1. Introduction

Tunable Fourier-transform-limited pulses are of high interest for various spectroscopy applications. The picosecond regime is especially used for time-resolved spectroscopy applications, including Raman spectroscopy [1], investigation of optical nonlinearities in confining structures [2], time-resolved measurement of carrier dynamics in optoelectronic devices [3], or coherent anti-Stokes Raman scattering thermometry in combustion facilities [4, 5]. In the mid-infrared, this type of tunable emission can be conveniently provided by optical parametric oscillators (OPOs). In this context, the use of a diffraction grating as an intracavity frequency selective reflector is a well-established approach to suitably narrow the emitted linewidth and precisely control the output wavelength [6, 7, 8, 9]. However, when fast (>kHz) and broad tuning is required, the accessible spectral range is limited by the parametric gain bandwidth that is typically of only a few nanometers for an OPO operating far from degeneracy [10].

Here, we investigate the use of an aperiodic, or chirped, quasi phase matched (QPM) crystal [11] to broaden the parametric gain bandwidth and thus enable fast tuning over a wide spectral range without changing the crystal temperature or the QPM period. Since the QPM grating period Λ(z) is an engineerable function of z, the phase matching wavelength can be varied and controlled along the position z in the crystal. These versatile properties have been extensively used for various applications such as nonlinear pulse compression [12], adiabatic frequency conversion [13, 14] or optical parametric chirped pulse amplification [15]. Moreover the large gain bandwidth properties of these chirped QPM crystals have been used to implement broadband femtosecond OPOs [16, 17].

In this paper, we report on a new approach that combines a picosecond SPOPO based on an aperiodically poled lithium niobate (APPLN) crystal and an intracavity fast spectral filter, in order to rapidly select and tune the emission wavelength within the wide parametric gain bandwidth offered by the APPLN crystal.

The paper is organized as follows. The experimental setup and the large bandwidth crystals properties are detailed in Section 2. Then, step-by-step tunability is developed in Section 3 and rapid wavelength tuning is demonstrated with our device in Section 4. Finally, an application to gas detection is reported in Section 5, where the transmission of a N₂O gas cell is recorded. The final Section summarizes the conclusions. The two appendices investigate respectively the influence of cavity length and cavity configuration to determine an optimal configuration.

2. Experimental setup

The aperiodic QPM crystal giving access to a wide gain bandwidth is a key element of our setup. Two kinds of aperiodic QPM gratings were studied. The first one was designed following the approach developed in [11] and consisted of a linearly chirped central section sandwiched between two nonlinearly chirped sections at the edges of the crystal for apodization, in order to reduce the spectral ripples in the parametric gain spectra. The calculated bandwidth and associated QPM period profile are shown in Fig. 1(a) and (b) respectively. The role of apodization has been largely discussed in [18] and is not developed here. Different gratings with different chirp rates were used in order to achieve different gain bandwidths. In the following, the chirp rate κ′ is defined as the rate of change of the grating wavenumber, K_g (z) = 2π/Λ(z), in the axial direction, in the center of the grating:

Table 1 summerizes the main properties of those gratings. Grating A shows the smallest chirp rate, κ′_A = 1.8 × 10⁴m⁻². Grating B has a larger central chirp coefficient and thus a broader gain bandwidth but consequently a smaller peak gain. Grating B chirp value is κ′_B = 3.9 × 10⁴m⁻² leading to a 13.4 nm signal gain bandwidth (Fig. 1(b)). Then, for grating C showing the broadest signal gain bandwidth of 40 nm, we used the approach developed by Lai et al. in [19] to design the QPM pattern. In this case, the widths of QPM domains obey to an iterative domino algorithm designed to optimize the crystal superlattice to further reduce the ripples in the gain bandwidth. All the involved crystals are based on 5 %-MgO-doped APPLN with a 60-mm length and were manufactured by HC Photonics.

 

Fig. 1 Theoretical single-pass, small-signal parametric gain spectra (a) and corresponding QPM domain widths (half periods) (b) for gratings A, B and C, respectively in grey, black and red. Grating C domain widths are calculated using Lai et al. algorithm [19] to improve the flatness of the gain spectrum.The corresponding C^* QPM domain widths (see Table 1) are shown.

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Table 1. Parameters used for chirped QPM grating and corresponding parametric gain bandwidth at the signal (Δλ_s) and idler (Δλ_i) wavelength. Grating C being aperiodic but not linearly chirped, grating C^* corresponds to the equivalent QPM grating with a linear chirp rate κ′_C^* that leads the same gain bandwidth (FWHM).

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The SPOPO is pumped by a 1.064-μm Nd:YVO₄ mode-locked laser delivering 8-ps duration pulses at a 76-MHz repetition rate (High Q Laser). As shown in Fig. 2, the SPOPO resonator has a standing-wave configuration with a central focused arm between two collimated arms. It is singly resonant at the signal wavelength around 1.47 μm while the idler beam at 3.85 μm and pump beam are output coupled through mirror M3 after the crystal output facet. The radius of curvature of both spherical mirrors, M2 and M3, is 500 mm. Mirrors M1, M2, and M3 are highly reflective at the signal wavelength. The plane output coupler M4 can have a signal reflectivity of 90 % or can be replaced by a 98 % reflectivity mirror, in order to reduce the threshold with grating C. It is mounted on a translation stage so that the cavity length can be precisely adjusted for synchronous pumping. All the cavity mirrors are based on undoped YAG substrates. The pump beam is focused in the middle of the crystal with a waist radius of 110 μm. The rotating mirror M1 is either mounted on a step-by-step piezoelectric rotating mount or replaced with a galvo-mirror controlled with a function generator. The diffraction grating (Horiba) has 600-lines/mm and is blazed for optimum reflectivity at 1.5 μm. The measured losses in the zero order are 22 % at 1470 nm.

 

Fig. 2 Experimental setup.

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The signal or idler beam profile is recorded with a camera (Spiricon) and the averaged signal spectrum is recorded with an optical spectrum analyzer (Ando) with a 10 pm resolution. The OSA can be replaced by the association of a highly dispersive fiber and a fast photodiode to record the pulse-to-pulse spectrum by dispersive Fourier transformation as described in [20].

In this device, the APPLN crystal gives access to a wide parametric gain bandwidth while the diffraction grating is the spectral filtering element. The FWHM spectral selectivity imposed by the diffraction grating can be expressed as [6, 7] :

The diffraction grating remains static but the rotating mirror M1 allows us to vary the incidence angle of the resonant beam on the diffraction grating. Due to the Littrow configuration, for one incidence angle θ₀ on the grating, only the associated wavelength λ₀ is exactly reflected on itself and is thus able to oscillate in the cavity. Slightly changing the incidence angle to θ₀ + δθ causes the geometrically favored wavelength to be tuned to λ₀ + δλ as shown in Fig. 3. This combination of a deflecting device and a static diffraction grating forms a fast spectral filter which allows us to select and tune the wavelength of the OPO within the broad gain bandwidth of the APPLN crystal. Such a fast tuning approach is similar to previous implementations in laser oscillators as in [21, 22]. Its application to an OPO enables here to deliver a rapidly tunable mid-infrared idler emission by controlling the signal wavelength with a reliable (off-the-shelf) near-infrared tuning element.

 

Fig. 3 Tunability within the gain bandwidth in the case of grating B. The emission can be controlled within the total gain spectral bandwidth represented in black (theoretical gain spectrum). The two blue signal spectra are experimental data, corresponding to different mirror M1 angle positions. The mirror deflection δθ is here of 0.52 mrad.

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3. Tunability: Step-by-step characterization

Rotating mirror M1 was first mounted on a step-by-step rotating mount. We performed extensive characterizations of the OPO tunability and behavior. The tunability was first measured with grating B, an output coupler reflectivity of 90 %, and a pump power of 9.6 W, corresponding to a pumping rate of 3 times above the oscillation threshold at central wavelength. It is shown with blue dots in Fig. 4. In this case, the demonstrated tuning range covers more than 85 % of the calculated gain bandwidth and the wavelength variation with mirror M1 angle is linear except at the very edge of the gain bandwidth, where the OPO is less stable. This shows the great potential of our tuning method. The typical extracted idler power was 120 mW and the corresponding signal output power was 600 mW. At the very edge of the tuning curve with grating B, the wavelength changes in the reverse direction (mirror rotation angle higher than 2.4 mrad in Fig. 4(a)). This behavior is concomitant with the sudden drop of power seen in Fig. 4(b) and is responsible for the data point around λ_s = 1466 nm (and λ_i = 3880 nm) with a lower power than the preceding point at the same wavelength.

 

Fig. 4 Wavelength tunability, for signal and idler waves, with M1 angle variation (a). Black dashed lines represent the theoretical slopes obtained with Eq. (4). The corresponding normalized output power as a function of the emitted wavelength is reperesented in (b). Measurements with grating B (blue dots) are performed at a pumping rate of 3. Measurements with grating C (red triangles) are performed at a pumping rate of 1.5 but nevertheless show a broader tuning range.

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Then, we tested grating C which provides a much broader gain bandwidth at the cost of a lower maximum peak gain (see Fig. 1(a)). The OPO threshold was indeed higher with grating C (7.7 W with the 98 % output coupler), but we could nevertheless reach a pumping rate of 1.5 and cover 58 % of the gain bandwidth. This reduced spectral coverage is attributed to the beam adaptation effects discussed in Appendix A that alter the overlap between the pump beam and the oscillating mode at the edges of the tuning range. Tunability is nevertheless greatly improved to a 160 nm range around 3.86 μm for the idler wave. To achieve this wavelength span with a periodically poled crystal, the required temperature change would have been over 110 ° C. The reference extracted idler power with grating C was 45 mW, and the corresponding signal output power was 150 mW.

In our case, the total wavelength variation Δλ with Δθ, the deflection of the resonant signal beam on the diffraction grating (due to M1 rotation), can be expressed as:

The first term is directly linked to M1 rotation and comes from Eq. (3), λ₀ is the initial signal wavelength and D is the diffraction grating pitch. It corresponds to a variation of 3 nm/mrad and is the main contribution to the total slope coefficient whose value is 3.2 nm/mrad in this case. The second term corresponds to a correction due to the beam path adaptation with cavity length variations. Indeed, moving mirror M1 changes the geometrical path of the signal beam and thus the total cavity length. This effect is detailed in Appendix A where the value of this coefficient is determined.

4. Dynamical characterization

To perform dynamical spectral measurements, we used a highly dispersive fiber associated with a fast detector as detailed in [20]. This method, referred as dispersive Fourier transformation [23], gives access to the spectrum for each cavity round-trip. This relative wavelength measurement is completed with an average OSA measurement during stationary regime, to know the absolute emitted wavelength.

We first investigated the pulse-to-pulse spectrum when the OPO is switched on while the angle of mirror M1 remains constant. As shown in Fig. 5, we can observe that, owing to spectral filtering provided by the grating, the wavelength is well constrained right from the first oscillating pulses. There is thus no transient spectral shift in this case, contrary to the situation of a free running SPOPO based on chirped QPM [20].

 

Fig. 5 Build-up of the oscillation recorded with highly dispersive fiber A (see text below) when the angle of mirror M1 remains constant. The build-up spectrum is constrained by the diffraction grating. The fast modulations on the spectrum are due to Fabry-Perot effect on a silicon plate placed before the dispersive fiber in order to filter the unwanted lower wavelength light.

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To demonstrate the fast tunability, we replaced mirror M1 by a galvanometer mirror controlled with a function generator. In this configuration, we were limited in power because of a thermally induced deformation of the mirror metallic surface, which occurred for pumping rates above two, with grating B and a 90 % output coupler. This limitation in terms of pumping rate reduces the achievable tunability range but could be fixed by replacing the metallic mirror by a dielectric one. Nevertheless, we were able to observe the dynamical behavior using a ramp function to drive the galvanometer mirror. The spectrogram was measured during the tuning as shown in Fig. 6. We can observe a linear tuning of the signal wavelength over 4 nm in 40 μs, which corresponds to a tuning of 30 nm of the idler wavelength during the same time interval. The tuning speed of the device is limited by the mechanical rotation of mirror M1.

 

Fig. 6 Spectrogram of the OPO emission with grating B, recorded with fiber B. Mirror M1 is a galvo-mirror driven by a sawtooth function. This figure shows the great potential for fast tuning of our device, the speed is over 30 nm in 40 μs for the idler wavelength.

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The span and resolution of the spectrograms depend on the dispersive coefficient or induced group delay dispersion (GDD) of the fiber we use. The spectrogram in Fig. 5 is recorded with fiber A inducing a GDD of −2000 ps/nm around 1.47 μm leading to a span of 6.5 nm and a resolution of 0.1 nm. The spectrogram in Fig. 6 is recorded with fiber B inducing a GDD of −500 ps/nm for the signal central wavelength leading to a larger accessible span of 26 nm but a lower resolution of 0.4 nm. The dynamical results confirm that our device has a great potential for fast tunability.

5. Gas detection

As a first test in a gas detection experiment, we chose to perform a local direct measurement of N₂O in a gas cell. N₂O displays strong absorption lines on a wide spectral range around 3.88 μm. We used the OPO with grating C to address the widest possible wavelength range.

As shown in Fig. 7, the idler beam was split into a reference path and a measurement path containing the 13 cm long gas cell, filled with 1.3 × 10⁴ Pa of N₂O partial pressure. For that purpose, we used a thin pellicle beamsplitter (Thorlabs BP145B4) in order to avoid Fabry–Perot interferences. The power in the two beams was recorded with identical HgCdTe photovoltaic detectors (Vigo System). We were thus able to measure the ratio of the measurement signal to the reference signal. We first recorded the baseline ratio for an empty cell and then carried out a second measurement of the ratio with the cell filled with gas. The transmission spectrum was then calculated as the measurement ratio over the baseline ratio. This approach enables to correct any spatial adaptation of the beam and spectral variation of the beamsplitter reflection/transmission coefficients over the large tuning range. The signal wavelength is recorded with the OSA and used to calculate the idler wavelength. To tune the OPO, we only changed the deflection mirror angle while all the other parameters remained unchanged. The idler was tuned over more than 160 nm around 3.88 μm using the step-by-step rotating mount and we obtained a transmission profile shown in Fig. 8. The theoretical fit corresponds to the convolution of the transmission spectral lines calculated with HITRAN database for N₂O and a Gaussian profile with a FWHM of 5 nm. This FWHM value corresponds to the average FWHM of the OPO idler spectra. In this case, the best fit is obtained for a partial pressure of 1.1 × 10⁴ Pa. The discrepancy between this value and the setpoint pressure measured with a manometer on the cell can be due to some leaks out of the cell.

 

Fig. 7 Experimental setup for local N₂O single pass detection in a gas cell.

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Fig. 8 N₂O transmission, measured in single pass in a gas cell at atmospheric pressure for a partial pressure of 1.3 × 10⁴ Pa, black squares (a) and (b). The HITRAN transmission lines are shown in grey (a), and the solid orange line in (a) and (b) corresponds to the convolution of this HITRAN transmission lines and a Gaussian profile with a FWHM corresponding to the mean OPO idler spectra FWHM within the addressed range.

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The y-error bars in Fig. 8 correspond to the standard deviation of the measurement-to-reference ratio as measured by the oscilloscope. This error is more important at the edges of the spectrum because the OPO is operated near the oscillation threshold, which results in higher power instabilities. The x-errors bars correspond to the standard deviation of the central wavelength for a fixed position of the rotating mirror, this value is smaller than the data points size in Fig. 8.

Despite the spectral linewidth of the OPO that does not allow to resolve fine absorption lines, the tuning over a broad spectral range enables to exploit the convolution profile to carry out correlation spectroscopy. The reported SPOPO scheme based on an APPLN crystal and an intracavity fast spectral filter has thus a great potential for fast gas detection. In the measurement, presented in Fig. 8, each data point is measured with a 200-pulse averaging. In terms of resolution and noise, this result is representative of what we could obtain with only one fast wavelength sweep. Owing to the high repetition rate (76 MHz), all the 42 data points of Fig. 8 correspond to an acquisition time of 110 μs. This means that, with improved galvanometer mirror and acquisition systems, a single fast wavelength ramp (speed of 0.7 nm/μs) would provide enough pulses to keep the resolution and signal-to-noise ratio.

6. Conclusion

In this article, we have demonstrated a new OPO architecture to obtain a rapidly tunable radiation over a broad wavelength range. This approach consists of the association of a broadband aperiodically poled nonlinear crystal and a fast tuning spectral filter.

Tuning over 160 nm around 3.86 μm has been achieved at fixed temperature and a fast tunability of 30 nm in 40 μs has been demonstrated for the idler and could be increased with a faster deflecting system such as an electro-optic modulator since the velocity is currently limited by the mechanical rotation of the intracavity mirror. We also used this device for detecting N₂O around 3.88 μm by absorption and we showed its potential for fast spectroscopy.

This approach could be generalized to other spectral ranges (e.g., visible) and temporal regimes (e.g., continuous-wave or nanosecond). Other intracavity spectral filters could also be used as filters based on a grazing-incidence grating [8], birefringent filters [10, 24] or Bragg gratings [25]. A grating with higher groove density or a prism beam expander could also be considered to improve spectral selectivity [26].

Appendix A – Influence of cavity length

In this appendix, we investigate the influence of cavity length on the OPO tunability.

As studied in [7], the change of the cavity length of a synchronously pumped OPO with an intracavity diffraction grating leads to a geometrical adaptation of the resonant beam path to cancel out the round-trip time detuning. This effect is illustrated in Fig. 9 where we consider a simplified unfolded configuration diagram, mirrors being replaced by lenses for the sake of clarity.

 

Fig. 9 Simplified representation of the unfolded SPOPO cavity. The mirrors are replaced by lenses and rotating mirror M1 is not represented. The detuning introduces a deflection δθ of the resonant beam.

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In our case, with the total cavity length fixed by the pump laser repetition rate and the 500-mm radius of curvature (f = 250 mm) for both M2 and M3, the distance d_M2–M3 has to be larger than 600 mm (i.e. δf >100 mm) to obtain a stable optical resonator. Since the beam must remain normal to mirror M4, the beam path adaptation, when the cavity length is varied, induces a small variation δθ of the incidence angle on the diffraction grating. As a consequence, the geometrically favored wavelength depends on the cavity length variations.

For such a standing-wave cavity SPOPO, this effect does not occur if we replace the diffraction grating by a plane mirror at normal incidence. Indeed, the beam has to keep a normal incidence on plane mirrors in both collimated arms in this case. In Fig. 10, we can actually see that the cavity length detuning tolerance with a plane mirror is about 100 μm while the tolerance is almost 10 times larger with an intracavity diffraction grating.

 

Fig. 10 Tolerance to cavity length detuning with a plane mirror (in grey) and a grating (in green). The data are recorded with grating A, when moving the output coupler M4 using a translation stage to vary the cavity length. The zero position corresponds to the cavity length that minimizes the OPO oscillation threshold.

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As shown in Fig. 11, the signal beam adaptation leads to a linear variation of the emitted wavelength as a function of the cavity length detuning, ΔL, at a rate Δλ/ΔL of 5.2 nm/mm in this case. Knowing the distance between the diffraction grating and the rotating mirror M1, the induced variation of cavity length with M1 rotation angle can be calculated, with ΔL/Δθ = 5.2×10⁻² mm/mrad in this case. The additional contribution to wavelength variation due to cavity adaptation is then deduced:

(5)$${\frac{\mathrm{\Delta }\lambda }{\mathrm{\Delta }\theta }|}_{\text{beam}\hspace{0.17em}\text{adaptation}}=\frac{\mathrm{\Delta }\lambda }{\mathrm{\Delta }K}\times \frac{\mathrm{\Delta }L}{\mathrm{\Delta }\theta }=0.27\hspace{0.17em}\text{nm}/\text{mrad}.$$

It corresponds to the correction term due to beam adaptation in Eq. (4). When we sum this cavity detuning contribution with the wavelength variation due to direct M1 angle variation, we obtain a good agreement with the experimentally measured coefficient as shown in Fig. 4(a).

 

Fig. 11 Wavelength tunability due to cavity length variation, induced by output coupler M4 translation. Wavelength shift is linear with respect to cavity length variations. The linear fit shows a coefficient of Δλ/ΔL = 5.2 nm/mm. Grating B is used here.

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Besides, one should note that the maximum beam deflection—of 4 mrad in our case—induces a cavity detuning of 400 μm that remains smaller than the 1 mm tolerance range shown in Fig. 10 and has thus a limited impact on the OPO performances. A way to enable even larger beam deflection angles could be to properly shift the beam spot out of rotating mirror M1 center (which is its rotating axis in our case) so as to maintain a constant beam path length while rotating the mirror.

Appendix B – Influence of cavity configuration

The results previously presented with grating B in Figs 4 and 11 or with grating A in Fig. 10 were measured for a fixed distance d_M2–M3 corresponding to δf = +145 mm.

In this appendix, we report on the investigation of the influence of parameter δf on the OPO behavior and tunability. For that purpose, mirror M3 was moved to vary δf while coupler M4 was translated to adapt the total cavity length. For each value of δf, we studied the wavelength tuning, spectral properties and oscillation threshold of the OPO.

In Fig. 12(a), we can see that the slope of the signal wavelength, as a function of the cavity length detuning, is smaller when δf is decreased (slope of 1.5 nm/mm for δf = 115 mm instead of 10 nm/mm for δf = 160 mm). This behavior is consistent with the analysis carried out in [7] where it was shown that the smaller is δf, the smaller is variation δθ of the incidence angle on the diffraction grating when the cavity length is detuned (see Fig. 9).

 

Fig. 12 Wavelength tuning with cavity length variation (a) and wavelength tuning with mirror M1 angle variation (b), for two configurations: δf = 115 mm (red circles) and δf = 160 mm (black squares). Output coupler M4 is translated to detune the cavity length. We observe a clear variation of the cavity length influence on wavelength due to the variation of the induced deflection angle (see Fig. 9). Grating B is used here.

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As expected from Eq. (4), Fig. 12(b) shows that parameter δf also affects the slope of the OPO wavelength tuning when the deflection angle of mirror M1 is changed. Indeed, a larger δf value leads to a higher correction term due to beam path adaptation and thus a higher tuning slope (slope of 3.3 nm/mrad for δf = 160 mm instead of 3 nm/mm for δf = 115 mm).

In addition to that, reducing δf reduces the beam waist size in the focused arm of the cavity, which increases the beam divergence and the incident beam size w on the diffraction grating. According to Eq. (2), this leads to a better selectivity of the spectral filter. Such a behavior is indeed confirmed by Fig. 13 that shows two typical signal spectra for the two configurations previously studied, and the corresponding beam profiles.

 

Fig. 13 Signal spectrum and output beam profile for the two previous configurations. The FWHM is around 0.7 nm for the larger δf (bigger waist radius and lower divergence of the beam in the focused arm of the cavity) and around 0.3 nm for the smaller δf (smaller waist radius and larger divergence of the beam in the focused arm of the cavity). The scale is the same for profiles (a) and (b), 1 tick = 1 mm.

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Moreover, to choose the best configuration we also have to consider the influence of parameter δf on the OPO oscillation threshold. For that purpose, Fig. 14 shows the oscillation thresholds for the different tested configurations. In our case, we obtained a minimum oscillation threshold for δf ≃ 130 mm which corresponds to the optimal matching of the signal and pump beam waists. For larger values of δf the signal waist is too large whereas it is too small for smaller values. The waist mismatch between pump and signal beams also favors the oscillation of higher order spatial modes in the cavity and is not desirable. This is why we chose the δf = 130 mm configuration, which is optimal, in our case, to perform the measurements with QPM grating C presented in red in Fig. 4(a) and (b).

 

Fig. 14 Pump thresholds with grating B and a 90 % output coupler, for the different tested values of δf.

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Designing a SPOPO with an intracavity diffraction grating thus requires to chose the best trade-off to have in the same time a low oscillation threshold, related with beam size matching between pump and signal, and a high tolerance to cavity length detuning taking into account the beam path adaptation effect detailed in Appendix A.

Acknowledgments

This work has been supported by Triangle de la physique (2011-028T-SAFIR) and “Laboratoire d’Excellence Physics Atom Light Matter”–LabEx PALM (SYCLOP and SORA) part of ANR Investissements d’Avenir (ANR-10-LABX-0039).

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