We report ~22 dB of Raman gain in single mode As2Se3 chalcogenide glass fiber using 15 ps optical pump pulses from 1470 nm to 1560 nm. We employ a novel technique of cross-phase modulation induced sideband amplification to map out the Raman gain spectrum of this glass, and investigate the role of both degenerate and non-degenerate (ND) two-photon absorption (TPA). We find that for materials such as As2Se3 where the Raman gain coefficient (gR) and TPA are comparable, it is critical to know and account for the role of both of these in order to achieve appreciable Raman gain. This is highlighted by our results, where we achieve significantly higher Raman gain at the longest pump wavelength (1560 nm), despite the fact that the Raman gain coefficient itself (gR) is smallest at this wavelength. This occurs because the TPA is significantly larger for shorter wavelengths in As2Se3. We conclude, therefore, that for Raman gain applications in As2Se3, L-band operation is strongly favored over C-band operation.
©2008 Optical Society of America
In recent years, much attention has been focused on highly nonlinear materials in the search for a platform for all-optical integrated photonic circuits, for future high bit rate telecommunications systems, where optical transparency, speed, cost, size and energy consumption must be addressed . The chalcogenide glasses are particularly attractive due to their large ultrafast χ (3) (third-order) optical response and good nonlinear figure of merit, allowing for a range of efficient nonlinear processes such as Raman gain [2–5], low-threshold four wave mixing  and spectral broadening via self and cross-phase modulation (SPM, XPM) [7–9]. Of the chalcogenide glasses, As2Se3 in particular possesses one of the highest nonlinearities at ~500× silica glass and has been the focus of a range of demonstrations including 2R optical regeneration , wavelength conversion [7, 8], and recent reports of tapering to sub-µm dimensions have yielded nanowires with nonlinearities in excess of 90,000 W-1km-1 . Additionally, photoinduced refractive index changes have led to recent demonstrations of Bragg gratings in As2Se3 fibers  and low-loss shallow-rib waveguides . The combination of these properties shows great potential for the development of an integrated all-optical device.
Stimulated Raman gain has significant potential in As2Se3 fiber since the Raman gain coefficient, with a spectral shift of ~7 THz and width of ~2 THz , is known to be 300-700× silica glass at communication wavelengths [2, 3]. Continuous wave (CW)  as well as nanosecond pulsed  Raman amplification have been reported in single-mode As2Se3 fiber, achieving gains of 3 dB and 20 dB, respectively, as well as in bulk As2Se3 glass . More recently, Raman lasing at ~2.1 µm was reported in As2Se3 fiber . However, no systematic investigation of the wavelength dependence of Raman gain through the C and L bands has been reported to date, despite the fact that both the Kerr nonlinearity (n 2 - related to the real part of χ (3)) and two-photon absorption (β TPA - related to the imaginary part of χ (3)) are known to vary significantly across the C-band in this material , as illustrated in Fig. 1 . It is well known that TPA poses a fundamental limit to the efficiency of nonlinear guided-wave switching devices , while a moderate TPA at 1550 nm has been shown  to be beneficial for 2R regeneration. The effects of TPA as a Raman gain-limiting process, however, have not been studied. Since the Raman gain coefficient g R, n 2 and TPA are different components of the third-order nonlinearity χ (3) , it is of significant interest to study how Raman gain and nonlinear absorption counteract across the C and L-bands. Finally, amplification of short (picosecond) pulses, which is critical for high bit rate systems, has not been reported.
In this paper, we present the first systematic study of picosecond pulsed Raman gain in single mode As2Se3 chalcogenide glass fiber. We employ a novel technique of cross-phase modulation induced sideband amplification by picosecond pump pulses on a CW probe signal to study Raman gain in this glass. By tuning the CW probe and measuring the amplification of its XPM induced sidebands (by the pump), we map out the Raman gain spectrum, as well as n 2 and the TPA coefficient, for pump wavelengths of 1470 nm, 1503 nm and 1560 nm. We investigate the role of both degenerate and non-degenerate (ND) two-photon absorption on Raman gain.
We find that in As2Se3 glass TPA plays a critical role in Raman gain – particularly non-degenerate TPA (simultaneous absorption of a pump and probe photon). We obtain higher Raman gain at longer pump wavelengths even though the Raman gain coefficient (g R) is smaller, since TPA is also smaller. We achieve up to 22 dB of gain in a 25 cm length of As2Se3 single mode fiber with 15 ps optical pulses at 80 W of peak pump power at 1560 nm and probe near 1619 nm. On the other hand, at the same pump power we only achieve ~7 dB of gain for a pump wavelength near 1470 nm, since TPA is significantly larger. We conclude that for Raman amplification in As2Se3 chalcogenide glass fiber, performance in the L-band is thus significantly better than the C-band.
2. Experimental approach
When high intensity pump pulses near the optical half band-gap co-propagate along a fiber with weak CW light that is within the Raman gain spectrum of the material, a number of nonlinear optical processes take place simultaneously. Both the pump pulses and probe spectrally broaden due to SPM and XPM, respectively. Sidebands thus emerge on the CW probe, and its output spectrum acquires a characteristic pedestal shape. Simultaneously, these XPM-induced sidebands are amplified due to Raman gain. A schematic of this process is illustrated in Fig. 2. The amplification of a CW probe by a low duty cycle pump pulsed laser is not resolvable on a spectrum analyzer, due to the small increase in average power. However, spectral measurements can easily detect the amplified sidebands, since they “background free”; ie., they are not present at the fiber input but generated and amplified by the pump pulses along the fiber.
In addition, if the sum energy of two co-propagating photons is greater than the optical bandgap, they can be absorbed by means of a TPA process. This can be degenerate, if caused by two pump photons (Fig. 3(a)), or non-degenerate, if induced by a pump photon and a signal photon (Fig. 3(b)). This results in pump and signal power depletion along the waveguide. Note that the presence of a long Urbach absorption tail in chalcogenide glass results in a TPA edge that can extend significantly below the optical half bandgap .
Figure 4 shows a schematic of the experimental setup. An optical parametric oscillator (OPO) generated pump pulses at a 100 MHz repetition rate and pulsewidth ~15 ps fullwidth at half maximum (FWHM) at 1470 nm, 1503 nm and 1560 nm. A CW probe signal from a wavelength tuneable laser diode (1500 nm to 1620 nm) was multiplexed with the pump in free space using a 50:50 beam splitter (BS), then both were coupled into the As2Se3 fiber. The power from the OPO was controlled using a variable attenuator (VA). Since Raman gain is polarization dependent, a polarization controller (PC) was used to vary the polarization of the CW signal. A 99:1 coupler was included between the laser source and the fiber, to monitor input power via a power meter (PM). The power distribution of the output wavelength spectrum was measured through an optical spectrum analyzer (OSA). Alternatively, the average output power was measured on a power meter.
The pulses were coupled into As2Se3 fiber via standard silica SMF28 fiber pigtails, with a short length of high numerical aperture (NA) fiber spliced on the end to improve coupling efficiency. The fiber has a mode area of A eff=21 µm2, and length L=25 cm. Using known dispersion parameters at our operating wavelengths (D=-504 ps/nm/km at 1550 nm ), we estimate that in our experiment walk-off between pump and amplified pulses due to group-velocity dispersion is small, so that the entire length of fiber contributes to Raman gain. Additionally, we operate in the normal dispersion regime (the zero dispersion wavelength being well into the mid-infrared ), therefore exponential parametric amplification does not occur, and Raman gain is the dominant effect. In order to avoid photo-induced effects such as photodarkening and anisotropy, which have been observed under prolonged exposure to sub-bandgap light in some chalcogenide glasses [23, 24], care was taken to minimize exposure time during each measurement.
Since sample to sample variations in the degenerate two-photon absorption coefficient β d and nonlinear index n 2 have been measured in the C-band for As2Se3 in the literature [3, 17, 21, 25, 26], possibly due to differences in glass purity, we first characterized these parameters for our specific fiber, at our pump wavelengths.
4.1 Degenerate TPA and n2
Figure 5 summarizes our measurements of nonlinear absorption. We varied the peak power incident on the fiber via the variable attenuator, and monitored the transmitted and incident average powers. Neglecting group-velocity dispersion, the output average power is a function of the degenerate TPA coefficient β d only, and its value can be determined by fitting the power transfer curves to theoretical results obtained using a generalized split-step Fourier method  which includes two-photon absorption. The data was fit to obtain β d at each wavelength (dotted curves), yielding β d=0.40±0.03 cm/GW, β d=0.78 ± 0.07 cm/GW and β d=1.3±0.1 cm/GW at pump wavelengths of 1560 nm, 1503 nm and 1470 nm, respectively. The uncertainties take into account output power fluctuations. As expected, degenerate TPA increases as the wavelength moves closer towards the half bandgap.
The nonlinear refractive index was obtained by measuring the output spectra of the pump pulses as a function of input power, at each pump wavelength. Knowledge of β d allows one to obtain n 2 by fitting the pump output spectra with simulation results, accounting for SPM-induced spectral broadening. In doing so we ignore the effects of β nd on the pump since this will be weaker by ~60dB (ratio of pump to probe powers) than β d. Figure 6 shows the output spectra of the pump pulses for different peak power levels, along with the theoretical fits, for a wavelength of 1560 nm. The values of n 2 are determined using the previously obtained values of β d. We obtain n 2=0.75±0.07×10-17 m2/W, n 2=0.82±0.08×10-17 m2/W and n 2=1.1±0.1×10-17 m2/W at pump wavelengths of 1560 nm, 1503 nm, 1470 nm, respectively. The uncertainties on β d influence our knowledge of n 2, since these two quantities counteract to induce the nonlinear phase shift responsible for SPM .
4.2 Raman Gain
Figure 6 illustrates the experimentally recorded output spectra (solid lines) of the CW probe beam at a wavelength of 1619 nm for a fixed pump wavelength of 1560 nm. The probe, kept constant at 50 µW input power, spectrally broadens with increasing pump power due to XPM, and the resulting CW sidebands are amplified due to Raman gain. Theoretical modeling was performed using a generalized split-step Fourier method which included stimulated Raman scattering via a temporal Raman response function , obtained from the Raman gain spectrum of this material . Simulations show good agreement with experiment, in this case suggesting a peak Raman gain of ~22 dB.
Figure 7(a) illustrates the experimentally recorded output spectra for different probe wavelengths for a fixed pump wavelength of 1503 nm and peak power ~80 W. The spectra are plotted in terms of the signal-probe Stokes shift λs - λp. By varying the input wavelength of the CW probe, the XPM-induced sidebands are amplified according to their position within the Raman gain spectrum for As2Se3. We observe peak gain at a wavelength shift of approximately 55 nm from the pump, in agreement with the expected ~7 THz frequency shift. The Raman gain spectrum can be extracted by integrating the power distribution of the amplified output sidebands. The result is shown in Fig. 7(b), showing a peak gain of ~15 dB at this pump wavelength (see Sec. 5).
5. Theory and analysis
The evolution of pump and stokes signal field intensities I p(z) and I s(z) co-propagating along z through a single mode fiber of length L is given by the following expressions ,
where β d and β nd are the degenerate and non-degenerate two-photon absorption coefficients, gR is the Raman gain coefficient and α is the linear propagation loss coefficient, assumed to be the same at pump and signal wavelengths. From Eq. (2) it becomes apparent that if gR and β nd are comparable quantities, then Raman gain and nonlinear absorption compete. Equation (1) can be readily solved, yielding
Substituting this result into Eq. (2) and integrating yields
From the experimental spectral data, one can estimate Raman gain as a function of pump intensity using two methods. The first involves isolating the amplified side-band component of the output wavelength spectrum and integrating the measured power distribution; the other requires optimizing the theoretical output gain spectrum, numerically filtering the signal wavelength, and extracting the amplification of the CW probe in the time domain from simulation. We found that the two methods yield comparable Raman gain to within a dB or so.
Figure 8 illustrates the measured Raman gain as a function of peak pump power, for different pump wavelengths, with the probe tuned to the Raman gain peak. We observe that gain is clamped at high intensities, and is significantly smaller for pump photon energies close to the optical half bandgap. The data is fit from Eq. 4 to obtain gR at each wavelength (dashed curves), using the values of degenerate two-photon absorption coefficient β d of Section 4.1. The linear loss in this fiber is α=1 dB/m in this wavelength range. The relationship between β d and β nd is described elsewhere . Here we approximate the non-degenerate TPA as an average of the degenerate TPA at the pump and probe wavelengths, with the assumption that the TPA at 1619 nm does not decrease substantially from 1560 nm, where it is already quite low. Doing this, we obtain β nd ~0.4 cm/GW, β nd ~0.6 cm/GW and β nd ~1.0 cm/GW for pump wavelengths of 1560 nm, 1503 nm and 1470 nm, and signal wavelengths of 1619 nm, 1560 nm and 1523 nm, respectively. By fitting the experimental data with the above parameters, we finally obtain gR=2.0±0.2 cm/GW, gR=2.3±0.2 cm/GW and gR=2.9±0.2 cm/GW at pump wavelengths of 1560 nm, 1503 nm and 1470 nm. For a given amount of Raman gain, the uncertainties on gR are related to the uncertainties on the TPA coefficients, via Eq. 4. Variations of n 2 do not influence our measurements of Raman amplification and estimates of gR. The results are summarized in Table 1.
These results therefore show that there are a number of competing effects on the Raman gain in this fiber as the pump wavelength is tuned from 1470 nm to 1560 nm. First, while both β nd and β d increase with decreasing wavelength, the effect of β nd on Raman gain is in fact more pronounced than that of β d (TPA of the pump alone), since β nd enters the gain equations in exactly the same manner as gR. In fact, the increase in β nd (with decreasing λ) actually overshadows a corresponding increase in gR of 50%. The result is that we actually obtain the largest gain (22 dB) for a pump wavelength of 1560 nm where gR is the smallest. It is thus critical to know these parameters (and their wavelength dependence) in materials where the Raman gain coefficient and TPA are comparable, in order to predict where the Raman gain is optimum. Finally, looking to future applications, we expect both degenerate and non-degenerate TPA to become negligible as we move further into the mid-infrared, with promising implications for Raman amplification and lasing in As2Se3 fiber in this region.
We demonstrate picosecond pulsed Raman amplification in single mode As2Se3 chalcogenide glass fiber and examine the effects of both degenerate and non-degenerate two-photon absorption, using a novel technique of cross-phase modulation induced sideband amplification to map out the Raman gain spectrum for this material. We investigate the dependence on pump wavelength from 1470nm to 1560nm, and achieve a maximum gain of ~22dB at 1560nm where both the Raman gain coefficient (gR) and two-photon absorption is smallest. We find that two-photon absorption (particularly non-degenerate) can dominate systems when it is comparable to gR and that for As2Se3 glass, the L-band is heavily favoured over the C-band for Raman amplification.
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