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Fiber based supercontinuum (SC) sources with output spectra covering the infrared atmospheric window are very useful in long-range atmospheric applications. It is proven that silica fibers can support the generation of broadband SC sources ranging from the visible to the short-wave infrared region. In this paper, we present the generation of an ultrahigh-brightness spectrally-flat 2-2.5 μm SC source in a cladding pumped thulium-doped fiber amplifier (TDFA) numerically and experimentally. The underlying physical mechanisms behind the SC generation process are investigated firstly with a numerical model which includes the fiber gain and loss, the dispersive and nonlinear effects. Simulation results show that abundant soliton pulses are generated in the TDFA, and they are shifted towards the long wavelength side very quickly with the nonlinearity of Raman soliton self-frequency shift (SSFS), and eventually the Raman SSFS process is halted due to the silica fiber’s infrared loss. A spectrally-flat 2-2.5 μm SC source could be generated as the result of the spectral superposition of these abundant soliton pulses. These simulation results correspond qualitatively well to the following experimental results. Then, in the experiment, a cladding pumped large-mode-area TDFA is built for pursuing a high-power 2-2.5 μm SC source. By enhancing the pump strength, the output SC spectrum broadens to the long wavelength side gradually. At the highest pump power, the obtained SC source has a maximum average power of 203.4 W with a power conversion efficiency of 38.7%. It has a 3 dB spectral bandwidth of 545 nm ranging from 1990 to 2535 nm, indicating a power spectral density in excess of 370 mW/nm. Meanwhile, the output SC source has a good beam profile. This SC source, to the best of our knowledge, is the brightest spectrally-flat 2-2.5 μm light source ever reported. It will be highly desirable in a lot of long-range atmospheric applications, such as broad-spectrum LIDAR, free space communication and hyper-spectral imaging.
© 2016 Optical Society of America
1. Introduction
Fiber based supercontinuum (SC) sources [1–3] have become the ultimate “white-light” sources in lots of applications in which they can play a decisive role, including frequency clocks [4], tomography [5], optical communication [6], broad-spectrum LIDAR [7], atmospheric science [8], etc. In particular, SC sources which locate at the atmospheric window benefit from low propagation loss and could be applied into long-range atmospheric applications [9–11]. These applications include active infrared illumination [12], hyper-spectral imaging [13], free space communication [14] and environmental sensing [15], where a broadband SC source is the prerequisite. It is worth to note that the working distance could be greatly extended if the SC source has a high brightness.
The atmospheric window at 2-2.5 μm locates at the short-wave infrared (SWIR) region, which bridges the SWIR region and the mid-infrared region. With the development of thulium-doped fibers (TDFs), many 2 μm fiber lasers with versatile output have been reported [16–23]. This development also provides an active approach for the generation of broadband 2-2.5 μm SC sources from thulium-doped fiber amplifier (TDFAs) directly [24]. Different from the traditional passive approach for SC generation where high intensity laser pulses are used to pump a piece of passive nonlinear fiber, this active approach takes advantages of both the gain and the nonlinearity in a TDFA. Note that this active approach is similar to the 1-2 μm SC generation in ytterbium-doped fiber amplifiers [25] which has been demonstrated as the most efficient way to obtain SC source with high power spectral densities [26, 27]. At present, there has been some reports on 2-2.5 μm SC generation from TDFAs [28–36]. And these reports show that this active approach brings at least two advantages: first, the gain from a TDFA could augment the power spectral density of the 2-2.5 μm SC source. Secondly, the long wavelength side of the SC source could be further extended about 200 nm deep into the high loss region of silica fibers.
In 2012, Geng et al reported an SC with a 3 dB bandwidth of ~600 nm from ~1.9 to 2.5 μm in a single-mode TDF [28]. However, the output power was limited at the ~100 mW level by the small core diameter of the single-mode TDF. Soon people found that by adopting the cladding-pumping scheme [37] with large core double-cladding TDFs, the average power of the 2-2.5 μm SC source could be scaled remarkably. In 2013, Alexander et al presented a high-power 2-2.5 μm SC source based on a large-mode-area (LMA) TDFA which was cladding pumped at 793 nm [38]. The generated SC source had a maximum output power of 25.7 W with a conversion efficiency of ~23% from the pump source. They also demonstrated this SC source could be used as an infrared illuminator to replace a halogen lamp in spectroscopy. However, due to the fact that the spectrum of the 2-2.5 μm SC source partly locates at the high loss region of silica fibers beyond 2.4 μm [39], it is difficult to reach much higher power level unless the SC conversion efficiency gets higher and an efficient thermal management is adopted. In 2015, by seeding a TDFA with a seed duty cycle of 1.4%, we scaled up the conversion efficiency of a 2-2.5 μm SC source to 35.4% [40]. This high conversion efficiency guaranteed the generation of a stable hundred-watt-level 2-2.5 μm SC source.
Regardless of these previous experimental studies [28–40], there is no detailed theoretical investigation on the 2-2.5 μm SC generation in a TDFA at present. In fact, the combined function of gain amplification, fiber dispersion and nonlinear effects is very complex so that related theoretical research has been rarely discussed. However, it is very essential and indispensable to find out the detailed SC generation process for better understanding the related physical mechanisms and for customizing the output power and spectral characteristics of the 2-2.5 μm SC source.
In this paper, a simplified model is employed to simulate the spectral and temporal evolutions of a seed pulse amplified in a cladding pumped TDFA. The amplifier model includes the gain, the loss, the nonlinearity, and the dispersion characteristics of the TDF (the host material is silica glass). Details of the SC generation process in the TDFA are investigated numerically, showing that a spectrally-flat 2-2.5 μm SC source could be generated as the result of the superposition of abundant soliton pulses (generated in the TDFA). The long wavelength side of the 2-2.5 μm SC source is limited by the intrinsic loss of silica. With the understanding of these physical mechanisms, a high duty cycle of the seed pulse and a short length of the gain fiber are adopted in the experiment to acquire a high SC conversion efficiency in the TDFA. An ultrahigh-brightness, spectrally-flat 2-2.5 μm SC source with the maximum output power of 203.4 W is obtained. The SC has a 3 dB spectral bandwidth of 545 nm ranging from 1990 to 2545 nm. The output SC source has a Gaussian-shaped beam profile. To the best of our knowledge, this is the brightest broadband light source at 2-2.5 μm ever reported.
2. Numerical modelling
2.1 GNLSE
In order to model the SC generation process inside a cladding pumped TDFA, we use generalized scalar nonlinear Schrödinger equation (GNLSE) in which the fiber gain and loss, the dispersive and nonlinear effects are considered [41–43]. For the sake of simplicity, the gain saturation, the time-dependent gain profile are neglected in the GNLSE.
where A is the field envelope in the time domain, z is the propagation distance along the gain fiber, α is the fiber linear loss, g is the fiber gain. T is the time parameter after the change of the variable T = t-z/β1. The βk represents the k-th order dispersion coefficient associated with the Taylor series expansion of the propagation constant β(ω) at ω0. γ is the nonlinear coefficient. The time scale parameter τshock is associated with effects such as self-steepening and optical shock formation. R(T) is the response function of silica fiber including both the instantaneous electronic and the delayed Raman contributions.
The TDF fiber used in the simulation is the same as the one used in the experiment which has a core/cladding diameter of 25/250 μm. The initial input pulse has a hyperbolic secant field profile to mimic the experimental seed pulse, with a pulse duration of 100 fs and a peak power of 10 kW. It has a central wavelength of 2000 nm. In the simulation, the input seed pulse also contains a shot noise by adding one photon per mode with random phase into each frequency bin [44]. The whole GNLSE is transformed into the frequency domain [2] and is sovled with a fourth-order Runge–Kutta method.
2.2 Gain and loss profiles
Here, the only role of thulium ions is to provide the gain in the simplified model. Note that the gain of TDFA around 2 μm depends not only on the absorption and emission cross sections of thulium ions [45] but also on the population of thulium ions in the upper 3F4 energy level [46]. So that the gain profile will vary along the fiber, depending on the pumping strength and configuration [47]. It has been shown that the gain per unit length for each signal frequency is given by [46, 48].
where N0 is the dopant concentration per unit volume of thulium ions in the fiber core, Г is the signal filling factor, n2 is the normalized excited population on the 3F4 energy level. Basically, the value of n2 relates to the accumulation and extraction of the stored energy in the gain fiber. The accumulation process depends on the pumping strength, while the stored energy will be extracted by the input seed pulse. Particularly, n2 could get very high when the amplifier is under strong pumping. Figure 1 plots the gain and loss distributions of the TDFA in the simulation for forward pumping regime. The gain is obtained by calculating Eq. (2). The adopted loss profile of the TDFA is the loss of silica fiber [39].
Fig. 1 Gain and loss distributions used in the simulation. The TDFA is forward cladding pumped at 793 nm. The normalized excited population n2 is exponentially distributed along the fiber length with values of 0.09 at z = 0 m and 0.033 at z = 3 m.
Obviously, as shown in Fig. 1 the gain and loss profiles could be divided into three areas by two curves (marked with “0”). The left area represents the high absorption region of the gain fiber. The middle area shows the z-dependent gain profile by adopting an exponentially distributed normalized excited population n2. As it shows that the gain peak wavelength of the TDF is red-shifted along with the fiber position [46] together with the decreasing of the gain. The right area is the high loss region of the gain fiber, showing that the longer the wavelength is, the higher the loss is.
3. Results and discussions
3.1 Spectral and temporal evolutions
The results presented here as shown in Fig. 2 illustrate the dynamics of the spectral and temporal evolutions of the seed pulse in the TDFA. It is shown on a logarithmic scale to illustrate the fine evolutions of the seed pulse.
Fig. 2 Results from numerical simulation showing the (a) spectral and (b) temporal evolutions for the SC generation process in a TDFA. The relative intensity are plotted on a logarithmic scale. (c) Output SC spectrum at the end of the TDFA.
As can be seen in Fig. 2(a), from z = 0 to 0.6 m, the energy of the seed pulse is scaled up and its spectrum is broadened slightly. Meanwhile, impacted by the anomalous dispersion of the gain fiber the seed pulse broadens to picosecond scale (see Fig. 2(b)). With propagation, the pulse energy is scaled continuously until it reaches a critical value where the pulse itself suffers dramatic temporal modulation, and then a high-peak-power soliton pulse is generated. After that, the soliton pulse is red-shifted towards the long wavelength side by the well-known optical nonlinearity of intra-pulse Raman soliton self-frequency shift (SSFS) rapidly [41]. However, when the central wavelength of the soliton pulse is red-shifted to ~2.5 μm, the high fiber loss of ~3dB/m attenuates the soliton pulse energy and stops the Raman SSFS. So that due to the decay of the peak power, the soliton pulse could not be red-shifted any more.
It is particularly clear to see that although the generated first soliton pulse is red-shifted off the gain area of the TDFA and cannot be amplified any more, the residual light around 2000 nm could be amplified continuously and emit a subsequent soliton pulse. Similarly, the new soliton pulse is red-shifted to the long wavelength side but halted at ~2.5 μm. This process is repeated until the input seed pulse gets through the amplifier, making the TDFA like a “soliton generator” in which abundant soliton pulses are generated. Finally, as can be seen from Fig. 2(c) the super-position result of abundant soliton pulses shapes an SC source with a spectrum from 2 to 2.5 μm. What’s more, the accumulation of a lot of soliton pulses results in a spectral peak around 2.5 μm on the SC spectrum which is also demonstrated in the latter experiment. The simulation result presented here shows that with sufficient gain in the TDFA, even a single ultrafast seed pulse could eventually form a 2-2.5 μm SC pulse.
3.2 Spectrogram representations
In order to better understand the SC pulse generation and the Raman SSFS process, we also plot the spectrogram representations of the SC pulse at z = 1.5 m and z = 3 m in Figs. 3(a) and 3(b), respectively. Two dotted lines are used to divide the soliton pulses and the residual light. As can be seen, the generated soliton pulses could be identified clearly with their ~100 fs temporal durations. The central wavelengths of these soliton pulses locates at 2 to 2.5 μm. Note that in the anomalous dispersion region, light with longer wavelengths travel much slower than those with shorter wavelengths. Due to the different group velocities of the soliton pulses and the residual light, the envelope of SC pulse broadens to a temporal width of ~25 and ~70 ps at the fiber position of z = 1.5 and 3.0 m, respectively.
Fig. 3 Spectrogram representations of the simulated SC pulse (a) at z = 1.5 m and (b) at z = 3.0 m. The inset in (a) shows a zoom view of a single soliton pulse. The relative intensity are plotted on a logarithmic scale.
Meanwhile, the previous generated soliton pulses have suffered with attenuation because that they have been already shifted into the high loss region of the fiber. As shown in Fig. 3(b), the relative intensities of these soliton pulses are decreased and the Raman SSFS processes are stopped, resulting that the central wavelengths of decayed soliton pulses locate at ~2.5 μm.
It is noted that the attenuation of these long wavelength soliton pulses brings a heat source along the gain fiber. The temperature of the fiber core will increase remarkably if a high-average-power 2-2.5 μm SC is generated. Although the silica glass has a high melting temperature of ~1700 degrees Celsius [49], the thermal performance of protective polymer coatings will limit the power scaling of the 2-2.5 μm SC. Therefore, a good thermal management is very critical for the high-average-power 2-2.5 μm SC generation.
4. Experiment details
4.1 Experimental setup
Figure 4 depicts the detailed experimental setup of the ultrahigh-brightness 2-2.5 μm SC source. The SC source has an all-fiber configuration with two parts: a low-power 1.5-2.3 μm SC as the seed SC and a TDFA. The seed SC is obtained by injecting high peak power laser pulses at 1550 nm into a 28 m-long of single-mode silica fiber. The seed SC pulse has a duration of ~7 ns with a repetition rate of 4 MHz. The anomalous dispersion of the single-mode silica fiber beyond 1500 nm leads to abundant ~100 fs pulses with central wavelengths locating at 1.9-2.2 μm in the seed SC pulse [41]. According to the numerical investigations, these ~100 fs pulses could be amplified since their spectra locate in the gain spectrum of the TDFA (as shown in Fig. 1). Spectral broadenings of these amplified seed pulses will result in the generation of a 2-2.5 μm SC. It is noted that although the temporal duration of each femtosecond pulse in the seed SC is at the scale of ~100 fs, the whole SC pulse duration of ~7 ns and the repetition rate of 4 MHz make the seed SC a nominal duty cycle of 2.8%.
Details of the TDFA are given in the following. Six LDs at 793 nm pigtailed with 200/220 μm multi-mode passive fibers are employed as the pump light. A (6 + 1) × 1 signal and pump light combiner is used to couple the pump light and the seed laser into the gain fiber. The total pump light could reach 518 W after the combiner. The gain fiber is a 3 m-long of LMA-TDF which has a core/cladding diameter of 25/250 μm. The cladding absorption coefficient of the LMA-TDF is ~9 dB/m at 793 nm. Therefore, the total absorption of the pump light at 793 nm is calculated to be as high as ~27 dB which ensures efficient absorption. The effective core NA values of the LMA-TDF is 0.11. The LMA-TDF is coiled on a radius of 7 cm to suppress high order modes. A high-power cladding light stripper with matched passive fiber is spliced to the LMA-TDF to dump the residual pump light. The fiber length of the stripper was cut to ~0.5 m to reduce the attenuation of the 2-2.5 μm SC source. An endcap made of a piece of multi-mode coreless silica fiber (a diameter of 400 μm) is spliced to the other end of the stripper to suppress the unwanted optical feedback due to the Fresnel reflection. The length of the coreless silica fiber is ~0.5 mm to ensure a good beam quality.
Due to the high pump absorption, quantum defect, nonradiative transition [50] and high attenuation of the generated SC source beyond 2.5 μm [39], a lot of heat will be loaded along with the gain fiber and the stripper. So that, both the gain fiber and the stripper are placed in a water-cooled conductive heatsink to dissipate the heat at a cooling temperature of 10 degrees Celsius. The passive fiber of the stripper before the endcap is placed into a water-cooled V-groove mounted on a 6-axis stage. The output SC is collimated with an off-axis gold parabolic mirror when characterizing its spectra and beam profiles.
4.2 Characterizing system
As shown in Fig. 4, the SC characterizing system includes a wavelength-insensitive thermal power meter to measure the SC power, a grating-based monochromator together with a liquid-nitrogen-cooled InSb detector (with integration time of 1 ms) to measure the SC spectrum, and an infrared HgCdTe camera to capture the beam profile of the SC. Considering the setup of 1 ms integration time of the InSb detector and the 4 MHz repetition rate of SC pulses, the measured SC spectra are averaged over 4000 pulses.
5. Experimental results and discussions
5.1 SC spectrum
The average output power of the seed SC is ~7 W. After the TDFA the spectral components from 1.5 to 1.95 μm are absorbed by the TDF, and only 2.56 W beyond 1.95 μm is left. By increasing the pump power at 793 nm, the output power of the SC light can be scaled up. Figure 5 plots the measured SC spectra at different output power. Note a femtosecond pulse in the seed SC could be amplified effectively as long as its spectrum matches the gain spectrum. By enhancing the pump strength, the total gain provided by the TDFA is increased too. As can be seen, the output spectrum firstly broadens to the short wavelength side slightly due to the fiber gain when the pump power is at a low level. At this time, no obvious nonlinearity happened. With the increasing of the pump power, the pulse energies of some seed femtosecond seed pulses can be scaled up remarkably and emit more and more soliton pulses. With the help of Raman SSFS, the output SC spectrum broadens to the long wavelength side gradually. More and more soliton pulses are generated which could be inferred from the increase of the spectral components beyond 2200 nm. As we have discussed in the section of numerical modeling, the superposition of those abundant soliton pulses finally forms a 2-2.5 μm SC source.
Fig. 5 Evolution of the SC spectrum by increasing the pump. The powers in the legend indicate the output SC power versus the pump power.
In the experiment, the higher the obtained SC power is, the broader the SC spectrum is. When the output SC power is 75.6 W, the long wavelength side of the output spectrum reaches ~2600 nm. But the output spectrum is not flat. Fortunately, the spectral components beyond 2200 nm could be scaled up by further increasing the pump. Finally, when the pump power is increased to 518 W, the output SC power is measured to be the maximum of 203.4 W. Meanwhile the spectral components of the SC source broaden to ~2700 nm. The SC spectrum at its maximum output power is very flat with a 3 dB spectral bandwidth of 545 nm spanning from 1990 to 2535 nm.
5.2 SC power
Figure 6 plots the evolution of the output SC power with respect to the pump power at 793 nm. Obviously, in the experiment the linear fitted slope efficiency of the TDFA decreased from 51.3% to 33.6% with the increasing of the pump power. In fact, when the pump power is higher than 200 W, the output SC spectrum has already become flat with comparative spectral components locating beyond 2400 nm. Note the decrease of the slope efficiency relates to the attenuation of the SC source beyond 2400 nm by the fiber. The maximum output SC power is 203.4 W with an optical conversion efficiency of 38.7% with respect to the 518 W pump power in the TDFA. Inset of Fig. 6 shows the photograph of the power meter when the SC power reaches its maximum.
Fig. 6 Evolution of the SC power with respect to the pump power at 793 nm. The inset shows the photograph of the power meter when the output power is 203.4 W.
5.3 Beam profile
Further, the beam profile of the output SC source is investigated with an infrared HgCdTe camera in the far filed. The collimated SC beam is directed onto an aluminum plate placed at a distance of 5 m. The camera is placed at another 5 m away from the SC spot to capture the diffuse reflection light. Gaussian-shaped beam profiles at different output powers are captured indicating that the beam profile of the SC is relatively well maintained during power scaling. The results are consistent with the fact that the output SC operates in fundamental mode (near diffraction limit) although the gain fiber supports a few modes. Figure 7 shows the measured beam profile when the SC output power is 203.4 W. The result are averaged over 200 frames.
5.4 Discussions
In order to show that the potential atmospheric applications of the obtained ultrahigh-brightness 2-2.5 μm SC source, we plotted the SC spectrum at the maximum output power of 203.4 W together with the atmospheric transmission spectrum for comparison in Fig. 8. The atmospheric transmission spectrum is simulated using the HITRAN database [51]. The atmospheric model used here is: middle latitude summer, rural aerosol model with 23 km visibility, altitude of 0 m, CO2 mixing ratio of 400 ppm and a horizontal path of 1 km. It is noted that the SC spectrum covers the 2-2.5 μm atmospheric window very well. The transparency window of the atmosphere and broadband spectrum make this SC source very useful for applications requiring long-range atmospheric propagation. Additionally, there are at least four gas molecules (H2O, CO2, CH4 and N2O) whose absorption lines locate in the spectral range of the SC source, which indicates the potential applications of this SC source in long-range air monitoring.
6. Summary
In conclusion, we present an ultrahigh-brightness, spectrally-flat SC source based on a cladding-pumping TDFA which has a broadband spectrum covering the atmospheric transmission window at 2-2.5 μm. Numerical investigations indicate the related physical process during the SC generation in the TDFA in details. It is found that the abundant soliton pulses generated from the TDFA together with the Raman SSFS process mainly shape the output SC spectrum. In the experiment, the obtained SC has a maximum output power of exceeding 200 W, and the corresponding SC spectrum has a 3 dB spectral bandwidth of 545 nm. The overall conversion efficiency from the pump power to the SC power is as high as 38.7%. The SC light has a good beam profile and it is believed to be useful in lots of long-range atmospheric applications.
Funding
National Natural Science Foundation of China (61235008, 61405254 and 61435009); National High Technology Research and Development Program of China (2015AA021101); Graduate Student Innovation Foundation of National University of Defense Technology (B150703).).
Acknowledgments
We thank Dr. Aijun Jin for his discussion with the numerical methods in solving the GNLSE. We also thank Dr. Wuming Wu for his help in simulating the atmospheric transmission spectrum.
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