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In this paper, we demonstrate that the the bandwidth of the supercontinuum spectrum generated in a large mode area sapphire fiber can be enhanced by employing triple pumping sources. Three pumping sources with wavelengths of 784nm, 1290nm, and 2000nm are launched into a single crystal sapphire fiber that is 5cm in length and has a core diameter of 115μm. The nonlinear interactions due to self-phase modulation and four-wave mixing form a broadband supercontinuum that covers the UV, visible, near-IR and lower mid-IR regions. Furthermore, we explore the possibility of generating a broadband supercontinuum expanding from the UV to far-IR region by increasing the number of pumping sources with wavelengths in the mid- and far-IR.
©2008 Optical Society of America
1. Introduction
Supercontinuum generation (SCG) refers to the creation of a broadband light source due to the nonlinear interactions of laser pulses inside an optical medium. Many applications in spectroscopy [1], confocal microscopy [2, 3], optical communication [4], medical imaging [5], optical coherence tomography [6], and remote sensing [7] require a broadband light source and may benefit from SCG.
Recently, the importance of a broadband light source covering the UV through mid-IR has increased. In spectroscopy, many chemicals have distinct peaks in UV, visible, near-, mid-, and far-IR. However, the spectra of many chemicals can only be differentiated by a small number of peaks in a certain range. Thus, the scanning range needs to be as wide as possible to distinguish these small differences. Remote sensing applications would also benefit from a broadband light source. The system described in Reference [8] utilizes both UV and mid-IR optical sources generated by an optical parametric oscillator (OPO) to perform remote-sensing for environmental conditions such as air pollution and water vapor, and for terrestrial monitoring. Even though conventional sources such as OPOs, tunable solid-state lasers, and quantum cascaded lasers (QCLs) can cover a wide spectral range by continuously tuning the wavelength [9], they cannot cover the entire range simultaneously because of the time delay during wavelength switching. Very wide range SCG from the UV to mid-IR (up to 4.5µm) in air has been previously reported [10]. However, this result was obtained in air by employing input pulses with an extremely high peak power density level on the order of a terawatt. Recently, broadband supercontinua from optical fibers covering more than an octave span have been demonstrated with relatively small intensity input pulses by many researchers [11–13]. Reference [13] shows that a SF-6 photonic crystal fiber (PCF) with a very small mode area (2.6µm diameter) and a nonlinear refractive index of 2.2×10-19m2/W can generate a spectrum that spans from 350nm to 3000nm. We previously reported supercontinua in a sapphire fiber with spectral spans from 450nm to 1350nm and from 1200nm to 2800nm [14, 15]. The fibers used in these papers were multimode and had a core diameter of 115µm. Sapphire fibers are well suited for SCG because they exhibit a high damage threshold (up to1.3kJ/cm2) and a nonlinear refractive index similar to silica fibers (3 × 10-20m2/W) [16–18]. They also have good transparency up to 5µm [17,18]. Additionally, sapphire fiber is fabricated using a technique based on laser heated pedestal growth (LHPG) [18–20], which is a matured technology. However, the nonlinear coefficient of a sapphire fiber (γ = 1.171 × 10-5/m·W at 1.55µm) is 14,000 times smaller than PCF fiber (γ = 0.1680/m·W at 1.55µm) due to its large mode area. Although the large mode area of the sapphire fiber significantly reduces its nonlinear coefficient, SCG in fibers with a larger mode area has generated a great deal of interest for the following reasons [21–23]: the coupling efficiency is very high, and the chance of surface damage decreases since the input light does not have to be as tightly focused as in the case of PCF fiber [18]. To maintain the advantages of a large mode area sapphire fiber (i.e. high coupling efficiency, high damage threshold, and good IR transparency) while improving the supercontinuum bandwidth, we adopt a multiple pumping source scheme.
Previously, SCG using dual-wavelength pumping has been reported [24–28]. Dual-wavelength pumping broadens the spectrum via cross-phase modulation (XPM) [24–26], generates peaks at sidebands due to XPM-induced instability [27], and causes nondegenerate four-wave mixing (FWM) [28]. But, the broadened spectrum created by dual-wavelength pumping in many papers has a discontinuity between the supercontinua generated by each pump wavelength [24,26–28]. Even though these spectra are overlapped in several papers, the total reported span is much less than two octaves [25].
In this paper, we employ triple pumping sources to generate supercontinuum in a single crystal sapphire fiber. Our supercontinuum covers a very broad spectrum from the UV to the lower end of the mid-IR without spectra discontinuity. By using triple pumping sources, we can generate a very broad spectrum despite using a large mode area. Also, an even broader spectrum may be generated by increasing the number of pumping sources in the longer IR wavelengths.
2. Technical approach
We followed the procedure in [29, 30] to derive the nonlinear Schödinger equation (NLSE) for the propagation of three pumping sources in an optical fiber. The generalized NLSE describing single pulse propagation in an optical fiber can be expressed as [29, 30]:
where R (T) represents the instantaneous and the delayed material response [29] while α is the fiber loss, and βn is the nth propagation constant.
The nonlinear part of Eq. (1) can be expressed in terms of new variable V as [29, 30]:
In that case, the multiple pumping sources propagating in an optical fiber can be expressed as [31]:
where NP is the total number of pumping sources, Pj and T0 are peak power and pulse width of jth pumping source, and Δωj is frequency difference between the jth pumping source and the carrier beam (NP=3 for our case). Each beam has high peak intensity on the order of 107 W, and three combined intensity carried through the fiber is very high. Thus, a sapphire fiber, which exhibits a high damage threshold, is a suitable optical medium for the propagation of three high power pulses simultaneously. In our experiments, we used a highly multimode sapphire fiber with a core diameter of 115µm. Even though our fiber is highly multimode, the fundamental mode is mainly considered because wave-vector mismatch between the fundamental and higher-order modes is extremely large [32, 33]. The total dispersion is dominated by the material dispersion of the fundamental mode [34]. The ordinary refractive index of a sapphire fiber is considered since only the c-axis is used. The Sellmeier equation describing the ordinary refractive index and material dispersion parameter D are given in previous papers [14, 15]. An optical parametric amplifier (OPA) produces signal and idler beams and an additional pumping source at 784nm according to the equation of ω784nm = ωsignal+ωidler. We have chosen the pumping sources at 784nm, 1290nm, and 2000nm to minimize intensity fluctuation in the overlapping region of each spectrum. The dispersion parameters in sapphire fiber at 784nm (-187.4ps/nm-km) and 1290nm (-3.374ps/nm-km) are within normal dispersion while the 2000nm pulse (57.28ps/nm-km) lies in anomalous dispersion.
To determine the length of a sapphire fiber, the dispersion length, LD, and the nonlinear interaction length, LNL, need to be calculated. Those lengths are given as LD = T02/|β 2| and LNL = 1/γP0, where P0 is the peak power of the propagating beam, and β2 is group velocity dispersion [35]. The group velocity dispersion at 784nm, 1290nm, and 2000nm can be calculated from β2=(λ3/2πc2)·(d2n0/dλ2), and the calculated values are 59.21ps2/km, 2.979ps2/km, and -121.5ps2/km, respectively. Based on pulse width of 150fs, the dispersion lengths are 38.01cm for 784nm, 755.34cm for 1290nm, and 18.52 cm for 2000nm. The effective mode area Aeff (10,386µm2) and the nonlinear refractive index n2 (3×10-20m2/W for 784nm, 2.9×10-20m2/W for 1290nm, and 2.8×10-20m2/W for 2000nm [16]) are substituted into γ = n2 ω0/cAeff = 2πn2/ λAeff to find the nonlinear coefficients. The calculated values are 2.268×10-5/m·W, 1.359×10-5/m·W, and 8.466×10-6/m·W for 784nm, 1290nm, and 2000nm, respectively. The calculated nonlinear interaction lengths according to the nonlinear coefficient above and the estimated peak power for our experiment (approximately 1.607×107W) are 0.274cm for 784nm, 0.457cm for 1290nm, and 0.735cm for 2000nm.
To minimize the dispersion-related interaction, we used a fiber length of 5cm, which is larger than calculated nonlinear interaction lengths, but smaller than dispersion lengths. Reference [15] discusses about the relationship between dispersion and fiber lengths in anomalous dispersion region. When the fiber length is shorter than the dispersion length, SPM is considered to be the dominant nonlinear effect [15, 35, 36]. However, when the fiber length is longer than the dispersion length, the soliton-related dynamics accompanied by the SPM can be observed [15, 35, 36]. The pumping wavelength and the fiber length used in [15] are 2000nm and 5cm, respectively. At 2000nm, the dispersion length LD for a sapphire fiber is 18.52cm, which is relatively larger than the fiber length. In that case, the dominant nonlinear effect is considered to be the SPM [15, 36]. Therefore, we believe that the dominant nonlinear effect caused by 2000nm source in 5cm sapphire fiber in this paper will be the SPM. The shape of the overall spectral broadening due to the propagation of three pumping sources can be predicted by the superposition of the supercontinuum generated by each of the sources individually. Also, a notable effect of the nondegenerate FWM that results from the interaction between two pumping sources can enhance the spectral broadening and increase the intensity level. The equations for the frequency (ω) and phase matching (k) conditions are as follows [37]:
where pj is jth pumping source, sj and ij are signal and idler beams generated by the FWM processes, and γpj and Ppj are the nonlinear coefficient and the peak power of jth pumping source.
3. Experimental procedures and results
To verify that FWM processes are involved in the SCG from three pumping sources, we calculated the frequency interaction and phase matching conditions of the three pumping sources. The frequency interaction condition between 1290nm and 2000nm is given as:
which is only satisfied when the following phase matching condition is matched [37]:
where kλ = 2πnλ/λ. By using the nonlinear coefficients, the peak power of 1.607×107W, and the refractive indices derived from the sellmeier equation [14, 15] to solve the phase matching condition, we find that the phase matching condition occurs when the signal and idler beams are at 1164nm and 2400nm. Also, two other interactions (784nm and 1290nm, and 784nm and 2000nm) generate the signal and idler peaks located at 595nm and 2700nm, and 727nm and 2500nm, respectively.
To compare the validity of our theory with the experimental results, three pumping sources launch pulses into the sapphire fiber. For the experimental setup shown in Fig. 1, the three sources are the signal and idler beams (1290nm and 2000nm) from the OPA and an additional source at 784nm. The beams have a 1kHz repetition rate and 150fs pulse width. Once the three beams overlap spatially and temporally, they are focused by an achromatic lens (f=5cm) and coupled into the 5cm sapphire fiber. The supercontinuum generated through the sapphire fiber is collimated by a silica lens (for UV, visible, and near-IR ranges) and a Zinc Selenide (ZnSe) IR lens (for near- and mid-IR ranges), and is detected by a monochromator (MicroHR, Horiba Jobin Yvon Inc.).
Figure 2 shows the experimental results of the supercontinuum spectra generated from the three individual pumping sources (blue dash: 784nm, green dash: 1290nm, and black dash: 2000nm) and the three pumping sources together (red solid). The spectrum produced by each individual pumping source is primarily a result of SPM. The spectra from the 784nm, 1290nm, and 2000nm sources range from 400nm to 1200nm, from 1000nm to 1800nm, and 1300nm to 2800nm, respectively. The supercontinuum generated by the three pumping sources together involves more than SPM. The three main spectra due to SPM are overlapped while the peaks due to nondegenerate FWM processes are created when the pulses from the three sources travel through the sapphire fiber simultaneously. The peaks created by FWM also undergo degenerate FWM processes with other peaks [38] to stack multiple peaks in the UV area, but the later interactions occur over a very short distance due to walk-off. Other effects such as Raman scattering and XPM also contribute to the increase in both ends of spectra. Therefore, idler beams can enhance the intensity level in mid-IR region via nondegenerate FWM processes while signal beams involved in nondegenerate and degenerate FWM processes can increase the intensity level in the UV and visible regions. As a result, an ultra-broadband supercontinuum ranging from the UV to mid-IR regions is generated by employing three pumping sources. The calculated peaks due to nondegenerate FWM processes match well with those of the experimental spectra shown in Fig. 2.
To verify the relevance of our experimental results, a simulation of the NLSE was performed with the same parameters as the experiments. We followed similar procedures in [29, 30] to numerically simulate the SCG in a sapphire fiber due to the propagation of three pumping sources. The frequency shift of the Raman gain was around 418cm-1 [39]. The fractional contribution of the instantaneous Raman response to the nonlinear refractive index, fR used was 0.25, which was derived from n2 and nR given in [40], and from the equation in [41]. Other parameters τ1, and τ2 used to decide delayed Raman response hR were 182fs, and 200fs, respectively [40].
Figure 3 shows the simulated spectra of the supercontinuum emitted from the sapphire fiber due to the interaction of the three pumping sources. The spectra of three pumping sources are broadened by SPM and overlapped while peaks and intensity enhancement in the UV, visible, and mid-IR are observed due to complex FWM processes. The peaks due to nondegenerate FWM processes in the simulation results are in good agreement with the experimental results.
To check whether the peaks shown in Figs. 2 and 3 are the nondegenerate FWM caused by each interaction between two pumping sources, we evaluated the interaction between 1290nm and 2000nm with simulation and experimental results. Figure 4(a) shows the simulation spectrum caused by the interaction between 1290nm and 2000nm pumping sources. The peak powers of 8.035×106W and 4.821×106W are utilized for 1290nm and 2000nm peaks, respectively. As shown in Fig. 4(a), signal and idler peaks due to the FWM are observed. To verify that the peaks observed in Fig. 4(a) are due to the FWM, we increased the peak power of 1290nm pumping source to 1.286×107W while the peak power for 2000nm source is unchanged. As shown in Fig. 4(b), the main spectrum caused by 2000nm source is very similar to that in Fig. 4(a) while the intensities of both peaks due to the FWM are increased. Figure 4(c) shows three simulation spectra when 2000nm pumping source is presented alone (dot line), and it is accompanied by 1290nm source with the peak powers of 8.035×106W (dashed line) and 1.286×107W (solid line). While the spectra due to 2000nm pumping source remains very similar, the peak at 2400nm intensifies when the intensity of 1290nm source increases. Also, the peak at 2400nm is not ovservable when 1290nm source is not coupled together. This seems to be due to the increased FWM gain [42]. According to papers that discuss cross-phase modulation (XPM) effect caused by dual-pumping, the spectrum of an interested source dramatically expands in wavelength when it is affected by another pumping source at different wavelength [25, 26, 43]. Therefore, compared to the FWM, the XPM effect does not seem very dominant in this simulation. To verify our simulation results shown in Fig. 4(a)–(c), we experimentally evaluated two pumping sources of 1290nm and 2000nm. The peak power used for this experiment was 8.035×106W. As shown in Fig. 4(d), two peaks due to the FWM are clearly observable. Therefore, many peaks appearing on Figs. 3 and 4 seem to be caused by the FWM effect.
Fig. 2. The experimentally measured spectra generated from the three individual pumping sources (blue dash: 784nm, green dash: 1290nm, and black dash: 2000nm) and the three pumping sources together (red solid)
Fig. 4. The simulation and experimental spectra of two pumping sources located at 1290nm and 2000nm: (a) simulation spectra of 1290nm source with 8.035×106W and 2000nm source with 4.821×106W, (b) simulation spectra of 1290nm source with 1.286×107W and 2000nm source with 4.821×106W, (c) three simulation spectra when 2000nm pumping source is presented alone (dot line), and it is accompanied by 1290nm source with the peak powers of 8.035×106W (dashed line) and 1.286×107W (solid line), and (d) experimental spectra of 1290nm and 2000nm sources with the peak power of 8.035×106W.
4. Conclusions
We experimentally demonstrated that the spectral bandwidth of SCG, generated from a large mode area sapphire fiber, could be enhanced by employing triple pumping sources. A broad supercontinuum spectrum from the UV to the mid-IR was successfully demonstrated. The mechanisms of SCG using the three pumping sources were theoretically and experimentally investigated. When three pulses at different wavelengths propagated through the sapphire fiber, their spectra were broadened due to SPM and the complex FWM processes. It is also anticipated that by increasing the number of pumping sources in the longer IR wavelengths, this scheme has the potential to create an even broader spectrum. This ultra-broadband source may have a significant impact in variety of applications including multiple region spectroscopy, remote sensing, standoff chemical detection, biomedical researches, and communications.
Acknowledgments
Partial financial support of this work by ONR grant, N00014-05-1-0844 is greatly appreciated.
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