1 Introduction

Stimulated Raman scattering (SRS) is one of the nonparametric third-order nonlinear optical effects with a distinctive threshold. It is an inelastic scattering process which has been observed in solid, liquid and gaseous media [1–3]. In this process, the incoming laser beam is scattered by the molecular vibrations of the medium. Depending on the molecular vibrational energy of the medium, the frequency of the scattered light can be lesser or more than the input frequency, referred to as the Stokes and anti-Stokes generation, respectively [4]. The gain for Stokes generation is higher than that of the anti-Stokes due to energy considerations, and hence, the new frequency generation is often dominated by Stokes frequencies. In the case of SRS, the use of the laser for excitation provides a large signal-to-noise ratio for the generation of new frequencies and enables the threshold of the process to be crossed. However, very high input powers can lead to some other nonlinear effects such as the stimulated Brillouin scattering and Kerr effect, which can reduce the efficiency of SRS. Hence, the power level of excitation is often kept just above the threshold for SRS process.

Since the Raman shifts are governed by the Raman-active vibrational modes of the material under study, they are independent of the input pump wavelength. Raman scattering can be generated from molecular vibrations, molecular rotations and combined vibration–rotations, depending on the material which is being used for observing it. There exist some selection rules for transitions from vibrational and rotational energy levels. Spontaneous scattering is present even at very low levels of excitation. But in the presence of higher input power, the threshold for stimulated scattering process is crossed and SRS occurs with significant efficiency.

Stimulated scattering leads to narrower linewidth and higher intensities than spontaneous scattering. Stimulated scattering also has a directional dependence with reference to the input beam for the generation of every new sideband. While the spontaneous scattering occurs in all directions, the stimulated process is predominant only in the forward and backward directions of the excitation beam. The spontaneously scattered light in directions other than the forward and backward is lost from the sidewalls of the sample cell. The scattered light in SRS propagating in the forward direction is known as forward stimulated Raman scattering (FSRS), and the light generated in the backward direction is known as backward stimulated Raman scattering (BSRS) [5–9]. SRS is used to get more than one new lasing wavelength in longer as well as in shorter wavelength region using the available conventional lasers. The new sidebands can be generated even at detunings larger than 100 nm from the input laser wavelength, depending on the Raman shifts in frequency and the gain bandwidth for the chosen medium.

We performed the SRS experiment using toluene as a nonlinear medium. Toluene shows efficient SRS effect, and it has been studied earlier by other authors [10–14]. Raman effect in toluene is seen due to different Raman-active vibrational modes of toluene such as those arising due to the ring-breathing mode, ring deformation mode [15], C–H bending mode, methyl (CH3) stretching mode [13] and C–H stretching mode [11]. There are some conflicting reports in the literature on SRS in toluene, such as those related to the experimentally observable Stokes lines, studies restricted to a few selected modes, extremely low intensity of Stokes lines reported in neat toluene indicating the need for mixing it with other solvents, absence of anti-Stokes lines even though sufficient energy was used and the spectral linewidth of the Stokes frequencies [10–14]. This necessitated a detailed study here to understand the process better, since toluene can be used as a reference in SRS measurements of novel materials.

In the present work, factors such as the relative threshold energy required for observing all the different modes in neat toluene, a justified assignment of the Raman modes from the values of shift seen for them, the relative gain of different modes and the spectral broadening associated with some of the modes are brought out clearly. In contrast to earlier reports, we emphasize that all the Raman modes can be observed in neat toluene without the need to mix it with other solvents. In addition, we have also analyzed the FSRS and BSRS in simultaneous measurements along with the phase-matching condition leading to the generation of the anti-Stokes line.

Highly intense new spectral lines generated by SRS have sparked further work on Raman amplifiers and lasers [18, 19]. Novel effects such as the surface-enhanced Raman scattering in metal colloids dispersed in standard solvents can increase the efficiencies further [20]. Thus, a precise understanding of the threshold energy, gain and spectral line shape is essential for analyzing the characteristics of the newly generated wavelengths in the SRS process and to design suitable applications.

2 Theoretical details

2.1 Conservation of energy and momentum

The conservation of energy as well as momentum is essential to the process of SRS. The scattered light has its energy lower or higher than the input light, as molecules of the medium absorb or lose their energy through scattering. The frequencies of the newly generated Stokes and anti-Stokes modes are obtained from Eqs. (1) and (2):

$${\text{Stokes}}:\omega_{\text{s}} = \, \omega_{\text{i}} - \, n\omega_{\text{vib}}$$
(1)
$${\text{anti-Stokes}}:\omega_{\text{as}} = \, \omega_{\text{i}} + \, n\omega_{\text{vib}}$$
(2)

where ω i , ω vib , ω s , ω as represent the frequencies of input light, molecular vibration, Stokes and anti-Stokes, respectively. In the case of Stokes generation, molecules dissipate a part of the incident energy leading to the generation of a frequency lower than the input light. In the case of anti-Stokes generation, molecules in higher vibrational states add their own vibrational energy to input light producing anti-Stokes modes with frequency higher than the input light. The factor n represents the order of the process, and it takes the value of 1, 2, 3… for order one, two, three, etc. Generally, n is not an exact integer due to the anharmonicity between the different vibrational energy levels, leading to some variation in the values of the generated output frequencies.

Figure 1 shows the energy level diagram corresponding to the frequencies of input light, Stokes and anti-Stokes modes, with n 1 and n 2 being the ground and excited electronic energy state of the system, respectively, while the dashed lines represent the molecular vibrational energy levels of the corresponding energy state [4]. With a single frequency of pumping, as used in this work, first-order Stokes generation has the lowest threshold. At higher pump energies, the steady buildup of vibrational energy facilitates the eventual generation of higher-order Stokes and first-order anti-Stokes through the contribution from virtual phonons [21]. In this process, several mechanisms can be contributed, such as thermal photons as well as virtual phonons. The contribution from the virtual phonons, leading to the simultaneous generation of a Stokes and an anti-Stokes photon, is given by,

$$2\omega_{\text{i}} = \, \left( {\omega_{\text{i}} + \, \omega_{\text{vib}} } \right) + \, \left( {\omega_{\text{i}} - \, \omega_{\text{vib}} } \right) \, = \, \omega_{\text{as}} + \, \omega_{\text{s}}$$
(3)
Fig. 1
figure 1

Schematic diagram of energy levels depicting the frequencies of input light and the transitions resulting in Stokes and anti-Stokes generation

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Apart from energy conservation, momentum of all the light waves should also be conserved. The momentum conservation explains the phase-matching angle. The newly generated modes are direction-dependent in their propagation and emerge at a special angle known as the phase-matching angle with the input beam direction, in order to satisfy the phase-matching condition [18, 22].

$$k_{\text{s}} = \, k_{\text{i}} {-} \, k_{\text{vib}}$$
(4a)
$$k_{\text{as}} = \, k_{\text{i}} + \, k_{\text{vib}}$$
(4b)
$$2k_{\text{i}} = \, k_{\text{s}} + \, k_{\text{as}}$$
(4c)

The momentum conservation law in terms of wave vectors is given in Eq. (4a), (4b) and (4c). Here, k i , k s , k as , k vib are the wave vectors of input light, Stokes mode, anti-Stokes mode and molecular vibration, respectively. Figure 2a and b shows the generation of Stokes and anti-Stokes as implied by Eq. (4a) and (4b), respectively. The magnitude of k s and k as is defined by k in and k vib. It is lesser than k i in the case of k s and more in the case of k as as seen from Fig. 2a and b, respectively. Figure 2c shows the phase-matching condition expressed by Eq. (4c). Since the anti-Stokes mode is generated only after or along with Stokes mode generation of the same vibrational mode, the Stokes wave vector will already be fixed to generate an anti-Stokes mode and it will follow the wave vector diagram shown in Fig. 2c. In Fig. 2c, the Stokes mode is fixed at an angle θ i with 2k i while the anti-Stokes is generated at an angle θ as known as the phase-matching angle. The angle θ i will be decided by the magnitude of k s and k vib. Thus, the newly generated Stokes and anti-Stokes modes will emerge spatially separated from the input beam. The phase-matching angle θ as can be calculated using Eq. (4c) and is given by Eq. (5) for the anti-Stokes mode [22].

Fig. 2
figure 2

Wave vector diagram for a Stokes and b anti- Stokes, along with c the depiction of phase-matching angle

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$$\theta_{as} = Cos^{ - 1} \left[ {\frac{{4k_{in}^{2} + k_{as}^{2} - k_{s}^{2} }}{{4k_{in} k_{as} }}} \right]$$
(5)

The anti-Stokes mode satisfies the condition shown in Fig. 2c and the magnitude given by Eq. (5) and emerges at θ as from the input beam. As a result, the output beam profile will consist of concentric rings due to anti-Stokes and higher-order Stokes generation.

2.2 Toluene as gain medium for SRS

In this work, we have used toluene liquid as a nonlinear medium. Toluene is a well-known member of the benzene group which has a significant Raman gain coefficient of 1.2 × 10−12 m/W, and it shows efficient Raman spectra due to its Raman-active vibrational modes. Earlier work has reported Raman peaks at shifts of 786 cm−1 due to ring-breathing modes [10, 15], 1006 cm−1 due to ring deformation modes [15], 1210 cm−1 due to C–H bending modes [11], 2979 cm−1 due to CH3 stretching modes [13] and 3060 cm−1 due to C–H stretching modes [11].

2.3 Forward and backward stimulated Raman scattering

When Raman scattering occurs in the medium, it scatters in both forward and backward directions. To start with, the input pump power is utilized to stimulate forward Raman scattering. When FSRS has built up to a certain level, then the remaining input pump power is utilized by back-scattered light and BSRS is initiated. FSRS utilizes the entire length of the sample. Due to the larger nonlinear interaction length seen by it than by BSRS, it acquires more gain [5]. BSRS does not have the input beam traveling in its direction. Hence, its buildup of stimulated process from the spontaneous part gets initiated only at a certain longitudinal position and effectively has a lesser nonlinear interaction length. As a result, FSRS and BSRS have different threshold levels and output power levels. The threshold power for FSRS and BSRS can be calculated from the expression given in Eq. (6a) and (6b), respectively, as [23]

$$P_{\text{FSRS}} = \frac{{16A_{\text{eff}} }}{{g_{\text{R}} L_{\text{eff}} }}$$
(6a)
$$P_{\text{BSRS}} = \frac{{20A_{\text{eff}} }}{{g_{\text{R}} L_{\text{eff}} }}$$
(6b)

In our work, the effective area of the input laser beam A eff is 0.9 × 10−12 m2, Raman gain co-efficient g R of toluene is 1.2 × 10−12 m/W, and the effective length of toluene cell L eff is 6.5 cm. The threshold power of BSRS is larger than that of FSRS. The threshold value for toluene is calculated using the expression given in Eq. (6a) and (6b) as 16 kW (pulse energy of 0.128 mJ) for FSRS and 20 kW (pulse energy of 0.16 mJ) for BSRS.

3 Experimental Details

Figure 3a shows the experimental setup for the SRS experiment. We used a frequency-doubled Nd:YAG laser (Litron Lasers, LPY707G-10) with 8 ns pulse width and 10-Hz repetition rate as the pump laser. The laser beam at 532 nm is of very high pulse energy requiring a variable neutral-density (ND) filter to lower it to the required operating energy range relevant to the medium. A mirror M diverts the beam into a lens L1 of 50 cm focal length, followed by the toluene cell of 5 cm length containing toluene. Whenever required, a linear polarizer is used just before the toluene cell in order to lower the input laser energy with finer control. The focal spot is midway in the toluene cell. The divergent output beam is passed through a notch filter to block 532 nm and then analyzed for its wavelength content with the Ocean Optics USB4000 VIS–NIR spectrometer with a wavelength resolution of 1.5 nm. The photograph of the divergent light on the screen is also shown in Fig. 3a. The divergent beam contains a colored ring pattern which is formed due to the newly generated Raman lines.

Fig. 3
figure 3

Experimental setup designed to study SRS process a to observe ring pattern at the output using detector with linear scale and b to observe diffracted light using a grating at the output. L1 & L2 lenses, P polarizer

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Figure 3b shows the experimental setup to obtain Raman lines diffracted using a grating at the output. In this setup, the divergent output beam coming from the toluene cell is collimated with a lens L2 of 20 cm focal length, passed through the notch filter and diffracted through the grating used at the output. The photograph of the diffracted wavelengths is taken at the screen and is shown with the setup in Fig. 3b. Only one red (3086 cm−1) and one green color (1035 cm−1) is shown in the photograph as these peaks are most intense to be visible easily on the screen.

We have also designed the experiment to record the spectra in the backward direction. In this case, the setup is modified in such a way that it can record BSRS as well as FSRS simultaneously at the same input energy. Figure 4 shows the experimental setup for simultaneous FSRS and BSRS detection. A glass plate G1 kept at an angle of 45o in the path of incoming pump beam transmits 90–92 % and reflects 8–10 % of input energy. The transmitted light passes through the toluene cell, and SRS process is initiated. In order to compare BSRS with FSRS, an identical glass plate G2 is kept after the toluene cell. The light traveling in the backward direction is collected after reflection from G1, and the output beam in the forward direction is collected after reflection from G2. To measure with the detector, lens L2 and L3 of focal length 20 cm are used at the output.

Fig. 4
figure 4

Experimental setup showing SRS process studied simultaneously in forward and backward directions. L1, L2 and L3 are lenses, and G1 and G2 are glass plates

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4 Results and discussion

4.1 Spectral measurement of ring pattern

In the first part of the experiment (see Fig. 3a), we have measured the spectra just after the toluene cell using a notch filter at the output. This is depicted in Fig. 5a for four different pump energies. The intensity is plotted in a log scale to observe the significance of peak heights. The newly generated spectral lines are measured in wavelength and assigned to their respective Raman shifts plotted in wavenumbers on x-axis.

Fig. 5
figure 5

a SRS spectra measured axially just after the toluene cell for different input energies. b SRS spectra measured at a distance from toluene cell at an input energy of 1.8 mJ and with the detector at different angle positions. S4 is not visible in this figure as it is observed only after divergence at a certain distance from the sample cell

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The newly generated wavelengths are at 506.5 nm (AS1), 557.6 nm (S1), 563 nm (S2), 596.5 nm (S3), 631.7 nm (S4) and 636.5 nm (S5) with corresponding Raman shifts of −946.3, +862.9, +1035, +2032.5, +2967 and +3086 cm−1 relative to the input wavelength of 532 nm. Only two Stokes lines (S2 and S5) at 1035 and 3086 cm−1 are seen at the input energy of 0.33 mJ, while Stokes lines (S1, S3 and S4) at 862.9, 2032.5 and 2967 cm−1 and one anti-Stokes line (AS1) at 946.3 cm−1 are seen additionally when the input energy is increased to 0.54 mJ. The intensity of Raman peaks increases with an increase in input energy. Hence, a further increase in the input energy to 0.86 mJ leads to higher intensities of all the generated peaks. At the highest input energy of 1.10 mJ, the spectral output broadens as the nearby peaks start merging into each other. It can be seen from Fig. 5a that the Stokes at 862.9 and 2967 cm−1 merge into 1035 and 3086 cm−1, respectively, at 1.10 mJ. We will discuss the spectral broadening aspects further in Sect. 4.4.

It is clear that the threshold level is different for the generation of different Raman lines. To obtain a precise threshold level for each peak, we have collected the data with a finer control of input energy by using a polarizer just before the toluene cell as shown in Fig. 3a. The measured counts at the wavelength of the Stokes and anti-Stokes modes show a linear dependence on excitation laser energy only above the threshold energy of that mode. The threshold energy values thus obtained are shown in Table 1.

Table 1 Stokes and anti-Stokes generation obtained from the experiment and the associated vibrational modes, threshold energies and Raman shifts
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The shift of +862.9 cm−1 corresponds to the first-order Stokes due to the ring-breathing mode, while the shift of −946.3 cm−1 is the first-order anti-Stokes due to the ring deformation mode. The Stokes line at 1035 cm−1 is the first order of ring deformation mode. Figure 5a shows that the Stokes line at 2032.5 cm−1 is generated at an input energy of 0.54 mJ only after the generation of Stokes line at 1035 cm−1 at 0.33 mJ. Hence, the Stokes line at 2032.5 cm−1 is assigned to a second order generated from the first-order Stokes line (1035 cm−1) of the ring deformation mode. The Stokes lines at 2967 and 3086 cm−1 are the first order of CH3 stretching mode and C–H stretching mode, respectively. All the peaks correspond to Raman-active vibrational modes of toluene with associated Raman shifts. Some difference between the observed and earlier reported values of the shift may be attributed to the detector resolution limit of 50 cm−1. The Stokes (S1, S2, S3, S4 and S5) and anti-Stokes (AS1) lines, along with the frequency shifts, wavelength values and threshold energies, are summarized in Table 1 and compared with the earlier reported values from others’ work.

Our results show that the neat toluene is able to generate the SRS spectra with sufficient gain even at input energy values as low as 1.1 mJ. The mixing of any other solvent is not required to obtain all the Raman peaks of toluene as seen in Fig. 5a. It is reported in [11] that neat toluene requires mixing of chloroform to observe the enhanced modes S2 and S3 of 1006 cm−1 shift and S5 of 3060 cm−1 shift. To observe the modes with a shift of 2979 and 3060 cm−1, it is mentioned in [14] that neat toluene is not sufficient, and hence, it is mixed with m-xylene resulting in the threshold level being higher than that for the shift of 1002 cm−1 mentioned in Table 1. Ref [17] reports anti-Stokes generation in toluene at 1003 cm−1, wherein inverse Raman scattering process in toluene is followed by Raman scattering in another liquid cell.

In the second part of the measurement, we have kept the detector at some distance from the toluene cell in order to observe the well-separated Raman peaks in the divergent beam. The detector is kept on a translation stage perpendicular to the beam so that position-dependent measurements can be carried out. Since the output beam spreads out in a ring-like fashion, the measured result is shown with the detector spatial position varied along the diameter of the ring. The intensity is shown in log scale to highlight the significant change in peak heights with radial position. Since the intensities are not perfectly symmetric on either side of the axis, measurements are recorded on both the left and right sides of the axis and the measured angles are shown as negative and positive values, respectively. All the first-order Stokes lines have the highest intensity at the center of the ring, while the peak value of first-order anti-Stokes is maximum when it is away from the center at the detector position of ±4 mm corresponding to the angular position of ±1°34′ on both sides. The anti-Stokes AS1 is found to be symmetrically present on both sides of the center, while the Stokes line S2 is slightly asymmetrical. We associate the small asymmetry to the fluctuation in the spatial position of the transmitted beam itself due to scattering. One may note that in Fig. 5a the spectrum is measured along the axis of the input beam and does not show any significant change in gain of AS1 with increase in the input energy. But in Fig. 5b, the amplitude of AS1 is maximum when the detector is at +1°34′ and −1°34′. This confirms that AS1 is not centered on the axis but appears at a small angle from the propagation direction of the input beam.

Some deviation is found in the shifts of generated modes with reference to the reported values as seen in Table 1. This is due to anharmonicity of energy levels which can be calculated by subtracting the output frequencies of S1 and AS1 from the input frequencies and the value is obtained as 0.025 × 1014 Hz. Due to this discrepancy, the phase-matching angle can be different from the expected value. This angle is calculated as 3°37′ by inserting the observed Stokes and anti-Stokes wavelengths into Eq. (5). The phase-matching angle is also found from the experiment by noting the angle (or position) at which the anti-Stokes intensity is the highest in the divergent beam. This comes out to be in the range from 2°21′ to 2°44′, since our measurements had a spatial accuracy of the order of 1 mm. The value of phase-matching angle for anti-Stokes is given as 2°54′ in [24], but no experimental result has been shown.

4.2 Analysis of individual modes

Figure 6 shows the diffracted SRS spectra using a grating in the experimental setup (see Fig. 3b). The purpose of using the grating is to record only one wavelength at a time among all the newly generated wavelengths. Figure 6a and b shows the first-order Stokes at 1035 and 3086 cm−1, respectively, with the intensity plotted in a logarithmic scale. For both the peaks, the peak heights differ significantly for the same input energy in the range of 0.55–1.20 mJ. This implies that the Raman line with a shift of 1035 cm−1 has more gain than the line at 3086 cm−1. The former corresponds to the first-order Stokes S2, while the latter is associated with the first-order Stokes S5 in Table 1. The other peaks (AS1, S1, S3 and S4) are not detected after dispersion by the grating since higher energies may be required to observe them to compensate for diffraction loss.

Fig. 6
figure 6

SRS output at input energies of 0.55, 0.75, 0.97 and 1.20 mJ showing the a Stokes at 1035 cm−1 and the b Stokes at 3086 cm−1 after diffraction from a grating

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4.3 BSRS and FSRS spectra

The measured spectra of BSRS and FSRS (see Fig. 4 for the experimental setup) are shown in Fig. 7 with a logarithmic scale for the y-axis. As the threshold levels are lower in the case of FSRS as reported in [23], FSRS begins at the pump energy of 0.33 mJ while BSRS starts only at the pump energy of 0.50 mJ. As a result, FSRS shows higher peak heights than BSRS. At an input energy of 0.88 mJ, S1 and S4 are generated only in FSRS but existing modes S2 and S5 grow in amplitude in both the directions. The mode S1, which is already generated in FSRS at 0.88 mJ, is found in BSRS only at 1.23 mJ. The mode S3 is found to be generated at the same input energy as that of FSRS at 1.23 mJ, while the peak height is lesser than that of FSRS. Anti-Stokes generation is present in BSRS at the same input energy of 1.23 mJ as well as the same amplitude as FSRS. In view of the above, it can be concluded that the threshold is comparable in the case of AS1 and S3 generation in FSRS and BSRS while the value is direction-dependent in the case of first-order generation (S1, S2, S4 and S5).

Fig. 7
figure 7

FSRS and BSRS output at input energies of 0.55, 0.88 and 1.23 mJ

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4.4 Spectral broadening and gain analysis of Raman modes

Figure 8 shows the measured SRS output at six different input energies by tuning the polarizer as shown in the experimental setup in Fig. 3a. The peak position of all the modes observed in our experiment is shown in Fig. 8a by vertical dashed lines, while the reported modes are shown in Fig. 8b by (i) vertical solid lines with their relative heights for shifts in the range of 200–1600 cm−1 taken from [12] and (ii) arrows for shifts in the range of 2800–3100 cm−1 taken from [13]. In [12], the peak positions have been computed using BPW91 functional in density functional theory. In Fig. 8b, the numbers 1–8 are assigned to arrows which indicate the modes at 2921, 2952, 2979, 3003, 3029, 3039, 3055 and 3063 cm−1, respectively, as reported in [13]. The length of the arrows is kept the same and is not indicative of their amplitude.

Fig. 8
figure 8

a Measured SRS output at different input energies with vertical dashed lines representing the observed Raman lines, while b vertical solid lines and arrows represent the reported bands of [12] and [13], respectively

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As the input energy increases from 0.25 to 1.10 mJ, the gain due to all the available Raman-active vibrational modes around the peak becomes very significant leading to broadening (and eventually crossing the saturation limit of our detector). All the Raman peaks S1, S2, S3, S4, S5 and AS1 are shown for six different input energies at 0.25, 0.40, 0.52, 0.55, 0.86 and 1.10 mJ in Fig. 8a. The energy values with a small step size were possible only by using a polarizer in the setup as shown in Fig. 3a. A neutral-density filter was essential after the toluene cell in order to obtain the systematic increase in peak heights at the input energies of 0.40, 0.52 and 0.55 mJ shown in Fig. 8a. The multiplying factor is shown for these energy values in the figure.

The strongest Raman peaks S2 and S5 are seen at the input energy of 0.25 and 0.52 mJ, respectively, in Fig. 8a. The peaks S1 and S4 are seen when the input energy is 0.55 and 0.86 mJ, respectively. They seem to merge with their neighboring modes S2 and S5 at the energy of 0.86 mJ. As the input energy increases further, S1 is totally merged with S2 and S4 is partly merged with S5 at 1.10 mJ in Fig. 8a. In Fig. 8b, one may notice that the number of modes around S1 and S2 is more than those near S4 and S5 which leads to larger broadening at S2 than at S5. The broadening is not present for AS1 and S3 since they do not have any neighboring modes to provide additional gain as seen in Fig. 8b. Spectral broadening to the extent of 1946 cm−1 (61 nm from 533 to 594 nm) and 1255 cm−1 (50 nm from 613 to 663 nm) is observed around the peaks S2 and S5 at an input energy of 1.10 mJ as shown in Fig. 8a.

The broadening seen in Fig. 8a in the range of 200–1600 cm−1 and in the range of 2800–3100 cm−1 can be explained due to the presence of multiple Raman modes reported by others through numerical calculations [12, 13]. Apart from [12, 13], the Raman-active vibrational modes from 200 to 1600 cm−1 and 2800 to 3100 cm−1 have been reported also in [25] and are comparable. The broadening seen in our work in the range of 3100–3500 cm−1 cannot be explained precisely since there are no reported modes in that range.

In [11], the broadening at 3060 cm−1 is observed and has been explained as resulting from the superposition of Raman modes of both the chloroform and toluene, while in our case (see Fig. 8), the broadening is more in neat toluene due to several Raman modes (shown by vertical solid lines and arrow lines for data from [12, 13]) which are present near the observed Raman shifts at S1, S2, S4 and S5 (vertical dashed lines).

From our experimental data, it is very clear that the gain is present not only at the shifts corresponding to the Raman peaks, but it is of different bandwidths distributed around a peak in an asymmetric way. Moreover, it appears that the relative gain reported in [12] for the different modes may not be appropriate for the stimulated process. It is also apparent that it is quite difficult to observe the individual lines in an experimental arrangement with moderate resolution due to the extreme asymmetry in gain due to a few modes.

5 Conclusions

The characteristics of SRS have been studied in liquid toluene using suitable experimental setups in different configurations. SRS spectra have been recorded together for all the Raman modes using a detector placed immediately behind the toluene cell. This is complemented by angle-dependent Raman peaks obtained by collecting the diverged output and well-separated Raman peaks recorded using a grating at the output, as well as by collection of the scattered output even in the backward direction for different input energies. The gain is compared at different input energies and also among all the peaks in both the forward and backward directions. Anti-Stokes generation has been observed here at a very low input energy of 0.54 mJ with sufficient gain at 946.3 cm−1 (506.5 nm) due to the ring deformation mode. Large spectral broadening is observed around the Raman modes at 1063 and 3086 cm−1 in neat toluene, quite in contrast to earlier work. The phase-matching angle for anti-Stokes is also measured in the experiment. The comprehensive approach used here which includes wavelength-, angle- and input energy-dependent measurements has enabled us to understand the process effectively and to clarify certain conflicting results in the earlier reported work. The assignments of all the Raman shifts to their respective Raman-active vibrational modes of toluene are shown in a tabulated form. Our work also highlights the discrepancies in mode assignments seen in earlier work. The present work emphasizes that neat toluene can generate all the prominent Stokes lines of first order as well as higher order and anti-Stokes line of first order, without the addition of other solvents. A second-order Stokes line at 2032.5 cm−1 and an anti-Stokes line at 946.3 cm−1 are observed in our work at 0.54 mJ using neat toluene, which have not been reported earlier at such low energy values. We have measured the relative change in the pulse energies for the observation of different lines, and we have analyzed the extent of broadening with change in pump energy. Simultaneous observation of forward and backward SRS provides a convenient handle on the role of gain length.