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Backward stimulated Raman scattering is generated in water, pumped by pre-compressed pulses from a single-cell stimulated Brillouin scattering pulse compressor. The maximum energy efficiency of 9% is achieved by employing a circularly-polarized pump pulse at its energy of 50 mJ, around which point the backward stimulated Raman scattering also exhibits a ring-shaped profile. The correlations between spatial and temporal profiles as well as the intensities of the backward stimulated Raman and the stimulated Brillouin scattering generated from Raman cell indicate that the ring-shaped backward stimulated Raman is driven by intense stimulated Brillouin scattering. We demonstrate the latter process to be much more efficient for the backward Raman generation than the conventional process in which the laser itself pumps a backward stimulated Raman beam. It is shown that a further increase in pump energy leads to a drop in efficiency, combined with a break-up of the ring pattern of backward stimulated Raman. These effects are associated with filament generation above a certain threshold.
© 2015 Optical Society of America
1. Introduction
Stimulated Raman scattering (SRS) was first observed in organic liquids [1, 2] pumped by Q-switched pulses, and later reported from water excited by a higher intensity mode-locked subnanosecond laser [3]. It has been noticed that, using nanosecond pulses, stimulated Brillouin scattering (SBS) is the dominating process because of its larger steady-state gain coefficient as compared to the SRS process [3–5]. Recent experiments have demonstrated that the SBS efficiency could reach as high as 98% in liquid fluorocarbon [6] and 75% in water [7] provided that a single-longitudinal-mode Q-switched laser is used. SBS however is reduced when the pump pulse-width is close or smaller than the phonon life time, due to the smaller transient SBS gain. With reduced depletion into SBS, mode-locked picosecond [8] and subnanosecond [9] pulses were employed to enhance the forward SRS. Extremely efficient forward SRS conversion up to 80% has been obtained.
Besides SBS and forward SRS, backward stimulated Raman scattering is a third process pumped simultaneously by the input laser. The early theory [10] predicts that the backward to forward SRS intensity ratio should be unity under steady-state condition. However, experiments have shown large discrepancies, i.e., the ratio is less than 10−2 if pumped with subnanosecond or shorter pulses [9, 11]. A ratio of more than unity has also been reported by Maier et al. [5], where a Q-switched nanosecond pulse (15 ns) is used to obtain a maximum backward SRS energy of 1.5 mJ from CS2. The competition between SBS and SRS is again attributed to the suppression of backward SRS. Several factors, such as cross section difference, multimode excitation and self-focusing, appear to contribute to the backward to forward SRS ratio. Among those three, self-focusing has clearly shown its importance in changing the ratio by favoring the forward emission [12, 13]. Therefore, both SBS and self-focusing should be minimized in order to achieve better backward SRS efficiency. Based on this fact, Chevalier et al. [14] have demonstrated a very high backward SRS efficiency of 40% by choosing a material (i.e. acetone) with a maximum Raman gain (g) to nonlinear index (n2) ratio, and by pumping with mode-locked picosecond pulses. It is worth noticing that the maximum backward SRS energy is obtained at the pump energy of 1 mJ. A further increase in pump intensity leads to a quick drop of the backward SRS generation, associated with an efficient build-up of filaments inside the liquid. It is concluded that the backward SRS energy is not scalable if picosecond pump pulses are used.
Other than the common competition existing between SBS and SRS, Zhang et al. [15] have reported the pumping effect of SBS on SRS by focusing single-mode nanosecond pulses into a liquid droplet. The droplets provide whispering gallery mode resonators for the SBS generated from the pump laser and confine both SBS and SRS along the entire droplet circumference for maximum spatial overlap. The highly correlated spatial profiles of SBS and SRS indicates that the SRS is pumped by SBS. This is further confirmed by the temporal correlation as well as the SRS threshold measurements. Very recently, Liu et al. [16, 17] have extended the pumping effect of SBS on backward SRS into a more universal case of optical cell experiment. By focusing single-mode nanosecond pulses into a water cell with focused depth up to 1.8 m, the correlation on SBS and backward SRS energies is found to support the existence of pumping of SRS by SBS. A maximum backward SRS energy of 0.25 mJ, corresponding to an efficiency of 0.03%, has been achieved. It has also been shown that the backward SRS excited by the pump laser and by SBS co-exist and could not be distinguished [17].
In this work, we demonstrate backward SRS generation of high energy (4.5 mJ) and high conversion efficiency (9%) from a water cell. For the first time, a special ring-shaped backward SRS profile, which is associated with the spatial dependent pulse-width distribution of pre-compressed pump pulse, is reported. We present evidence that the backward SRS results from forward pumping by backward SBS, based on different correlations between SBS and backward SRS generated from Raman cell. Our study on the evolution of filament generation in water under different pump inputs leads to an understanding of our measurements on SRS, as well as the results [5, 14] obtained earlier with pump pulses of different duration.
2. Pump source for the Raman cell
In most prior experiments of stimulated Raman scattering, the pump is produced by a standard inversion laser. The source used in the present investigation is based on backward SBS. The pulse compression mechanism has been described in detail in [18]. The pump source for Raman generation is a single 2.5 m long oscillator, and does not include an amplifier cell as in [7]. The primary pump for the 2.5 m long SBS cell is a home-built frequency-doubled Q-switched Nd:YAG laser delivering single-longitudinal-mode laser pulses [19] with up to 3.5 J energy and pulse-width of 12 ns at 532 nm.
The theoretical analysis involved a system of 3 differential equations for the forward pump field, the backward signal and the phonon field. The slowly varying envelope approximation was only applied to the optical fields. This theoretical model was verified to match the experimental results for the two liquids evaluated: water and FC-72. The main result relevant for the present work is that the duration of the pulse generated in an SBS generator follows the intensity profile of the pump, with the shortest (300 ps at full power) pulses being at the beam center. The resulting pulse duration profile is shown in Fig. 1(a). The energy of this pulse is plotted as a function of primary pump pulse energy in Fig. 1(b). The beam profile of the SBS generated in this cell ranges from 25 mm at 50 mJ output, to 30 mm at maximum output energy (400 mJ).
Fig. 1 (a) Spatial pulse-width distributions of the pump generated in the first cell, at the energies of 10 and 50 mJ; (b) Energy and efficiency of the SBS cell generating the pump pulse, as a function of the primary Nd:YAG pulse energy
3. Experimental setup
The experimental setup sketched in Fig. 2(a) includes the SBS generator described in the previous section, followed by a 54 cm long water cell (SRS cell). The pump beam is coupled out through TP2 [Fig. 2(a)], focused by the lens L2 and directed by two mirrors into the SRS water cell. The latter is slightly tilted to spatially separate the backward signal and surface reflections. The polarization of the SRS pump can be manipulated with the quarter-wave plate QW2. The position of the lens L2 is adjusted to have the focal spot at 27 cm from the entrance window, a depth chosen to match half of the spatial length of the 2 to 3 ns pulses.The coupling optics between the two cells implies a reduction factor of 2.8, hence an input diameter ranging from 9 mm at 50 mJ to 11 mm at 400 mJ. The dichroic mirror (DM) with >99% reflectivity at 532 nm and ∼95% of transmittance around 650 nm allows the backward SRS to be coupled out and characterized. We measure the output energy, the spatial and temporal profiles for both SBS and SRS as well as the filament generated by the pump beam.
Fig. 2 (a) Schematic of experimental setup for SRS generation. The combination of a half-wave plate HW and a thin film polarizer TP1 is used to control the energy of the pulse (the pulse radial profile is I(r) = exp(−2r4/w4) with w = 15 mm) focused by the lens L1 (effective focal length of 2.2 m in water) into a first SBS cell. The quarter-wave plate QW1 makes the SBS p-polarized to transmit through the thin film polarizer TP2, to provide a pump for the second (SRS) cell. This pump is focused (lens L2 of 50 cm focal length) onto the 54 cm Raman cell via the dichroic mirror DM. Its polarization is controlled by the quarter-wave plate QW2. Different color filters (CF) are used to block the unwanted beams after both backward SRS and forward SRS are collected by lens L3 and L4, respectively. Throughout the paper, “backward SRS” refers to the propagation of the Raman radiation towards the left of the second cell. (b) Ring-shaped backward SRS profile at the pump energy of 50 mJ. (c) Typical forward SRS profile with the pump energy of more than 50 mJ.
4. Experimental results
4.1. Stimulated Brillouin scattering: energy and efficiency
The energy characteristic of the SBS generated by the compressed source differs significantly to those of nanosecond pumped SBS shown in Fig. 1(b). In the latter, the energy efficiency increases monotonically to approach 76% at 500 mJ, in agreement with previous reports [6,20]. The backward SRS is observed to appear randomly at an input energy around 400 mJ (SBS output energy of ∼300 mJ) and becomes stable when the input energy exceeds 500 mJ. A similar behavior has been reported by Liu et al. [16]. This energy behavior of SBS generator is characteristic of steady state generation [21]. By contrast, the energy characteristic of the SBS generated in the second cell [Fig. 3] shows a transition from steady state at low energy to transient. Because of the compression in the first cell, the pump in the second cell is of higher power (up to 1 GW) but less energy. As a result, the energy efficiency curve shown in Fig. 3 saturates at a relatively low energy, to peak at 45 mJ, and subsequently drops with increasing energy. The maximum SBS efficiency obtained is only about 20%, which can be explained by the shorter pump pulse duration (closer to the phonon lifetime of 295 ns in water at 532 nm) implying a smaller backward gain and SBS energy conversion to backward SRS.
Fig. 3 SBS output energy (left scale) and the corresponding efficiency (right scale) from the short SRS generating cell
4.2. Stimulated Raman generation: energy and stability
The pump radiation into the second cell results not only in generation of backward SBS, but also both backward SRS (with respect to the pump) and forward SRS (in the direction of the pump). Chevalier et al. [14] have reported that the backward SRS conversion efficiency in some materials could be enhanced by choosing circular pump polarization. Therefore, the backward SRS generations with both linearly and circularly polarized pump are compared. Figure 4(a) shows the SRS output energies at two different pump polarizations.
Fig. 4 (a) SRS output energies at both linear and circular pump polarization; (b) Relative Standard Deviation (RSD) of SRS energy at circular pump polarization. Forward and backward denote the SRS propagation direction with respect to the pump; Linear and circular refer to the pump polarization.
The energy dependence of the SRS does not follow the exponential dependence shown in [22], except at the lowest pump energies. In the case of forward generation, the energy dependence of the Stokes signal turns to linear, typical of saturation. Consistent with Chevalier et al. [14], a larger conversion for circular polarization than for linear polarization is observed at low energies. With increasing energy, the pump pulse duration reduces, resulting in (i) a decrease in backward conversion, and (ii) filamentation, as the peak intensity of the pump pulse increases.
The SRS energy fluctuation is also measured, as illustrated in Fig. 4(b), for the case of circular pump polarization. Similar behavior is observed for the pump with linear polarization (not shown here). It should be noted that the maximum 532 nm pump energy used in the first cell for SBS is below the threshold (400 mJ) for backward SRS generation. Therefore, no SRS signal from the first cell is seeded into the second cell. Several observations regarding the SRS generation are worth emphasizing. First, the generation of backward SRS is more efficient and more stable than that of forward SRS when the pump energy is below a certain threshold. The same observation indicating that the backward SRS to forward SRS ratio could even be larger than 1, has also been reported in the early work of Maier et al. [5] where a nanosecond pump pulse is used. Next, both backward SRS and forward SRS generation are pump polarization dependent. Backward SRS generation with a circularly polarized pump is more efficient, while forward SRS shows the opposite trend. The maximum backward SRS energy and conversion efficiency achieved are 4.5 mJ and 9%, respectively, when circularly polarized pump is employed. Last, the backward SRS generation saturates around a pump threshold and drops at higher pump energy. By contrast, forward SRS generation shows a sharp increase once the pump energy exceeds the same threshold as mentioned above. Since the circularly polarized pump excites backward SRS more efficiently, further experimental measurements presented below are based on the circularly polarized pump.
4.3. Spatial profiles and their corresponding intensities
The evolution of the spatial profiles of backward SRS presented in Fig. 5 shows some correlation with the energy plots of Fig. 4. Not shown in the figure are the profiles at the lowest pump energies, between 2 mJ (threshold for backward SRS) and 10 mJ, where the backward SRS profile evolves from a single spot (2 to 5 mJ) to 2 spots (8 mJ). This evolution continues from 5 spots (10 mJ) to a increasingly large number, as seen in Fig. 5(a). The same observation has been reported by Chevalier et al. [14]. As the pump energy increases from 10 to 50 mJ, a ring-shaped pattern appears in the backward SRS profile [Fig. 5(b)]. The ring shape starts to break up into spots again [Fig. 5(c)] with a further increase of the pump energy and the corresponding backward SRS energy also gradually drops from its maximum value. Irregular backward SRS profiles are later observed if higher pump energies (>100 mJ) are used.
Fig. 5 Spatial profiles of backward SRS and SBS taken with a digital camera at different pump energies; (a) and (d), 10 mJ; (b) and (e), 50 mJ; (c) and (f), 100 mJ; Fringes next to SBS profile are due to the leakage of back-scattering through the edge of the dichroic mirror.
The pump SBS itself can generate its own backward SBS signal, which then propagates in the same direction as the backward SRS shown in Figs. 5(a)–(c). It is interesting to compare the corresponding profiles of SBS, which are recorded in Figs. 5(d)–(f), with that of backward SRS. The profiles of SBS and backward SRS are highly correlated at pump energies around 50 mJ. By choosing appropriate filters to balance the contrast of green and red colors, the overlap of two rings is observed, which shows clear evidence that the backward SRS is driven by the SBS under current experimental conditions. It is worth emphasizing that, if backward SRS were to be excited by the pump itself, the high intensity portion of the backward SRS profile should be at the beam center [see forward SRS profile in Fig. 2(c)], where the pump beam exhibits its highest intensity.
In addition, we have measured the ratio of the intensity of the radiation in the ring and in the center of the hole, for both SBS and backward SRS. At the pump energy of 50 mJ, this ratio in the backward SRS beam is about 3 times of the ratio measured in the SBS beam. This is to be expected, since the generation of backward SRS is nonlinearly dependent on the SBS (pump) intensity before the saturation is reached, as discussed in Section 4.2.
4.4. Spatial pulse-width distributions
Measurements of the spatio-temporal profile of the pump pulse further demonstrate that the backward SBS is generating the backward SRS. A cross-section of the pulse-width distribution in the pump beam at 10 mJ and 50 mJ was shown in Fig. 1(a). This pulse-width distribution finds its origin in the first cell where the pump SBS is generated from a 532 nm pulse [7, 23]. The SBS gain in the second cell is decreasing with decreasing pulse-width, with the steepest dependence when the pulse duration approaches the phonon lifetime of 295 ps. The SBS reflectivity is moderate and uniform at the pump energy of 10 mJ, where the pump pulse duration remains above 1 ns across the beam. The backward generated SBS beam has a Gaussian like profile [Fig. 5(d)]. However, when the pump energy is increased to 50 mJ, the minimum pump pulse-width reduces to be 500 ps [Fig. 1(a)], quite close to the phonon lifetime. The corresponding SBS reflectivity around the beam center is then dramatically lowered due to the reduced transient SBS gain. The gain remains however high on the edges of the beam, where the pulse duration exceeds 1 ns. Therefore, a ring-shaped SBS profile is formed. As a result of the increasing hole in the center of the beam, the SBS efficiency decreases [Fig. 3]. At increasing pump energies, the portion of the pump beam with a few hundred ps duration increases in diameter, resulting in further reduction in efficiency. This is verified by the SBS profile with a larger hole taken at the pump energy of 100 mJ [Fig. 5(f)].
If the backward SRS were to be excited directly from the pump, it would have a profile with a higher intensity at the left side, corresponding to the shortest pump pulse duration seen also at the left side of the beam. However, the intensity distribution of backward SRS simply follows that of SBS beam, which exhibits less intense beam at the left side.
The spatial pulse-width distribution of SBS beam at the pump energy of 50 mJ is presented in Fig. 6. The horizontal axis is normalized such that the pulse-width of input and output could be compared directly. Since the focused depth is chosen to match the longest pulse-width at the beam edge, pulses within the whole beam area are efficiently compressed. It is worth mentioning that the shortest pulse-width achieved is below the phonon lifetime, which further increases the SBS intensity. The backward SRS pulse-width at the corresponding position is also measured and presented together with the SBS pulse-width. The pulse-width of backward SRS is seen in Fig. 6 to be shorter than the SBS pulse-width, which agrees to prior theoretical [17] and experimental [5] observations. The backward SRS and SBS appear to be correlated. For instance, the backward SRS shows shorter pulse-width at the position where the SBS pulse-width is also shorter. This provides further evidence of the pumping effect of SBS on backward SRS.
Fig. 6 Spatial pulse-width distributions: pulse-width of SBS and that of backward SRS at the corresponding positions at the pump energy of 50 mJ. Due to the limited temporal resolution of the pulse detection setup (140 ps rise-time), the actual SRS pulse-width could be much shorter than indicated in the figure.
4.5. Evolution of filament generation
Based on the correlations existing between different parameters of SBS and SRS, we have established that backward SRS could be efficiently driven by SBS. In this section we investigate the propagation of the pump, and the evolution of the backward SRS profile. It has been shown that the backward SRS is initiated by self-focusing [5] and its evolution related to filament generation [14]. The tracks of filaments are recorded in the photographs of Fig. 7, for different pump energies. At low pump energy of 2 mJ, both backward SRS and forward SRS generations are observed to appear randomly as a single small spot. As the pump energy increases, the number of backward SRS spots increases because of the generation of transversely distributed multiple filaments, which could not be resolved because of the limited spatial resolution [Fig. 7(b)]. At higher pump energy longer filaments are generated. As reported in [14], with increasing pump pulse energy, those backward SRS spots gradually disappear or become irregular areas. As mentioned in the previous sections, the ring-shaped SBS also starts to build up and excites the backward SRS, giving it a similar profile. At the pump energy of 50 mJ, only two main filaments [Fig. 7(c)] are shown to co-exist inside the beam center area, which ensures the generation of a regular ring shape. However, more filaments [Fig. 7(d)] are at the beam edge with even higher pump energy. Spots are observed again within the ring-shaped backward SRS profile [Fig. 5(c)]. The backward SRS energy also drops since the forward SRS generation is enhanced by the filament generation. Because of the competition existing between backward SRS and forward SRS, the stability of their energies thus shows opposite tendency.
Fig. 7 Evolution of filament generation in water under different pump energies; (a) 2 mJ; (b) 10 mJ; (c) 50 mJ; (d) 100 mJ; The pump beam propagates from left to right.
5. Optimization of the conversion efficiency in Raman
In this section we analyze the factors influencing the efficiency and high energy conversion into backward SRS, based on our data and those of [14, 16]. Our understanding of the mechanism of SRS generation leads to the conclusion that it is only possible to meet the conflicting requirements of high energy and high efficiency to backward SRS in a setup with multiple cells.
All observations converge to the conclusion that, in the backward direction, SBS is the primary and more efficient mechanism, and is a source of SRS in the same direction. The first element of the cascade pump SBS – backward SBS — SRS requires high efficiency and efficient compression of the pump SBS. Intensity enhancement could readily be satisfied since the SBS process is well known for its application in pulse compression [18]. In order to achieve best intensity enhancement, i.e., single compressed pulse and high energy efficiency, a focused depth (of the pump) of ≥1 m inside the medium is typically required to match half to full of the spatial length [cτp/n, where τp is the pulse-width (FWHM) and n is the index of refraction of the SBS medium] of the single-mode nanosecond input pulse. After the focused depth (f) is chosen, a small f-number (f/D) therefore a large input beam diameter (D) is also needed to keep the Rayleigh range small such that the point, where SBS starts to build up, is less dependent on the pump energy. Both larger f-number and higher pump energy tend to move the SBS build-up point towards the entrance, which equivalently reduces the focused depth and therefore lowers the efficiency of intensity enhancement. The generated backward SBS is amplified towards the cell entrance, to reach its maximum intensity near the peak of the pump, which, given the optimum design configuration for SBS, is close to the entrance window [24]. This is the region where the SRS is effectively generated, which happens — counter-intuitively — to be where the beam size is the largest. This explains the previous observation that backward SRS could barely be observed when the focused depth is short [16], and that a single-cell setup cannot drive very efficiently backward SRS generation.
A multiple-cell setup makes it possible to pre-shape the pump SBS pulse for optimum backward SRS generation. In the two-cell configuration presented here, a pre-compressed pulse (≤3 ns) serves as pump in the second cell, resulting in a much faster accumulation of SBS energy than in the case of a ∼10 ns pump pulse (as is the case in a single-cell setup [16]). Therefore, the SBS intensity reaches backward SRS threshold much earlier. Another advantage of the two-cell setup is that small beam diameter of 9 mm, which is defined by the f-number and focused depth chosen for the second cell, requires much less energy to obtain the same intensity as achieved from single-cell setup. As a result the energy efficiency could be dramatically enhanced. Last, the compressed SBS pulse-width could reach below the phonon lifetime with a two-cell setup design [25], which further enhances the SBS intensity to drive backward SRS more efficiently.
There are different configurations and liquids to be used depending on the energy to be achieved in the final process. For instance, if the initial pump energy of the first cell is highest, a liquid of small Brillouin gain, such as water, will be chosen to create a high energy SBS. This pump SBS could further be scaled up using a SBS amplifier cell, as demonstrated in [7, 18]. In the final cell for Raman generation, the efficiency can be optimized by a judicious choice of liquid with high Raman gain coefficients [8].
6. Conclusion
Efficient backward SRS generation from an optical cell driven by intense SBS is realized by exploiting a two-cell setup. The mechanism of backward SRS generation is interpreted as being a forward Raman process pumped by a backward SBS. This two step mechanism explains a ring-shaped backward SRS, as mimicking the spatial dependent pulse-width distribution of the pump beam. We show that filament generation plays a crucial role in suppressing the backward SRS generation. A circularly polarized pump is therefore employed to enhance the backward SRS generation by lowering the efficiency of filaments generation. A conversion efficiency of 9% for backward SRS is achieved in water. The evolution of SRS energy and its stability as well as the change of backward SRS profile are also investigated and explained in relation with the evolution of filamented beams. Higher SRS energies and efficiency can be obtained using different Raman media, and multiple cells.
Acknowledgments
This work was supported by DTRA grant HDTRA-11-1-0043 and the ARO MURI grant W911NF1110297.
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