1. Introduction

Stimulated Raman Scattering (SRS) is an inelastic process arising from the third-order nonlinearity of Raman active materials. It has been widely used for frequency conversion to extend the spectral coverage of solid-state lasers, not only in the infrared region but also in the visible through sum-frequency generation (SFG) of fundamental and Stokes output or through second harmonic generation (SHG) of either of these [1, 2]. Compact, efficient, all-solid-state lasers generating visible emission spanning the green-to-yellow are attractive for applications in ophthalmology, biomedicine and display technologies. Motivated by these applications, significant effort has been directed at optimizing such laser sources. The most efficient and practical solid-state CW Raman lasers reported to date have been mainly based on a variety of tungstate crystals including BaWO₄, SrWO₄, KGW, and vanadate crystals including Nd:YVO₄, Nd:GdVO₄, and Nd:LuVO₄ [3–6].

Previous methods for optimizing CW Raman lasers have focused on managing three key resonator parameters, these being resonator mode size, resonator losses and thermal lensing. However, with the drive for higher output powers, and the desire to generate wavelength-selectable Raman lasers, it has become apparent that the dynamics of whole resonator is indeed very complicated due to the interplay between SRS and SFG/SHG processes [5]. Understanding and managing this interplay is critical in order to improve the design and operation of such lasers.

In this paper, we present the performance of an efficient miniature self-Raman laser that generates either lime or yellow output by tuning the intracavity LBO crystal temperatures for phase-matching of either SFG or SHG. Despite the very modest diode pump power of 3.8 W, output powers of 320 mW at 588 nm and 660 mW at 559 nm were achieved with high diode to visible conversion efficiencies of 8.4% and 17% respectively, comparable to the best conversion efficiencies previously reported for order-of-magnitude higher pump powers. Contrary to usual expectations, the best laser performance is achieved with a short LBO crystal, a consequence of the interplay between SRS and frequency mixing, as well as crystal losses. We compare laser operation using two LBO crystals of different length, and make estimates of the round trip losses by laser threshold measurements. By measuring the residual fundamental and Stokes emission through the output coupler, along with the visible emission, we show that complex interplay between the intracavity fields occurs in these lasers, originating from competition between the non-linear effects. We use rate equation analysis to explain this complex behavior leading to new understanding of factors limiting power and efficiency.

2. Laser design

The cavity layout for our compact lime–yellow wavelength selectable laser is shown in Fig. 1 . The laser was designed for low-threshold and high-efficiency operation, and to achieve these we used small spot sizes and kept cavity losses as low as possible. The fundamental (1064 nm) and Stokes (1176 nm) wavelengths were resonated in the high Q cavity, and we used temperature tuning of an LBO crystal to select the visible output wavelength of the laser: the output was 559 nm (lime) when the LBO was phase-matched for SFG of the fundamental and Stokes fields, and 588 nm (yellow) when the LBO was phase-matched for SHG of the Stokes field.

 

Fig. 1 Cavity layout for self-Raman experimental laser.

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The pump source used in this work was a high-brightness free-space diode laser (Unique Mode: UM4200-M20-CB-TEC), providing horizontally-polarized pump light with a maximum output power of 3.8 W at 808 nm. We used a telescope arrangement for expanding and collimating the diode output and then focusing it into the Nd:YVO₄ crystal through a 50 mm focal length lens. The focal spot radius was estimated to be 80 µm. Over 98% of the pump was absorbed in the laser crystal.

We chose an a-cut, 1 at.% Nd:YVO₄ crystal with dimensions of 4 mm × 4 mm × 3 mm long as the combined laser/Raman medium, taking account of the high Raman gain (4.5 cm/GW [7]) and high emission cross-section (14.1×10⁻¹⁹ cm² [8]) of this material. The Nd:YVO₄ crystal was oriented so that the pump light was polarized along its ‘c’ axis, to take advantage of the high 808 nm absorption (48.4 cm⁻¹), a factor of four times higher than for light polarized along the ‘a’ axis [8]. In order to reduce the number of intracavity surfaces and minimize resonator losses, a high-reflectivity (HR) coating (R>99.994% @ 1064 /1176 nm) was deposited directly onto the pumped face of the Nd:YVO₄ crystal. Here and below the quoted reflectivities are as specified by the suppliers. On the other side, the crystal was anti-reflection (AR) coated (R = 0.026% @ 1064nm, R = 0.045% @ 1176 nm). The crystal was water cooled to 20°C.

Two lithium triborate (LBO) crystals (Castech Inc.) with dimensions of 4 mm × 4 mm (cross section) and either 10 mm or 5 mm long were evaluated for intracavity frequency-mixing. They were cut for noncritical phase matching (NCPM) (θ=90°, φ=0°), AR coated (R = 0.42%-0.47% @1064 nm, R=0.095%-0.098%@1176 nm). A copper block incorporating a resistive heater was used to house the LBO crystal and enable heating of the crystal from ambient up to 160°C, and the temperature of this mount was monitored using a PT100 sensor.

The resonator was formed by the combination of the HR coating on the pumped face of the Nd:YVO₄ crystal, and an output coupler with radius of curvature (ROC) 50 mm. The total cavity lengths were ~17 mm and ~15 mm when the 10 mm and 5 mm long LBO crystals were used respectively (the minimum cavity length was set by the component mounts). The output coupler was coated for high transmission (T~80%) at 559 nm and 588 nm (T~95%), and high reflectivity (R>99.994%) at 1064 and 1176 nm. The spectral properties of the output were monitored using a fibre-coupled spectrometer having 0.05 nm resolution.

3. Experimental results using LBO crystals with different lengths

3.1 Laser output powers at 559 nm and 588 nm

Figure 2(a) shows results obtained using the 5 mm long LBO crystal. We observed the maximum visible output powers (at 3.8 W maximum pump power) were 660 mW and 320 mW, at 559 nm and 588 nm respectively, for which the LBO mount temperature was 98°C and 45°C. The corresponding conversion efficiencies were 17% and 8.4%. Figure 2(b) shows the experimental results for the 10 mm long LBO crystal. The maximum power at 559 nm was 420 mW, and at 588 nm 195 mW, obtained for the same 3.8 W incident pump power and LBO mount temperatures set at 88°C and 50°C respectively. The temperatures for the two LBO crystal lengths were noticeably different. Threshold pump powers were identical for the two visible wavelengths, 0.34 W for the 5 mm LBO case and 0.6 W for the 10 mm LBO case. Note that the thresholds for both visible lines are the same as threshold for SRS. The output beam quality parameter (M2) of the outputs were 2.5 and 1.5 at 559 nm and 588 nm respectively, at maximum output power.

 

Fig. 2 Visible output power as function of incident pump power (a) using 5 mm long LBO (b) using 10 mm long LBO.

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Given that each LBO crystal had identical coatings, the substantially lower threshold and higher maximum output powers for the lasers utilizing the shorter LBO crystal indicate that bulk losses in these crystals are significant. This is discussed further in Section 4.

The diode to visible conversion efficiencies achieved here are very high, approaching those obtained in [5] where pumping with a much higher power of 29 W delivered conversion efficiencies of 12.1% and 16.9% in the yellow and lime respectively. The powers reported here are also substantially higher than the yellow power of 220 mW reported in [9] using the same 3.8 W pump diode (operation at 559 nm was not reported in [9]). Note that, for simplicity, only the visible emission propagating through the output coupler was measured in this work. Even higher powers and efficiencies may be possible by using an intracavity mirror as in [5] and [9] to collect the back-propagating visible emission. The improvements in this work are due to many factors including the directly-deposited HR coating on the Nd:YVO₄ crystal, a shorter resonator with consequently smaller cavity mode and higher intensities, and most particularly a shorter LBO crystal for reasons associated with laser dynamics and losses that are developed in the following sections.

3.2 Optical dynamics: dependence on phase matching temperature

To further investigate the behavior of the laser operating with 5 mm or 10 mm long LBO crystals, we monitored the visible output power along with the residual fundamental and Stokes fields leaking through the output coupler, as functions of LBO temperature (affecting the phase matching within the resonator). Normally highest yellow and lime outputs would be expected for LBO temperatures which correspond to optimum calculated phase matching conditions for those wavelengths, with considerably lower output away from these temperatures. However, we see from Fig. 3(a) and 3(b), the observed behavior is not the case, particularly for the longer crystal.

 

Fig. 3 Experimental measurements of visible, Stokes and fundamental field intensities as a function of LBO temperature tuning for (a) 5 mm LBO crystal, and (b) 10 mm LBO crystal along with theoretical plots, (c) and (d), of the non-linear coupling strengths for the associated LBO crystals.

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For comparison with the experimental results, we also plotted in Figs. 3(c) and 3(d), the relative strength of the SHG and SFG non-linearity $\eta$, which is proportional to crystal length $l_D{}^2$ and sinc² term. This takes the form [10]

The results using the 5 mm long LBO, show that the yellow output was maximized around 45°C, and the lime at around 98°C, with fairly symmetric behavior above and below these temperatures. The temperatures that we recorded experimentally, corresponding with the maximum visible emission at these two wavelengths, are notably higher than the theoretical phase matching temperature (with a larger discrepancy for the higher phase matching temperature) consistent with the measured LBO mount temperature being higher than the temperature on the axis of the LBO crystal. The measured widths (span of temperatures) of the emission peaks are consistent with the expected sinc² dependence on temperature, with the total width of central peak of the sinc² function being 28.6°C for the yellow output, and 24.8°C for the lime output for the 5 mm crystal. What is surprising is that substantial visible output power was still generated at LBO temperatures far from the optimum value, in the wings of the sinc² curve. This result indicates that even for non-linear strengths of only a few percent of the peak value, there was still sufficient coupling to generate substantial visible laser output.

The results for the 10 mm long crystal are significantly different from those for the shorter crystal. We expect the peak non-linear coupling to be four times higher compared to the 5 mm case due to the $l_D^2$ dependence, and the temperature acceptance bandwidths to be half as wide. In fact, around where maximum lime emission was generated using the 5 mm long LBO crystal (~98 ^o C), no lime at all was generated when using the 10 mm long LBO, and the 1176 nm field completely stopped lasing over a significant temperature range (92°C-100°C). The cessation of the 1176 nm field over this temperature range is even more surprising given that there was strong intracavity fundamental (1064 nm) intensity, evidenced by the direct measurement of the residual fundamental field through the output coupler. The maximum lime emission was observed on either side of the temperature range seeing cessation of 1176 nm field, and the maximum output power was lower compared to the 5 mm case. Yellow emission was observed at similar temperatures to what was observed in the 5 mm case, but the output power appeared largely independent of temperature over a 30°C temperature range. Again, the weak non-linear coupling in the wings of the sinc² function was strong enough even to provide near-maximum output, suggesting that there was far more non-linearity than required at the phase matched temperature,

There are two aspects of these experimental results that require further explanation and confirmation. Firstly, why does the 5 mm long LBO crystal give much more output power than the 10 mm LBO? Secondly, why does the lime and Stokes output completely and suddenly cease near the peak of the temperature tuning of the 10 mm LBO crystal?

4. Estimation of round trip losses

The relative thresholds and output powers when using the 5 mm and 10 mm LBO crystals are clearly related to round trip losses. We now find an estimate of the cavity losses by considering the Raman thresholds of lasers constructed with and without LBO. Cavity losses are of critical importance in CW Raman lasers where extremely high cavity Q’s are required in order to reach threshold for SRS. Here, we show that bulk crystal losses caused by scattering and absorption, which are typically of little consequence in traditional frequency-doubled lasers, must now be considered in designing Raman lasers with low thresholds.

At Raman threshold, the Stokes field is, by definition, extremely small and so the effective output coupling of the LBO crystal can be neglected. The total cavity losses at threshold are then comprised of the unwanted losses due to mirror leakage, surface reflections, and bulk losses in the crystals. The threshold for Stokes oscillation can be written [13]. Note the original work in [13] did not consider backwards SRS. It has been included here, giving rise to an additional factor of 2 in the denominator.

As an aside, we note that more complex methods using multiple measurements, such as Caird analysis [14] and Findlay-Clay method [15] are normally required to measure the losses of conventional lasers. Such methods are not viable here because the losses are not dominated by a fixed output coupler transmission in our Raman lasers. The output couplers have very low transmission, and for the yellow and lime lasers, the effective output coupling due to frequency mixing within LBO crystal actually goes to zero at Raman threshold. In this case, the crystal losses are the dominant contributor to resonator losses, and therefore can be reasonably estimated by a single measurement.

Table 1 shows the measured thresholds, experimental parameters, and calculated round trip losses for the yellow lasers constructed with the 5 mm and 10 mm long LBO crystals, as well as for a self-Raman laser with no LBO crystal in the cavity. For all the three cases, we used the same output coupler with T_F=0.0064%, T_S=0.0042% and adjusted the physical length of the cavity to achieve the same cavity mode size of 96 µm inside the Nd:YVO₄ crystal, determined using LASCAD (software package for Laser Cavity Analysis and Design). The M² beam quality was measured to be 1.2 near threshold for each case.

Table 1. Round Trip Losses Calculation

View Table

From the measured thresholds, we calculated the round trip loss for each laser: 0.145% for the self-Raman laser; 0.214% for the 5 mm LBO yellow laser, and 0.286% for the 10 mm LBO yellow laser. We estimated the accuracy of the above values to be approximately 10%, primarily due to the uncertainties in the radius of the Raman cavity mode and the observed laser threshold. Uncertainty in the Raman gain coefficient would also impact on the loss measurements; no error is estimated in [7], however the gain coefficient is said to be “no less than 4.5 cm/GW”, leading to (if anything) our underestimating the round trip loss. From these cavity losses, we inferred the additional insertion loss caused by 5 mm and 10 mm LBO crystals to be 0.07% and 0.14%, respectively. This 1:2 ratio of losses indicates that the insertion losses caused by LBO crystals are dominated by bulk losses rather than the surface losses that are identical in both cases. It is interesting then that in this laser, the AR coatings on the LBO (R=0.42% - 0.47% @1064 nm, R=0.095% - 0.098%@1176 nm) do not appear to contribute to the intracavity loss. We believe that laser runs on longitudinal modes that experience no coating losses due to etalon effects, a contention which is supported by our observation of spectral mode selection effects associated with the LBO. We also note that experiments performed using a different 10 mm crystal with much better AR coatings (0.004% at 1064 nm, 0.064% at 1173 nm) showed the same Raman threshold. This gives further confirmation that the AR coatings do not contribute significantly to the round trip loss in this laser. Here, we present only the results for the 10 mm and 5 mm long LBO crystals coated by Castech (as detailed in the method section) to allow immediate comparison and conclusion regarding the effect of crystal length.

Likewise, we attribute the losses in the self-Raman laser to bulk scattering losses in the 3 mm long Nd:YVO₄ crystal, noting the excellent coatings on the intracavity faces of the Nd:YVO₄ crystal. The round trip scattering loss 0.145% determined for the Nd:YVO₄ self-Raman resonator corresponds to a per centimeter loss of 0.24% for the highly doped Nd:YVO₄ crystal used in this work.

5. Theoretical analysis

We now move on to analyze theoretically the complex behavior of the yellow and lime output for our two lasers, with a view to understanding the complete suppression of the Stokes and lime fields for the laser with 10 mm long LBO at temperatures where we would usually expect the most output.

For the yellow laser, we can think of the SHG process as a non-linear output coupler for the Stokes field, with the effective output coupling being zero at Raman threshold, increasing as the Stokes field grows with increasing pump power. To get optimum output power at our maximum pump power, we require this effective output coupling to take its optimum value for that Stokes field strength, just as the fixed output coupler for a conventional laser needs to be optimized. If the SHG strength is too low or too high, the yellow output will be less than its potential maximum, quite similar to the case of frequency doubling a conventional laser [16]. For the 5 mm LBO, the yellow output peaked symmetrically as the temperature was tuned, indicating that the coupling strength at the phase matching temperature was at or below its optimum value. For the 10 mm LBO, the yellow output power was flat or even slightly dipped around the same phase matching temperature, suggesting that the peak coupling strength may have been too high, i.e. the Stokes field was over-output-coupled.

For the lime laser, the SFG process also acts as a non-linear output coupler, in this case presenting a loss to both the fundamental and Stokes fields. In contrast to SHG, if the SFG strength is too high, the Stokes field is extinguished – there is a critical coupling strength over which the Stokes field suddenly does not lase. We can gain further insight into the dynamics of this effect by considering the form of the differential rate Eq. (3) for the power in the Stokes field:

When the LBO temperature is in the region for lime emission by sum frequency generation (SFG), we can approximate that ${\kappa }_{SHG}\approx 0$ and so the last term in Eq. (3) can be neglected. We also note that the terms for Raman gain and SFG have the same dependence on the powers of the intracavity field and thus we can combine them for the case of SFG to get the simplified Eq. (4)

Of course, if a 10 mm crystal provides too much non-linear coupling, it makes sense to try a shorter crystal: the 5 mm crystal has a peak value of $\beta$a factor of ¼ as high, and our experiments show that even at the peak of the phase matching, this value is less than the value required to turn off the Stokes field and lime output. Furthermore, because the shorter crystal presents less cavity loss, as determined in the previous section, the peak lime output is enhanced.

6. Conclusions

Our comprehensive investigation of lime and yellow wavelength-selectable Raman lasers using 5 mm and 10 mm LBO crystals has led to two important observations that have enabled us to demonstrate an efficient wavelength-versatile Raman laser pumped by only 3.8 W of diode power.

First, in the high-Q resonators that are typical of efficient intracavity CW Raman lasers, bulk crystal losses (e.g. due to scattering and absorption) become increasingly important. For the lasers presented here, the intracavity losses are dominated by the bulk losses of the crystals themselves, rather than losses at the AR-coated crystal surfaces or unwanted transmission through cavity mirrors. This unusual situation leads to new conclusions regarding the optimum length of the intracavity crystals, notably that shorter Raman and SHG/SFG crystals are favored to reduce losses. This is why in this work, lasers with 10 mm LBO generate lower output powers than those with 5 mm LBO, and is one reason why miniature Raman lasers with just 3 mm of Raman active material in the cavity have relatively similar efficiencies to more standard designs with up to 20 mm of Raman active material [5]. The dominance of crystal losses is also a significant factor favoring self-Raman laser designs over those using separate laser and Raman crystals, for which the total length of material in the cavity can be substantially reduced.

Second, we have observed experimentally a complete suppression of the first-Stokes optical field in a Raman laser using intracavity SFG, and explained this phenomenon by considering the rate equation for the first-Stokes optical field in the presence of SFG. Understanding these dynamics is absolutely critical to the design of efficient Raman lasers incorporating intracavity SHG.

While for the last few years the output and efficiency of visible Raman lasers have been substantially boosted by improvements to mirror and crystal coatings, these improvements appear to be approaching a limit. The present results show that future advances might now be driven by improvements of crystal quality both of the laser and nonlinear materials. We have also demonstrated the potential for making practical miniature visible laser sources based on mm-scale crystal Raman lasers, giving ~100 mW CW powers using low-power (1-2W) diode-pumping.