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In this paper, an investigation on broadband IR supercontinuum generation in single crystal sapphire fibers is presented. It is experimentally demonstrated that broadband IR supercontinuum spectrum (up to 3.2µm) can be achieved by launching ultra-short femtosecond laser pulses into single crystal sapphire fiber with a dimension 115µm in diameter and 5cm in length, which covers both the near IR spectral region and the lower end of the mid-IR spectral range. Furthermore, the mechanism of supercontinuum generation in single crystal sapphire fibers is briefly addressed. When the fiber length is shorter than the dispersion length, the self-phase modulation dominates the broadening effect. In this case, the broad supercontinuum spectrum with a smooth profile can be obtained. However, when the fiber length is longer than the dispersion length, the soliton-related dynamics accompanied by the self-phase modulation dominates the broadening effect. There are discrete spikes in the spectrum (corresponding to different order solitons). The above assumption of supercontinuum generation mechanism is quantitatively modeled by the computer simulation program and verified by the experimental results. Thus, one can adjust the spectral profile by properly choosing the length of the sapphire fibers. The broad IR spectral nature of this supercontinuum source can be very useful in a variety of applications such as broadband LADAR, remote sensing, and multi-spectrum free space communications.
©2008 Optical Society of America
1. Introduction
Extreme broadening of a narrow spectral laser pulses can be realized via the nonlinear interactions between the laser pulses and the optical medium in which they are traveling. This process is often referred as supercontinuum generation (SCG).
In recent years, the interest in broadband mid-IR light sources has increased due to the critical need of a variety of applications such as IR spectroscopy, broadband laser radar (LADAR), and combustion monitoring [1,2]. Conventional sources such as optical parametric amplifiers (OPOs), tunable solid-state lasers, and quantum cascaded lasers (QCLs) are currently utilized for these applications [3]. However, wavelengths of OPOs and QCLs need to be continuously tuned to cover the entire spectral range needed. Compared to these conventional sources, a supercontinuum source has the advantage of covering a wider range of spectrum without the time delay caused by the wavelength tuning of conventional sources.
In the past decade, near IR (<2µm) ultra-broadband supercontinuum (broadened by >1000 nm) sources have been successfully created by launching femtosecond laser pulses into highly nonlinear silica fibers [4–6]. Such kinds of near IR supercontinuum sources have also been applied for several applications including optical coherence tomography [7, 8], optical metrology [9, 10], telecommunications [11, 12] and spectroscopy [13].
Even though some papers have shown SCG in silica-based fibers that extend into mid-IR region, SCG in silica materials are limited by heavy material absorption in the mid-IR region [1]. To realize the SCG in the mid-IR region, IR glass fibers are commonly employed [2,14,15,16]. Although mid-IR SCG have been successfully generated in these IR glass fibers, it is difficult to achieve very high power supercontinuum sources because of the lower softening temperature of these IR glass fibers [e.g., around 455 °C for ZBLAN Fluoride fiber [17], 600 °C to 900 °C for Chalcogenide fiber [15], and 538 °C for SF-6 fiber [18], which are lower than that of silica fibers (~1175 °C) [19]].
Besides glass materials, single crystal sapphire materials (in both the bulk and fiber form) can also be harnessed for the mid-IR SCG because sapphire materials (1) are transparent up to 5µm, (2) have a good value of nonlinear refractive index around n2=2.8×10-20m2/W [20], and, in particular, have a very high melting temperature (>2,000 °C) that enables high power mid-IR SCG. Furthermore, the growing of single crystal sapphire fibers [e.g., by using the laser heated pedestal growth (LHPG) [21–23]] has become a mature technology. In a recent previous paper [24], we demonstrated that, indeed, SCG could be realized in single crystal sapphire fiber and the fiber form offered a higher SCG generation efficiency due to the light confinement effect of the fiber. However, due to the limitation of the experimental setup at that time, we were unable to achieve SCG beyond 2µm. Moreover, there was also a lack of detailed investigation on the mechanism of SCG in sapphire fibers in this previous paper.
To overcome the aforementioned limitations of the previous paper [24], in this paper, we report the recent advances on SCG in single crystal sapphire fibers, including (1) a very broad supercontinuum spectrum (from 1.2µm to 2.8µm and from 2µm to 3.2µm) that also covers a portion of mid-IR spectrum (i.e., beyond 2µm) and (2) a more detailed study on the mechanism of SCG in single crystal sapphire fibers by analyzing and experimentally demonstrating the relationships among the shape of spectral profile, the geometrical length of the sapphire fiber, and the dispersion length of the sapphire fiber.
2. Technical approach
It is well known that SCG can be mathematically described by the nonlinear-Schödinger equation (NLSE) [24, 25]:
where A(T,z) is the complex amplitude of the light field at the axial location z at time T, α represents the fiber loss, βk(k=2,3) denote the second and the third coefficients of the Taylor-series expansion of the propagation constant β around ω0, and γ represents the nonlinearity coefficient. Since the sapphire fiber, used in our experiment, is highly multimode (with a diameter over a hundred micron), the dispersion effect is dominated by the material dispersion of the fundamental mode [26]. Furthermore, because a c-axis sapphire fiber is employed in the experimental study, only the ordinary refractive index needs to be considered. The ordinary refractive index of the sapphire material as a function of wavelength can be described by the following Sellmeier equation [27]:
Then, the material dispersion parameter, D, can be determined from the second derivative of n(λ), as given by [28]:
Figure 1 shows the calculated material dispersion as a function of wavelength for the sapphire fiber based on Eq. (3). At 2µm, the pumping wavelength, used in our experiments, the dispersion parameter, D, is about 57.28ps/nm-km, which falls within the anomalous dispersion region.
To investigate the mechanism of SCG in a sapphire fiber, we need to estimate the dispersion length and the nonlinear interaction length of the sapphire fibers, as given by [25]
where T0 is the pulse width, β2 is the group velocity dispersion, P0 is the peak power, and γ is the nonlinear coefficient. To get the value of LNL, first, the nonlinear coefficient, γ, is determined by substituting the following values, including the nonlinear refractive index coefficient n2=2.8×10-20m2/W, the effective area of sapphire fiber Aeff=10,386µm2 (corresponding to 115µm fiber diameter), and λ=2µm into the expression of nonlinear coefficient γ=n2ω0/cAeff=2πn2/λAeff. The calculated nonlinear coefficient is about γ=8.47×10-6/m·W. Then, the nonlinear lengths, LNL, corresponding to different peak powers, can be derived. For example, substituting γ=8.47×10-6/m·W, P0=30.94GW/cm2×Aeff=3.213×106W and P0=154.7GW/cm2×Aeff=1.607×107W into Eq. (4b), the corresponding nonlinear lengths are 3.67cm and 0.735cm, respectively.
To calculate the dispersion length, LD, we first calculate the value of group velocity dispersion, β2, which can be expressed in the form of
where c is the light speed in vacuum. Substituting λ=2µm and the value of d2n0/dλ2=-8.592×10-3µm-2 [calculated based on Eq. (2)] into Eq. (5), the calculated β2 is about -121.5ps2/km at λ=2µm. Furthermore, substituting β 2=-121.5ps2/km and the pulse width T0=150fs into Eq. (4a), the value of LD is calculated to be LD=18.52cm.
According to the SCG theory [16, 25], when the fiber length is shorter than the dispersion length, the most dominating effect for supercontinuum generation is thought to be self-phase modulation. However, when the fiber length is longer than the dispersion length, the soliton-related dynamics accompanied by self-phase modulation dominates the broadening effect. For example, when pump pulses at 2µm travel into single crystal sapphire fiber, self-phase modulation is accompanied by anomalous dispersion, creating a soliton at another frequency [29–32]. The soliton is red-shifted because of Raman scattering, which is further involved in many other nonlinear effects such as soliton fission, cross-phase modulation, and four-wave mixing [29–31].
Although above SCG theory has been supported by the SCG experiments based on glass fibers, to the best knowledge of authors, there are no experimental results to verify the theory for the case of highly multimode single crystal sapphire fibers. To fulfill this gap between the theory and the experiment, an experimental investigation on the mechanism of SCG in single crystal sapphire fibers is provided in next section.
3. Experimental procedures and results
In the experiment, a c-axis single crystal sapphire fiber with a 115µm diameter was used for the SCG. Figure 2 shows the experimental set up for SCG in sapphire fiber. The 2µm pumping source is created by using an optical parametric amplifier (OPA) seeded by a femtosecond laser, which has a 784nm central wavelength, a 1 kHz repetition rate, a 150fs pulse width, and a 5mm diameter beam size. The ultra-short pulses were focused by a 5× microscope objective with a 25.4mm focal length. The fiber was placed 1.5mm behind the focal plane. The beam size at the input end of the fiber was measured to be 295.3µm, which was larger than the diameter of the sapphire fiber so that the cross section of the fiber end was fully illuminated. According to Fig. 1, the material dispersion D at 2µm is 57.28ps/nm-km and is considered to be within the anomalous dispersion region. The spectrum obtained from the sapphire fiber was collimated by a Zinc Selenide IR (ZnSe) lens, and measured by a monochromator (MicroHR, Horiba Jobin Yvon Inc.) with a lock-in amplifier. A grating with a blazing wavelength of 1.5µm and a PbS photodetector were used for the 1-2µm range spectral profile measurement and a grating blazed at 4µm and a HgCdTe cryogenic photoreceiver were used for the 2-3µm range spectral profile measurement.
To verify the SCG theory for the case of single crystal sapphire fiber, as discussed in the section of theoretical approach, we first conducted experiments using a sapphire fiber whose length was shorter than the dispersion length (i.e. LD=18.52cm at 2µm). The fiber chosen for the experiment was 5cm in length. Figures 3(a) and 3(b) show the experimentally measured spectra from the 5cm sapphire fiber using two different input peak power density levels (i.e. 30.94 GW/cm2, and 154.7 GW/cm2, respectively). The corresponding peak power levels within the sapphire fiber are 3.213×106W and 1.607×107W, respectively. Since the fiber length is shorter than the dispersion length, the most dominating effect that causes spectrum broadening is thought to be self-phase modulation [16, 25]. The relatively smooth spectral profiles, shown in Figs. 3(a) and 3(b) suggested that self-phase modulation was indeed the dominant factor for the spectrum broadening. In addition, the experimental result also shown that a very broad IR spectrum (ranging from 1200 nm to 2800 nm), which covered the near-IR and the lower end of mid-IR spectral range, could be achieved via SCG in single crystal sapphire fibers. Again, this was also the new experimental result, which was not shown in the authors’ previous paper [24].
Fig. 3. Experimentally measured spectra for a 5cm sapphire fiber at two different input peak power levels of (a) 3.213×106W and (b) 1.607×107W.
To verify that SCG can also be realized via soliton-related dynamics in single crystal sapphire fibers, we also conducted the experiments with a sapphire fiber whose length was longer than the dispersion length.
To illustrate the required experimental conditions, first, let us have a brief review on the soliton generation theory. Soliton can be created when the following phase matching condition is met [29]:
where ωR and ω0 are the radiation and the soliton frequencies, respectively, and P0 is the peak power. The soliton order, N, can be determined by [33]. Substituting LD=18.52cm and LNL=0.735cm (corresponding to the peak power P0=1.607×107W) into the expression of N, we obtain . Table 1 shows dispersion parameter β=(dmβ/dωm), where m=1, 2….., calculated based on Eqs. (2) and (3) [25, 28]. By using resonance condition Eq. (6) and β values given in Table 1, the fundamental soliton wavelength is approximately 1.155µm.
Table 1. dispersion parameter β
Figures 4(a) and 4(b) show the experimentally measured spectra for a 35cm long sapphire fiber (longer than the dispersion length) at two different input peak power levels of P0=3.213×106W, and P0=1.607×107W, respectively. In Fig. 4(a), there is a soliton peak appeared around 1.2µm accompanied by the self-phase modulation. Figure 4(b) shows a broader spectrum due to the self-phase modulation and higher soliton peaks. The locations of the experimental soliton peaks are slightly red-shifted (around 40nm), which may be due to the uncertainty in the dispersion curve of the sapphire fiber and complicated higher-order soliton periodic evolutions [29]. At any rate, the spike shape spectral profiles, shown in Figs. 4(a) and 4(b), confirmed that SCG could also be generated in single crystal sapphire fibers via soliton related dynamics when the fiber length was longer than the dispersion length.
Fig. 4. Experimentally measured spectra for a 35cm sapphire fiber at two different input power levels of (a) 3.213×106W and (b) 1.607×107W.
4. Discussion
To investigate the relevance of the experimental results, we performed the NLSE simulations with the parameters given in the previous sections and compared them with the experimental results. Simulations were performed for fiber lengths of 5cm and 35cm, the same lengths used in Fig. 3 and 4, respectively, and an input peak power density level of 154.7 GW/cm2 was employed. We used 418cm-1 for the frequency shift of the Raman gain spectrum [34]. Figure 5 compares the simulation results (dashed lines) to the experimental results (solid lines). Both the simulation and experimental results in Fig. 5(a) clearly show that when the fiber length is shorter than the dispersion length, 5cm in this case, the SCG in the sapphire fiber is mainly due to SPM. In Fig. 5(b), when the length of the sapphire fiber (35cm) is longer than the dispersion length, we observe soliton peaks in both the simulated and experimental results. As shown in Figs. 5(a) and 5(b), the simulation results are in good agreement with experiments.
It is a challenging task to generate supercontinuum in the mid-IR region due to the absorption of the silica material in the mid-IR regime [1]. Efforts have been made to extend the SCG at longer wavelengths. For example, in [35], the authors use germano-silicate fibers to generate a supercontinuum that extends to the lower end of the mid-IR region (up to 2.8µm) by shining UV light onto a 1cm fiber to shift the zero dispersion point by over 100nm. The further extend to the longer wavelength (i.e., beyond 2.8µm) is largely limited by the heavy absorption of the silica materials. As shown in Fig. 6, the absorption of silica in the mid-IR region is much stronger than in sapphire. To experimentally demonstrate that it is possible to generate SCG beyond 2.8µm by employing sapphire fiber, we conducted the SCG experiment by using a pump wavelength at 2.5µm. We launched the laser pulses into a 5cm sapphire fiber with an input peak power density level of 92.82GW/cm2. Figure 7 shows the experimentally measured spectra from the 5cm sapphire fiber pumped at 2.5µm. A spectrum from 2µm to 3.2µm was obtained. This result experimentally proves that a SCG from sapphire fiber can extend further into the mid-IR regime than a SCG from a silica fiber.
Fig. 5. Spectra comparison between simulation (dashed lines) and experimental results (solid lines) for (a) 5cm sapphire fiber and (b) 35cm sapphire fiber.
Fig. 7. Experimentally measured spectra for a 5cm sapphire fiber at the pump wavelength of 2.5µm and input power level of 9.640×106W.
5. Conclusions
We experimentally demonstrated that broadband SCG in the near- and mid-IR spectral region could be realized by launching femtosecond laser pulses into single crystal sapphire fibers. A spectrum ranging from 1.2µm to 2.8µm was obtained by pumping 2µm pulses into a 5cm single crystal sapphire fiber, and a spectrum ranging from 2µm to 3.2µm could be achieved by pumping at longer 2.5µm wavelength. Furthermore, the mechanisms of SCG in single crystal sapphire fibers were also theoretically and experimentally investigated. Experimental results confirmed that self-phase modulation was the dominant factor for the SCG when the fiber length was shorter than the dispersion length. On the other hand, when the fiber length was longer than the dispersion length, soliton related dynamics also played an important role in SCG. These experimental results agreed well with the theoretical simulations. The high laser damaging threshold of the sapphire fiber also enables high power broaden supercontinuum generations. Such a high power, broaden supercontinuum source can have a great impact in a variety of applications, such as IR spectroscopy, material identifications, broaden LADAR, biomedical research, and broadband multi-spectrum communications.
Acknowledgments
We are grateful to Dr. Zhiwen Liu, Dr. Kebin Shi, and Peng Li for their assistance on the simulation work and helpful discussion.
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36. Redrawn from http://optical-material.optical-components.com/
