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A mid-infrared synchronously pumped optical parametric oscillator pumped by a femtosecond erbium-doped fiber laser is demonstrated and characterised. The idler is tunable from 3.7–4.7 μm, with a maximum average power of 37 mW and a pulse length of ∼ 480 fs at 4 μm. We compare the experimental results with numerical results based on an extensive simulation model.
© 2010 Optical Society of America
1. Introduction
Femtosecond and picosecond laser sources in the mid-infrared (mid-IR) range have potential applications in spectroscopy, as mid-IR frequency combs, and in material characterisation. Nonlinear devices, such as synchronously pumped optical parametric oscillators (OPOs) represent an attractive alternative for generation of such pulses. Traditionally, this type of OPOs has been pumped by Ti:sapphire or Nd-based lasers [1–6], but the highest output power has been obtained by an OPO pumped by an Yb:YAG thin-disc laser [7], where 7.8 W at 3.6 μm was obtained.
Using a fiber laser as pump source may provide a number of advantages over traditional bulk oscillators, such as compactness and low power consumption. Synchronously pumped OPOs driven by femtosecond and picosecond Yb-doped fiber lasers have recently been reported [8–12], where idler powers of up to 4.9 W at 3.1 μm have been demonstrated [12].
Although they have lower power, there are several reasons for using an Er-fiber laser instead of an Yb-fiber laser as pump source. First, standard telecom components can be used at the wavelength of the Er-fiber laser. Second, in some applications it may be desirable that both the signal and idler beams are in the mid-IR range. Third, Er-fiber lasers operate at an eye-safe wavelength, compared to e. g. Yb-fiber lasers. Finally, the performance of short-pulse optical parametric amplifiers depends on the relation between the group velocities of the interacting beams [13, 14], and for some combinations of nonlinear crystal and output wavelengths a 1.55μm pump beam may be desirable. Er-doped fiber lasers can be used to pump CW and nanosecond OPOs [15–17], femtosecond optical parametric generators and amplifiers [18, 19], and femtosecond OPOs, which have recently been reported on conferences [20, 21]. This paper gives a more detailed characterisation of the OPO presented in Ref. [20].
The experimental setup is described in Sec. 2, and Sec. 3 gives a brief description of the simulation model. Experimental results are discussed in Sec. 4 and compared with simulations.
2. Experimental setup
2.1. Pump laser
The OPO is pumped by a commercial mode-locked Er-doped fiber laser/amplifier (FFS.SYS.HP from Toptica) with a repetition rate of 90.3 MHz. An optical isolator is used to avoid feedback into the laser. The measured spectrum and intensity autocorrelation of the pump laser pulses are shown in Fig. 1(a) and 1(b), respectively.
Fig. 1 (a) Measured pump spectrum. (b) Measured intensity autocorrelation for pump, and calculated autocorrelation for test pulse. (c) Test pulse for simulations.
The pulse shape could in principle be measured using e.g. the frequency-resolved optical gating technique [22], but such equipment was not available at our laboratory. To obtain an estimate of the pulse shape, a test pulse is constructed using the measured pulse spectrum and Taylor-expanding the spectral phase to fifth order around the central frequency. The expansion coefficients are varied to maximise the overlap between the autocorrelation of the test pulse and the measured autocorrelation. The resulting test pulse is shown in Fig. 1(c). Even though a perfect fit to the measured autocorrelation in Fig. 1(b) is not obtained, the test pulse serves as a useful input to the simulations to provide design guidelines for the OPO.
The maximum available pump power for pumping the OPO is ∼ 300 mW.
2.2. Nonlinear crystal
The nonlinear crystal is a 5 mm long and 1 mm thick 5% doped MgO:PPLN crystal. This crystal is chosen, because it can be periodically poled, has high figure of merit ( ), and has good transmission up to ∼ 5 μm (> 60% for a 5 mm long crystal [23]). If longer idler wavelengths are desired, nonlinear crystals such as AgGaS2 and AgGaSe2 could be more suitable due to their wide transmission range [2, 3].
The crystal is kept at a temperature of 150°C in all experiments, except for the temperature tuning experiments in Sec. 4.2. Room temperature operation is possible [24], but a crystal temperature of 150°C is chosen here to allow temperature tuning in both directions without cooling. The crystal has six grating periods in the range 29.5–34.5 μm. Five of them, 29.5–33.5 μm correspond to quasi phase-matched idler wavelengths in the 3–5 μm range. A fan-out grating would allow for continuous tuning of the idler wavelength [9], but is not used here because continuous tunability is not a major goal in the present work.
The length of the crystal must be chosen as a compromise between gain and temporal walk-off. A long crystal leads to large temporal walk-off and consequently long output pulses.
Figure 2 shows the calculated idler-signal and pump-signal temporal walk-off for PPLN, using the Sellmeier equations from Ref. [25] and a pump wavelength of 1.55 μm. The pump-signal walk-off is less than 30 fs/mm for idler wavelengths in the range 3.5–5 μm, while the idler-signal walk-off increases from 80 fs/mm at 3.5 μm to 440 fs/mm at 5 μm. We chose a 5 mm long crystal in order to get enough gain, but this leads to significant signal-idler walk-off, which limits the minimum idler duration that can be obtained. Note that the pump-signal temporal walk-off changes sign for an idler wavelength of 4.4 μm. This corresponds to a transition between the bad group velocity regime with vp outside [vs, vi] (for λi < 4.4 μm) and the good regime with vp between vs and vi (for λi > 4.4 μm) [13, 14]. However, since the idler-signal walk-off is much greater than the pump-signal walk-off, the group velocity relations are far from optimal even for the longer idler wavelengths.
Fig. 2 Calculated temporal walk-off, between idler and signal, and between pump and signal, where v is the group velocity in the nonlinear crystal. The pump wavelength is 1.55 μm.
The pump acceptance bandwidth is related to the temporal walk-off [26, 27]. If the idler frequency is fixed and the signal frequency adapts to the pump, the acceptance bandwidth is Δνps ≈ 1/|Δtps|, where Δtps is the temporal walk-off between the pump and signal. Similarly, if the signal frequency is fixed and the idler varies, Δνpi ≈ 1/|Δtpi|. Figure 2 shows that |Δtpi| > |Δtps|, so Δνps > Δνpi. In our case, neither the signal nor the idler-frequency is fixed, and either spectrum can adapt to the pump. Therefore the greater pump acceptance bandwidth, Δνps, is the most relevant. At 3.66 μm, the smallest idler wavelength in our work, the pump-signal walk-off in the 5 mm crystal is about 100 fs. This corresponds to Δνps ≈ 10 THz, which is comparable to the width of the pump spectrum. On all the other wavelengths we have reported, the pump acceptance bandwidth is greater than the pump bandwidth.
2.3. Resonator
The OPO layout is shown in Fig. 3. The resonator is singly resonant for the signal at 2.3–2.7 μm. Although a ring cavity would have lower round-trip loss, a standing wave cavity is chosen because it is simple to align. M1 and M2 have a radius of curvature of 75 mm, while HR (high-reflectivity mirror) and OC (signal output-coupler) are flat. The distance between M1 and M2 is ∼ 79.5 mm, and the total cavity length is 1.66 m. The cavity forms a resonator mode for the signal with a calculated waist radius of 26–28 μm for a signal wavelength of 2.3–2.7 μm, corresponding to a confocal parameter of 3.9 mm in the nonlinear crystal.
All mirrors are highly reflective for the signal, except for OC, which has a signal transmission of ∼1%. The signal transmitted through OC is used for monitoring purposes, since only the idler beam is of interest in this work. HR is placed on a motorised stage for partially automated adjustment of the cavity length. The angles OC-M2-M1 and HR-M1-M2 are 8°. Calculations based on the ABCD-matrix for the resonator show that this is sufficiently low to avoid problems with astigmatism. The OPO cavity is purged with N2 to avoid the water vapour absorption band centred at 2.7 μm. The contribution to the signal round-trip loss from the mirror- and crystal coatings is estimated to be ∼ 5%, based on the coating specifications. However, there may also be additional contributions to the loss due to e.g. residual water vapour in the resonator, and the total signal round-trip loss is therefore estimated to be in the range 5–10%. Dispersion compensation of the cavity for the signal pulses is not attempted in this work, because the signal is only of interest for monitoring purposes here, and the idler duration is mainly determined by temporal walk-off effects in the nonlinear crystal.
The idler is coupled out through M2 and is collimated by L2. The total idler loss in the end surface of the nonlinear crystal, M2, and L2 is estimated to vary in the range 20–40%, depending on the wavelength.
The pump beam is focused to a waist radius of ∼ 32 μm in the nonlinear crystal. This waist radius corresponds to a confocal parameter of 8.7 mm in the crystal. This is longer than for optimal focusing [28], but a more tightly focused pump would lead to a strongly divergent idler, which would be difficult to collect without vignetting. The total loss for the pump in L1, M1, and the front surface of the nonlinear crystal is estimated to be 14%. The pump is coupled out of the cavity through M2 and OC, and reflection back into the cavity is negligible. The pump is separated from the idler using a long-pass filter after L2.
3. Simulation model
The OPO is simulated using an advanced numerical model [29], which includes crystal and mirror dispersion, diffraction, resonator geometry, and idler absorption in the nonlinear crystal. The input pump beam has 32 μm waist radius, as measured in the experiment, and the spatial profile is taken to be Gaussian because the beam originates from a single-mode fiber laser. The spectrum and pulse shape are shown in Fig. 1(a) and 1(c), respectively. The nonlinear coefficient, d33, of the MgO:PPLN crystal is taken to be 18 pm/V, and the refractive index is computed by the Sellmeier equations in Ref. [25]. The mirror dispersion for the signal is taken from the dispersion curves calculated by the manufacturer. The total round-trip loss for the signal is taken to be 8% as an estimate. Simulations show that the quantum efficiency at full pump power is not critically sensitive to small variations in the signal round-trip loss.
The signal builds up from quantum noise, with an average intensity of 1/2 photon per mode. A signal pulse typically starts forming after ∼ 100 round-trips, and the simulations are terminated when the signal power has reached a stable value, typically after ∼ 200 round-trips. The exact number of round-trips depends on how far the OPO is above threshold and the random noise.
4. Results
4.1. Output power
Figure 4(a) shows the measured and simulated input-output curve for the 32.5 μm grating, corresponding to an idler wavelength of 3.96 μm. This grating period gives the highest idler energy. Up to 37 mW idler power after the lens L2 is obtained for a pump power of 299 mW incident on the lens L1. Taking into account the pump loss from outside L1 to inside the nonlinear crystal and the idler loss from inside the nonlinear crystal to after L2, the internal quantum efficiency is ∼ 46%.
Fig. 4 (a) Measured and simulated input-output curve for 32.5 μm grating. (b) Measured and simulated idler output at full pump power for different grating periods. The pump power is measured in front of L1, and the idler power is measured after L2. The simulations are corrected for the 14% pump loss from outside L1 to inside the nonlinear crystal and the estimated idler losses in the range 20–40% from inside the crystal to after L2.
Figure 4(b) shows the measured and simulated idler power at full pump power for the different grating periods. The cavity length was adjusted to maximise power at each wavelength. The 33.5 μm grating (giving 3.66μm idler) could only be used with N2 flushing, because the corresponding signal wavelength is in the water vapour absorption band around 2.7 μm. The measured idler power at 4.2 μm is reduced by CO2 absorption in air, because parts of the path from the nonlinear crystal to the power meter is not purged with N2. We estimate that up to 20% of the idler power at 4.2 μm is lost due to CO2 absorption, but the simulation is not corrected for this loss contribution. The simulation is not carried out for the grating period corresponding to an idler wavelength of 4.7 μm, because we lack data for the mirror dispersion at this wavelength.
With exception of the point at 3.66 μm, the idler power decreases with increasing idler wavelength. This is due to a combination of different effects. First, the idler absorption in the nonlinear crystal increases with wavelength [23]. Second, the idler photon energy also decreases with wavelength, and third, the effective nonlinear gain coefficient decreases with increasing idler wavelength [28]. The transition from the poor to the good group velocity regime, shown in Fig. 2, should improve conversion efficiency at longer wavelengths, but this is not sufficient to compensate for the negative effects just mentioned. On the other hand, the relatively large pump-signal walk-off at 3.66 μm may explain the decrease in power from 4 μm to 3.66 μm.
The difference between the simulated and measured power is not greater than one must expect given the uncertainty of the pump pulse shape. The dispersion of the mirror M2 increases sharply for the shorter signal wavelengths, so an uncertainty of the dispersion data may explain the relatively large discrepancy at 4.48 μm. The variation of idler loss with wavelength also contains uncertainties.
Figure 5 shows measured and simulated pump depletion spectra for full pump power using the 32.5 μm grating. The simulated pump depletion is 60%. The measured output spectrum has a strong peak at 1.527 μm at high pump power. We ascribe this to back-conversion. The absence of this peak in the simulations could be due to the difference in experimental and simulated pump pulse shape.
Fig. 5 Measured and simulated depleted/undepleted pump spectra, 32.5 μm grating period and full pump power.
4.2. Idler spectra
Figure 6(a) shows measured idler spectra (normalised) for different grating periods at full pump power. We observe that the idler spectrum for the 31.5 μm grating is affected by the CO2 absorption band at 4.2–4.3 μm, because the path from the OPO to the monochromator is not purged with N2. It can also be noted that the idler spectrum for the 29.5 μm grating has a high noise level due to the small idler power.
Fig. 6 (a) Measured idler spectra (normalised) for for different grating periods, (b) Measured idler spectra, 32.5 μm grating period, for varying crystal temperature.
The measured spectral widths are compared with the simulated ones in Table 1. There is reasonable agreement for all gratings, except for the 31.5 μm grating, since the CO2 absorption is not included in the simulations. Because the idler has large temporal walk-off with respect to the signal and pump, its spectral width can be estimated by the acceptance bandwidth Δνi ≈ 1/|Δtsi|, where Δtsi is the temporal signal-idler walk off from Fig. 2, assuming a 5 mm long crystal. The data in Table 1 shows that the simple estimate gives reasonable values for the idler bandwidth, although the discrepancy increases at shorter idler wavelengths.
Table 1. Measured and simulated idler bandwidth (FWHM). The table also shows an estimated idler bandwidth based on the phase-matching acceptance bandwidth
Measured idler spectra for different crystal temperatures are shown in Fig. 6(b).
4.3. Idler duration
The duration of the idler at full pump power and 32.5 μm grating is measured using non-collinear intensity autocorrelation with a 1 mm LiIO3 crystal. The autocorrelation, which is shown in Fig. 7(a), has an FWHM width of ∼ 680 fs. This corresponds to a pulse width (FWHM) of 480 fs assuming a Gaussian pulse shape. This width and the measured FWHM spectral width of 0.96 THz from Table 1 gives a time-bandwidth product of 0.46. For comparison, the value of the time-bandwidth product for an ideal Gaussian pulse is 0.44. The simulated pulse shape of the idler is shown in Fig. 7(b), and its autocorrelation agrees well with the measured one, as shown in Fig. 7(a). The reason why the idler autocorrelations agree well in spite of the differences between the corresponding autocorrelations for the pump, in Fig. 1(b), is probably that the idler spectrum is limited by the phase matching bandwidth and therefore not very sensitive to details of the pump pulse.
Fig. 7 (a) Measured and simulated intensity autocorrelation for the idler with 32.5 μm grating period. (b) Simulated pulse shape for the idler.
4.4. Beam quality
The beam quality (M2) of the idler is measured by focusing the idler with a lens with 75 cm focal length and recording the beam profile with a pyroelectric camera in the focus and in the far field. From the measured beam profiles, we obtain a beam quality of M2 = 1.8. This agrees reasonably well with the simulated beam quality of M2 = 1.9. The simulations and experiments are performed at full pump power and using the 32.5 μm grating. The beam quality of the signal is not measured, but is near diffraction-limited according to the simulations.
4.5. Power stability
To test the stability of the idler power, we logged the idler output at maximum pump power for a grating period of 32.5 μm. For a measurement time of 30 min, the average idler power varied about ±1 mW, i.e. ±3%. For long-term operation over several hours, the idler power may drop significantly due to thermal drifts, and the cavity-length should be adjusted to maintain the desired idler power.
We also measured the idler power as a function of resonator length at full pump power and for a grating period of 32.5 μm. The results are shown in Fig. 8, along with the simulated results. The measured curve is seen to be in reasonable agreement with the simulated one. The idler wavelength is found to be fairly stable when the resonator length is adjusted. A 6 μm change in resonator length leads to a change of 14 nm in idler wavelength.
Fig. 8 Measured and simulated idler power (normalised) as a function of resonator length, 32.5 μm grating period.
5. Conclusion
We have demonstrated and characterised a mid-IR source based on a synchronously pumped optical parametric oscillator driven by a femtosecond Er-doped fiber. We estimate an internal quantum efficiency of 46% for a pump power of 299 mW. The maximum idler power is 37 mW at a central idler wavelength of 4.0 μm, with a beam quality of M2 = 1.8. The idler wavelength is tunable in the range 3.7 μm to 4.7 μm using different quasi phase-matching periods in the MgO:PPLN crystal.
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