1. Introduction

Stimulated Raman scattering (SRS) is a third-order nonlinear optical process that transfers power from an inelastically scattered pump beam to a Stokes-shifted beam. Lasers based on SRS gain provide an efficient route to extend wavelength coverage with the benefits of automatic phase-matching and beam clean-up, so that high brightness output can be obtained from simple and robust Raman laser setups [1–3].

Despite a long history of Raman laser development, single longitudinal mode (SLM) Raman lasers have only been observed in a small fraction of cases despite intense interest for such lasers in coherent laser applications [4–14]. One advantage for obtaining SLM output in Raman lasers is that the spatial hole-burning effect that tends to induce multi-longitudinal modes (MLMs) in conventional inversion lasers is essentially absent so that the laser design complexity can be reduced [4]. Consequently, Raman laser designs that exploit this effect provide a promising practical route towards SLM lasers with potential applications such as precision sensing, spectroscopy, quantum operations, atom cooling, and atmospheric detection. [7,15–19].

The Raman lasers that have exploited the lack of spatial hole burning for SLM are mainly based on diamond [4,7,9,10] in addition to the reports of YVO₄[20] and BaWO₄[12]. Diamond is well suited for stably generating SLM at power levels higher than other Raman materials due to its outstanding thermal properties and, therefore, a reduced coupling between Stokes power and cavity length. A 4 W continuous-wave (CW) SLM DRL at 1240 nm has been achieved in a free-running standing-wave resonator without additional stabilizing elements [4]. However, above 4 W the mode was unstable and MLM for higher powers. Stability is perturbed by thermal effects, the onset of stimulated Brillouin scattering (SBS) and any residual effects that may inhomogeneously broaden the gain [21–24]. To date, the highest SLM CW power for a simple standing wave cavity was 7.2 W, which had an output wavelength of 1240 nm and stabilized using Hänsch-Couillaud cavity locking [9].

Additional stabilization and higher power is obtained using an intracavity χ⁽²⁾ crystal, which is a technique for suppressing weaker competing modes through mode sum frequency generation [10,25]. It has been demonstrated to increase the range of SLM Stokes output power up to 12 W in CW and quasi-CW lasers [10,26,27]. However, these systems were optimized for efficient generation of the frequency-doubled (visible) output with Stokes output obtained as a residual beam. Recently, a χ⁽²⁾-stabilized diamond Raman laser was optimized for maximum Stokes power by using a higher output coupling at the Stokes wavelength and detuning the phase-matching temperature of the χ⁽²⁾ crystal to reduce the loss to the second harmonic, but not so much as to cause the laser to become MLM [28]. The laser achieved 20 W of SLM power at the Stokes. An interesting overall finding from reports of χ⁽²⁾-stabilized SLM diamond lasers is that SBS is typically not observed.

In this paper, we consider the role of the χ⁽²⁾ crystal and cavity design on mode suppression in more detail. We demonstrate a V-shaped high-power DRL with χ⁽²⁾ SLM stabilization that is optimized for Stokes output. In contrast to two-mirror designs (e.g., [28]), the V-shaped cavity was found to be more susceptible to SBS mode generation. We experimentally determined the phase-matching conditions necessary to suppress secondary modes generated by SRS and SBS as a function of pump power. We also find that SBS modes often appear as higher order spatial modes that can be suppressed with an appropriate aperture. The greater susceptibility of the V-cavity to SBS modes, and the appearance of higher order spatial modes, is explained with the aid of a numerical model for the axial mode structure as a function of cavity length.

2. Experimental setup

The experimental setup is shown in Fig. 1. The pump source used in the experiment was a linearly-polarized single-frequency fiber laser at 1064 nm with a CW output power up to 68 W. A free-space optical isolator protected the fiber laser from the back-reflected beam. The diamond Raman resonator was configured as a V- cavity using three plano-concave mirrors, which provided a pump double-pass architecture while enabling independent beam alignment of the pump and the Stokes and minimized potential pump enhancements observed in [4]. A beam-expanding telescope system and a plano-convex focusing lens (f = 50 mm) was used to mode-match the pump with the Stokes beam in the diamond crystal. The calculated beam waist radius of the pump and Stokes in the diamond was 15 µm and 43.7 µm, respectively. The radius of curvatures of the input coupler (M1), output coupler (M2), and M3 were 75 mm, 100 mm, and 100 mm, respectively, and the optical length of the cavity was 379.8 mm. Mirrors M1 and M3 had identical optical coatings, which were highly transmissive (T = 98.2%) at 1064 nm, highly reflective (R = 99.8%) at 1240 nm, and partially transmissive (T = 75.5%) at 620 nm. M2 was highly reflective (R = 99.9%) at 1064 nm and partially transmissive at 1240 nm (T = 0.6%) and 620 nm (T = 50.1%). The Raman gain medium was a 2 × 2 × 7 mm³ single-crystal diamond (Type IIa, Element Six Ltd.) with anti-reflective coatings at 1064 nm and 1240 nm, cut for propagation along a < 110 > direction. The diamond was placed on a water-cooled copper holder at 22 °C. A 4 × 4 × 4 mm³ LiB₃O₅ (LBO) cube (cut at θ = 85.6° and φ=0°, type I phase-matching, Castech Ltd.) was inserted into the resonator to provide SHG and MLM suppression. The LBO crystal was placed at the second focusing point in the cavity, between M1 and M3, where the Stokes waist radius was 130 µm. A temperature control module with the adjustment accuracy of 0.1 °C was used to stabilize the LBO temperature and control the phase-matching condition and SHG output power. The pump polarization direction was aligned with the diamond <111 > axis by using a half-wave plate to get the highest Raman gain [29]. The LBO was rotated to have its slow axis parallel to the polarization direction of the Stokes field.

 

Fig. 1. Schematic of the Raman laser setup, HR, highly reflector; λ/2, half-wave plate; BS, beam sampler; PM, Power meter.

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3. Results and discussion

3.1 Multi-longitudinal mode suppression

Figure 2(a) displays the output Stokes power curves as a function of pump power at different LBO temperatures. The Stokes power curve without LBO is also added in Fig. 2(a) for comparison. Without LBO in the cavity, the cavity length was 377.5 mm, making the beam waist 43.5 µm at the diamond center. As the black dashed line shows, the Stokes reached a threshold at 32.3 W. The maximum Stokes output power generated was 16.7 W for a 68 W pump with a slope efficiency of 46.5%. However, the Stokes output became MLM above 34.8 W of pump power.

 

Fig. 2. (a) Stokes power input/output curve with different LBO temperatures. The black dash line (with squares) is the Stokes output curve without LBO inside the cavity. The red line (circles) shows the SLM power for the LBO temperature for perfect phase matching. The blue line (diamonds) shows the Stokes power for the maximum LBO temperature at which SLM was obtained. The green line (triangles) is the Stokes power for LBO temperature for the minimum nonlinear coupling. The Stokes is SLM in the beige area, and MLM in the grey area. (b) and (c) are the F-P interferometer spectrum at points A and B.

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In order to investigate how much χ⁽²⁾ coupling is required to suppress secondary modes, an LBO crystal was placed in the long arm of the cavity, where the Stokes field was relatively insensitive to cavity length changes. The LBO extended the optical cavity length by 2.4 mm, which changed the Stokes waist size by only 0.2 µm. The extra LBO insertion loss (scattering and absorption) slightly increased the Stokes generation threshold to 34.8 W, and the slope efficiency decreased to between 30% and 40%. The multi-mode suppression was investigated by LBO phase-matching conditions for fixed pump powers until a change from SLM to MLM operation was observed using a scanning Fabry-Perot (F-P) interferometer (SA210-8B with 10 GHz FSR, Thorlabs Inc.). We adjusted the LBO temperature to modify the phase-matching without altering the cavity alignment. Note that the Stokes power also changes due to the nonlinear loss.

When the LBO was under the optimal phase-matching temperature of 38.5 °C, the maximum Stokes power (red line) dropped to 10.4 W with reduced 31.3% slope efficiency due to the nonlinear loss calculated as 0.17%. The Stokes field remained SLM from the threshold to maximum pump power of 68 W. To determine the range of temperatures required to maintain SLM, we increased the LBO temperature above the optimum point for SHG, and therefore reducing the mode suppression effect and simultaneously increasing the Stokes power. The investigated temperature ranges from 38.5 °C to 57.6 °C, a span corresponding to the calculated temperature acceptance of LBO at 1240 nm (19.1 °C). The blue line shows the maximum Stokes power that can maintain SLM operation for each pump power. This curve is the boundary between the SLM area (marked with the beige color) and the MLM area (marked with the grey color). Specifically, during the LBO temperature increase from the optimal phase-matching, the Stokes gradually degenerated from SLM to MLM. The marked temperatures are the maximum temperatures of observed SLM Stokes operation. The maximum SLM Stokes power was 11.7 W, obtained at 68 W of pump power and the slope efficiency was 34.9%. Note that the blue line approaches the line of maximum SHG conversion (red line) as pump power increases. This indicates that higher power Stokes operation requires more χ⁽²⁾ coupling to suppress the neighboring modes. The maximum SHG nonlinear loss for the SLM to MLM boundary curve was 0.06% at 49 °C

Increasing the LBO temperature further resulted in MLM Stokes output. The green line is the Stokes power for the LBO temperature at its highest value in the investigated range (55 °C), and we expect a minimum in the χ⁽²⁾ coupling. The MLM Stokes power reaches 12.5 W with a slope efficiency of 37.5%. Note that the Stokes was SLM for Stokes output powers up to 3.2 W (pump powers up to 39 W) in good agreement with [4] where it was shown that SLM can be obtained at lower powers without the aid of LBO. It is worth mentioning that the LBO temperature tuning does not affect the Stokes behavior near the threshold, as the nonlinear loss is insignificant compared to output coupling.

We selected two representative points (A and B in Fig. 2(a)) with similar Stokes power (8.8 W) but different mode behavior, and measured the spectrum using the F-P interferometer. As seen in Fig. 2(b) and Fig. 2(c), the spectrum shows that output was SLM at spot B while at spot A the Stokes was MLM.

Figure 3 shows the SHG power expressed as a fraction of the total output power plotted as a function of the pump power for different LBO temperatures. The SHG power was measured after M3 and the total SHG power was calibrated using the reflectivities of M3 (R_M3= 24.5%), M1 (R_M1= 24.5%), and M2 (R_M2= 50.1%) mirrors at 620 nm (assuming the forward and backward generated SHG powers were equal). The total SHG power P_total is given by ${P_{total}} = 2{P_{measured}}\left( {1 - {R_{M3}}{R_{M1}}{R_{M2}}{R_{M1}}} \right)/\left[ {\left( {1 + {R_{M1}}{R_{M2}}{R_{M1}}} \right)\left( {1 - {R_{M3}}} \right)} \right]$. For the LBO phase-matching temperature at optimal value, the SHG power increases to 5.9 W and forms 36.0% of the total output (red line). In contrast, when the LBO phase-matching is detuned as much as possible while still SLM (blue line), the SHG power can be as low as a few milliwatts at low pump powers and increases to 2.2 W (15.6% of the total output power) at full pump power. For comparison, the two mirror resonator in [28], the second harmonic output was only 30 mW (about 0.2% of total output) for 16 W output of Stokes power. This result indicates that the V-resonator requires phase-matching conditions that yield more SHG to suppress secondary modes compared to the two-mirror cavity.

 

Fig. 3. SHG proportion as a function of pump power. The red line (circles) the case for the optimum phase-matching temperature, whereas the blue line (diamonds) is for the LBO temperature that gave the maximum SLM Stokes output power at that pump power. At the highest LBO temperature investigated (55°C), the SHG power was always less than 0.08% of the total output power (green line with triangles).

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3.2 SBS investigation

As a major difference between this work and that of the two-mirror cavity of Ref. [28] is the greater prevalence of SBS, we have investigated its influence on lasing for the two cavity designs in more detail. SBS had been observed in a V-cavity without SHG stabilization before [30]. In the present work, the generated Stokes output was characterized using an optical spectrum analyzer (AQ6370D Yokogawa Inc.). Without LBO in the cavity, the SBS threshold was 37 W of the pump with Stokes output of 3.3 W.

We investigated whether the parasitic mode suppression effect of the χ⁽²⁾ crystal also suppresses the SBS. We compared the spectrum of Spot A and Spot B - refer to Fig. 2(a) - that have similar Stokes intracavity fields but different amounts of χ⁽²⁾ coupling. Figure 4 shows that for Spot A with less than 0.1% of SHG output, there is an SBS satellite peak (1239.8 nm) at the expected Brillouin shift from the Raman line at 1239.5 nm. For Spot B, where the SHG power proportion was much higher (5.3%), no SBS was observed. This suggests that the suppression effect of the SHG conversion is also helpful in suppressing the SBS. Since the acceptance bandwidth of the LBO (40 nm; calculated by SNLO software) greatly exceeds the Brillouin shift (0.36 nm), the effect of the χ⁽²⁾ interaction on SBS modes is likely to be similar to that on neighboring SRS modes.

 

Fig. 4. Spectra for Spot A and Spot B in Fig. 2.

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Prior studies [21] have noted that only specific cavity lengths have a cavity mode at the SBS frequency; the window of cavity lengths for SBS resonance is relatively small (less than 100 µm) and should be readily avoided. However, in contrast, when we slowly scanned the cavity length by 1.5 mm, SBS lasing was always present. The SBS theory in [21] only includes TEM₀₀ cavity modes, and we propose that this difference is caused by the SBS lasing in higher-order transverse modes.

To test this hypothesis, we removed the LBO and inserted an aperture inside the cavity to increase the loss for higher-order transverse modes. Figure 5 depicts the spectrum with the open and closed aperture at identical Stokes output power. For an open aperture, SBS is observed in the spectrum and the CCD image (Fig. 5(a)) and is suppressed upon narrowing the aperture (Fig. 5(b)).

 

Fig. 5. The spectrum of the output beam when a) aperture is open and b) aperture is closed. The inset the CCD graph of the output Stokes.

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To predict the gain of different SBS transverse modes in the cavity, we adapt the external cavity Raman laser model derived in [31]. From [31], the Stokes output power can be written as

Combining Eq. (1), Eq. (2) and Eq. (4) a pump power factor for SBS threshold ${r^{SBS}}$ is

The factor ${r^{SBS}}$ is the factor above the pump threshold for SRS we expect to observe SBS. We have ${g_{SBS}}$ = 14.9 cm/GW at 1 µm, ${g_{SRS}}$ = 10 cm/GW at 1 µm [22,32], $T$ is 0.6%, and $\eta $ was measured as 37.5%. For SBS and SRS in a TEM₀₀ mode and with the measured pump spot size, we calculate $\frac{{{A_{SBS}}}}{{{A_{SRS}}}} = 1.62$, which makes ${r^{SBS}} = 1.016$. This means that the SBS is predicted for pump powers 1.6% above the Stokes threshold for the peak of the SBS gain profile resonant with a TEM₀₀ cavity mode. As the cavity length is tuned away from this resonance we can calculate how the gain decreases [21], and find that the gain is Lorentzian with an FWHM of about 25 µm, showing that changing the cavity length from resonance by 97 µm drops the effective gain by a factor $0.016$ and so the ${r^{SBS}}$ value increases to 2.

Now, let us consider the gain and positions of higher order modes. The locations of higher-order modes within one FSR depend on their Gouy phase. Higher-order modes will inherently have lower SBS gain due to their larger effective area when interacting with a TEM₀₀ Stokes cavity mode. For example, the TEM₃₃ has a normalized overlap of $\frac{{{A_{SBS}}}}{{{A_{SRS}}}} = 16.61$. Considering the effective area and locations of TEM_mn gain curves, the effective gain for SBS lasing is calculated as a function of cavity length to determine the cavity lengths that provide the best SBS suppression.

We first consider a two-mirror quasi-concentric cavity. In such a cavity nearing its stability limit, the Gouy phase approaches $2\pi $ and the frequency spacing between higher order transverse modes narrows. At the stability limit, all the higher order modes have frequencies identical to TEM₀₀­. With no astigmatism, there is no difference in the Gouy phase in the T and S plane, and modes with equal $({m + n} )$ are degenerate. Figure 6 shows the SBS gain as a function of cavity length, normalized to the gain for SBS in resonance with a TEM₀₀ mode. Resonance for TEM₀₀ occurs for cavity lengths near 134.8 mm and 136.9 mm, with the width of the resonant peaks approximately 100 µm. For higher order modes, resonances are fanned out towards longer cavity lengths from each TEM₀₀ resonance. For example, TEM₂₀ resonances at 135.3 mm and 137.2 mm have a lower effective gain of 37.5% due to the reduced field overlap. (Note that these locations are also resonant with TEM₀₂ with the same gain, and with TEM₁₁ with lower overlap and lower gain). Note that Fig. 6 is reminiscent of plots of mode position versus mode frequency, which simply repeats after each FSR. In contrast, the pattern does not exactly repeat since the Gouy phases vary with the cavity stability parameter.

 

Fig. 6. The effective gain for SBS for modes up to TEM_16-0 as a function of the cavity length in a linear cavity. The stability parameter is shown on the top axis.

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We have plotted for m + n ≤ 16 since higher order modes are unlikely to lase, despite the normalized gains still up to 20%, due to vignetting by cavity optics. Figure 6 shows there are many cavity lengths for which the SBS gain into any mode diminishes and SBS modes are suppressed.

For the V cavity, however, the situation is not as favorable for two reasons. First, such cavities usually operate well away from the stability limit so that the Gouy phase is no longer near a multiple of $\pi $ and modes are spread across the FSR. Second, astigmatism from the turning mirror (M1) splits the degeneracy of the Gouy phase between the T and S planes and no modes are degenerate. Figure 7 shows that for effective SBS gain for m +­n ≤ 8, mode locations are more widely spread throughout the FSR. As a result, there are fewer cavity lengths where the gain diminishes to levels that are able to suppress SBS. We suggest that this explains the prevalence of SBS in the V-cavity regardless of cavity length compared to the two-mirror of [28]. These findings are also consistent with the higher-order modes observed and the suppression effect of an aperture for cavity lengths away from the TEM₀₀ mode resonance.

 

Fig. 7. The effective gain curve of SBS for modes up to TEM₈₀/TEM₀₈ as a function of the cavity length for a V-cavity.

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It is clear that consideration of the cavity mode structure can play an important role in controlling SBS in Raman lasers. To avoid SBS resonances, it is beneficial to use a cavity near the stability limit, in agreement with the two-mirror cavity results in [28], or to use an aperture to limit higher order spatial modes.

4. Conclusion

By introducing a χ⁽²⁾ element in the cavity, we have demonstrated a V-shape external cavity Raman laser with 11.7 W of stable SLM Stokes output and 34.9% slope efficiency. We have quantified the χ⁽²⁾ coupling necessary to suppress secondary modes as a function of pump power. Further work is required to derive a Raman laser model that would include SHG mode suppression and predict SLM or MLM laser operation.

Without χ⁽²⁾ stabilization, we find the SBS is more prevalent in V-cavity and coincides with observed higher order transverse modes. Contrary to simple two-mirror cavity, we were not able to suppress the SBS by cavity length changes. We have theoretically derived the SBS gain as a function of cavity length, which takes into account higher order transverse cavity modes. The model shows that in simple two mirror cavities close to the stability limit, the SBS frequency is less likely to overlap with any modes, and thus SBS can be avoided by small changes in cavity length. Folded cavities with astigmatism, on the other hand, exhibit higher order modes spread across their FSR. As a result, for almost any cavity length, the SBS frequency overlaps with a higher order cavity mode with significant gain. SBS suppression in folded cavities can be achieved by using intracavity appertures to limit the number of possible higher order modes, adjusting the cavity length to avoid the main low order resonances, or introducing appropriate level of χ⁽²⁾ coupling.