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The characteristics of a barium tungstate (BaWO4) anti-Stokes Raman laser at 968 nm are studied theoretically and experimentally. The BaWO4 Raman resonator is pumped by a Q-switched Nd:YAG laser at 1064 nm with its axis tilted from the pumping laser axis. The non-collinear phase matching for the generation of the first anti-Stokes wave in the same BaWO4 crystal is achieved. The output energy, temporal and spectral informations are investigated. At a pumping laser energy of 128 mJ, the anti-Stokes laser energy obtained is 2.2 mJ. The second Stokes radiation at 1324 nm as well as the first and the third Stokes waves at 1180 nm and 1509 nm is also generated at the same time. The maximum total Stokes energy output is 42.5 mJ. In the theory, the anti-Stokes laser intensity expression as a function of the pumping and the first Stokes laser intensities for the extracavity anti-Stokes Raman laser is deduced. The properties of the anti-Stokes Raman laser are simulated theoretically by solving the rate equations of the extracavity Raman laser and using the derived expression. The theoretical results are in good agreement with the experimental results.
© 2013 Optical Society of America
1. Introduction
Stimulated Raman scattering (SRS) is an extensively used nonlinear effect which widely extends the spectral range of present lasers. The crystalline Raman media have the advantages of favorable thermal and mechanical properties, high Raman gain, and narrow linewidth of the vibrational modes. As the development of the high quality Raman crystal, solid-state Raman lasers have received much attention in recent years [1-13]. The generation of Stokes radiation is a frequency down conversion process which is easy to be realized with high conversion efficiency and no need of phase matching. Most of the researches are focused on the first order Stokes radiations, some are focused on the second and higher order Stokes radiations.
To make full use of SRS to obtain more wavelengths, the anti-Stokes generation is necessary. In contrast to Stokes generation, anti-Stokes laser generation is a frequency up conversion. It is a four-wave mixing (FWM) process of two pumping photons, one first Stokes photon, and one first anti-Stokes photon. When ultrashort laser pulses are focused into a Raman medium, many Stokes and anti-Stokes lines can be generated. But these laser radiations have poor spatial or spectral characteristics and have little practical applications except the study of the Raman medium’s properties [14-16]. To generate nanosecond anti-Stokes waves with high beam quality for practical applications, non-collinear phase matching is needed [17, 18]. That is to say, there should be an exact phase-matching angle between the intense pumping beam and the first order Stokes beam. So far, only a few reports have been related to crystalline anti-Stokes lasers [17, 18]. A simple setup is proved to be an available approach to generate anti-Stokes radiation by R. P. Mildren et al. in 2009 [18]. An extracavity KGd(WO4)2 Raman resonator whose axis tilted from the pumping axis generated Stokes radiation at the phase-matching angle for FWM interreaction. The Stokes and the anti-Stokes radiations were generated in one Raman medium which greatly reduced the complexity of the experimental installation. The maximum anti-Stokes output energy of 0.27 mJ was obtained at 0.46% conversion efficiency from the pump.
BaWO4 crystal is a promising Raman gain medium. It has a high gain coefficient of 8.5 cm/GW [19], a large thermal conductivity, and a wide spectral transparency range [20]. Many results have been reported with regard to the Stokes Raman laser based on BaWO4 crystal [6-10] In 2005, Chen et al. reported an actively Q-switched intracavity Nd:YAG/BaWO4 Raman laser, generating 1.56 W of the first Stokes average output power, corresponding to a conversion efficiency of 16.9% [6]. In 2010, Cong et al. studied an actively Q-switched intracavity frequency doubled Nd:YAG/BaWO4/KTP Raman laser with 8.3 W 590 nm radiation [8]. However, anti-Stokes Raman lasers based on BaWO4 crystal have not yet been studied.
In this paper, a BaWO4 anti-Stokes Raman laser at 968 nm pumped by an actively Q-switched Nd:YAG laser is investigated. It has the potential to generate blue radiation at 484 nm by frequency doubling for applications such as color holography, laser display, and optical countermeasures. The oscillating first Stokes radiation is obtained by an extracavity Raman laser with its axis at a phase-matching angle from the pumping laser axis. Besides the first anti-Stokes radiation at 968 nm, the second Stokes radiation output at 1324 nm is also obtained with some first and third Stokes radiations at 1180 nm and 1509 nm. At the pumping laser energy of 128 mJ, 2.2 mJ anti-Stokes laser radiation is obtained with the pulse width of 6.8 ns; the corresponding conversion efficiency is 1.7%. Meanwhile, the total Stokes energy obtained is 42.5 mJ with 29.4 mJ second Stokes component included. The conversion efficiency from the pumping radiation to the anti-Stokes and the Stokes laser radiations is 34.9%. We deduce a simple expression for the anti-Stokes laser intensity as a function of the pumping and the first Stokes laser intensities for the extracavity anti-Stokes Raman laser. The rate equations and the deduced equation are used to simulate the characteristics of the anti-Stokes laser. The theoretical results are in well accordance with the experimental data.
2. Theory
2.1 Relationship between the pumping, the first Stokes and the first anti-Stokes laser intensities
In this section, a straight-forward equation is deduced to express the anti-Stokes laser intensity IAS by the incident pumping laser intensity IL0 and the first Stokes laser intensity IS1. The theory and the experiment are based on the experimental arrangement shown in Fig. 1.The Raman crystal is single-pass pumped by intense nanosecond pumping laser pulses. The Stokes laser radiation oscillates inside the Raman cavity with its axis at an external angle θˊ−1 offset from the pumping laser axis. Considering that rate equations will be used to analyze the anti-Stokes Raman lasers, the first Stokes intracavity intensity IS1 is defined as the spatial averaged value in the laser resonator as the first Stokes laser radiation oscillates in the Raman cavity. That is to say, the Stokes laser intensity is assumed to be uniform along the propagation direction. The anti-Stokes laser beam is generated with its axis at an external angle θˊ+1. The phase-matching condition is Δk = 2kL-kS1-kAS = 0 (shown in Fig. 2) where kL, kS1, and kAS are the wave vectors of the pumping, the first Stokes, and the first anti-Stokes laser radiations. Under the plane-wave approximation, the laser beams are assumed to be uniform in the laser beam cross sections.
In Fig. 2, θ+1 and θ−1 represent the phase-matching angles inside the Raman crystal. They are calculated to be 1.0° and 0.8°, respectively. The walk-off between the pumping and the first Stokes laser beams is much smaller than the beam diameters, so is that between the pumping and the first anti-Stokes laser beams, which will be analyzed in section “Experimental results and discussion”. So, we consider approximately that the three beams are coaxial. Assuming the laser radiations propagate along z axis, in the slowly varying amplitude approximation, the evolution of the anti-Stokes field amplitude AAS (z) is given by [21]
where ωAS is the angular frequency of the anti-Stokes radiation, c is the light speed in vacuum, nAS is the refractive index of the anti-Stokes radiation, ε0 is the free space permittivity. P(ωAS) is the third-order polarization at the anti-Stokes frequency which can be expressed as [21]where χR(ωAS) is the anti-Stokes Raman susceptibility, χF(ωAS) is the anti-Stokes FWM susceptibility. These two parameters can be connected by the Stokes Raman susceptibility χR(ωS1) [21].Substituting Eqs. (2) and (3) into Eq. (1), we obtain
χR(ωS1) can be calculated through the Raman gain coefficient at the first Stokes laser wavelength gR by [22]where nL and nS1 are the refractive indexes of the pumping and the first Stokes laser radiations. χR″(ωS1) is the imaginary part of χR(ωS1) which is negative. At the exact Raman resonance (ωS1 = ωL−ωv, ωv is the frequency shift of the Raman medium), we haveThe first term of Eq. (4) is the conversion process from the anti-Stokes laser radiation to the pumping radiation and the second term describes the FWM process of the anti-Stokes generation. As the anti-Stokes laser intensity is much lower than the Stokes laser intensity and the first term of Eq. (4) can be ignored. Under the phase-matching condition (Δk = 0), AAS(z) and AAS(z)* are yielded by integrating Eq. (4). AAS(z) and AS1 can be transformed into laser intensities IAS(z) and IS1 by Ij(z) = nj(ε0/μ0)½Aj(z)Aj(z)*/2 (j = AS, S1).where IS1|FWM is the first Stokes laser intensity involved in the FWM process. Because the pumping laser radiation can only interact with the forward first Stokes laser radiation to generate a unidirectional anti-Stokes laser radiation, IS1|FWM is half of the total first Stokes laser intensity inside the cavity (IS1).The pumping laser amplitude AL(z) is given in the slowly varying amplitude approximation by [21, 22]
At the exact Raman resonance, the real parts of χF(ωAS) and χF(ωAS)* are both 0, χF(ωAS) + χF(ωAS)* = 0. As the same approximation with Eq. (4), the second term can also be ignored. So, the pumping laser amplitude is simplified toAL(z) and AL(z)* can be yielded by integrating Eq. (11) and using Eqs. (5) and (6). where AL0 is the initial pumping laser amplitude, g0 = ωLgR/ωS1 is the Raman gain coefficient at the pumping laser wavelength.Substitute Eqs. (12a) and (12b) into Eq. (9), we obtain
where λAS is the anti-Stokes laser wavelength, IL0 is the initial pumping laser intensity. Parameter η is introduced to mark the ability for the Raman medium to realize the FWM process, which is written asη can be also expressed with commonly used parameter g0 by substituting Eq. (5) into Eq. (14).Equation (13) is valid for constant fields in the medium. When the fields vary with time, the integral transformation from Eq. (11) to Eq. (12) is not tenable. However, in our experiment, the crystal length is 45.5 mm. The time that the lights pass through the Raman crystal is 0.27 ns. The durations of the pumping, the first Stokes, and the anti-Stokes laser pulses are longer than 6 ns. So, with in 0.27 ns, the laser fields in the crystal can be regarded as constants. Therefore, in our case, Eq. (12) can also be yielded and Eq. (13) is reasonable at time t. Considering temporal distribution, the output anti-Stokes laser intensity is written as2.2 Rate equations
In this section, the rate equations of the extracavity Raman laser are utilized to calculate the output energy of the anti-Stokes laser. Compared with the Stokes laser intensity, the anti-Stokes laser intensity is very low. The first Stokes generation caused by the anti-Stokes generation can be neglected. The rate equations of the extracavity Raman laser with up to the third Stokes taken into consideration are [23]
where IS2(t) and IS3(t) are the second and the third Stokes laser intensities, tr = 2lc /c is the round-trip transit time of light in the cavity, ksp is the spontaneous Raman scattering factor, gSj = g0ωSj /ω0 (j = 1, 2, 3) is the Raman gain coefficient for the corresponding Stokes laser radiation, L is the intrinsic loss of the resonator, υL and υS1 are the frequencies of the pumping and the first Stokes laser radiations, Rj1 and Rj2 (j = 1, 2, 3) are the reflectivities of the output coupler and the input mirror at the corresponding Stokes laser wavelengths.The single pulse energies of the anti-Stokes laser radiation EAS and the jth order Stokes laser radiation ESj (j = 1, 2, 3) can be expressed as
where RAS is the reflectivity of the output coupler at the anti-Stokes laser wavelength, So is the average overlapping area of the pumping and the first Stokes laser beams in the Raman crystal, SS is the Stokes laser beam size. Numerically solving Eqs. (17a)-(17c), we can obtain ISj(t). Substituting IS1(t) and IL0(t) into Eq. (18), we can calculate the output anti-Stokes pulse energy. Substituting ISj(t) into Eq. (19), we can calculate the jth order Stokes pulse energy. The theoretical pulse traces of the first anti-Stokes and the jth order Stokes radiation can be given by IAS(t) and ISj(t), respectively.3. Experimental setup
The schematic of the pulsed BaWO4 anti-Stokes Raman laser is shown in Fig. 1. The pump source is a flash-lamp-pumped actively Q-switched Nd:YAG laser at 1064 nm. The repetition rate is 1 Hz. The pumping laser beam has a top-hat distribution. A half-wave plate is used to change the pumping laser polarization to obtain the maximum Raman gain. An extracavity BaWO4 Raman laser is arranged to realize the anti-Stokes generation. Flat cavity mirrors M1 and M2 are mounted on a motorized rotation stage (Zolix RSA100) which is precisely controlled by a motorized stage control box (Zolix SC300). The rotation accuracy is 0.00125° per step. The rear mirror (M1) is coated for high transmission (HT) at 1064 nm (T > 99.3%) and high reflection at the first Stokes wavelength (1180 nm) (R > 99.5%). The output mirror (M2) is coated for HT (T > 92.0%) at the first anti-Stokes wavelength (968 nm) and 1064 nm (T > 95.5%) and partial reflection at 1180 nm (R = 90.4%). The transmissions of the cavity mirrors are shown in Fig. 3.A 5 × 5 × 45.5 mm3 a-cut BaWO4 crystal is placed between M1 and M2 with its c-axis perpendicular to the rotation plane. The whole cavity length is 58 mm. The output anti-Stokes energies are detected by a pyroelectric energy sensor (Ophir PD300-IR-ROHS) with a laser energy meter (Ophir NovaII). The pulse shapes are recorded by a Tektronix digital phosphor oscilloscope (TDS 3052B, 500 MHz) with a fast photodiode (1 GHz). The spectral information is monitored by a wide-range optical spectrum analyzer (YokogawaAQ 6315A).
4. Experimental results and discussion
All the generated radiations have the same polarization as the pumping laser radiation that is parallel to the c-axis of the BaWO4 crystal. The typical laser spectra of the output radiations with a resolution of 5 nm are shown in Fig. 4. Besides the first anti-Stokes radiation, up to three orders of Stokes laser radiations are obtained for the high pumping laser intensity. Since the output coupler has high reflectivity at the first Stokes wavelength, the main part of the output Stokes radiations is the second Stokes component. The frequency shift between the output lines agrees very well with the optical vibration modes of tetrahedral WO4−2 ionic groups of BaWO4 (925 cm−1). The anti-Stokes laser radiation can be observed when θˊ−1 is 19.1 mrad. The most effective anti-Stokes generation occurs when θˊ−1 is 34.1 mrad. Meanwhile, θˊ+1 is measured to be 27.6 mrad. The theoretical external angles are calculated by the phase-matching condition. The refractive indexes are obtained by the Sellmeier equations reported in [24]. The comparisons between the experimental and the calculated values are shown in Table 1. It can be seen that the calculated results are consistent with the experimental results.
Table 1. Parameter comparisons of the output beams between the calculated and the experimental values.
Two pumping laser beams with diameters of Dp1 = 2.5 mm and Dp2 = 3.0 mm are respectively used to investigate the characteristics of the anti-Stokes generation. The walk-off between the pumping and the Stokes laser beams is 0.23 mm (θ−1lR /2nS1, θ−1 = 18.1 mrad) for the crystal length lR = 45.5 mm. The walk-off between the pumping and the anti-Stokes laser beams is 0.18 mm (θ+1lR /2nAS, θ+1 = 14.8 mrad). They are much smaller than the laser beam diameters and cannot make a strong impact on the interactional spatial overlap of the pumping, the first Stokes and the first anti-Stokes laser beams. Therefore, the coaxial assumption in the simulation is reasonable. The output anti-Stokes pulse energies for different pumping laser energies are shown in Fig. 5. The solid symbols are the experimental results and the lines are the theoretical results. The parameter values adopted in the theoretical calculations are listed in Table 2.
Table 2. The parameters for the theoretical calculation.
It can be seen that under the phase-matching condition, the anti-Stokes conversion efficiency strongly depends on the pumping laser beam size. At the same pumping laser energy, smaller beam size corresponds to higher laser intensity. High conversion efficiency and low threshold are obtained using the smaller 2.5 mm pumping laser beam. The anti-Stokes laser radiation is generated above the threshold of 22 mJ. At the maximum pumping laser energy of 128 mJ, the highest output anti-Stokes laser energy is 2.2 mJ. The corresponding conversion efficiency from the pumping laser radiation is 1.7%.
Three order Stokes radiations are generated together with the anti-Stokes laser radiation. Figure 6 shows the output energies of the three order Stokes radiations with the pumping beam diameter of 2.5 mm. The solid symbols are the experimental results and the lines are the theoretical results. Being highly reflective at the first Stokes, the output coupler achieves high conversion efficiency of the second Stokes laser radiation. The second Stokes pulse energies increase with increasing pumping pulse energy. When the pumping pulse energy is above 83 mJ, the third Stokes radiation appears. At the maximum pumping energy, the total output Stokes laser energy is 42.5 mJ with the pulse energies of 5.5 mJ, 29.4 mJ, and 7.6 mJ for the first, the second, and the third Stokes components, respectively. The total conversion efficiency from the pumping laser radiation to the Stokes and the anti-Stokes laser radiations is about 34.9%. By using proper cavity mirrors, we can obtain only the first anti-Stokes and the second Stokes radiations.
The pulse shapes for the incident pumping, the depleted pumping, the first Stokes, and the first anti-Stokes laser radiations are shown in Fig. 7 under the highest anti-Stokes output. The anti-Stokes pulse width is 6.8 ns. The corresponding peak power is about 320 kW. The pulse shapes are calculated at the pumping laser energy of 128 mJ.They are shown in Fig. 8. It can be seen that the anti-Stokes laser radiation is generated at the temporal overlapping area of the pumping and the first Stokes laser pulses. As shown in Figs. 5-8, the theoretical results are well coincide with the experimental results. Some discrepancies can also be observed. In Fig. 5, the model predicts much faster anti-Stokes energy growth than the measured data. When the pumping energy is large, the theoretical results are larger than the experimental ones. In Fig. 6, the first Stokes experimental data grow linearly with increasing pumping laser energies. The theoretical curve grows fast at the beginning and flattens out when the second Stokes reaches the threshold. There are two main reasons. First, the pumping, the first Stokes and the anti-Stokes beams are assumed to be coaxial. Actually, there are small angles between the three laser beams. The interaction of the FWM process and the Raman conversion from the pumping radiation to the first Stokes radiation in theory are stronger than the reality. Second, the Raman conversion from the first anti-Stokes radiation to the pumping radiation is neglected, this also results in higher theoretical results in Fig. 5. In Eq. (4), the first term is the conversion process from the anti-Stokes radiation to the pumping radiation and the second term describes the FWM process of the anti-Stokes generation. From Eq. (4), when Δk = 0, the ratio of the anti-Stokes decrease due to the Raman conversion to the anti-Stokes increase due to the FWM process can be expressed as
where IL(z), IAS(z), and IS1 are the intracavity intensities of the pumping, the anti-Stokes, and the first Stokes radiations, respectively, when the output anti-Stokes intensity is the maximum. Table 3 shows the values of r estimated at different pumping energies. The values are calculated at the anti-Stokes peak intensity, so they are even smaller at other time. Compared with the anti-Stokes generation rate due to the FWM process, the anti-Stokes depletion rate due to the Raman conversion is very small. If this term is considered in the theoretical model, the derivation process will become very complicated. So, it is reasonable to neglect it. But, in fact, it can produce a little discrepancy.
Fig. 7 Oscilloscope traces of the pumping, the depleted pumping, the first Stokes and the first anti-Stokes laser pulses.
Fig. 8 Numerically calculated traces of the pumping, the depleted pumping, the first Stokes and the first anti-Stokes laser pulses.
Table 3. The ratio of the anti-Stokes decrease due to the Raman conversion to the anti-Stokes increase due to the FWM process for different pumping energies.
Raman conversion in crystalline materials is one of the most efficient methods to produce new laser lines. Stokes lasers can generate longer laser wavelengths than the pumping wavelengths with high conversion efficiency. Shorter wavelengths can be obtained by anti-Stokes lasers than that of the pumping radiations. The anti-Stokes conversion efficiency is relatively low. Compared to other methods for new wavelength generation, e.g. second harmonic generation, sum-frequency generation, optical parametric oscillation, the anti-Stokes Raman lasers are very suitable for the generation of three or more wavelengths simultaneously. In this paper, including the residual pumping laser radiation, five wavelengths are easily obtained from one pumping laser and an anti-Stokes Raman laser.
5. Conclusion
In summary, an efficient BaWO4 extracavity Raman laser that generates both three orders of Stokes and the first anti-Stokes laser radiations has been investigated in this paper. The phase-matching of the anti-Stokes generation process is achieved by inclining the Raman cavity axis at about 34.1 mrad from the pumping laser axis. At the maximum pumping laser energy of 128 mJ, the highest pulse energy obtained is 2.2 mJ for the first anti-Stokes laser radiation with the pulse width of 6.8 ns; the corresponding conversion efficiency is 1.7%. The total conversion efficiency from the pumping laser radiation to the Stokes and the anti-Stokes laser radiations is about 34.9%. An equation that indicates the relationship between the pumping, the first Stokes and the anti-Stokes laser intensities for the extracavity anti-Stokes Raman laser is deduced from the propagation equations. Together with this equation, the rate equations of extracavity Raman laser are used to simulate the properties of the anti-Stokes laser. The theoretical predictions agree well with the measured data. The theoretical model is also applicable to other extracavity pumped anti-Stokes lasers arranged as the experimental installation in this paper.
Acknowledgments
This research is supported by the National Natural Science Foundation of China (11174185, 10974168), the Research Fund for the Doctoral Program of Higher Education of China (20100131110064).
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