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An efficient multi-frequency extracavity Raman laser for nanosecond pulses was realized by taking advantage of the anisotropic optical property of the KGd(WO4)2 crystal. The conversion efficiencies of the converter were investigated versus the pump pulse energy, pump polarization, and output coupling rate experimentally and theoretically. Based on the coupled radiation transfer equations, a theoretical model was deduced to predict the performance of solid-state extracavity Raman lasers. This model was solved numerically to analyze the operation of the extracavity Raman laser with the KGd(WO4)2 crystal, and the numerical results had a good agreement with the experimental ones.
©2005 Optical Society of America
1. Introduction
The stimulated Raman scattering (SRS) has been widely adopted to realize frequency shifters, pulse compressors and power amplifiers with liquids and gases as the nonlinear media since its discovery. In recent years there has been a resurgence of interest in SRS as a result of the discovery and development of new synthesis Raman crystals, e.g. Ba(NO3)2, Pb(NO3)2, BaWO4, and KGd(WO4)2 [1–4]. At the same time, various Raman laser configurations were also investigated, including Raman generators, extracavity Raman lasers, intracavity Raman lasers, coupled cavity Raman lasers, etc. Comprehensive reviews on the progresses of solid-state Raman lasers have been made recently [5,6].
Extracavity Raman lasers, where the Raman crystal is placed in an independent resonator from the pump laser as depicted in Fig. 1, can substantially lower SRS threshold, selectively produce the output at the aimed order Stokes, and improve the quality of output beam as compared with Raman generators. Meanwhile, this configuration is a versatile and simple add-on to an unaltered pump laser, and its design and optimization are relatively simple being compared with the intracavity Raman lasers. Thus, the extracavity Raman lasers have attracted research interests, and very efficient lasers have been demonstrated [7–10].
The KGW crystal is an increasingly popular Raman material [15–18], which features high thermal conductivity, low dn/dT and high damage threshold. The KGW crystal possesses monoclinic lattice structure (space group-C2/c), which leads to the anisotropic optical and thermophysical properties. In the KGW crystal, the mutual positions of the crystallographic axes relative to the optical indicatrix axes are given in Fig. 2 [19]. The crystallographic b-axis also known as the second-fold symmetric axis coincides with the optical indicatrix axis Np , while the Nm and Ng axes are located under 24 and 20 degree with the a- and c-axes, respectively. The edge shared [WO6] octahedrons form molecular groups in the KGW crystal, which have complicated polarized Raman spectra. Two intensive Raman lines are observed in the polarized SRS spectra of the Np -cut KGW crystal. One SRS line is registered with the Raman shift at 901 cm-1 under the p[mm]p excitation geometry, and one stimulated vibronic line is observed at 768 cm-1 under the p[gg]p geometry [19]. Here, p[mm]p and p[gg]p adopt the notation of Damen and Porto [20]. Much richer spectral lines can be obtained for other excitation configurations in the KGW crystal.
Fig. 2. Unit cell of KGW, constructed on W atoms. The positions of the crystallographic axes a, b and c are given relative to the optical indicatrix axes. α=γ=90°, β≠ 90°.
Relative to the experimental works, there have been less theoretical efforts reported on extracavity Raman lasers with the crystalline Raman media. The coupled radiation transfer equations derived by Shen and Bloembergen [11] were used to predict the conversion efficiency of Raman generators [12, 13]. Murray et al. [14] solved the coupled radiation transfer equations by the fast Fourier transform (FFT) method to predict the temporal profiles of the first Stokes and pump beams of the extracavity Raman lasers, and Kazzaz et al. [22] also adopted these equations to model the performance of the extracavity Raman laser with the pressurized methane gas as the nonlinear medium. However, the high order Stokes weren’t taken into consideration in these two works, which are not negligible for the SRS processes in the Raman crystals.
In this paper, an efficient multi-frequency extracavity Raman laser was realized by taking advantage of the anisotropic optical property of the KGW crystal, and the SRS processes were investigated with both the Ng - and Nm -polarized pumping configurations. The output couplers with different reflectivity spectral profiles were experimented to obtain the output of the first or second Stokes wave. The conversion efficiencies of the Stokes beams were investigated versus the pump pulse energy, pumping polarization, and output coupling rate. The maximum conversion efficiency of the first Stokes obtained was 45%, and that of the second Stokes 48%. Meanwhile, we gave a modified radiation transfer equation model for the extracavity Raman laser with the crystalline nonlinear medium by taking up to the third Stokes and the backward Raman scattering into consideration. These coupled equations were solved numerically to predict the performance of the extracavity Raman laser, and the results had a good agreement with the experimental ones.
2. Theory
In the Raman medium, the evolution of the intensities of the pumping and Stokes beams can be described by the following set of coupled radiation transfer equations for the steady state regime by assuming that the beams propagate along the z axis [21, 22]. Because of the cascade property of the SRS, up to the third Stokes beams are considered in the coupled equations. The equations are based on the plane-wave approximation and dispersion neglect.
where Ii (i=L, 1, 2, 3) is the intensity of the pump or each order Stokes beam, respectively. gi =g 0 ω i/ω L is the Raman gain coefficient of each order Stokes beam with ωi and ωL the angular frequencies of the Stokes and pump beams, respectively, and g 0 the Raman gain coefficient at the pumping wavelength. n is the refractive index of Raman medium, α the dissipative loss coefficient in the Raman medium, Ksp the spontaneous Raman scattering factor, and c the light speed in the vacuum. Note that Ii is the function of t and z, i.e. Ii =Ii (t, z), here we adopt the simplified form for convenience.
Including the backward SRS terms, the following set of coupled differential equations is obtained for the extracavity Raman laser.
where (i=L, 1, 2, 3) is the intensity inside the Raman cavity, i.e. 0≤ z≤ lc , and plus (minus) sign means forward (backward) propagating direction. α is the dissipative loss coefficient of the extracavity Raman laser defined as α=L/lc =Σj Lj /lc , where L=Σj Lj represents the sum of dissipative losses of a single pass through the resonator except the output coupling rate, and lc stands for the optical length of the resonator. It is assumed that the Raman gain coefficient of the backward SRS is equal to that of the forward one.
The boundary conditions are imposed by the resonator mirrors referring to Fig. 1,
where R i1 is the reflectivity of the output coupler at the pump or each order Stokes beam, R i2 that of the input mirror at each order Stokes, TL the transmission of the input mirror for the pump pulse, and IL (t) the intensity function of the input pump pulse with respect to t.
In this numerical model, the generation and interaction with anti-Stokes waves are neglected, and the term describing four waves mixing is omitted. The validity of these assumptions can be verified by the experimental results of us and other researchers, which shows that higher order Stokes beams were observed commonly in extracavity Raman lasers with the crystalline nonlinear media, however the anti-Stokes beams were usually negligible [18–21].
The coupled radiation transfer equations are partial derivative equations with respect to t and z, and numerically solved by the method of characteristics by considering the boundary conditions. The spatial profile of the pump and Stokes beams are nonuniform usually, and for simplicity the beam intensities are assumed to have the average values in the theoretical calculations.
3. Experimental setup
Fig. 3. Experimental arrangement, showing the pump laser, coupling optics, and external Raman resonator.
The experiment system is depicted in Fig. 3. An actively Q-switched Nd: YAG laser system operating at 1064 nm was used as the pump source with the output energy up to 80 mJ. The pump radiation was re-imaged by a focusing lens of 40 cm focal length. Two polarizers were used for the adjustment of the pump energy. The Raman laser output was separated into the first and second Stokes beams by a dichroic mirror. The energies of the pump and Stokes beams were registered with an energy-calibrated pyroelectric probe (Molectron J50) connected to Molectron EPM2000.
The b-cut KGW crystal used in the experiment was of dimensions φ 6 mm×45 mm. The crystal had antireflection from 1040 nm to 1300 nm. The optical indicatrix axes Nm and Ng were oriented by using the pleochroism. The input mirror of the Raman resonator was highly transmissive (HT; >90%) at the fundamental and highly reflective (HR; ~99%) from 1130 nm to 1330 nm. Three kinds of output couplers were experimented, which have high reflectivity at 1064 nm (to realize the double-pass pumping) and different reflectivity values at the Stokes beams given in Tables 1 and 2 for the Ng - and Nm -polarized pumping configurations, respectively. For each output coupler, the experiments were carried out for both the Ng - and Nm -polarized pumping configurations.
Table 1. The reflectivities of the output couplers at the pump and Stokes beams with 768cm-1 Raman shift for Ng -polarized pumping
Table 2. The reflectivities of the output couplers at the Stokes beams with 901cm-1 Raman shift for Nm -polarized pumping
4. Results and discussion
4.1. Conversion efficiency of the extracavity Raman laser
The conversion efficiency is defined as the ratio of the output Stokes pulse energy to the pump pulse energy transmitted into the Raman resonator. The experimental results versus pump energy for three kinds of output couplers are shown in Figs. 4–6, respectively. A diffraction lattice monochromator was used to monitor the spectral information of the output, and the first and second Stokes beams were observed, but no output at the third Stokes and anti-Stokes wavelengths were detected even for the highest pump energy. The theoretically calculated results are also given in Figs. 4–6, and the parameter values adopted in the calculations are listed in Table 3.
Table 3. The parameters for the theoretical calculation [5]
The performance of the extracavity Raman laser is related to the parameters of the pump pulses (i.e. the pulse duration and energy), those of the resonator (including the resonator length, the curvatures and reflectivity spectral profiles of the resonator mirrors), and the features of the Raman medium (such as the length and Raman gain coefficient). Especially, the operation of the extracavity Raman laser closely depends on the reflectivity spectral profiles of the resonator mirrors.
As illustrated in Figs. 4 and 5, the conversion efficiency of the first Stokes rises with the pump energy at the initial stage; however once the first Stokes intensity inside the resonator surpasses the threshold of the second Stokes, the energy will flow to the second Stokes. With the other parameters fixed, there is an optimum pump energy value corresponding to the maximum conversion efficiency of the first Stokes, which is also the threshold of the second Stokes. For the No.1 output coupler, the optimum values of the pump energies are approximately 35 mJ and 20 mJ for the Nm - and Ng -polarized pumping configurations, respectively, as shown in Fig. 4, and for the No.2 output coupler they are 40 mJ and 30 mJ, respectively, in Fig. 5. Due to having higher reflectivities at the Stokes beams, the No.1 output coupler has lower thresholds of the second Stokes than the No. 2. Possessing higher Raman gain coefficient, the Ng-polarized pumping has lower thresholds of the second Stokes than the Nm -polarized pumping. The maximum conversion efficiency of the first Stokes achieved in the experiment is 45% with the No. 1 output coupler and Nm -polarized pumping as shown in Fig. 4(a).
Fig. 4. Conversion efficiency versus the pump pulse energy with the No.1 output coupler for the Nm -polarized pumping (a) and Ng -polarized pumping (b). Solid lines represent the calculated results of the first Stokes, dash lines those of the second Stokes, doted line that of the third Stokes. The solid squares stand for the experimental results of the first Stokes, and the open squares those of the second Stokes.
Being highly reflective at the first Stokes, the output coupler No.3 achieved high conversion efficiency of the second Stokes. The maximum conversion efficiency of the second Stokes obtained is 48% for the Nm -polarized pumping, where the conversion efficiency of the first Stokes is 12% referring to Fig. 6(a). The threshold of the second Stokes for the Ng -polarized pumping is lower than the Nm -polarized pumping, also because the reflectivities and the Raman gain coefficient are higher for the Nm -polarized pumping. The optimum value of the pump energy for the second Stokes is approximately 43 mJ, which is also the threshold of the third Stokes for the Ng -polarized pumping as shown in Fig. 6(b).
For given pump energy and other parameters, an optimum output coupling rate can be found to achieve the maximum conversion efficiency of the first or second Stokes. The higher pump pulse energy is, the lower optimum output coupling rate is. The optimization procedure of the extracavity Raman laser is purely experimental up to now, and this theoretical model can help select the appropriate reflectivity spectral profile of resonator mirrors to construct Raman lasers emitting radiation at the aimed order Stokes frequency or multi-frequencies simultaneously.
We can see that the calculated results have a good agreement with the experimental ones. However, the experimental conversion efficiencies are smaller than the theoretical counterparts for most situations, and the conversion efficiency of the first Stokes declines not as sharply as the theory predicts after the second Stokes presents. These discrepancies can be partially attributed to the assumptions made for the radiation transfer equations, for example, assuming the beam intensities to be uniform inside the resonator, neglecting the anti-Stokes generations, and omitting the four-photon parametric process. Besides, the imperfect pump beam quality, and mode mismatch also limit the SRS conversion efficiency.
4.2. Polarization dependence of the first Stokes conversion efficiency
With the extracavity Raman laser, the polarization dependence of the first Stokes conversion efficiency in the KGW crystal was investigated. The crystal was held on a rotatable stand. The stand was rotated to change the pump polarization, and the optical axis of the resonator was kept to be perpendicular to the crystal end surface. The experimental results are shown in Fig. 7. The conversion efficiency of the first Stokes varies periodically with the pump beam polarization, and four peaks are corresponding to the Nm - and Ng -polarized pumping configurations. The Ng -polarized pumping has the higher conversion efficiency than the Nm -polarized one.
Referring to the polarization characteristics of the SRS spectra in the KGW crystal [19], for the Np -cut KGW crystal, one SRS line is observed in the p[mm]p excitation geometry with the Raman shift of 901 cm-1, and for the p[gg]p excitation, the stimulated vibronic line is found at 768 cm-1. In the experiment, with the pump pulse energy of 23 mJ, one spectral line at 1177 nm (1159 nm) was registered in the output, which was linearly Nm - (Ng -) polarized, when the pump pulse was linearly Nm - (Ng -) polarized. For the other polarization direction, the incident beam was decomposed into the Nm - and Ng -polarized components to stimulate the SRS separately, and two lines were observed at 1177 nm and 1159 nm, which were linearly Nm - and Ng -polarized, respectively.
Fig. 7. Dependence of the conversion efficiency of the first Stokes on the pump polarization with the pump pulse energy Ep =23 mJ and No.2 output coupler. The solid squares represent the experimental results, and the line the calculated one.
The numerical calculation was carried out with the radiation transfer equations, and the results are also given in Fig. 7. Probably due to the discrepancy of experimental conditions, there are different Raman gain coefficient values reported for the KGW crystal at 1064 nm. Basically, two results are adopted most frequently, which are 3.3 cm/GW and 4.4 cm/GW given by Kaminskii for the Nm - and Ng -polarized pumping configurations, respectively [23], and 6 cm/MW measured by Bernenberg for both polarizations [24]. In our theoretical calculation, when the data of the Kaminskii were adopted, the calculated results had a better agreement with the experimental ones as shown in Fig. 7.
5. Conclusions
In the paper, we have demonstrated an efficient multi-frequency converter of high energy pump pulse with KGW as the Raman medium. Due to the monoclinic lattice structure, the optical and thermophysical properties of the KGW crystal are anisotropic, and much richer spectral lines can be observed in the Raman laser based on the KGW crystal. Two SRS lines with different Raman shifts were obtained for the Nm - and Ng -polarized pumping configurations in our experiments. The conversion efficiencies of the converter were investigated versus the pump pulse energy, pump polarization, and output coupling rate experimentally and theoretically. By considering up to the third Stokes waves and backward SRS in the coupled radiation transfer equations, a theoretical model was established for the extracavity Raman laser with the crystalline nonlinear medium, and verified to be able to predict the performance of the Raman lasers. This theoretical model can help design the extracavity Raman lasers emitting radiation at the aimed order Stokes frequency or multi-frequencies simultaneously.
Acknowledgments
This research is supported by the Science and Technology Development Program of Shandong Province, and the Project-sponsored by SRF for ROCS, SEM.
References and links
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