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Singly resonant optical parametric oscillator in periodically poled KTiOPO4 pumped by a Bessel beam V. Pasiskevicius, H. Karlsson, J. A. Tellefsen, and F. Laurell Department of Physics-Optics, Royal Institute of Technology, 100 44 Stockholm, Sweden
R. Butkus, A. Piskarskas, V. Smilgeviˇcius, and A. Stabinis ˙ Laser Research Center, Vilnius University, Sauletekio 9, Building 3, 2040 Vilnius, Lithuania Received March 2, 2000 Conical pumping was used in a periodically poled KTiOPO4 optical parametric oscillator for singly resonant idler generation in a nearly diffraction-limited axial beam. A single signal – idler pair was generated over the whole tuning range by use of asymmetric ref lectivity of the OPO mirrors. Pump depletion of 40% and total conversion efficiency of 27% were obtained. Additional OPO tuning capability was demonstrated by adjustment of the angle of the conical pump beam. © 2000 Optical Society of America OCIS codes: 190.4410, 190.4400, 190.4970, 230.4320.
Since the introduction of Bessel beams1 and early demonstrations of their potential in nonlinear optics experiments,2 there has been growing interest in using experimentally realizable apertured Bessel beams (Bessel–Gauss beams) for frequency-conversion applications. Bessel beams can produce a strongly peaked pump-intensity distribution over relatively long spans in nonlinear media. It was recently demonstrated that the increase in interaction length with Bessel beam results in more-efficient thirdharmonic generation in gasses.3 Pumping of optical parametric oscillators (OPO’s) with conical beams is attractive because the tight and quasi-nondiffracting gain channel provided by the Bessel pump distribution facilitates diffraction-limited parametric beam generation in the axial direction. According to recent investigations,4,5 frequency-conversion efficiency should not be limited by pump depletion in the main lobe of the Bessel beam, since the Bessel distribution is continuously self-reconstructing in the Bessel zone. Parametric generation with conical pumping was recently studied.6,7 However, the demonstrated frequency-conversion eff iciency was rather low, probably owing to the low nonlinearity of the crystal employed. To increase conversion efficiency, we employed noncritical phase matching in periodically poled KTiOPO4 (PPKTP) crystal as a nonlinear medium in an OPO pumped by a conical beam. The noncollinear geometry of the conical pumping allows OPO wavelength tuning by adjustment of the angle of the pumping cone. Here we demonstrate that singly resonant OPO operation can be achieved even in the spectral region close to degeneracy. The phase-matching properties in parametric generators realized with birefringence phase-matched crystals excited by a Bessel beam were studied in detail in Refs. 6 and 8. Here we recall the main results of these theoretical developments and adapt them to the materials with quasi-phase matching. The phase-matching geometry is depicted in Fig. 1(a). Here the coordinate axes x, y, and z correspond to crystal 0146-9592/00/130969-03$15.00/0
axes a, b, and c. The Bessel pump beam can be analyzed as consisting of plane waves propagating on the surface of a cone with a unique angle ap relative to the cone axis. The quasi-phase-matching grating vector, kg 苷 2p兾L, is parallel to the axis of the pump cone. In addition to the energy-conservation condition, vp 苷 vs 1 vi , the momentum-conservation conditions should hold for the wave-vector components: ksz 1 kiz 苷 kpz , ksy 1 kiy 苷 kpy , and ksx 1 kix 1 kg 苷 kpx , where ksj , kij , and kpj are the components of the signal, the idler, and the pump-wave vectors, respectively. The parametric gain depends on the coupling between the interacting waves in the transverse 共 y z兲 plane.
Fig. 1. (a) Schematic geometry of a PPKTP OPO excited by a Bessel beam. ( b) Experimental setup. © 2000 Optical Society of America
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By integration of the product of the field distributions of the Bessel – Gauss beams in the transverse plane, it can be shown6 that maximum coupling is obtained for three combinations of the azimuthal angles: (i) cs 苷 ci 苷 cp ; (ii) cs 苷 cp , ci 苷 cp 1 p; and (iii) cs 苷 cp 1 p, ci 苷 cp . Condition (i) represents collinear phase matching, and conditions (ii) and (iii) are the two cases of noncollinear phase matching. Here we aim to generate OPO output along the axis of the pump cone, so only conditions (i) and (iii) are important. Using condition (ii) in momentum-conservation equations, we arrive at ks cos as 1 ki cos ai 1 kg 苷 kp cos ap ,
(1a)
ks sin as 2 ki sin ai 苷 kp sin ap ,
(1b)
and condition (iii) yields ki cos ai 1 ks cos as 1 kg 苷 kp cos ap ,
(2a)
ki sin ai 2 ks sin as 苷 kp sin ap .
(2b)
Equations (1) and (2) ref lect the fact that two independent signal– idler pairs can be generated in the noncollinear parametric process simultaneously. We can obtain the equations for the axial idler and signal generation by setting ai 苷 0 and as 苷 0 in Eqs. (1) and (2), respectively. The experimental setup is shown schematically in Fig. 1(b). The Bessel pump beam was formed by an axicon prism with an apex angle of 174± placed between two telescope lenses, L1 共 f 1 苷 100 mm兲 and L2 共 f 2 苷 75 mm兲. We employed the frequency-doubled output from a f lash-lamp-pumped Q-switched Nd:YAG laser for OPO pumping, which generated 1.5-mJ, 5-ns-long pump pulses in a nearly diffraction-limited beam. The collimated Gaussian pump beam that illuminates lens L1 is transformed by the axicon into a ring intensity distribution in the focal plane of lens L1. This ring distribution is then transformed into a Bessel-like distribution in the focal plane of lens L2. By moving the axicon on a translation stage along the axis of the optical system, we could vary the radius of the ring in the focal plane of lens L1, which in turn resulted in variation of the pump-cone angle in the PPKTP crystal. So, by translation of the axicon by a distance of 50 mm from lens L1, the angle between the pump-wave vector kp lying on the surface of the cone and its axis was smoothly varied from 12.7 to 30.9 mrad. A 1-mm-thick PPKTP crystal with a domain-inversion period of 9.01 mm and a quasi-phase-matched grating length of 10 mm was used in the OPO.9 The temperature of the crystal could be varied from 0 to 100 ±C. The optical surfaces of the PPKTP crystal were slightly wedged by approximately 0.5± and left uncoated. The polarization of the Bessel pump was parallel to the crystal’s c axis. Both OPO cavity mirrors, M1 and M2, were f lat, with low ref lectivity 共R ⬃ 5%兲 at the pump wavelength. We adjusted the cavity mirrors to resonate the parametric
waves that were generated along the axis of the pump cone. The noncollinear geometry, as described by Eqs. (1) and (2), allows the generation of two independent signal–idler pairs, which can be a disadvantage because the available pump power is then shared by four parametric waves. We verified experimentally the generation of two signal– idler pairs in the PPKTP sample by use of a conf iguration without cavity mirrors. For symmetric conical pumping, one of the two independent pairs of the parametric waves cannot be easily suppressed by choice of the geometry of the resonator, e.g., by tilting of the resonator axis. As we were interested in generating a single parametric wave (e.g., the idler) in the axial direction with maximum efficiency, we employed OPO mirrors with asymmetric ref lectivity, i.e., high ref lectivity for the idler and low ref lectivity for the signal. The input mirror, M1, had a ref lectivity that varied from R 苷 99.5% to R 苷 95% in the idler spectral region from degeneracy at 1064 to 1300 nm. The ref lectivity in the signal region, from 900 to 1050 nm, was ⬃20%, with a sharp cutoff 共Dl 苷 3 nm兲 between the two spectral ranges. First, we tested an output coupler, M2, that was similar to input mirror M1, with the cutoff edge at 1070 nm. In this OPO cavity with high f inesse for the idler, in addition to the axial idler beam and the associated conjugated signal cone we still observed the appearance of a second pair of parametric waves with the signal generated in the axial direction. However, when we employed the output coupler, which had a ref lectivity of R 苷 40% in the idler region and R 苷 20% in the signal region, we generated a single signal– idler pair (axial idler) at each pumping power and pump-cone angle. At the same time, the efficiency of the axial idler output increased signif icantly. Moreover, single-pair generation was retained when we removed the output coupler altogether, so that the PPKTP end face served as an output coupler, with essentially equal ref lectivity at the signal and idler wavelengths. These observations suggest that the second parametric pair (the axial signal) appears only in the OPO cavity with high finesse for the idler. This result can possibly be explained by scattering of a fraction of the intracavity idler photons in an off-axis direction in which phase-matched interaction with the conical pump could take place, thus producing a conjugated signal wave in the axial direction. The OPO threshold increased approximately quadratically with the angle of the pump cone. Such dependence is generally expected, owing to the increase in the nonresonated signal-cone angle. With the R 苷 40% output coupler and a half-angle of the pump cone of 25.5 mrad, the OPO reached threshold at 170 mJ of the pump energy (see Fig. 2). The efficiency of the axial idler generation exceeded 13% for a pump energy of 880 mJ, whereas the total OPO efficiency, including the signal core, was 27%. Here we reference the pump power to the input of the PPKTP crystal by taking into account losses in the optical system. The pump depletion was evaluated by measurement of the transmission difference of the pump when the OPO cavity was properly adjusted
July 1, 2000 / Vol. 25, No. 13 / OPTICS LETTERS
Fig. 2. PPKTP OPO output efficiency and pump depletion versus pump energy.
Fig. 3. OPO output wavelength versus PPKTP temperature for different pump-cone half-angles.
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account the losses incurred by the parametric waves as a result of Fresnel ref lections at the uncoated faces of the PPKTP crystal. We could achieve tuning of the OPO output wavelengths by translating the axicon prism and (or) by changing the PPKTP temperature (see Fig. 3). We obtained idler tuning of up to 1241 nm and signal tuning of down to 931 nm by increasing the pump-cone half-angle to 30.9 mrad at the PPKTP temperature of 100 ±C. We measured the transverse prof ile of the OPO output by scanning the bare end of an optical fiber (core diameter, 10 mm; N.A., 0.12) across the central part of the transverse pattern. The output of the fiber was focused onto a p– i –n photodiode. Transverse scans performed at a distance of 22 cm from the cavity and at two different temperatures are shown in Fig. 4. The OPO generated an axial idler beam with a Gaussian intensity prof ile in a mode supported by the cavity. When the temperature was increased, only the angle of the conjugated signal cone decreased, as required by the phase-matching conditions. The measured divergence of the axial idler beam was 2.3 mrad, nearly diffraction limited for a Gaussian beam. Note that the divergence did not change appreciably when the M 2 of the pump beam that illuminated the axicon was increased to M 2 苷 6, although the conversion efficiency was lower in this case. In conclusion we have demonstrated singly resonant, diffraction-limited axial idler generation in a PPKTP OPO pumped by a Bessel beam. Conical pumping provides additional tuning capabilities and a rather simple way to separate the signal and the idler waves even in the spectral region close to degeneracy. Finally, the conversion efficiency in Bessel-pumped OPO was still lower than the saturated eff iciency of 40% demonstrated in noncollinear OPO pumped by Gaussian beam at similar interaction angles (21 mrad) (Ref. 10); however, the output beam in this case was substantially nondiffraction limited. V. Pasiskevicius’s e-mail address is
[email protected]. References
Fig. 4. Transverse scan of the OPO output across the center of the intensity distribution at two PPKTP temperatures: (f illed areas) T 苷 19 ±C and (open areas) T 苷 90 ±C. The axial idler prof ile remains unchanged with temperature.
and when it was detuned from oscillation. At the highest available power, pump depletion reached 40%. One can explain the difference between the total OPO efficiency and the pump depletion by taking into
1. J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987). 2. T. Wulle and S. Herminghaus, Phys. Rev. Lett. 70, 1401 (1993). 3. C. Altucci, R. Bruzzese, D. D’Antuoni, C. de Lisio, and S. Solimento, J. Opt. Soc. Am. B 17, 34 (2000). 4. V. N. Belyi, N. S. Kazak, and N. A. Khilo, Opt. Commun. 162, 169 (1999). 5. L. Niggl and M. Maier, Opt. Lett. 22, 910 (1997). 6. A. Piskarskas, V. Smilgeviˇcius, A. Stabinis, and V. Vaiˇcaitis, J. Opt. Soc. Am. B 16, 1566 (1999). 7. A. Piskarskas, V. Smilgeviˇcius, and A. Stabinis, Appl. Opt. 36, 7779 (1997). 8. R. Gadonas, A. Marcinkeviˇcius, A. Piskarskas, V. Smilgeviˇcius, and A. Stabinis, Opt. Commun. 146, 253 (1998). 9. H. Karlsson and F. Laurell, Appl. Phys. Lett. 71, 3474 (1997). 10. V. Smilgeviˇcius, A. Stabinis, A. Piskarskas, V. Pasiskevicius, J. Helström, S. Wang, and F. Laurell, Opt. Commun. 173, 365 (2000).
