Issue 
J. Eur. Opt. SocietyRapid Publ.
Volume 20, Number 1, 2024
EOSAM 2023



Article Number  7  
Number of page(s)  5  
DOI  https://doi.org/10.1051/jeos/2024006  
Published online  15 March 2024 
Research Article
μJlevel normaldispersion fiber optical chirpedpulse parametric oscillator
^{1}
CORIA, UMR 6614 CNRS – INSA Rouen – Université de Rouen Normandie, 675 avenue de l’Université, 76801 Saint Etienne du Rouvray, France
^{2}
Photonics Bretagne, 4 rue Louis de Broglie, 22300 Lannion, France
^{*} Corresponding author: thomas.godin@coria.fr
Received:
30
January
2024
Accepted:
16
February
2024
We demonstrate the generation of broadband tunable and synchronized pulses exceeding the microjoule level using the new concept of Fiber Optical Parametric ChirpedPulse Oscillation (FOPCPO). The oscillator is based on a collapsedends photonic crystal fiber pumped in the normal dispersion regime by an ytterbium fiber laser delivering highlychirped pulses. The experimental results are compared with the results of numerical simulations and highlight that the feedback ratio appears as a key parameter for optimizing the system’s efficiency and dynamics.
Key words: Parametric Sources / Nonlinear Fibers / Fiber laser / Ultrafast laser / Parametric oscillator / FOPCPO
© The Author(s), published by EDP Sciences, 2024
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
1 Introduction
Optical parametric amplifiers and oscillators delivering ultrashort pulses are a wellestablished technology that has enabled considerable progresses in many research and industrial applications [1]. MultimJ energies and few cycles pulse durations are now reached using solidstate optical parametric sources but their complexity, cost, and alignment sensitivity hinder their use outside the laboratory environment. In the last years, significant advances have been made in their fiberbased counterparts which rely on Degenerate FourWave Mixing (DFWM – thirdorder nonlinearity of silica). Nonlinear wavelength conversion of ultrashort pulses has then been obtained with a variety of fiber systems. In particular, using the concept of Fiber Optical Parametric ChirpedPulse Amplification (FOPCPA) [2–4] has allowed to overcome the saturation of the nonlinear process and the μJ level has been reached, by either using complex optical fiber designs or using Raman gain assistance. However, such systems operate in the anomalous group velocity dispersion of the fiber which restricts the parametric sidebands near the pump wavelength. FOPCPA pumped in the normal dispersion regime and delivering subpicosecond pulse with wide wavelength separations have been reported but are still limited in terms of tunability as they require a seed source [5–7]. A way to circumvent this limitation is to use a resonant fiber optical parametric oscillator (FOPO) where the dispersion map can be tailored. High energy levels and ultrashort pulses – along with excellent signaltonoise ratios – have then been obtained in FOPOs combining DFWM in Photonic Crystal Fibers (PCF) with pumping in the normal dispersion regime [8, 9]. Further energy scaling is however quite limited due to high peak powers and subsequent nonlinearities. To overcome this limitation, a natural idea is then to combine FOPCPAs capabilities in terms of energy scaling by using chirped pulses with FOPO’s flexibility and wavelength tunability. Such a concept – termed FOPCPO – was first investigated numerically and showed significant potential for bandwidth control of parametric waves [10]. We then demonstrated experimentally the feasibility of this concept by generating broadlytunable highly chirped pulses with energies exceeding 200 nJ in such a FOPCPO [11]. By combining highlychirped pump pulses with a collapsedends photonic crystal fiber, we now confirm this idea and report on the generation of broadband signal and idler waves exceeding the μJ level at MHzrepetition rates from a FOPCPO pumped in the normal dispersion regime.
2 Experimental setup
The experimental setup is depicted in Figure 1. The pump laser is a commercial ytterbium fiber laser (Active Fiber Systems GmbH), delivering highlychirped pulses of 800 ps at 1032 nm (200 fs transformlimited) with 15 W average power at 1 MHz repetition rate. The pump pulses are injected into the nonlinear fiber through a combination of a dichroic mirror and an aspheric lens (11 mm focal length).
Figure 1 Experimental setup. ISO: Isolator, CESUP5125: Collapsedends SUP5125 fiber, DM: Dichroic mirror, PBS: Polarization beam splitter, ODL: Optical delay line. 
The nonlinear fiber is an airsilica microstructured 8 cm long SUP5125 (Product line Perfos^{®}) fiber, developed and drawn at Photonics Bretagne facilities. It exhibits a nonlinear coefficient of 15 W^{−1}·m^{−1}, a 5 μm mode field diameter, and a zerodispersion wavelength of 1055 nm. Both ends of the fiber are collapsed in order to mitigate the laser induced damages due to the high peak power coming from the pump laser (up to 20 kW). The collapsed region is tailored to avoid beam diffraction on the fiber tip, resulting in an excellent output beam quality, as shown in Figure 2c on the beam profile taken at directly at the output of the fiber. As the phasematching diagram depicted in Figure 2a suggest, such a fiber should generates a signal wave in the 800 nm band, along with an idler wave in the 1500 nm band.
Figure 2 a) Phase matching diagram of the SUP5125 fiber. b) Collapsedend of the SUP5125 fiber. c) Beam profile at the output of the SUP5125 fiber 
The cavity is closed with a 200 m PM780 spool, so the signal wave propagates in the normal dispersion regime allalong the intracavity components, and match the repetition rate of the pump laser. In order to finely adjust the roundtrip delay of the cavity, we also implemented an Optical Delay Line (ODL), which allows us to tune the emission wavelength using a dispersive filtering effect [12]. This indeed gives the possibility to overlap different spectral components of the pump pulses and the signal pulses, hence changing the phasematching condition of the parametric process. The feedback ratio is controlled via an adjustable optical circulator before the ODL, and the polarization of the signal is controlled in the cavity in order to improve the parametric conversion and to mitigate any polarizationdependent phase mismatching in the nonlinear fiber.
3 Numerical simulations
3.1 Numerical FOPCPO model
In order to predict the FOPCPO performances, we developed a script for a typical cavity as depicted in Figure 3. The script propagates the complex optical envelop through the different fibers and components, and reuse a fraction of the output field into the next cavity roundtrip. Numerical simulations along the fiber segments were performed using an inhouse Generalized Nonlinear Schrödinger Equation (GNLSE) solver, with a RungeKutta 4 in Interaction Picture (RK4IP) method [13]. The main idea is to solve the following GNLSE:$$\begin{array}{c}\frac{\partial A\left(z,T\right)}{\partial z}=\underset{\widehat{L}}{\underbrace{\frac{\alpha \left(\omega \right)}{2}A\left(z,T\right)+\sum _{k\ge 2}\mathrm{}\frac{{i}^{k+1}}{k!}{\beta}_{k}\frac{{\partial}^{k}A\left(z,T\right)}{\partial {T}^{k}}}}+\dots \\ ...\underset{\widehat{N}}{\underbrace{\mathrm{i\gamma}\left(1+{\tau}_{\mathrm{shock}}\frac{\partial}{\partial T}\right)\times \left(A(z,T){\int}_{\infty}^{\infty}\mathrm{}R\left({T}^{\mathrm{\prime}}\right)\leftA\right(z,T{T}^{\mathrm{\prime}}){}^{2}\mathrm{d}{T}^{\mathrm{\prime}}\right)}}\end{array}$$(1)
Figure 3 Outline of the cavity simulation. 
By applying the following transformation,$${A}_{I}(z,T)={e}^{(z{z}^{\mathrm{\prime}})\widehat{L}}A(z,T)$$(2)it is possible to solve equation (1) using standard RungeKutta 4 algorithm. The fibers parameters (i.e. the Taylor coefficients β _{ k } and the nonlinear coefficient γ) were determined using an inhouse developed fiber mode solver based on a finitedifference method, while the material loss α are approximated using the fused silica losses model presented in [14]. The pump pulses are modeled using:$$A\left(t\right)=\sqrt{{P}_{0}}{e}^{\frac{1}{2}{\left(\frac{t\tau}{{t}_{0}}\right)}^{2}}{e}^{i\left(\frac{{C}_{2}}{2}\right(\omega {\omega}_{0}{)}^{2})i{\omega}_{0}t}$$(3)where C _{2} is the 2nd order phase coefficient that control the quadratic phase (i.e. the chirp) of the pulse [15]. In order to initiate the parametric fluorescence in the nonlinear fiber, the pump pulses are injected with a noise of one photon per spectral mode.
The numerical parameters used in the simulations are detailed in Table 1.
Simulation parameters of the FOPCPO.
The pump pulses are defined as linearly chirped gaussian pulse, with a Fourierlimited duration of 200 fs, energies of 10 μJ, and a 2nd order phase coefficient of 5.8 · 10^{−23} s^{2}, leading to a pulse duration of 800 ps at 1032 nm.
3.2 Numerical results
Simulations were performed for 100 roundtrips in the cavity. As depicted in Figure 4, we extracted narrowband signal pulses of 1.2 μJ centered at 785 nm, along with broadband idler pulses of 650 nJ, exceeding our previous numerical predictions [11]. The FOPCPO is selfstarting from noise and is stable after roughly 60 roundtrips. As predicted by Brinkmann et al. [10], all the pulses are linearly and positively chirped, allowing compression using standard gratingbased compressors. By defining the compressor dispersion coefficients using the model given in [16], it is possible to compress the pulses below 950 fs for the idler and 3 ps for the signal. The feedback ratio given by the losses of the coupler was carefully adjusted in order to allow a stable operation with coherent output pulses.
Figure 4 Numerical results. a) Output spectrum of the FOPCPO. b) Output spectrogram. c) Signal wave buildup. d) Autocorrelation traces of the dechirped signal and idler pulses. 
4 Experimental results
The FOPCPO output measured at 10 μJ pump energy are summarized in Figure 5a. Using timedispersion tuning, the FOPCPO output pulses can be widely tuned over the gain bandwidth with a tunability of 30 nm for the signal (from 780 to 810 nm), and 70 nm for the idler (from 1440 to 1510 nm), with a maximum gain obtained at 800 nm and 1450 nm and a pulse duration of 260 ps has been measured using a fast detection system (25 GHz photodiode and 33 GHz oscilloscope). The output signal energy scales linearly with the pump energy and reaches 1.4 μJ, see Figure 5b.
Figure 5 a) FOPCPO tunability for a pumping energy of 10 μJ. Power is normalized to the highest value obtained at 800 nm (see inset). b) FOPCPO energy scaling. Inset: Output spectrum at nominal power. 
It is worth noting that both idler and signal pulses are relatively broadband (from 5 to 10 nm), which is a major difference with the numerical simulations as narrower signal pulses were expected. The physical reason behind this discrepancy is still being investigated. However, it appears that several regimes are actually accessible by adjusting the feedback ratio. We identified two specific regimes, one with a low feedback ratio that appears slightly narrower than the one with a high feedback ratio, as depicted in Figure 6. In addition, the highest energies were obtained with the highfeedback regime.
Figure 6 Impact of the feedback ratio on the output signal spectrum. 
As discussed by Zhang et al. [17], it appears that the output spectrum broadens as the feedback ratio increases, before reaching an unstable regime for a critical feedback ratio. Although this phenomenon is easy to detect in numerical simulations, it is no mean feat experimentally. Because of the spectrum analyser integration time, one should track the FOPCPO output dynamic pulse by pulse, by means for example of dispersive Fourier transform, however it needs a spool of normal dispersion optical fiber at the wavelength of interest. Pulse compression is an ongoing work, as it can be a challenging task for oscillators that exhibits several dynamic behaviors.
5 Outline and prospects
We demonstrate that using highly chirped pulses in combination with PCF ends functionalization to mitigate fiber tips damage, energy scaling of the FOPCPO scheme beyond the microjoule barrier is possible. This opens the path for the development of widely tunable parametric oscillators delivering high energy levels at highrepetition rates. These features would make FOPCPOs prominent sources for stimulated coherent Raman spectroscopy (SRS) [18], or multiphoton imaging [19]. Further experiments should now be done on pulse compression and the impact of the feedback ratio on the dynamics of the pulses. However, the chirp properties of such a system could also be used without compression in a spectral focusing based SRS setup [20, 21].
Funding
The authors acknowledge the support of the Conseil Régional de Normandie and the European Regional Development Fund, the Région Bretagne, the Département des Côtes d’Armor, LannionTrégor Communauté (LTC) and the Agence Nationale de la Recherche et de la Technologie (ANRT).
Conflict of Interest
The authors declare no conflict of interests
Data availability statement
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Author contribution statement
All authors made significant contributions to this work.
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All Tables
All Figures
Figure 1 Experimental setup. ISO: Isolator, CESUP5125: Collapsedends SUP5125 fiber, DM: Dichroic mirror, PBS: Polarization beam splitter, ODL: Optical delay line. 

In the text 
Figure 2 a) Phase matching diagram of the SUP5125 fiber. b) Collapsedend of the SUP5125 fiber. c) Beam profile at the output of the SUP5125 fiber 

In the text 
Figure 3 Outline of the cavity simulation. 

In the text 
Figure 4 Numerical results. a) Output spectrum of the FOPCPO. b) Output spectrogram. c) Signal wave buildup. d) Autocorrelation traces of the dechirped signal and idler pulses. 

In the text 
Figure 5 a) FOPCPO tunability for a pumping energy of 10 μJ. Power is normalized to the highest value obtained at 800 nm (see inset). b) FOPCPO energy scaling. Inset: Output spectrum at nominal power. 

In the text 
Figure 6 Impact of the feedback ratio on the output signal spectrum. 

In the text 
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