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We report an analytical model describing power and efficiency of a 23 W quasi-continuous-wave diamond Raman laser. The model guides the optimization of the first Stokes output power as a function of resonator and crystal parameters. We show that, in the limit of a weak thermal lens, efficient operation requires strong focussing, low output coupling and low-absorption crystals. Efficient damage-free operation at higher pump powers is predicted to benefit greatly from increased optimum output couplings that act to limit the intracavity Stokes field.
© 2015 Optical Society of America
1. Introduction
Stimulated Raman scattering (SRS) is a practical method for achieving step-wise decreases in laser frequency that has been most extensively applied to pulsed laser sources. Being a third order (χ(3)) nonlinear interaction, high intensities are needed to drive the process which places much greater demands on system design for continuous-wave (cw) conversion. To date, several approaches have been used to achieve cw conversion including using waveguide enhancement [1, 2], doubly resonant cavities (ie., cavities resonant at the pump and Stokes wavelengths) [3–5] and singly resonant cavities with high gain bulk media [6, 7]. The latter represents a highly attractive method for beam conversion that is applicable to a wide variety of multimode pump lasers. In 2012, it was shown that synthetic diamond when used as the Raman medium enables efficient and high power cw Raman conversion using a cavity singly resonant at the first Stokes [7]. Recently, this work has been extended to demonstrate 108 W of Stokes output at 1240 nm in a quasi-cw (steady-state) temporal regime [8]. These devices exploit the excellent thermal properties of diamond (high thermal conductivity and low thermal expansion coefficient), to enable efficient and high beam quality output at average powers much higher than achieved in other Raman materials. To date, these empirical studies have been performed as functions of pump power with most cavity parameters fixed. It is important to better understand the importance of other cavity parameters on laser behaviour in order to assist in future optimization of designs.
Theoretical and numerical models are important tools for understanding and predicting laser performance. Numerical studies of pulsed Raman lasers have enabled inclusion of pump pulse temporal dynamics (see for example [9]) and the interaction of Raman and inversion gain media in intracavity Raman lasers [10–12]. The time independent nature of cw doubly-resonant gas Raman lasers has enabled modelling using an analytical approach [5,13]. In this latter case, conversion is described in terms of impedance matching of the pump with the Raman cavity without explicit consideration of depletion of the pump beam as it propagates through the Raman medium. For singly resonant external cavity Raman lasers, on the other hand, the pump is strongly depleted within a single or double pass of Raman medium. Therefore, a new solution of the Raman laser equations, which includes pump depletion, is required to adequately describe behaviour of cw external cavity Raman lasers.
In this paper we report an analytical model for steady-state first-Stokes generation. The calculations are compared to the previous 10 W diamond Raman laser (DRL) experiment [7] and also a new quasi-cw (q-cw) pumped DRL with a 23 W on-time output power. We use the model to find optimal laser parameters maximizing output power and efficiency as functions of pump power, crystal loss and optical design parameters.
2. Model equations
In order to achieve moderate laser thresholds, the pump and mode-matched Stokes field are tightly focussed which for a simple two-mirror cavity imposes the use of a near-concentric geometry. Furthermore, low output couplings, typically around 0.5%, are necessary for moderate pump powers (approximately 10–20 W). These practical implications dictate the assumptions of the theoretical model. The propagation and focussing of Gaussian beams are considered and large depletion of the pump is a necessary requirement for efficient conversion. In the paraxial approximation, the growth of the intracavity Stokes field and depletion of a single pass pump are governed by the following two differential equations
where IP, IS are pump and Stokes intracavity intensity, respectively, η = λP/λS is the quantum defect of the inelastic Raman process, where λP and λS are pump and Stokes wavelengths, respectively, and αP and αS are the parasitic losses at pump and Stokes wavelength, respectively.It is assumed that the pump IP, Stokes IS, and residual pump, have TEM00 intensity distributions
with the power in each beam of where IP,S(0, z) is intensity of the pump and Stokes field on the beam axis and it is described by the change of the beam radius wP,S(z) from waist wP,S(0) due to focusing where are beam confocal parameters, and nP,S, λP,S and are the indices of refraction, wavelengths and beam quality factors, respectively.Assuming that the forward and backwards gain are equal, and in the present steady-state case of a high Q-cavity, for which the dependence of the intracavity Stokes field on z can be neglected, the equation for pump depletion in (1) is integrated in polar coordinates (radius r from 0 to ∞ and θ from 0 to 2π) using a method similar to [14] to become (assuming losses are small on a single pass of the Raman crystal)
Solution to (5) is straightforward by separation of variables to give where G is the Raman power gain in the focused geometry [14]. The PRes is the residual pump power after the depletion. The dimensionless parameter ξ depends on the ratios of crystal length, L, and bP and bS according to where bP/bS = bPS and for simplicity. The parameter Λ contains a gain reduction factor for the pump and Stokes wavelength mismatch (the first bracket in Eq. (9)) and beams overlap mismatch (the second bracket in Eq. (9)), respectively. In order to maximize G the arctan(ξ) has to approach its maximum of π/2, thus , and Λ has to be minimized. For x > 0 the function x + 1/x acquires its minimal value of 2 for x = 1. Therefore the highest gain is achieved by strong focussing, bP = bS and, in principle, η′ = 1.By conservation of energy, the generated Stokes power from the pump depletion is
In a linear Raman resonator the total intracavity Stokes power is the sum of a left and right directed beams. Therefore the out-coupled Stokes power PS is
where T is the transmission of the output coupler. In the steady-state, is dissipated by loss through the output coupler and parasitic mechanisms such as surface and bulk scatter loss and bulk absorption losses in optical components. We have bundled all the major parasitic loss mechanisms into a bulk absorption term in the diamond, α. Hence, substitution of (11) into (10) leads to a solution predicting the pump power needed for a particular Stokes output, Combining equations (6) and (11) gives the residual pump To obtain the maximum slope efficiency σ, which equals the maximal conversion efficiency, the Eq. (12) is differentiated with respect to PS and PS is limited to ∞, The initial slope efficiency at the threshold (PS = 0) is 2σ which, in principle, can be greater than η. The laser threshold PThr is obtained by limiting the Stokes output in (12) to zero, This general expression accounts for the focusing conditions of the pump and Stokes beams. Fig. 1 shows how the threshold reduces as bP and bS decrease. For a special case of bS/L = 1 or bP/L = 1 there are optimal ratios of bP and bS of approximately 0.4 minimizing the threshold. A similar ratio was obtained in ref [14], however, here the ratio and thus Fig. 1 are not symmetrical due to not assuming equality of pump and Stokes wave vectors. Note that the theory presented is restricted to TEM00 Stokes waist sizes equal to or greater than the pump and thus for bP < bS. Outside this regime (wS < wP) the model assumption of Gaussian beams is likely to be invalid due to the increasing likelihood of excitation of higher order spatial modes and to strong depletion of the beam in the central region of the beam (leading to a large departure from a Gaussian profile). From a practical point of view, operation in this regime is undesirable for applications requiring high beam quality output. Also, it is often convenient to fix the pump focus conditions and maximize the Stokes power using small adjustments to the mirror spacing. In this case, the optimal threshold and high slope efficiency are obtained for bS = bP = b (M2 = 1 is assumed for the pump and Stokes beams) and where the wS > wP requirement for TEM00 Stokes generation is fulfilled due to λS > λP. Under this assumption the ξ and Λ parameters simplify to which accounts for the difference in waist sizes of the pump and Stokes fields of the same confocal parameter. Alternatively, we can make the assumptions wP = wS and bP,S ≫ L to find It is noted that Eq. (17) provides the same threshold as for a collimated top-hat beam profile [15].
Fig. 1 Normalised Raman laser threshold as a function of pump and Stokes confocal parameters normalised on crystal length. Ideal Gaussian pump and Stokes beams were assumed.
In general a portion of the pump is reflected back through the Raman crystal by the output coupler and experiences additional depletion. In practice, it is beneficial to have 100% reflection of the pump to reduce the threshold as well as to provide pure Stokes output. It is often convenient to fabricate an output coupler that is highly reflecting at the pump wavelength due to its close spacing with the Stokes wavelength. For 100% reflectance and for a path exactly the same as the forward pass, the gain coefficient G in Eqs. (12,13) and (15) is multiplied by 4 instead of 2. Compared to single-pass pumping, the threshold is halved, and the slope is unchanged.
The results of Eqs. (12,13) for double-pass pumping normalized on generation threshold together with conversion efficiency are shown in Fig. 2 for parameters of the 23 W DRL discussed below (see Table 1). Above threshold, the Stokes power asymptotically approaches the slope σ. Over the same range, the residual pump approaches zero. The efficiency is limited by the Stokes intracavity loss.
Fig. 2 Stokes output power, conversion efficiency and residual pump power as a function of threshold pump power for a double pass pump. Powers are normalized to the threshold pump power.
Table 1. Variables used to model the cw 10 W and q-cw 23 W extra-cavity DRLs.
3. Experiment
The model output is compared with the performance of the 10 W cw DRL reported by us previously [7], as well as with characteristics of a new DRL pumped with up to 50 W of quasi-cw pump power. The quasi-cw DRL, shown in Fig. 3, was pumped by 30 ms pulses at a rate of 15 Hz (45% duty cycle). Given that such power levels are in a regime of a weak thermal lens [7, 8], and that the pulse duration is several orders of magnitude longer than the establishment of thermal gradients in diamond (approximately 10 μs [8]), the results are expected to be representative of steady-state cw operation. After passing through optical isolator and a half-plate the pump radiation was focused in the diamond by a 50 mm-focal-length lens to a 42 μm pump spot radius. The pump beam profile was Gaussian-shape with beam quality factor of 2 (see Fig. 5 for far-field images). The pump laser was configured with an output linear polarization aligned to the 〈111〉 crystallographic axis of the diamond.
Fig. 3 Schematics of experimental setup of the q-cw pumped DRL. The residual pump power is rejected from the optical isolator on a calibrated power meter.
The DRL resonator consisted of an input coupler, IC, 97% transparent for the pump 1064 nm wavelength and 99.98% reflective at the first Stokes 1240 nm wavelength. The output coupler, OC, was highly reflective for the pump to provide double pass pumping and had 0.5% transmission at the first Stokes wavelength. The input and output coupler radius of curvatures were 25 and 50 mm, respectively, and cavity length was 78 mm. The diamond used was 8 mm long CVD-grown single-crystal with ultra-low birefringence (Element 6, UK) and anti-reflection coated at the first-Stokes wavelength. The length of the near-concentric resonator was adjusted to achieve maximum output with TEM00 profile. Figure 4(b) shows that the laser attained threshold at 20 W of pump power and generated a maximum of 23 W of Stokes output power with 47% efficiency.
Fig. 4 Stokes output power and residual pump power as a function of pump power for a 10 W and 20 W DRLs compared with the model.
Fig. 5 Intensity profiles of residual pump, left, and Stokes, right, exiting the diamond imaged on the CCD camera. Black full line - residual at maximum 48 W pump in the absence of Stokes output, Blue dashed line - residual at threshold 18 W, Red dotted line - residual at maximum pump 48 W and maximum Stokes 23 W.
Figure 4(a) and 4(b) shows the measured Stokes output and residual pump power for the 10 W and 23 W DRLs, respectively, compared with Eqs. (12) and (13) with double-pass gain for parameters summarized in Table 1. As T and L are well known, α is used as an adjustable parameter to fit the slope of measured output power. As can be seen in both cases, the model reproduces the output power reasonably well. The higher slope efficiency in the 23 W DRL compared to the 10 W system (34% compared to 55%) is attributed to the lower fitted absorption coefficient (0.17% cm−1 compared to 0.28% cm−1) of the diamond sample. Both absorption values are within the range expected for diamond samples with 20±10 ppb nitrogen content [16].
The threshold depends on resonator loss, Raman gain coefficient and pump and Stokes focusing properties (Eq. (15)). The cavity round-trip loss can be determined by the slope efficiency and pump and Stokes beams characteristics (beam quality and spot sizes) are measured. Therefore, gS is used as a free variable. In order to best fit the output power measurements, gain coefficients of 9 cm/GW and 7.5 cm/GW were required for the two DRLs having the 10 W and 20 W thresholds. The difference is attributed to uncertainties in intracavity waist sizes and M2 measurements. The reported Raman gain coefficient of diamond ranges from 8 to 17 cm/GW [17] for 1064 nm pumping linearly polarized in 〈111〉 direction, thus this work supports a gain coefficient at the lower end of this range.
There is a notable discrepancy between model and observation in respect to the residual pump power; the calculated residual pump power approaches zero more rapidly with pump power. We attribute this disagreement to the deviation in experimental spatial and polarization properties of the beams from the ideal conditions in the model. In experiment, optimal overlap between pump and Stokes beams is achieved by maximizing conversion efficiency at the highest pump power, however, this may not necessarily coincide with the focusing conditions of the model. Also, the use of Gaussian beams in the models does not explicitly consider the detailed spatial dependence of conversion and effects of beam diffraction. The tight focussing (and resulting strong diffraction) ensures that the residual pump spatial distribution is near Gaussian as shown in Fig. 5. However, some beam degradation is evident, as expected by the stronger conversion in the central part of the beam, causing an increase in the pump waist size of the pump beam as it makes a double pass of the diamond. This is likely to result in lower conversion efficiency compared to the model. We have also found that birefringence in the diamond may also significantly perturb performance. Localised stress-induced birefringence, which is present in the material due to lattice defects [16] (and possibly exacerbated by local heat deposition at very high powers), is likely to significantly influence the polarization of the Stokes beam. Indeed, some parts of the crystal are observed to perform very poorly which appear to be correlated with detailed birefringence properties in the mode volume. Overall, the fact that the model predicts higher depletion than observed suggests that the model derived gain and loss coefficients are likely to be overestimates. In the case of the 10 W laser, the model predicts α = 0.28% cm−1 which is higher than the 0.13% cm−1 value determined using a power budget analysis [7].
4. Optimization
The analytical model was used to study the principal factors that govern DRL behaviour at higher pump powers, as well as to explore tolerances on cavity and diamond material parameters and to find optimal variables maximizing conversion efficiency. In particular, we have investigated the Stokes output power as functions of output coupling, beam focusing (the bP/bS = 0.5 ratio from experiments was kept constant), crystal length and parasitic loss. As a reference point, we selected initial model parameters that correspond to the 23 W DRL detailed above (see Table 1).
4.1. Output power
The focal spot-size of the pump beam is one of the most important design variables as the intensity and thus the small-signal gain scales inversely with the beam area. When reducing spot-size (for a fixed output coupling), a point is reached where the Stokes power linearly increases as a function of pump with the slope σ. Thus there is an experimental optimum spot size, small enough to get close to the maximum output power, but not so small to be experimentally problematic. As shown in Fig. 6, the Stokes output power saturates for waist sizes less than 40 μm when using a 50 W pump and tighter focusing beyond what was used would result only in a marginal (less than 10%) increase in output power. Small waists are more challenging to achieve in practice due to the high numerical aperture optics required and may lead to increased thermal lens strengths in the diamond crystal. As a result, operation is preferred at the large-spot-size end of the plateau region. The red curve indicates how the optimal waist size increases for higher pump powers.
Fig. 6 Stokes output power as a function of pump waist radius (bottom axis) for pump powers in the range 10 to approximately 160 W for T = 0.5%, L = 8 mm, α = 0.17% cm−1. Top axis shows corresponding pump beam confocal parameter. The two data points show measured output power of the q-cw DRL at 30 W and 48 W pump power. The red curve indicates the waist size required to reach 99% of maximal Stokes output for a given pump.
Output-coupling influences slope efficiency and threshold according to Eqs. (14) and (15), respectively. As shown in Fig. 7, the 0.5% output-coupling used in the experiment is similar to the optimum value determined by the model. The output coupling maximizing the Stokes output increases with pump power, as indicated by the red curve.
Fig. 7 Stokes output power as a function of output coupling for pump powers in the range 10–160 W for wP = 42 μm, L = 8 mm, α = 0.17% cm−1. The red line indicates optimal values of output coupler transmission maximizing Stokes output power. The squares show the measured output power for the q-cw DRL when pumped at 30 W and 48 W.
Crystal length directly influences performance via the absorption loss and the length of the Raman interaction. For L ≫ b, increasing L leads to proportional increases in loss that are not counter-balanced by an increase in Raman gain. Figure 8 shows that the optimal crystal length decreases with increasing pump power. The results show that the 8 mm long crystal used in the experiments was well suited to pump powers above 30 W and in the range investigated in the present experiments.
Fig. 8 Stokes output power as a function of crystal length for different pump powers in the range 10–160 W for T = 0.5%, wP = 42 μm, α = 0.17% cm−1. The red curve Lopt shows optimal length of the crystal and the squares show output power of the q-cw DRL at PP = 30 W and 48 W.
4.2. Efficiency
Crystals and optics with negligible losses lead to conversion efficiency quantum limited irrespective of the output coupling. Low thresholds are achieved by using strong focusing, low output coupling and long crystals. When loss is present, however, these associated parameters (bP, T and L respectively) require optimization to maximize conversion efficiency at a given pump power.
For a fixed loss value, the efficiency is a function of L, bP and T. Due to the approximate arctan(L/bP)/T dependence in Eq. (12) for L ≪ bP, increases in L are equivalent to decreases in T. For L ≫ bP the arctan function approaches its maximum value of π/2 such that further increases in L only lead to reduced efficiency due to escalating losses. Strong focussing and simultaneous output coupling optimization along with the use of a shorter crystal thus significantly increases efficiency. These dynamics are shown in Fig. 9(a), 9(b) and 9(c) for pump power of 48 W and conditions of fixed bP, L and T respectively.
Fig. 9 Output conversion efficiency PS/PP as a function of (a) output coupling T and crystal length L, (b) output coupling and pump waist radius wP, and (c) crystal length and pump waist radius wP. The contours show corresponding Stokes output power. The maximum operation point of the 23 W laser is indicated by the black square. Plots are shown for a typical value of α = 0.17% cm−1 and pump power of 48 W.
The absorption loss varies over a fairly large range of values between different diamond samples. These losses directly impact the efficiency (according to Eq. (14)) and increase the laser threshold according to Eq. (12). In general, designs providing higher T, shorter L and shorter bP are favoured to reduce the impact of absorption loss as shown in Fig. 10(a), 10(b) and 10(c) for pump power of 48 W and for conditions of fixed T and bP, L and bP, and T and L, respectively.
Fig. 10 Output conversion efficiency PS/PP as a function of parasitic absorption α and crystal length L (a), output coupling T (b), and pump waist radius wP (c). The contours show corresponding Stokes output power. The maximum operation point of the laser 23 W DRL for 48 W of pump power is indicated by the black square.
5. Discussion and conclusion
The optimization analysis presented assumes that the thermal lens induced in the diamond does not significantly change the pump and Stokes waist sizes. We have shown previously [17] that the thermo-optic effect will be the likely primary cause for saturation at elevated power levels as a result of diamonds low susceptibility for other thermal lensing mechanisms that involve stress-optical effects (namely stress fracture, birefringence and end-facet distortion). Based on calculations for the thermo-optic lens strength for the operating conditions of the 10 W laser of [18], we expect that such effects are small for powers deposited in the crystal up to at least 70 W, corresponding to output powers well in excess of a hundred watts, depending upon the levels of absorption loss in the crystal. Indeed, recently a quasi-cw pumped DRL with a 100 W of on-time Stokes output power [8] has been demonstrated without evidence of a thermal lens.
In our device, we have seen up to approximately 45% of the output Stokes power deposited as heat in the crystal, a large fraction of which is due to absorption loss. Thus the onset of thermal effects can be offset substantially by, according to Eq. (13), selecting operating conditions allowing high output coupling (thus lower intracavity fields) and short crystal lengths. Using elevated pump powers, although generally adding to the total heat load, enables higher optimum output couplings and thus higher efficiency in the presence of parasitic losses. Although it may be ultimately necessary to increase the pump and Stokes spot sizes to avoid damage, it is noted that the intracavity Stokes intensity required to effectively deplete the pump beam (of the order of a 0.5 GW/cm2 for the current system), which is a necessary condition for efficient operation, is fixed for any pump power as long as the intracavity Stokes field can be considered stationary upon round-trip (see Eq. (6)). Since the total intensity experienced by the diamond facets is primarily due to the resonant Stokes field, the system has the benefit of being scalable to higher powers without greatly increased risk of optical damage, as well as operating more efficiently.
The minimum threshold observed to date is 10 W [7], yet there is interest in reducing this value to enable efficient devices at low power. Reductions in threshold require designs that can enhance the intracavity Stokes field, which is achieved by reducing cavity losses and output coupling and tighter focussing of the laser fields. Low loss diamond is therefore crucial. Reducing the pump spot size is relatively straightforward by using suitable focusing optics, however, keeping the Stokes field mode-matched is challenging in a near-concentric resonator. Folded cavities or cavities with internal lenses may be beneficial for supporting smaller mode waists. Using lowest loss available material, and for waist sizes approaching 10 μm, we expect thresholds as low as a few watts may be achievable. Waveguide structures represent a key approach to further reductions in laser threshold [19, 20]. These same strategies for reducing threshold also hold for increasing conversion efficiency (see Eq. (12)). Even lower thresholds may be obtained by using pumps of shorter wavelength in accordance with the increasing gain coefficient with Stokes frequency (although this advantage will need to counteract the generally increased cross-sections for scatter and absorption loss).
Operation far above threshold increases the possibility of generating higher-order Stokes components which would saturate the first Stokes output. The relatively large and isolated Raman mode in diamond compare to other crystals makes it relatively straightforward to design mirror coatings with reflectivities minimized at the wavelength of the higher-order Stokes component. In our experiments to date, we have designed the cavity to ensure the round-trip losses at the second-Stokes wavelength to be sufficiently large (greater than 80%) to avoid generation of the second-Stokes. However, with a large number of applications near 1.5 μm, there is a substantial interest in cw DRL converters to the second-Stokes wavelength of 1485 nm, or to even higher Stokes orders. By adding suitable equations for the cascade, the model is readily adaptable to accommodate higher order generation. Furthermore, intracavity harmonic conversion of the Stokes field into visible spectrum could be simulated by introducing a Stokes-power dependent output coupling. The model may also be readily adapted to pumps at other wavelength, from the UV to mid-IR, such as high power cw sources at second harmonic wavelengths in the visible and tunable fibre lasers.
Acknowledgments
The authors would like to acknowledge stimulating discussions on model design with Ing. Jan Sulc, Ph.D., Czech Technical University, FNSPE, Prague, Czech Republic. This material is based on research sponsored by the Australian Research Council Future Fellowship ( FT0990622) and Discovery Grant ( DP130103799) Schemes, and the US Air Force Research Laboratory under agreement number FA2386-12-1-4055.
References and links
1. H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature 433, 725–728 (2005). [CrossRef] [PubMed]
2. C. Headley, M. Mermelstein, and J. C. Bouteiller, “Raman fiber laser,” in Raman Amplifiers for Telecommunications 2, M. N. Islam, ed. (Springer, 2004). [CrossRef]
3. J. A. Piper and H. M. Pask, “Crystalline Raman Lasers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 692–704 (2007). [CrossRef]
4. J. K. Brasseur, K. S. Repasky, and J. L. Carlsten, “Continuous-wave Raman laser in H2,” Opt. Lett. 23(5), 367–369 (1998). [CrossRef]
5. K. S. Repasky, J. K. Brasseur, L. Meng, and J. L. Carlsten, “Performance and design of an off-resonant continuous-wave Raman laser,” J. Opt. Soc. Am. 15(6), 1667–1673 (1998). [CrossRef]
6. A. S. Grabtchikov, V. A. Lisinetskii, V. A. Orlovich, M. Schmitt, R. Maksimenka, and W. Kiefer, “Multimode pumped continuous-wave solid-state Raman laser,” Opt. Lett. 29(21), 2524–2526 (2004). [CrossRef] [PubMed]
7. O. Kitzler, A. McKay, and R. P. Mildren, “Continuous-wave wavelength conversion for high-power applications using an external cavity diamond Raman laser,” Opt. Lett. 37(14), 2790–2792 (2012). [CrossRef] [PubMed]
8. R. J. Williams, O. Kitzler, A. McKay, and R. P. Mildren, “Investigating diamond Raman lasers at the 100 W level using quasi-continuous-wave pumping,” Opt. Lett. 39(14), 4152–4155 (2014). [CrossRef] [PubMed]
9. S. Ding, X. Zhang, Q. Wang, F. Su, S. Li, S. Fan, S. Zhang, J. Chang, S. Wang, and Y. Liu, “Theoretical models for the extracavity Raman laser with crystalline Raman medium,” Appl. Phys. B 85(1), 89–95 (2006). [CrossRef]
10. D. J. Spence, P. Dekker, and H. M. Pask, “Modeling of continuous wave intracavity Raman lasers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 756–763 (2007). [CrossRef]
11. J. T. Murray, W. L. Austin, and R. C. Powell, “Intracavity Raman conversion and Raman beam cleanup,” Opt. Mater. 11(4), 353–371 (1999). [CrossRef]
12. D. J. Spence, “Spatial and spectral effects in continuous-wave intracavity Raman lasers,” IEEE J. Sel. Top. Quantum Electron. 21(1), 1400108 (2015). [CrossRef]
13. P. Peterson, A. Gavrielides, and M. P. Sharma, “Modeling of high finesse, doubly resonant cw Raman lasers,” Opt. Commun. 160(1–3), 80–85 (1999). [CrossRef]
14. G. D. Boyd, W. D. Johnston, and I. P. Kaminow, “Optimization of the stimulated Raman scattering threshold,” IEEE J. Quant. Electron. 5(4), 203–206 (1969). [CrossRef]
15. A. Penzkofer, A. Laubereau, and W. Kaiser, “High intensity Raman interactions,” Prog. Quant. Electron. 6(2), 55–140 (1979). [CrossRef]
16. I. Friel, S. L. Geoghegan, D. J. Twitchen, and G. A. Scarsbrook, “Development of high quality single crystal diamond for novel laser applications,” Proc. SPIE 7838, 783819 (2010). [CrossRef]
17. R. P. Mildren and J. R. Rabeau, Optical Engineering of Diamond (Wiley-VCH Verlag GmbH & Co. KGaA, 2013). [CrossRef]
18. O. Kitzler, A. McKay, and R. P. Mildren, “High power cw diamond Raman laser: Analysis of efficiency and parasitic loss,” in Conference on Lasers and Electro-Optics 2012, (Optical Society of America, 2012), paper CTh1B.7.
19. L. J. McKnight, M. D. Dawson, and S. Calvez, “Diamond Raman waveguide lasers: Completely analytical design optimization incorporating scattering losses,” IEEE J. Quant. Electron. 47(8), 1069–1077 (2011). [CrossRef]
20. B. J. M. Hausmann, I. Bulu, V. Venkataraman, P. Deotare, and M. Loncar, “Diamond nonlinear photonics,” Nature Photon. 8(5), 369–374 (2014). [CrossRef]
