February 15, 2011 / Vol. 36, No. 4 / OPTICS LETTERS
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Stable operation of a cw optical parametric oscillator near the signal–idler degeneracy Markku Vainio1,2 and Lauri Halonen1,* 1
Laboratory of Physical Chemistry, Department of Chemistry, P.O. Box 55 (A.I. Virtasen aukio 1), FIN-00014 University of Helsinki, Finland 2
Centre for Metrology and Accreditation, P.O. Box 9, FIN-02151 Espoo, Finland *Corresponding author:
[email protected]
Received October 25, 2010; revised December 28, 2010; accepted January 2, 2011; posted January 12, 2011 (Doc. ID 137111); published February 4, 2011 The frequency stability of a cw optical parametric oscillator (cw OPO) near the signal–idler degeneracy has been studied. The strong tendency of a near-degenerate OPO to mode hop has been suppressed by using a bulk Bragg grating as a spectral filter in the OPO cavity. An experimental demonstration of stable parametric oscillation in a single longitudinal mode of the OPO cavity is reported, together with the capability of tuning the signal–idler difference frequency from 1 to 4 THz. The OPO has potential use in cw terahertz generation. © 2011 Optical Society of America OCIS codes: 050.7330, 190.4360, 190.4410, 190.4970.
Perhaps the most common method for generating widely tunable, coherent, and cw terahertz (THz) radiation is optical heterodyning in a photoconductive mixer [1]. The method requires two laser beams whose difference frequency is in the THz regime. The beams are often produced by two tunable lasers or by a single laser that emits two frequencies simultaneously. The advantage of the latter approach is the good spatial overlap of the beams emitted from the same source, which improves the efficiency of the photomixing process. In addition to lasers, optical parametric oscillators (OPOs) can be used for THz generation by optical heterodyning. The reported dual-frequency cw bulk OPOs suitable for THz generation rely on the use of cascaded nonlinear processes or on a dual-crystal configuration [2,3]. A more straightforward approach would be to use an OPO that oscillates near the optical degeneracy, so that the difference frequency of the signal and idler waves generated in the OPO falls directly in the THz regime [4–6]. [The OPO is pumped at frequency νp , and it produces output beams at frequencies νs (signal) and νi (idler), fulfilling the law of energy conservation, νp ¼ νs þ νi ]. The problem with the near-degenerate OPO is its inherent tendency to mode hop. In this Letter, we show that it is possible to stabilize the operation of a near-degenerate OPO into a single pair of signal and idler frequencies. Controlled tuning of the difference frequency, νTHz ¼ jνs − νi j, is achieved over a wide range of THz frequencies. In the experiments reported here, we have used two different OPOs. Both of them are pumped by a singlefrequency Ti:sapphire laser (Coherent MBR-PS, Coherent, Inc., USA) at ∼800 nm, which sets the degeneracy wavelength to approximately 1600 nm. The first OPO is referred to as an all-mirror OPO. It has a bow tie ring cavity formed by four mirrors [7]. The optical length of the cavity is 0:7 m, which corresponds to a longitudinal mode spacing of 428 MHz. All mirrors are highly reflective (R ¼ 99:9%) at signal–idler wavelengths between 1450 and 1725 nm. Therefore, the all-mirror OPO is doubly resonant. Two of the mirrors are plane mirrors, and the other two are concave, with radii of curvature of 0146-9592/11/040475-03$15.00/0
100 mm. A 5-cm-long, MgO-doped (5%), periodically poled lithium niobate (MgO:PPLN) crystal is placed between the concave mirrors. A poling period of 20:5 μm was used in the experiments. The dimensions of the cavity and the focusing of the pump beam were adjusted to give a focusing parameter [8,9] of ξ ¼ 2:3 at all three wavelengths. The second OPO design is otherwise like the first one, but it has one of the plane mirrors replaced by a Bragg grating (BG). We call this design BG-OPO. The grating has been recorded in a bulk of photosensitive glass (Optigrate, Optigrate Corp., USA). It is highly reflective (R ∼ 98:5%) at 1584 nm, which is the center wavelength of the grating reflection at an angle of incidence of 8°. This is the angle that corresponds to the folding angle of the OPO cavity. The reflectance bandwidth of the grating is ∼30 GHz (FWHM). As the BG reflects only at a narrow frequency band at a time, it makes the OPO singly resonant. We have previously used the same grating in a cw OPO based on a standing-wave cavity and pumped at 1 μm [10]. Here, we demonstrate that the effective reflectivity of a bulk BG can be sufficiently high so as to reach the oscillation threshold of a singly resonant cw OPO even in an oblique angle, which is required for a ring cavity. A detailed study of the characteristics of a BG with an oblique angle of incidence has been given by Hellström et al. [11]. In the case of first-order quasi-phase matching, the wave–vector mismatch is given as Δk ¼ 2π½ðνp np − νs ns − νi ni Þ=c − 1=Λ, where c is the speed of light in a vacuum and np;s;i are the crystal refractive indexes at the pump, signal, and idler frequencies, respectively [12]. The poling period of the crystal is Λ. The wavelength tuning curve of the OPO can be calculated by finding the wavelengths that fulfill both the phase matching condition Δk ¼ 0 and the law of energy conservation. The calculated tuning curve of the all-mirror OPO is shown as a function of pump wavelength, λp , for three different temperatures of the crystal in Fig. 1. The refractive indices of MgO:PPLN were computed using the Sellmeier coefficients from reference [13]. The tuning curve gives the signal–idler wavelength pairs for which the optimal phase matching © 2011 Optical Society of America
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Fig. 1. (Color online) Theoretical phase-matching curves of the near-degenerate OPO at three different temperatures of the MgO:PPLN crystal. Poling period of the crystal is 20:5 μm.
is achieved. Parametric oscillation is possible also at other wavelengths close to this optimum, as long as the phase mismatch, Δk, is small enough for reaching the OPO threshold. Because the signal and idler waves have nearly the same refractive index near the degeneracy, the parametric gain bandwidth becomes exceptionally large. This is illustrated in Fig. 2, which shows the calculated gain profiles for three different pump wavelengths at signal wavelengths close to the degeneracy wavelength, 2λp . The calculation was done for a fixed temperature of the crystal, assuming a singly resonant OPO that resonates at the signal wavelength [14]. As an example, curve (c) shows the parametric gain at T ¼ 57:2 °C, λp ¼ 797:27 nm, where the phase-matched (Δk ¼ 0) case corresponds to a signal–idler frequency difference of νTHz ¼ 2:4 THz. The gain bandwidth of >4 THz is approximately 30 times wider than in a more typical OPO pumped at 1 μm and resonating at 1:5 μm. An important characteristic of a near-degenerate OPO is that the center frequency, or the “Δk ¼ 0” point, of the gain profile moves fast in the frequency domain as the crystal temperature or the pump frequency is varied. The effect of pump frequency tuning is exemplified in Fig. 2, where the dashed curves show the parametric gain curves as the pump wavelength is shifted by 0:06 nm from 797:27 nm. In Fig. 3, the shift of the phase-matched signal frequency, νs;PM ¼ νs ðΔk ¼ 0Þ, is studied for a
Fig. 2. (Color online) Solid curves, calculated parametric gain of the singly resonant OPO with (a) λp ¼ 796:25 nm, (b) λp ¼ 796:75 nm, and (c) λp ¼ 797:27 nm. Dashed curves, the same but with the pump wavelength shifted from λp ¼ 797:27 nm by 0:06 nm (28 GHz). Vertical lines denote the signal wavelength, λs , of the peak gain and the degeneracy wavelength, 2λp , for case (c). Crystal temperature T ¼ 57:2 °C.
wider range of operating parameters. The operating point marked with dots in the figure is the same as the one used in the previous example. At this point, a small change in the pump frequency leads to a 200 times bigger change in the phase-matched signal frequency. A change of the crystal temperature by as little as 1 mK changes the frequency of the phase-matched signal wave by 7 GHz. The wide gain bandwidth, together with the high sensitivity of the phase-matched wavelengths to the changes of the operating conditions, make the OPO prone to mode hops. This is evident from Fig. 4(a), which shows a measured spectrum of the all-mirror OPO for the same operating conditions as used in the simulations. The spectrum was recorded using a scanning grating spectrometer (Ando AQ6317B, Ando Electric Co., Ltd., Japan). The stability of the pump frequency was better than 50 MHz, and the stability of the temperature of the MgO:PPLN crystal was better than 10 mK. Note that the pump frequency was not locked to the OPO cavity. Therefore, the power of the doubly resonant all-mirror OPO fluctuated between zero and the maximum during the measurement. The maximum total output power extracted through one of the cavity mirrors was 20 GHz around each set point was achieved by tuning the pump laser only. When pumping at 1.75 times the phase-matched threshold, the total tuning range that could be obtained with pump tuning— without adjusting the crystal temperature—was approximately 60 GHz. Beyond this, the parametric gain dropped below the OPO threshold. This observation is in good agreement with the pump tuning range estimated from
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the calculated gain profiles. [See Fig. 2, which shows how the normalized gain at λs ¼ 1584 nm drops to about 0.6 ð∼1=1:75Þ as the pump frequency is tuned by 28 GHz from that corresponding to a phase-matched case]. The oscillation threshold of the BG-OPO was obtained at a pump power of ∼1:65 W. At the maximum pump power of 2:92 W, a total output power (signal þ idler) of 820 mW was obtained through the BG. Idler power was estimated to be roughly two times higher than the outcoupled signal power. The measured output power is significantly higher than what is required for optical heterodyning in a photoconductive mixer. However, if needed, the power can be further increased by using an Yb fiber laser as the pump source [10]. This could make the near-degenerate BG-OPO suitable for quasi-phasematched difference-frequency generation in GaAs [15]. The financial support of the Academy of Finland is gratefully acknowledged. We thank F. Manoocheri and E. Ikonen for the loan of the spectrum analyzer. References 1. E. R. Brown, K. A. McIntosh, K. B. Nichols, and C. L. Dennis, Appl. Phys. Lett. 66, 285 (1995). 2. R. Sowade, I. Breunig, I. C. Mayorga, J. Kiessling, C. Tulea, V. Dierolf, and K. Buse, Opt. Express 17, 22303 (2009). 3. I. Breunig, J. Kiessling, R. Sowade, B. Knabe, and K. Buse, New J. Phys. 10, 073003 (2008). 4. J. E. Schaar, K. L. Vodopyanov, and M. M. Fejer, Opt. Lett. 32, 1284 (2007). 5. J. Saikawa, M. Fujii, H. Ishizuki, and T. Taira, Opt. Lett. 32, 2996 (2007). 6. B. Jacobsson, V. Pasiskevicius, F. Laurell, E. Rotari, V. Smirnov, and L. Glebov, Opt. Lett. 34, 449 (2009). 7. W. R. Bosenberg, A. Drobshoff, J. I. Alexander, L. E. Myers, and R. L. Byer, Opt. Lett. 21, 1336 (1996). 8. M. Vainio, J. Peltola, S. Persijn, F. J. M. Harren, and L. Halonen, Appl. Phys. B 94, 411 (2008). 9. G. D. Boyd and D. A. Kleinman, J. Appl. Phys. 39, 3597 (1968). 10. M. Vainio, M. Siltanen, T. Hieta, and L. Halonen, Opt. Lett. 35, 1527 (2010). 11. J. E. Hellström, B. Jacobsson, V. Pasiskevicius, and F. Laurell, IEEE J. Quantum Electron. 44, 81 (2008). 12. L. E. Myers, R. C. Eckardt, M. M. Fejer, R. L. Byer, W. R. Bosenberg, and J. W. Pierce, J. Opt. Soc. Am. B 12, 2102 (1995). 13. O. Gayer, Z. Sacks, E. Galun, and A. Arie, Appl. Phys. B 91, 343 (2008). 14. S. E. Harris, Proc. IEEE 57, 2096 (1969). 15. K. L. Vodopyanov, Laser Photon. Rev. 2, 11 (2008).
