and is far from the ZDW, FWM is difficult to occur. Additionally the pump pulse is not short enough for effective self phase modulation. So only separated SRS peaks were observed. Therefore, in Fig. 2(a) the broadening of SC occurs mainly after the segment with the core diameter of 2.8 μm, mainly in the segment with the core diameter of 0.9 μm. To confirm this, we simulated the SC generation in a 30-cm-long fiber with the core diameter of 0.9 μm by solving the generalized nonlinear Schrödinger equation with split-step Fourier method. We adopted the dispersion data at 1064 nm shown in Fig. 1(b). Up to tenth-order dispersion was used. The peak power of the pump pulse was 375 W. The simulated curve is shown in Fig. 2(c). It indicates the broadest spectrum of the demonstrated SC can be generated by the last 30-cm-long nanofiber.
In Fig. 2 (a), FWM is the dominant mechanism of the SC broadening. The phase matched conditions of FWM can be calculated by [17]:
In Eq. (2) P0 is the pump power, and is the linear phase mismatch, where β2,4 are the dispersion parameters at the pump wavelength, and Ωs is the frequency shift. The phase matched conditions under different pump powers for the microstructured fiber with the core diameter of 0.9 μm is shown in Fig. 3(a) . The parametric wavelengths approximately coincide with the blue and red shift wavelengths of SC spectra, if the weak visible emissions are neglected.
Fig. 3 (a) Phase matched conditions of FWM in the tellurite microstructured fiber with the core diameter of 0.9 μm. Legend shows the peak power of the pump pulse. (b) Soliton wavelength vs. wavelength of dispersive wave for the tellurite microstructured fiber with different core diameters.
In this SC demonstration, the core diameter and dispersion profile of the last 30-cm-long nanofiber are crucial to the flatness and bandwidth of the spectrum. If the core diameter is larger than 0.9 μm, as shown in Fig. 1(b), the fiber is in the deep normal dispersion region at the pump wavelength. The gain of FWM will be low. Meanwhile the fiber nonlinearity will be reduced. If the threshold of FWM is higher than SRS, FWM will be depressed. The SC spectrum will not be so flat due to the SRS peaks. An example of this situation can be found in [13]. If the core diameter is smaller than 0.9 μm, the fiber is in the anomalous dispersion region at the pump wavelength. Modulation instability and solitons will be dominant and they will depress FWM. In this case the SC spectrum only exhibits red shift, which has been proved in [11].
The weak visible emissions are ascribed to the dispersive waves of solitons. A similar situation can be found in Fig. 2 of [18]. The ZDW of the fiber with the core diameter of 0.9 μm is 1070 nm, the SC components with wavelengths longer than the ZDW are in the anomalous dispersion region. The modulation instability can induce the breakup of the pulse envelope and lead to the formation of solitons. Additionally, it can be found from Fig. 1(b) that the dispersion curve has a large slope. The difference in dispersion between the blue and red shift components is large. The walk-off length is short. For example, for the core diameter of 0.9 μm, the calculated walk-off length between 1600 nm and the pump wavelength is only 17 cm. The walk-off between input pulse and generated frequencies must occur, which also leads to the formation of solitons. Dispersive waves are often accompanied with solitons. The phase matched conditions between dispersive wave and solitons are given by Eq. (3) [19]:
where ωs and Ps are the soliton’s centre frequency and peak power respectively, ωDW is the frequency of dispersive wave, and βn is the n-th order derivative of the frequency-dependent wave vector. The calculated wavelengths of dispersive waves vs. the soliton’s center wavelengths with various core diameters are shown in Fig. 3(b). In this calculation Ps was 375 W, which was the highest peak power of the input pulse. For a fiber with a core diameter of 0.9 μm, the solitons at the wavelengths around 1600 nm correspond to the dispersive wave in the blue band.
Table 1 lists the SC generations by various highly nonlinear fibers in picoseconds regime. Conventionally, for the SC generation in silica fibers, the pump power has to be very high to obtain a flat spectrum and an octave-bandwidth. However, for our highly nonlinear tapered microstructured fiber, a pump source with an extremely high power is not indispensable to obtain a broad and flat SC generation.
Table 1. Various highly nonlinear fibers and their SC generations in picosecond regime. 10 dB bandwidths were obtained from the SC spectra in the publications. When determining the 10 dB bandwidth, the strong pump peak was excluded.
4. Summary
By using a highly nonlinear tapered tellurite microstructured fiber with an elaborately chosen dispersion profile and an extremely high nonlinear coefficient, we demonstrated broad and flat SC generation by the pump of a 15-ps-pulsed laser with the input peak power of 375 W. The SC light spans from UV to mid IR. The 10 dB spectrum is from 780 to 1890 nm. For the applications of SC where just the flatness and wide bandwidth are highly required, our scheme provides a cost-effective option, since neither femtosecond pulsed laser nor high power picosecond pulsed laser is necessary.
Acknowledgments
Meisong Liao acknowledges the support of the JSPS Postdoctoral Fellowship. The authors acknowledge the support of MEXT, the Support Program for Forming Strategic Research Infrastructure (2011-2015).
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