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This paper presents the tunable Stokes laser characteristics of KTiOAsO4 (KTA) crystal based on stimulated polariton scattering (SPS). When the pumping laser wavelength is 1064.2 nm, the KTA Stokes wave can be discontinuously tuned from 1077.9 to 1088.4 nm with four gaps from 1079.0 to 1080.1 nm, from 1080.8 to 1082.8 nm, from 1083.6 to 1085.5 nm, and from 1085.8 to 1086.8 nm. When a frequency doubling crystal LiB3O5 (LBO) is inserted into the Stokes laser cavity, the frequency-doubled wave can be discontinuously tuned from 539.0 to 539.5 nm, from 540.1 to 540.4 nm, from 541.3 to 541.8 nm, from 542.7 to 542.9 nm and from 543.4 to 544.2 nm. With a pumping pulse energy of 130.0 mJ and an output coupler reflectivity of about 30%, the obtained maximum Stokes laser pulse energy at 1078.6 nm is 33.9 mJ and the obtained maximum frequency-doubled laser pulse energy at 543.8 nm is 15.7 mJ. By using the most probably coupled transverse optical modes obtained from the literature, the polariton refractive indexes, and the simplified polariton Sellmeier equations, the polariton dispersion curve is obtained. The formation of the Stokes frequency gaps is explained.
© 2016 Optical Society of America
1. Introduction
Potassium titanyl arsenate (KTiOAsO4, KTA) is one of the isomorphs of potassium titanyl phosphate (KTiOPO4, KTP). KTA crystal at room temperature possesses excellent qualities such as high nonlinear coefficient [1] and high damage threshold [2], it has established itself as an efficient and reliable material for nonlinear converting process to expand the laser wavelength range. Based on its second-order nonlinearity, KTA has been widely used in optical parametric oscillators (OPOs) [3,4 ], second-harmonic generation [5,6 ], sum frequency generation [7] and difference frequency generation [8]. Based on the stimulated Raman scattering (SRS) in it, KTA has been widely used in various Raman lasers [9,10 ]. Based on the stimulated polariton scattering (SPS) in it, a terahertz (THz) wave parametric oscillator (TPO) was constructed and the intermittently tunable THz waves from 3.59 to 3.96 THz, from 4.21 to 4.50 THz, from 4.90 to 5.16 THz, from 5.62 to 5.66 THz and from 5.92 to 6.43 THz were obtained [11].
When a pumping photon is consumed in the process of SPS, a Stokes photon and a polariton will be generated. A TPO is a special OPO. In the TPO, three waves including the pumping wave, the generated Stokes wave and the polariton wave interact in the overlapped beam area. In general, the reflectivities of the two Stokes wave oscillating mirrors are nearly 100% to keep a high Stokes wave intensity in the cavity which is beneficial to the terahertz wave generation. If one of the oscillating mirrors is partially reflective, the tunable Stokes laser output will be obtained [12,13 ]. The tunable Stokes laser characteristics based on the SPS in KTA crystal have not been investigated so far. And the formation mechanism of the frequency gaps in the tunable wavelength range is not very clear.
This paper focuses on the tunable Stokes laser characteristics of KTA crystal based on SPS. In section 2, the experimental setup will be described. In section 3, the experimental results will be given. The dependences of the output Stokes laser pulse energies on the cavity mirror reflectivity is first studied. The optimum reflectivity for the maximum pulse energy is about 30%. When the pumping laser wavelength is 1064.2 nm, the KTA Stokes laser can be discontinuously tuned from 1077.9 to 1088.4 nm with four gaps. By inserting the frequency doubling crystal LBO into the Stokes laser cavity, the frequency-doubled laser can be discontinuously tuned from 539.0 to 544.2 nm with four gaps. When the pumping pulse energy is 130.0 mJ, the obtained maximum Stokes laser pulse energy at 1078.6 nm is 33.9 mJ and the obtained maximum frequency-doubled laser pulse energy at 543.8 nm is 15.7 mJ. In section 4, the formation mechanism of the Stokes frequency gaps is analyzed. Section 5 is the conclusion.
2. Experimental setup
The experimental setup for the tunable Stokes laser based on the SPS in KTA crystal and the frequency-doubled Stokes laser accomplished by LBO crystal is shown schematically in Fig. 1 . The line in yellow represents the pumping beam and the line in red represents the Stokes beam. The x-cut KTA crystal had dimensions of 30 (x) mm × 5 (y) mm × 5 (z) mm. Its two ends were anti-reflection (AR) coated at 1060–1100 nm (T > 99.8%). The Stokes resonant cavity was formed by the KTA crystal and two parallel flat mirrors M1 and M2 which were D-shaped, with the aim that the pumping beam could directly pass close to the cutting-edge of the mirrors. The rear mirror M1 was coated for high-reflection (HR) at 1060–1100 nm (R > 99.8%) and the output mirror M2 had partial reflection (PR) at 1060–1100 nm (R ≅ 20%, 30%, 40% and 50%, respectively). The physical length of the Stokes resonant cavity without the LBO crystal was 17 cm. It was the minimum length for the pumping beam to spatially separate from the oscillating Stokes beam in the non-collinear phase matching geometry. The Stokes resonant cavity was located on a rotatable platform. The KTA crystal center and the center of the overlap area between the pumping beam and the Stokes beam were located in the same position. By rotating the platform, the external angle θex t between the Stokes cavity axis and the pumping beam was easily adjusted.
In the process to investigate the frequency-doubled Stokes wave, the total length of the resonator was stretched to 28 cm resulted from the inserting of the LBO crystal. It was cut at θ = 90° and φ = 10.4° and had dimensions of 7 × 7 × 15 mm3. Both faces were AR coated at 1064–1096 nm and 532–548 nm (R < 0.5%). While tuning the Stokes laser wavelength, the LBO crystal was also adjusted to satisfy the phase matching angle. The resonant cavity was formed of mirror M3 which was HR at 1064–1100 nm and 538–544 nm (R > 99.6%) and the output mirror M4 which was HR at 1060–1100 nm (R > 99.6%) and high transmission at 538–544 nm (R < 5%).
The pumping source was a 1064.2 nm Q-switched laser. The pulse width, repetition rate and beam size were 10 ns, 10 Hz and 3.3 mm, respectively. The polarization of the pumping beam and the Stokes beam was parallel to the z-axis of the KTA crystal based on the near-forward scattering configuration X(ZZ)X + ∆φ. And the Stokes beam propagated along the x-axis of the KTA crystal with the internal angle θin to the pumping beam (θext = npθin, np is the refractive index of the pumping beam in the crystal). The Stokes laser pulse energies were measured by an energy sensor (J-50MB-YAG, Coherent Inc.) connected to an energy meter (EPM2000, Coherent Inc). The wavelengths were measured by an optical spectrum analyzer (YOKOGAWA AQ6315, 350–1750 nm). The pulses were monitored by a Si biased detector (THORLABS, DET10A/M, 200–1100 nm) connected to a digital phosphor oscilloscope (Tektronic TDS5052B, 500MHz, 5GS/s).
3. Experimental results
Considering the size of the pumping beam and the KTA crystal, the external angle θex t between the pumping and Stokes beams was set to range from 1.875° to 6.500°. Figure 2 shows the dependences of the Stokes pulse energies on the external angle θex t with different Stokes output mirrors (the mirror reflectivities were about 20%, 30%, 40%, 50%, respectively) in the case of pumping pulse energy of 130.0 mJ. We can see that the optimum output mirror reflectivity was in the vicinity of 30% for getting the maximum output Stokes wave energy. In the following Stokes wave experiment, we selected the mirror with 30% reflectivity as the output coupler.
Fig. 2 Dependences of the Stokes laser pulse energies on the external angle θext with different Stokes output mirrors.
Figure 3 shows the dependences of the Stokes laser wavelength (in black color) and the frequency-doubled laser wavelength (in red color) on the external angle θex t. It can be seen that the Stokes laser wavelength can be tuned from 1077.9 to 1079.0 nm, from 1080.1 to 1080.8 nm, from 1082.8 to 1083.6 nm, from 1085.5 to 1085.8 nm and from 1086.8 to 1088.4 nm. The frequency-doubled laser wavelength can be tuned from 539.0 to 539.5 nm, from 540.1 to 540.4 nm, from 541.3 to 541.8 nm, from 542.7 to 542.9 nm and from 543.4 to 544.2 nm. Four gaps appear in the tunable wavelength range of the Stokes wave and it will be explained in Section 4.
Fig. 3 Dependences of the Stokes laser wavelength and the frequency-doubled laser wavelength on the external angle θext.
Figure 4 shows the dependence of the Stokes laser pulse energy on the wavelength. The measured maximum Stokes laser pulse energy was 33.9 mJ at 1078.6 nm of Range A when the pumping energy was 130.0 mJ. The optical-optical conversion efficiency was 26.1%. The other peak energies were 27.8 mJ at 1080.3 nm of Range B, 25.0 mJ at 1083.2 nm of Range C, 6.2 mJ at 1085.6 nm of Range D, 28.8 mJ at 1087.6 nm of Range E, respectively. Figure 5 shows the relations between the output Stokes wave energies and the input pumping wave energies at 1078.6 nm, 1080.3 nm, 1083.2 nm, and 1087.6 nm, respectively.
Fig. 5 Dependences of the Stokes laser pulse energies on the pumping pulse energy at different Stokes laser wavelengths.
Figure 6 shows the frequency-doubled laser pulse energy as a function of the wavelength. The measured maximum frequency-doubled laser pulse energy was 15.7 mJ at 543.8 nm of Range E when the pumping pulse energy was 130.0 mJ. The other peak energies were 10.7 mJ at 539.3 nm of Range A, 10.3 mJ at 540.2 nm of Range B, 11.5 mJ at 541.7 nm of Range C, 2.2 mJ at 542.8 nm of Range D, respectively. Figure 7 shows the output frequency-doubled laser pulse energies as function of the input pumping pulse energy at 539.3 nm, 540.2 nm, 541.7 nm and 543.8 nm respectively.
Fig. 7 Dependences of the frequency-doubled laser pulse energies on the pumping pulse energy at different wavelengths.
4. Discussion
In the process of SPS, the momentum conservation and the energy conservation must be satisfied simultaneously:
where k s, k pu, and k po are the wave vectors of the Stokes wave, the pumping wave and the polariton wave, respectively. ωs, ωpu, and ωpo are the photon energies of the three waves. The pumping wave and Stokes wave refractive indexes can be calculated by using the following Sellmeier equations [14] where λ is the wavelength in units of micrometer. Due to the large refractive index of the polariton wave, only non-collinear phase matching can be realized, shown in Fig. 8 . By using the relations shown in Figs. 3 and 8 and Eqs. (1)–(5) , it is easy for us to calculate the experimental results for the polariton refractive indexes at different frequencies.The essential condition for SPS in a crystal is the existence of one or more intense transverse optical (TO) modes which are both infrared- and Raman- active. The theoretical expression for the polariton frequency-dependent dielectric constant can be written as [15]
where ΩjTO and ΓjTO are the wavenumber and the damping coefficient respectively of the jth TO mode, Sj is its oscillator strength, and ε∞ is the high-frequency dielectric constant. Currently we cannot obtain the values of ΩjTO, ΓjTO, ε∞, and Sj for the KTA crystal from the literatures. Fortunately, it is relatively easy for us to obtain the Raman spectrum of the KTA crystal. Considering that polaritons are formed by the coupling of phonons and the incident infrared waves [16], the wavenumbers of the most probably coupled TO modes are 111.5, 132.9, 156.3, 175.1, 188.4, 209.4 and 233.8 cm−1, obtained from the KTA crystal TO Raman spectrum [17]. Following the assumption in the general Sellmeier equations that Ω is far from ΩjTO and Ω2 jTO - Ω2 >> ΓjTOΩ, Eq. (6) can be simplified asPerforming curve fitting by using Eq. (7) and the experimental results for the polariton refractive indexes at different frequencies, we obtained Sj of the coupled TO modes, shown in Table 1 . The generated polariton dispersion curve is shown in Fig. 9 .
Table 1. The fitted values of Sj for the coupled TO modes of KTA crystal.
Fig. 9 Dispersion relation of the polariton. The dots represent the experimental results, the lines represent the fitted results.
It can be seen that the experimental results of the polariton refractive index are well in consistent with Eq. (7). When the polariton wavenumber Ω approaches to ΩjTO, the polariton refractive index (and therefore the polariton loss) will approach to infinity. It should be pointed out that this is the result of neglecting ΓjTO. If ΓjTO was not neglected, the polariton refractive index and the polariton loss will not approach to infinity at ΩjTO. But we can infer that they will still be very large [18,19 ].
In SPS, the pumping wave, the generated Stokes wave and the polariton wave interact in the overlapped beam area. There are 7 areas (Area A–G) in Fig. 9. When θext is between 1.875° and 2.625°, the polariton frequency is located in the central part of Area A. The polariton has suitable gain and loss. The Stokes wave and the polariton wave can be generated and amplified. When θext is between 2.750° and 3.250°, the polariton frequency is located in the central part of Area B. The polariton also has suitable gain and loss. The waves can also be generated and amplified. When θext = 2.625°, the polariton frequency has a jump leading to a Stokes frequency gap between 1079.0 and 1080.1 nm. This is because the loss becomes very large when the polariton frequency approaches to 132.9 cm−1, one of the coupled TO mode frequencies. The causes of the Stokes frequency gaps from 1080.8 to 1082.8 nm, from 1083.6 to 1085.5 nm, from 1085.8 to 1086.8 nm, are similar.
5. Conclusion
In conclusion, the tunable Stokes wave properties based on the SPS in KTA crystal have been investigated for the first time. When the given pumping laser wavelength was 1064.2 nm and the pumping pulse energy was 130.0 mJ, discontinuous Stokes wave was obtained from 1077.9 to 1079.0 nm, from 1080.1 to 1080.8 nm, from 1082.8 to 1083.6 nm, from 1085.5 to 1085.8 nm, from 1086.8 to 1088.4 nm when the external angle between the pumping and Stokes beams changed from 1.875° to 6.500°. The maximum pulse energy of output Stokes wave was 33.9 mJ obtained at the wavelength of 1078.6 nm and the optical-optical conversion efficiency was 26.1%. The intracavity frequency-doubled Stokes wave characteristics were studied by using the LBO crystal. The discontinuously tunable frequency-doubled Stokes wavelength varied from 539.0 to 539.5 nm, from 540.1 to 540.4 nm, from 541.3 to 541.8 nm, from 542.7 to 542.9 nm, from 543.4 to 544.2 nm and the maximum frequency-doubled Stokes wave energy was 15.7 mJ obtained at 543.8 nm. The polariton dispersion curve is obtained by using the most probably coupled transverse optical modes obtained from the literature, the polariton refractive indexes obtained in the experiment, and the simplified polariton Sellmeier equations. The formation of the Stokes frequency gaps in the tunable wavelength range is explained.
Acknowledgments
This research is supported by the National Natural Science Foundation of China (NSFC) (61475087, 11204160), the Shandong Provincial Natural Science Foundation for Distinguished Young Scholars (2013JQE27056), the Natural Science Foundation of Shandong Province (ZR2014FM024), and the Fundamental Research Funds of Shandong University (2014QY005).
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