1. Introduction

Periodically poled lithium niobate (PPLN) is a widely used nonlinear material for generating tunable mid-IR radiation by frequency conversion of shorter wavelength lasers. High conversion efficiencies are achieved with the high gain possible in PPLN, which has led to rapid advances in both cw and pulsed optical parametric oscillator (OPO) devices.^1–3 These advances are significant for applications of tunable 1.3- to 5-μm radiation including spectroscopy, laser radar imaging, and atmospheric sensing.^1,4,5 High gain, however, can result in secondary effects that can be either beneficial or detrimental.

We present experimental and numerical investigations of a PPLN OPO operating in the 1.3- to 5-μm region pumped by a 1.064-μm Nd:YAG laser. In addition we have observed efficient secondary parametric oscillations pumped by the resonant primary OPO signal. The energy conservation relationships between the OPO frequencies are ω _s1+ω _i1=ω_p and ω _s2+ω _i2=ω _s1, where ω_p is the frequency of the pump radiation; ω _s1 and ω _i1 are the frequencies of the primary signal and idler; and ω _s2 and ω _i2 are the frequencies of the secondary signal and idler. Phase matching is described by the equations k_p- k _s1- k _i1-2π/Λ=0 and k _s1- k _s2- k _i2-2π/Λ=0 where the k’s represent the optical wavevectors and Λ is the grating period for the quasi-phase-matched (QPM) interaction. The secondary oscillation is made possible by the fortuitous simultaneous phase matching of both OPO processes by the same grating period Λ. The occurrence of these coincidentally phase-matched processes is not unique to QPM devices (Fig. 1). The observation of cascaded OPO’s in our case was enhanced by the use of broad-band cavity mirrors and by pumping many times over threshold.

 

Fig. 1 Calculated (based on the dispersion formulas of ref. 6) phase-matching wavelengths for primary (blue line) and secondary (red dash) OPO interactions in (a) QPM PPLN and (b) type I LiNbO₃. The primary pump wavelength is 1.064 m m, and the secondary pump wavelength is 3 the primary signal wavelength at the given grating period or phase matching angle. Wavelengths observed in operation of our OPO with the 25-mm-long PPLN crystal are shown as circles in (a).

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2. Experiment

The experimental layout (Fig. 2) consisted of a diode-pumped, Q-switched, 1.064-μm Nd:YAG laser pumping a PPLN crystal inside a linear singly resonant oscillator (SRO) cavity. The laser produced 1-mJ pulses of 43-ns full width at 1/e² peak intensity at 200-Hz repetition rate. A half-wave plate/polarizer combination was used to vary the laser pump energy incident on the crystal. The pump beam was focused to a 150-μm spot size (1/e² peak intensity radius) inside the crystal. The multiple-grating PPLN crystal² had adjacent poled regions with grating periods ranging from 26 to 31 μm in 1-μm steps. The end faces of the crystal were anti-reflection coated at the pump and signal wavelengths. The resonator mirror separation was 70 mm with one of the crystal surface 5 mm from the flat mirror. The crystal was enclosed in an oven, and the temperature was varied from room temperature to 300° C. The output wavelength of the OPO was tuned by translating different period gratings into the pump beam and by subsequent temperature tuning.²

Parametric oscillation using the 28-μm-period region of a 10-mm-long PPLN crystal was investigated initially. For a 1-mJ pump, the measured pump depletion was 35%. The spectral content of this output consisted of strong primary signal and idler, strong secondary signal and idler, and several other relatively weaker spectral components due to mixing of the various fields. The 1.064-μm pump produced primary signal and idler outputs at 1.428 μm and 4.184 μm, respectively. In addition, the primary signal pumped a secondary parametric oscillation with signal and idler outputs at 1.992 μm and 5.040 μm, respectively. The wavelengths of both OPO’s tuned simultaneously with temperature change of the PPLN crystal. The relative power distribution for the primary and secondary OPO signal was monitored using a monochromator/InSb detection system. Figure 3a shows the measured peak intensities for the two OPO signals as a function of pump energy for the 10-mm-long PPLN crystal. The measured pump thresholds for the primary and secondary signals were 250-μJ and 800-μJ, respectively.

 

Fig. 2 Experimental layout of the PPLN OPO. Mirror M1 has 85.9-mm radius of curvature, R>99% at 1.4–2.1 μm and T=80% at 1.064 μm. Mirror M2 is flat with R=70% at 1.4–2.1 μm and T>80% for the idler wavelengths.

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The secondary parametric oscillation became much stronger when we switched to a longer (25 mm) PPLN crystal (the crystal was simply inserted with no changes to the cavity length and with one face still 5 mm from the flat mirror). In this case, secondary oscillations were also observed for other grating periods as indicated in Fig. 1a. Figure 3b shows data obtained for the 28-μm grating of a 25-mm-long crystal. Pump thresholds for the primary OPO (1.428-μm signal) and secondary OPO (1.992 μm) decreased to 60-μJ and 150-μJ, respectively. Above 0.4-mJ of pump energy, the secondary OPO became dominant and significantly depleted the signal power of the primary OPO. Variations in the measured output were apparent at higher levels of pumping, as shown in Fig. 3b. We believe that this is the result of a combination of factors including the cascading, the dynamic nature of pulsed OPO’s, and back conversion processes.

3. Discussion

Threshold calculations for the primary parametric oscillations were performed using the model of Brosnan and Byer⁷ for pulsed singly resonant OPO’s with modifications appropriate for our experiment. We assumed a Gaussian signal mode determined by the stable oscillator cavity. Threshold was taken as the pumping level at which the energy of the circulating signal oscillation reached P_m = 0.2 μJ resulting in a value of ln(P_m/P_o) = 28 where P_o is the single-photon signal energy. The length of time that the gain exceeded loss was calculated iteratively, and approximations appropriate for arbitrary single-pass gain were used. For the measured pump parameters, pump-energy thresholds of 300 μJ and 58 μJ for the 10- and 25mm PPLN crystals, respectively were calculated. This is in reasonable agreement with the measured thresholds of 250 μJ and 60 μJ for these crystals. All pump energies are given before encountering the 80% transmission at the input mirror.

The performance of the cascaded OPO’s above threshold was analyzed numerically with a model that included both diffraction and time dependence. The time increment was taken as one round-trip cavity transit. The nonlinear interaction was modeled by dividing the PPLN crystal into 50 segments and alternately calculating the effects of diffraction and nonlinear wave coupling. Circular symmetry was assumed in the diffraction calculation, which employed Hankel transform techniques.^8,9The coupled mode equations are solved using a fourth-order Runge-Kutta solution of the five waves with the primary signal wave also acting as the pump for the secondary OPO. The model allows arbitrary depletion and back conversion. The lithium niobate absorption coefficient of 1 cm^-1 at the 5.040-μm secondary idler wavelength was also included.

 

Fig. 3 Measured (blue circle 1.428 μm; red circle 1.992 μm) and calculated (blue line 1.428 μm; red dash 1.992 μm) energy for the dual OPO’s as a function of pump energy for a) 10-mm- and b) 25-mm-long PPLN crystals. The QPM grating period was 28 μm. The calculated values are output energies while the measured values are unscaled peak intensities.

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Figure 3 also shows the calculated OPO output energy at the 1.428 μm and 1.992 μm signal wavelengths as a function of pump energy for the 10-mm- and 25-mm-long PPLN crystals. Our model gave results that agree qualitatively with many aspects of experimental observations. For example, the secondary OPO signal energy grows to exceed that of the primary when pumped approximately eight times above threshold for the 25-mm crystal.

There is also qualitative agreement between the measured and calculated time dependence of the OPO pulses. Figure 4 shows plots of the observed and calculated temporal profiles of the incident pump, transmitted pump, and the primary and secondary OPO signal outputs at the maximum pump energy. The experimental data shown in Fig. 4a was displayed on a 1.5-GHz digital oscilloscope with a 10-GHz sampling rate and obtained with either a 0.2-ns-rise-time Si detector for the pump or a 0.2-ns-rise-time InGaAs detector for the OPO signal wavelengths. For these pumping conditions the model predicts a chaotic behavior that is apparent in the calculated transmitted pump pulse. We could not experimentally observe these fluctuations perhaps due to the multimode character of the pump pulse and parametric oscillations and limitations of our detection system.

The beam divergence for the OPO with the 25-mm-long crystal was also measured. In this case, the OPO was operated at 1.667-μm signal and 2.914-μm idler, corresponding to a grating period of 31 μm, and at near maximum pump level of 1 mJ. This operating point was chosen because it eliminated secondary OPO oscillation (due to reduced cavity finesse). The measured half-angle beam divergence’s were 5.3 mrad and 24.4 mrad for signal and idler, respectively. The calculated 1.667-μm-signal-beam-waist (fundamental mode; near threshold) for this OPO is 147 μm, which yields a beam divergence half angle of 3.6 mrad. The calculated idler in the SRO near threshold has a 105-μm beam waist and 8.9-mrad divergence. Due to pump depletion and back conversion,¹⁰ the signal beam transverse distribution will develop additional intensity structure after amplification resulting in slightly higher divergence. The nonresonant idler beam, however, can have phase changes of π in its transverse profile resulting in a low fundamental mode projection and significantly higher divergence.

 

Fig. 4 Temporal profiles for the incident pump, transmitted pump, primary OPO and secondary OPO signals for 25 mm long PPLN crystal: a) measured and b) calculated. The measured data in (a) are averaged over 1000 pump pulses.

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Our results for the PPLN OPO are similar in many respects to the results obtained by other investigators for different nonlinear materials and devices. Smith et al.¹¹ presented detailed experimental and theoretical analysis of a pulsed, singly resonant OPO based on KTP that showed deterioration of optical quality of the OPO output when the pumping level was increased from 2.3 to 3.5 times threshold. Even without the secondary OPO, we find the best optical quality in the resonated primary signal is attained by not exceeding 2.5 times threshold. Tandem OPO’s, analyzed by Moore and Koch,¹² have the potential of high efficiency in the secondary oscillation over a large range of pumping levels. We observe an increase in pump depletion when the second oscillation grows in intensity. We do not, however, observe high depletion over a large range of pumping levels as predicted for cw pumping of the two-crystal tandem OPO.¹² The dynamic nature of pulsed oscillation with rapidly changing pump intensity could well explain this difference.

4. Conclusion

Pulsed OPO’s based on PPLN can easily be pumped twenty times above threshold (based on pumping 1 mJ into a 0.5 mm thick sample and a 50 μJ OPO threshold). At such high levels of pumping, cascading processes can become dominant in OPO operation as shown in this work. The secondary parametric oscillation is due to the coincidental phase matching that is not unique to QPM nonlinear interactions. For example, secondary parametric oscillation has been observed for high levels of incident fundamental in doubly resonant second-harmonic generation.¹³ Cascaded optical parametric oscillation offers simultaneous multiple wavelength outputs. Resonated OPO signal intensities can exceed pump intensities resulting in increased gain for phase-matched secondary oscillations; we have observed a secondary oscillation even though the absorption coefficient at the secondary idler was 1 cm^-1. The secondary oscillation could be either beneficial or detrimental depending on the application. On the one hand, the secondary process may introduce unwanted frequency components and reduce the efficiency of the primary process. On the other hand, optimization of cascaded optical parametric oscillation can provide conversion to additional wavelengths and improved pump utilization.