Optical amplification based on stimulated Raman scattering (SRS) in optical fibers offers the potential to generate gain at any arbitrary wavelength with an appropriate pump source, limited only by the fiber’s transparency range. Furthermore, cascaded SRS can generate gain at wavelengths further away from the initial pump wavelength than a single Stokes order [1
1. L. G. Cohen and C. Lin, “A universal fiber-optic (UFO) measurement system based on a near-IR fiber Raman laser,” IEEE J. Quantum Electron. 14(11), 855–859 (1978). [CrossRef]
3. P. T. Rakich, Y. Fink, and M. Soljacić, “Efficient mid-IR spectral generation via spontaneous fifth-order cascaded-Raman amplification in silica fibers,” Opt. Lett. 33(15), 1690–1692 (2008). [CrossRef] [PubMed]
]. This has proved a very effective way of providing gain at those wavelengths not directly available with rare-earth (RE) doped fibers, as well as providing some advantages over RE doped fiber amplifiers such as distributed amplification. So far however most of this success has been achieved using continuous-wave (CW) pump sources for developing fiber Raman lasers (see [4
4. E. M. Dianov and A. M. Prokhorov, “Medium-power CW Raman fiber lasers,” IEEE J. Sel. Top. Quantum Electron. 6(6), 1022–1028 (2000). [CrossRef]
] and references in it). However, pulse-pumping opens up new opportunities for controlling the SRS process which are not available with CW pumping. In recent years there has been renewed interest in the pulse-pumping of fiber Raman amplifiers (FRAs). This has been mainly in the telecommunications area through time–division multiplexed (TDM) pumping schemes [5
5. L. F. Mollenauer, A. R. Grant, and P. V. Mamyshev, “Time-division multiplexing of pump wavelengths to achieve ultrabroadband, flat, backward-pumped Raman gain,” Opt. Lett. 27(8), 592–594 (2002). [CrossRef]
], but also in other areas due to advances in high power fiber master oscillator-power amplifier (MOPA) systems [3
3. P. T. Rakich, Y. Fink, and M. Soljacić, “Efficient mid-IR spectral generation via spontaneous fifth-order cascaded-Raman amplification in silica fibers,” Opt. Lett. 33(15), 1690–1692 (2008). [CrossRef] [PubMed]
6. P. Dupriez, C. Farrell, M. Ibsen, J. K. Sahu, J. Kim, C. Codemard, Y. Jeong, D. J. Richardson, and J. Nilsson, “1 W average power at 589 nm from a frequency doubled pulsed Raman fiber MOPA system,” Proc. SPIE 6102, 348–352 (2006).
]. The idea behind TDM pumping is to multiplex several pump wavelengths together with each one producing its own individual Raman gain spectrum. The result of this is several overlapping Raman gain spectra which can be tailored to produce a flat ultra-broadband Raman gain profile. The pump wavelengths are separated in time (i.e., through pulse-pumping) so they are never simultaneously present at the same location within the fiber and therefore pump-to-pump Raman interactions are avoided [7
7. C. R. S. Fludger, V. Handerek, N. Jolley, and R. J. Mears, “Novel ultra-broadband high performance distributed Raman amplifier employing pump modulation,” Optical Fiber Communications Conference, (Anaheim, CA, USA, 2002), paper WB4.
]. This work is primarily concerned with generating gain from multiple pump sources over a single Raman conversion step in optical communication systems. Therefore, it targets only the 1.5 µm region of the spectrum and uses long amplification lengths (tens of kilometers) to enable the use of low-power pump sources. Pulse-pumping schemes based on cascaded SRS have also been investigated in the telecommunications area as a way of improving the noise performance [8
8. J.-C. Bouteiller, K. Brar, J. Bromage, S. Radic, and C. Headley, “Dual-order Raman pump,” IEEE Photon. Technol. Lett. 15(2), 212–214 (2003). [CrossRef]
], but again this work only targets the 1.5 µm spectral region and only considers gain across one Stokes order.
Here we investigate the Raman gain spectra produced from pumping a Raman gain fiber with well controlled shaped optical pulses delivered from a fiber MOPA source. Since SRS is an essentially instantaneous process, the Stokes order at which gain is achieved depends on the instantaneous pump power, which, with the right pump source, allows the gain spectrum to be controlled over several Stokes orders. The MOPA configuration, with a low-power seed source, allows for excellent control of the pump pulse parameters which is not easily available from Q-switched or mode-locked lasers. The power level can then be amplified up to those required for SRS in a cascade of amplifiers. Thus, a diode-seeded high power Yb doped fiber source emitting around the 1050 to 1100 nm region constitutes a flexible pump source that can in principle be used to generate gain for any signal from ~1100 to 2000 nm in a silica-based fiber via cascaded SRS limited by the host material propagation loss. The unique properties of a pulsed MOPA pump source therefore opens up new opportunities for control of the Raman gain spectrum through control of the pulse parameters (i.e., shape, peak power, duty cycle, etc [9
9. C. Farrell, C. Codemard, and J. Nilsson, “A counter-propagating cascaded Raman fiber amplifier pulsed pumped with a 1.06 µm source,” in Frontier in Optics, (16–20 Sept 2007, San Jose, CA, 2007), paper FWB2.
10. C. Farrell, C. Codemard, and J. Nilsson, “A Raman fibre amplifier generating simultaneous gain across multiple Stokes orders by using step shaped optical pulses,” in 3rd EPS-QEOD Europhoton Conference, (31 Aug - 05 Sep 2008, Paris, France, 2008), paper THoC5.
We report counter-propagating Raman gain measurements up to seven Stokes orders from a pump wavelength of 1064 nm and optionally also at 1090 nm in a silica-based highly nonlinear fiber (HNLF). We used quasi-rectangular pump pulses to increase the conversion efficiency between Stokes orders. Furthermore, we also investigate the Raman gain spectra produced from pumping the HNLF with step-shaped pump pulses. Such pulses consist of multiple levels with different instantaneous powers which can be controlled by adjusting the height of each level. By tailoring the height (i.e., instantaneous power) of each level appropriately we make different parts of the pulse transfer their energy to different Stokes orders, leading to a controllable gain spectrum covering multiple Stokes orders. We can further control the gain spectra by manipulating the individual duty cycle of each section of the step-shaped pump pulse as well as using multiple pump wavelengths in a TDM pumping scheme. We believe this could open up opportunities for an ultra-broadband FRA with near-instantaneous electronic control of the gain spectrum.
2. Experimental set-up and fiber specifications
The experimental set-up is depicted in Fig. 1
Fig. 1 Schematic of the dual wavelength MOPA pump source. AWG: Arbitrary waveform generator; CP: Cladding pumped; YDFA: Ytterbium-doped fiber amplifier; HR: High reflectivity; HT: High transmission.
. The MOPA source used for pumping the HNLF was capable of emitting two wavelengths at 1064 nm and 1090 nm, either on their own or both together. The diode lasers that seeded the pump MOPA were driven by electrical pulses from an arbitrary waveform generator (AWG) to provide the desired optical pulse shapes. The pump pulse durations used in this work were of the order of several hundred nanoseconds so that walk-off effects are negligible and the quasi-CW regime applies. The pulse repetition frequency (PRF) of the pump pulses was between 2 and 4 MHz. Both pump seed sources were then combined into a single fiber using a 1064/1090 nm WDM coupler before entering the pre-amplifier comprising a cladding pumped (CP) Yb-doped fiber amplifier (YDFA). This boosted the total power up to ~400 mW before entering a polarization scrambler to reduce the polarization-dependence of the gain. The polarization scrambler, Fiberpro model PS-155-A, is designed for 1550 nm but works well at 1064 – 1090 nm as well, with an insertion loss of ~1.5 dB when spliced directly into the MOPA set-up (i.e., the connectors on the polarization scrambler were replaced by splices). At the output of the polarization scrambler another 1064/1090 WDM coupler split the two pump wavelengths for amplification in separate YDFAs. The separate power amplifiers reduced interactions between the two wavelengths which simplified and improved the control of the output power at each wavelength. To optimize the gain peak for each amplifier, the 1064 YDFA used a 12 m long cladding pumped phosphosilicate fiber, while the 1090 YDFA used a 12 m long cladding pumped aluminosilicate fiber. Both power-amplifiers were capable of boosting the average powers up to 5 W. The power amplifier outputs were then recombined into one delivery fiber for pumping the cascaded FRA, again using a 1064/1090 WDM coupler. We note however that YDFAs can work simultaneously at 1064 and 1090 nm, so the two YDFAs can be replaced by a single one for a simplified optical scheme, albeit with more difficult control.
The MOPA output was then free-space coupled into a tap coupler, which was in turn spliced to a HNLF to enable pumping and cascaded Raman conversion. A dichroic mirror could then be used in the free-space path to separate the Raman pumps (at 1064 and 1090 nm) and an ultra-broad range of Raman signal wavelengths (~1100-1700 nm). The seed source for the cascaded FRA comprised a nanosecond supercontinuum (SC) source with a PRF of 100 kHz and a conventional diffraction grating monochromator. The SC spectrum comfortably spans from 1100 to 1700 nm (see inset of Fig. 1
), as sufficient for this work. The monochromator was set to a resolution of 2 nm. Thus, the SC source followed by a monochromator provided a pulsed spectrally narrow tunable input seed signal to the cascaded FRA. The free-space output from the monochromator was launched into the HNLF through its pump output end, through a lens and a short piece of SMF-28 pig-tailed to the HNLF. The seed power launched into the cascaded FRA varied from ~2 µW to ~6 µW, depending on wavelength. In order to find the gain the output from the HNLF was measured with a lock-in amplifier locked to the SC source. The on-off gain was then determined as the ratio between the output signal with the pump on and off. The net gain was determined by subtracting the background loss of the HNLF. Thus, the signal in-coupling losses were disregarded.
The key specifications of the HNLF used for cascaded Raman conversion are shown in Fig. 2
Fig. 2 (a) Raman gain efficiency spectrum measured at 1064 nm for the HNLF. (b) Measured attenuation and chromatic dispersion profiles for the HNLF.
. Figure 2(a)
shows the Raman gain efficiency coefficient spectrum measured at 1064 nm. The Raman gain efficiency coefficient is defined as
, where gR
is the Raman gain coefficient and Aeff
is the effective area of the fiber [11
11. J. Bromage, “Raman amplification for fiber communications systems,” J. Lightwave Technol. 22(1), 79–93 (2004). [CrossRef]
]. The peak value of the Raman gain efficiency coefficient for the HNLF at a pump wavelength of 1064 nm is 14.26 km−1
(unpolarized), which can be compared to a typical value of less than 1 km−1
for SMF-28. The HNLF was fabricated by Sumitomo Electric Industries, Ltd and designed specifically for enhancing the nonlinear response with an increase in germanium (Ge) content and a smaller core diameter than standard single mode fibers (SMFs). The Sumitomo HNLF is composed of ~30% (mol) GeO2
Furthermore, Fig. 2(b)
shows the attenuation and dispersion profiles of the HNLF. The dispersion profile is important for clean cascaded Raman conversion across a wide range of wavelengths. The presence of a zero-dispersion wavelength (ZDW) located within the bandwidth of operation of the cascaded FRA can be detrimental as four-wave mixing, which requires phase-matching, would take over from SRS, thus causing the cascaded Raman conversion to break down. The HNLF is optimal for wide band wavelength conversion using cascaded SRS since the chromatic dispersion is always negative (i.e., normal) across the transparency range of the fiber.
3. Gain characteristics of different Stokes orders
Pulse-pumping leads to different gain characteristics for a co-propagating and a counter-propagating signal. A signal only experiences gain when and where it overlaps with a pump pulse. Due to the instantaneous nature of SRS, the instantaneous Raman gain will have a temporal profile which follows that of the pump pulses, thus leading to temporal gain variations. However, in case of counter-propagating pump and signal, the variations are averaged over the transit time through the fiber, and therefore over several pump pulses if the fiber is sufficiently long. Thus, the impact of temporal gain variations in a counter-pumped set-up can be reduced so that the temporal profile of the input signal (whether CW or pulsed) can be maintained at the output of the amplifier [12
12. P. J. Winzer, J. Bromage, R. T. Kane, P. A. Sammer, and C. Headley, “Repetition rate requirements for time-division multiplexed Raman pumping,” J. Lightwave Technol. 22(2), 401–408 (2004). [CrossRef]
]. In this regime, the gain in the counter-propagating direction is determined by the average pump power and is therefore proportional to the duty-cycle of the pump pulses. A low duty cycle then makes it difficult to generate high counter-propagating gain. On the other hand, for a co-propagating signal, a given part of the signal always overlaps with the same part of the pump, insofar as walk-off is negligible. Then, the highest gain is determined by the pump peak power. It can therefore be quite high even at low duty cycles, higher than the counter-propagating gain by the inverse of the duty cycle, and readily leads to cascaded SRS even at low duty cycles and average powers. Thus, the pump experiences cascaded SRS in the co-propagating direction, and generates a high (peak) gain in the co-propagating direction and a reduced gain in the counter-propagating direction. Since SRS limits the co-propagating gain to roughly 55 dB according to our simulations, it follows that the counter-propagating gain is limited to this value times the duty cycle. Spectrally, the peaks of the gain match the spectral peaks of the SRS cascade. For the computer simulations we employed a cascaded FRA model for co-propagating CW pumping from the commercial software package, VPIphotonics [13
]. This is based on the conventional equations for the evolution of the power of the pump and Stokes waves [14
14. G. P. Agrawal, Nonlinear Fiber Optics, 3rd Ed. (Academic Press Inc, San Diego CA, 2001).
]. The model is fully spectrally resolved across the whole wavelength range we consider. Note that counter-propagating light is not included. The recorded co-propagating CW gain was then multiplied by the duty cycle of the pump pulses to provide the counter-propagating gain. The computer model includes the attenuation profile of the HNLF (as shown in Fig. 2(b)
) across the full wavelength range of operation. It also includes the full Raman gain efficiency spectrum (as shown in Fig. 2(a)
) along with a scaling factor that takes into account the inverse dependence of gR
on the effective pump wavelength as the gain shifts further away from the initial pump wavelength of 1064 nm in the cascaded process. However no attempt has been made to fully solve for the modes in the HNLF or to accurately calculate the effective area at different wavelengths. Furthermore, we did not include Rayleigh scattering or dispersion in our simulations.
We have measured the counter-propagating Raman gain up to seven Stokes orders with a 2 km length of the HNLF. The cascaded Raman gain measurements were performed for pump pulses with duty cycles of 20% and 40%. The pump pulses were approximately rectangular with pulse durations ~150 ns. Figure 3(a)
Fig. 3 (a) Counter-propagating on-off gain and (b) counter-propagating net gain over seven Stokes orders for the 2 km HNLF: (‒●‒) corresponds to a 20% duty cycle; (‒▲‒) corresponds to a 40% duty cycle. (c) Simulated data for the counter-propagating on-off gain over seven Stokes orders for the 2 km HNLF: (‒♦‒) corresponds to a 20% duty cycle; (‒x‒) corresponds to a 40% duty cycle. (d) A simulated gain spectrum for a pump power of 0.8 W, where the maximum gain is located at the 1st Stokes order. 1st Stokes (▬) = 1116 nm, 2nd Stokes (▬) = 1172.4 nm, 3rd Stokes (▬) = 1235.6 nm, 4th Stokes (▬) = 1305.8 nm, 5th Stokes (▬) = 1384.8 nm, 6th Stokes (▬) = 1473.6 nm, 7th Stokes (▬) = 1573.6 nm.
shows the on-off gain measured at the different Stokes peaks for the 20% and 40% pump duty cycles. For this measurement, we used a single pump wavelength of 1064 nm with the counter-propagating gain at the 7th Stokes order, corresponding to a wavelength of 1573.6 nm. The measurement was stopped there since the 8th Stokes order with a wavelength of ~1690 nm was not observable on our optical spectrum analyzer and also the loss of silica-based fibers increases sharply around this wavelength. However we believe this is the first time a pulse-pumped cascaded Raman gain measurement over seven Stokes orders has been undertaken without the interference of supercontinuum effects from four-wave mixing (FWM) and for high duty cycles (> 1%), whereby the counter-propagating gain becomes important and a measurable quantity. For pump pulses with a 20% duty cycle the counter-propagating on-off Raman gain across the seven Stokes orders had an average value of ~7.2 dB. With a 40% duty cycle the counter-propagating on-off Raman gain across the seven Stokes orders had an average value of ~13.6 dB. We note also that the extra pump power required to cascade from one Stokes order to the next increases with the Stokes order, in experiments as well as in simulations. The reason for this is that the Raman gain efficiency decreases with increasing wavelength. Furthermore, the 1380 nm absorption peak reduces the amount of power that Raman-scatters beyond the fourth Stokes order, which further reduces the rate at which the cascade progresses for Stokes orders higher than that. In Fig. 3 (b)
, the on-off gain is converted to net gain by subtracting the background loss of the amplifier which comprises the attenuation of the HNLF and any splice loss between the HNLF and the SMF-28 pigtails. The on-off gain (in dB) is approximately 30-40% lower than that estimated by our computer simulations depending on the Stokes order, which we tentatively attribute to limitations with our current experimental set-up. For example, the polarization scrambling may be inadequate for complete depolarization for co-propagating SRS which then speeds up due to a higher gain, but may still be adequate for counter-propagating SRS, the gain of which is then reduced relative to the co-propagating value. However, we did not investigate polarization effects. See [15
15. Q. Lin and G. P. Agrawal, “Vector theory of stimulated Raman scattering and its application to fiber-based Raman amplifiers,” J. Opt. Soc. Am. B 20(8), 1616–1631 (2003). [CrossRef]
] for a treatment of polarization effects on co- and counter-propagating Raman gain. Figure 3(c)
shows a numerical simulation of the on-off gain at different Stokes orders vs. instantaneous pump power with parameters corresponding to the experimental ones. The qualitative agreement is good, although the achievable gain is higher. Furthermore, Fig. 3(d)
shows a simulated gain spectrum for an instantaneous pump power set to 0.8 W, where the maximum gain is located at the 1st Stokes order. The full width at half maximum (FWHM) for the 1st Stokes order at maximum gain is 8.4 nm.
The results in Fig. 3
show that it is possible to get Raman gain over a wide range of wavelengths in the HNLF through pulse-pumping with a Yb-doped fiber MOPA source. The spectral location of the gain can be shifted to any of the Stokes orders by controlling the instantaneous power to the FRA at the final stage of the MOPA pump source. The pump wavelength from the Yb MOPA source can also be adjusted to change the spectral location of the peak Raman gain. Furthermore, we believe the FRA can operate with a shorter fiber length than we used which would further increase the net gain for a given duty cycle. However, even though the gain can cover a wide range of wavelengths, it was restricted to a relatively narrow wavelength range at any one time. Some applications call for gain that extends over a wide wavelength range at a given time. We therefore build on this work by investigating the Raman gain spectra generated from pumping the 2 km HNLF with step-shaped pulses consisting of multiple levels and target gain simultaneously over multiple Stokes order.
4. Multi-Stokes gain control with single-wavelength stepped pump pulses
We used two- and three-level step-shaped pump pulses from the 1064 nm MOPA source to generate close to equal gain simultaneously across two and three Stokes orders, respectively. The step-shaped pulses have a total duty cycle of ~50% (i.e., there was no pump 50% of the time). This duty cycle was chosen with a view to later adding the 1090 nm pump wavelength in a TDM pumping scheme, although the single pump wavelength source could be operated with multiple levels up to a total duty cycle of 100%. Figure 4 (a)
Fig. 4 Dual-level pulse-pumping of the 2 km HNLF. (a) Initial pump pulse with 50% total duty cycle. (b) Resulting counter-propagating Raman gain spectra; Curve A: 502 mW of average pump power, Curve B: 797 mW of average pump power. (c) Temporal profile of transmitted pump at 1064 nm after propagating through the 2 km HNLF for curve A. (d) Temporal profile of co-propagating 1st-Stokes power, as Raman-scattered from the pump pulse shown in (a) (corresponding to curve A). (e) Same as (d) but for the 2nd-Stokes power.
shows the two-step pump pulse and the resulting counter-propagating Raman gain spectrum is shown by curve A in Fig. 4(b)
. The height ratio between the levels was adjusted so that the instantaneous powers of each section of the pump pulse were close to being fully converted to their targeted Stokes orders (see Figs. 4(c)
). Thus, there is no shorter-wavelength pump power left that can generate additional Raman gain, i.e., the effective pump for respective Stokes order has been depleted.
At the same time, a higher launched pump power would lead to power conversion to higher Stokes orders, which reduces the gain at lower Stokes orders. Therefore the different steps supplied the maximum achievable gain to their targeted Stokes order. The resulting peak on-off gain values at the 1st and 2nd Stokes orders were 12.5 dB and 12.9 dB, respectively. The total average input power to achieve this gain was 502 mW. Furthermore, curve B in Fig. 4(b)
shows how the gain can be pushed out to the 2nd and 3rd Stokes orders by increasing the average pump power and adjusting the individual step-heights appropriately. The total average pump power to push the gain out to the 2nd and 3rd Stokes order was 797 mW. In this case the peak on-off gain at the 2nd and 3rd Stokes orders was 11.5 dB and 12.3 dB, respectively. We consider this slight reduction from the earlier result to be within the error margin of the measurements.
The composition of the overall gain spectrum given by curve A was confirmed by experimentally measuring the on-off gain for single-step quasi-rectangular pump pulses, each with a 25% duty cycle and the same instantaneous powers as each step of the dual-level pump pulses. Figure 5
Fig. 5 (a) Quasi-rectangular pump pulses with 25% duty cycle and (b) Counter-propagating on-off gain versus average pump power for the 1st and 2nd Stokes orders.
shows the pump pulses and the resulting on-off gain measurements at the peak of the 1st and 2nd Stokes orders using the 2 km HNLF. The height ratio of the dual-level pump pulse in Fig. 4
was approximately 0.55:1. Therefore from the total input pump power of 502 mW, the average input pump power for the first and second section of the dual-level pump pulse is estimated to be 178 mW and 324 mW. These power levels have been highlighted in Fig. 5(b)
. The single-step pump pulse with a 25% duty cycle and peak power of 178 mW operates in the depleted pump regime and generates 8.6 dB of on-off gain at the 1st Stokes order and 4.1 dB of on-off gain at the 2nd Stokes orders. Likewise, a similar pump pulse with a 25% duty cycle and peak power of 324 mW generates 8.8 dB of on-off gain at the 2nd Stokes order and 4.3 dB of on-off gain at the 1st Stokes orders. This gives a total on-off gain of 12.9 dB at the 1st Stokes order and 12.9 dB at the 2nd Stokes order. These results are in good agreement with those given by curve A in Fig. 4(b)
. Thus, an instantaneous power-level that maximizes the gain at a particular Stokes order also contributes some gain at neighboring Stokes orders, and the total gain at a Stokes order is the sum of the gain provided by the different steps in a multi-level pulse.
It follows, also, that a single step pulse can generate gain over two and even three Stokes orders at any given time. This can be seen in Fig. 3
and Fig. 5(b)
. However, equal gain is only possible across two neighboring Stokes orders and is also only possible over a narrow pumping region. Pumping with shaped pulses offers more control over which Stokes order the pump power is converted to, and non-neighboring Stokes orders can be targeted, too (e.g., 1st and 4th orders). This pulse-shaping is readily achieved by utilizing the advantages of a MOPA pump source.
In Fig. 5 (b)
, the residual gain at the 1st Stokes becomes negative, but only by a relatively small amount, as the average power increases to high average values corresponding to SRS to higher Stokes-orders. This is generally true, implying that the generation of high-order Raman gain is not associated with significant nonlinear loss at lower Raman orders. Nevertheless, the absence of positive gain at low Stokes orders for a high-order cascade limits the scope for high gain over a broad bandwidth. For pump powers sufficiently high for cascaded SRS, simulations show that the spectral integral over the region with positive gain is approximately equal to 1.1 × 1015
dB Hz × ηp
, where ηp
is the pump duty cycle. Thus, in this regime, a continued increase of the pump power shifts the Raman gain rather than increases it, insofar as the spectral bandwidth remains the same, and the spectral integral is limited to 1.1 × 1015
dB Hz for a duty cycle of 100% (see Fig. 6
Fig. 6 Spectral integral of gain over region with positive Raman gain versus instantaneous pump power for CW pumped cascaded SRS.
Fig. 7 Multi-level pulse-pumping of the 2 km HNLF. (a) Initial pump pulse with 47% total duty cycle. (b) Resulting counter-propagating Raman gain spectra. (c) Section of pump pulse transferred to the 1st Stokes order. (d) Section of pump pulse transferred to the 2nd Stokes order. (e) Section of pump pulse transferred to the 3rd Stokes order.
shows a further example using multi-level pump pulses with three steps at a single wavelength to generate a gain spectrum with approximately equal maximum on-off gain across three Stokes orders. It also shows the sections of the pump pulse which are transferred to the three Stokes orders. In this example the pump pulses have a total duty cycle of 47% (see Fig. 7(a)
) but in order to obtain equal maximum on-off gain across three Stokes orders the individual duty cycles of each level are not equal. The first level has a duty cycle of ~22%, the second level has a duty cycle of ~7% and the third level has a duty cycle of ~18%. The height ratio of the individual steps was set at 0.34:0.65:1 so that the instantaneous power of each section corresponded to that required for nearly full conversion to its respective Stokes order. The total average power required was 590 mW. Figures 7(c)
show the sections of the pump pulse which were Raman-scattered to the 1st, 2nd and 3rd Stokes orders, respectively. The average maximum gain across all three Stokes orders is approximately 7.9 dB, so close to two thirds of the gain obtained for the two Stokes orders case of Fig. 4
at a similar duty cycle. The gain could be doubled by simply doubling the duty cycle.
In this example, the duty cycle of the middle section of the multi-level pump pulse is lower than the other sections because the wavelength region of the 2nd Stokes order receives gain contributions from both the lower and higher level sections of the pump pulse. The power levels are again set so that each section of the multi-level pulse generates the maximum on-off gain at their targeted Stokes orders. However from Fig. 5
it can be seen that the maximum on-off gain extends over a wide pumping region of power. Over this range of pump powers there will always be some gain contributed to neighboring Stokes orders, the amount of which depends on the exact amount of pump power.
Perhaps most relevant would be to generate a required gain spectrum with pulses that are as easy to generate as possible (e.g., with the lowest bandwidth), but we have not investigated this. The noise properties can also be different with different pulse shapes, even if the gain spectra are similar.
These results show that it is possible to use shaped pump pulses with multiple levels to generate gain simultaneously across multiple Stokes orders with a high degree of control, albeit at the expense of the maximum gain. However, we can also see that it is impossible to realize a continuous, flat, Raman gain spectrum across multiple Stokes orders with a single pump wavelength in a silica fiber. There will always be gaps between neighboring Stokes orders due to the intrinsic characteristics of the Raman gain. The spectral location for each Stokes order is determined by the location of the peak gain at the previous Stokes order, which is ultimately determined by the initial pump wavelength. It follows that multiple pump wavelengths could be employed to fill in the gaps of lower gain between the peaks of neighboring Stokes orders seen with a single pump wavelength.
5. Ultra-broadband spectral gain control with two pump wavelengths
In using TDM pumping, pump-to-pump Raman interactions between pump sources at different wavelengths are avoided and the resulting Raman gain spectrum is a superposition of the individual Raman gain spectra from the individual pump wavelengths. A second pump at 1090 nm would be located in the middle of the 1064 nm pump source and the corresponding peak of the 1st Stokes order at 1118 nm. We therefore use the 1090 nm pump in combination with the 1064 nm pump to generate a flatter Raman gain spectrum extending over two Stokes orders.
Fig. 9 Dual-level pulse-pumping of the 2 km HNLF with two pump wavelengths at 1064 nm and 1090 nm; (a) initial pump pulse with 75% total duty cycle; (b) resulting counter-propagating Raman gain spectrum; (c) depleted pump pulses after propagating through the 2 km HNLF; (d) section of pump pulses transferred to the 1st Stokes order; (e) section of pump pulses transferred to the 2nd Stokes order.
shows a Raman gain spectrum optimized for flatness, generated from pumping the 2 km HNLF with dual-level pump pulses from the dual-wavelength MOPA source. The Raman gain spectrum covers the wavelength region from ~1110 to 1220 nm. The power levels of the pump pulses are set to target maximum gain at their respective 1st and 2nd Stokes orders (see Fig. 9(a)
). For all the pump pulses the height ratio between the two levels was approximately 0.6:1. The total average pump power used to produce the Raman gain spectrum in Fig. 9(b)
was 944 mW, and the total duty cycle was 75%. The ratio of average pump power at the two pump wavelengths closely followed that of their respective duty cycles. The ratio was approximately 0.74:1 with the 1064 nm pump having the higher average pump power.
shows the sections of the pump pulses which are left un-depleted at the launched pump wavelengths and the sections which are transferred to the 1st and 2nd Stokes orders after being Raman converted in the 2 km HNLF. It can be seen that the individual duty cycles of each level are heavily weighted at the lower level of the short wavelength pump and the higher level of the long wavelength pump. These two sections of the pump pulses correspond to the beginning and end of the composite Raman gain spectrum. As emphasized in Fig. 8
, there are significant overlapping gain contributions in the centre of the composite Raman gain spectrum. This is ultimately reflected in the pump pulse profiles with reduced individual duty cycles for the sections that directly target gain in the centre of the composite Raman gain spectrum. Again as shown in Fig. 8
, a similar gain spectrum could also be reproduced by modifying the instantaneous power and the individual duty cycles of each section of the pump pulses. Furthermore the flatness of the Raman gain spectrum can be improved by optimizing the wavelength location of the second pump source. This was verified using computer simulations.
Fig. 10 Counter-propagating Raman gain spectra (a) resulting from simulations of dual-level pulse-pumping of the 2 km HNLF with two pump wavelengths. The black curve shows a flattened gain spectrum using the pump pulse profiles in (b) and pump wavelengths of 1064 and 1090 nm. The red curve shows a flattened gain spectrum using pump wavelengths of 1064 and 1087 nm.
shows the simulated Raman gain spectra generated for pumping the 2 km HNLF with two pump wavelengths and dual-level pulses. Again, the CW-pumped cascaded FRA model described in section 3 is employed. This is still valid with a TDM pumping scheme since none of the pump wavelengths used to produce the step-shaped pulses are overlapping in time. Therefore they can all effectively be treated as separate pump sources whose resulting gain spectra can be simply added together, in the absence of signal-induced gain saturation and walk-off. The two pump wavelengths used to produce the black curve in Fig. 10(a)
are the same as those used in the experimental work, i.e., 1064 and 1090 nm. The pump pulses used to produce this gain spectrum are shown in Fig. 10(b)
. The power levels used in the simulation are similar to those used in the experiment and so the pump pulse profiles are very similar. The individual duty cycles for the 1st and 2nd section of the pump pulses were adjusted to 48% and 5% for the 1064 nm pump and 10% and 35% for the 1090 nm pump, respectively. A good correlation in the shape of the gain spectra can be seen between the simulated data of the black curve and the experimental data in Fig. 9
. The red curve in Fig. 10(a)
shows a flatter Raman gain spectrum produced by optimizing the wavelength spacing between the two pump wavelengths. The longer pump wavelength is shifted from 1090 nm to 1087 nm. In this case the power levels were kept the same but individual duty cycles for the 1st and 2nd section of the pump pulses were adjusted to 46% and 7% for the 1064 nm pump and 10% and 35% for the 1087 nm pump, respectively. Improvements in the flatness of the Raman gain spectrum can be seen albeit at the expense of a slight reduction in the overall bandwidth. Still, our example falls short of a complete optimization over five or six free parameters, so flatter and wider gain spectra may well be possible.
While experimental measurements were only taken using two pump wavelengths, the use of additional pump wavelengths was also investigated using computer simulations. It was concluded that three pump wavelengths was enough to achieve good flatness for a Raman gain spectrum covering multiple Stokes orders. The use of more pump wavelengths did not improve gain flatness. However, it should be noted that more pump wavelengths could potentially allow for more complex gain shapes with a higher resolution. The three pump wavelengths used for simulations were 1064 nm, 1081 nm and 1098 nm, whereby the wavelength spacing was approximately the first Stokes shift in the HNLF (52 nm) divided by 3. Figure 11
Fig. 11 Counter-propagating Raman gain spectra (a) resulting from simulations of multi-level pulse-pumping of the 2 km HNLF with three pump wavelengths. Black curve: Flattened gain spectrum across the 1st, 2nd and 3rd Stokes orders using pump pulse profiles shown in (b); Red curve: Flattened gain spectrum across the 5th, 6th and 7th Stokes orders; Blue curve: Flattened gain spectrum across seven Stokes orders (1st to 7th).
shows some examples of simulated flattened Raman gain spectra using the three pump wavelengths. For the black curve shown in Fig. 11(a)
, gain is targeted over the 1st, 2nd and 3rd Stokes orders. For this a combination of two-level and three-level pump pulses was used as shown in Fig. 11(b)
. The 1064 nm pump used a three-level pump pulse whose individual duty cycles for the pump pulse sections were set to 29%, 7% and 7%. The 1081 and 1098 nm pumps used two-level pump pulses whose instantaneous powers were set to target maximum gain directly at the 1st and 3rd Stokes orders. The individual duty cycles for the pump pulse sections were adjusted to 16% and 14% for the 1081 nm pump and 12% and 15% for the 1098 nm pump, respectively. The resulting simulated gain spectrum has an average on-off gain of ~15.5 dB across a gain bandwidth of ~180 nm or 37 THz. This implies that the maximum gain – bandwidth product of 1.1 × 1015
dB Hz was not reached. Finally the red and blue curves in Fig. 11(a)
show two more examples of pumping the cascaded FRA with multi-level pulses and the three pump wavelengths of 1064 nm, 1081 nm and 1098 nm. The red curve shows a Raman gain spectrum where the gain has been pushed out to the 5th, 6th and 7th Stokes orders. The resulting simulated gain spectrum has an average on-off gain of ~20 dB across a gain bandwidth of ~290 nm or 38 THz and covers the wavelength region from 1370 to 1660 nm. The blue curve used multi-level pump pulses up to seven levels and shows a Raman gain spectrum targeting gain from the 1st to the 7th Stokes order. The resulting simulated gain spectrum has an average on-off gain of ~9 dB across a gain bandwidth of ~500 nm or 80 THz. In these cases the integrated gain spectra come close to the limit of 1.1 × 1015
We have demonstrated spectral gain control in a counter-pumped cascaded FRA by employing shaped pump pulses delivered from a fiber MOPA source. For the Raman gain medium we used a silica-based HNLF which exhibits a high Raman gain efficiency, low attenuation and tailored chromatic dispersion profile making it ideal for cascaded Raman conversion over a wide wavelength range. Using this fiber we were able to measure Raman gain over seven Stokes orders showing the potential of covering the whole spectral region from ~1100 nm to ~1700 nm. Following on from this we also generated Raman gain simultaneously at multiple Stokes orders using multi-level pump pulses. This extends the Raman gain bandwidth of the cascaded FRA from those using single-level pump pulses. Experimental results were reported for controlled gain across two and three Stokes orders. Furthermore, the gain flatness of the multi-level pulse-pumped cascaded FRA was improved by employing two pump wavelengths in a TDM pumping scheme. We have also used theoretical predictions and simulations to support and explain the experimental results for the ultra-broadband Raman gain spectra covering multiple Stokes orders, as well as simulated the use of more than two pump wavelengths to improve the flatness of the Raman gain spectra and extend the gain bandwidth across seven Stokes orders.
Further investigations of this pulse-pumped cascaded FRA looking into the noise properties are ongoing, although early indications suggest the counter-propagating noise is dominated by the amplified spontaneously scattered light or Raman ASE that is Rayleigh backscattered from the co-propagating direction. While the noise figure is high compared to that required for optical communication systems, it is still acceptable for other applications. Therefore, we believe this work could open up opportunities for an ultra-broadband FRA with near-instantaneous electronic control of the gain spectrum, within the limited gain – bandwidth product of a cascaded Raman amplifier.