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Abstract
A concept to flexibly adjust the spectral bandwidth of the output pulses of a fiber optical parametric oscillator is presented. By adjusting the chirp of the pump pulses appropriate to the chirp of the resonant pulses, the energy of the output pulses can be transferred into a user-defined spectral bandwidth. For this concept of optical parametric chirped pulse oscillation, we present numerical simulations of a parametric oscillator, which is able to convert pump pulses with a spectral bandwidth of 3.3 nm into output pulses with an adjustable spectral bandwidth between 9 and 0.05 nm. Combined with a wavelength tunability between 1200 and 1300 nm and pulse energies of up to 100 nJ, the concept should allow to adapt a single all-fiber parametric oscillator to a variety of applications, e.g., in multimodal nonlinear microscopy.
© 2017 Optical Society of America
1. Introduction
Ultrashort pulsed lasers based on rare-earth doped fibers are very convenient devices for laser applications due to their robustness, compact foot print and cost-efficiency [1]. In order to extend the wavelength range of such laser systems, fiber optical parametric oscillators (FOPO), which are based on four-wave mixing (FWM) in a photonic-crystal fiber (PCF), are often the preferred choice [2]. With a previously shown wavelength tunability of up to 500 nm [3], FOPOs are attractive for several applications in, e.g., multiphoton-fluorescence imaging [4], coherent Raman scattering spectroscopy [5,6], sensing [7], and optical coherence tomography [8]. Thereby, the center wavelength of the generated pulses is typically tuned via the wavelength or repetition rate of the pump pulses in order to enable a fiber-integrated and thus alignment-free operation [9]. Most recently, we have presented an electronically tunable FOPO [10], which was based on a gain-switched pump laser diode in combination with the technique of dispersion-tuning [11]. The wavelength of the output pulses of this FOPO could be tuned between 1130 and 1310 nm without altering the resonator, but by simply matching the repetition rate of the pump laser pulses to the repetition rate of the desired specific wavelength component of the strongly chirped resonant pulses. In contrast to this fiber-integrated technique for wavelength tuning, no solution has been presented to flexibly adjust the output spectral bandwidth of a FOPO without comprising the FOPO’s fiber-integrability. A possible adjustment of the output bandwidth via a change of the bandwidth of the pump pulses [12] is usually connected to a cumbersome reoptimization of the pump pulse generation and amplification, and an adjustment via a spectral filter or dispersion management in the resonator [6] is likewise difficult to realize in a fiber-based and wavelength-tunable manner. Thus, as no convenient control parameters are available to flexibly adjust the spectral bandwidth of the output pulses, the versatility of a FOPO seems to be limited to a certain range of applications.
In this contribution we propose and numerically verify a concept, which allows to flexibly adjust the output spectral bandwidth of a FOPO almost independent of the spectral bandwidth of the pump pulses. Based on adjusting the chirp of the pump pulses relative to the chirp of the resonant pulses, the concept enables to transfer the energy of the output pulses into a user-defined spectral bandwidth. This possibility to adjust the spectral bandwidth of wavelength-tunable pulses paves the way to a very versatile light source, which will, e.g., be attractive for pump probe experiments [13] or for the combination of contrary nonlinear imaging modalities, which require different pulse parameters [14]. Related to the interaction of two chirped pulses in a parametric oscillator, we will refer to this concept as optical parametric chirped pulse oscillation (OPCPO). In contrast to optical parametric chirped pulse amplification (OPCPA) [15], in which one seed pulse is chirped to reduce its peak power and keep its spectral bandwidth constant during the parametric amplification process, in OPCPO two mixing pulses are precisely chirped in order to reorganize the spectral distribution of a third generated pulse. Therewith, OPCPO allows for instance the generation of narrowband output pulses from broadband pump pulses. This spectral reorganization can be compared to a spectral focusing, applied in coherent anti-Stokes Raman scattering spectroscopy, in which two broadband pulses are specifically chirped in order to arrange a well defined energy difference between these pulses for the excitation of a spectrally narrow vibrational resonance [16,17]. Further studies about pulse chirping as a convenient control parameter in nonlinear mixing processes can additionally be found in neighboring fields [18,19].
After a conceptual description of OPCPO in section 2, we will exemplify the potential of OPCPO in section 3 by numerically modeling a FOPO, which can be tuned in the spectral bandwidth of its output pulses by two orders of magnitude. Therewith, output pulses with a bandwidth-limited duration as short as a few hundred femtoseconds or up to tens of picoseconds can be generated with a single setup by applying only variable group velocity dispersion (GVD) to the pump pulses. In section 4, we emphasize how the concept of OPCPO is compatible with the wavelength tunability of a FOPO, such that a fixed output spectral bandwidth can be retained while tuning the output wavelength without the need to re-adjust the chirp of the pump pulses.
2. Optical parametric chirped pulse oscillation
In Fig. 1 an outline of the FOPO is shown, which was investigated for the exemplification of OPCPO. First, the FOPO comprised a piece of highly nonlinear PCF, in which the pump pulses with center frequency ν0,p were converted via degenerate FWM into spectrally upshifted signal pulses with center frequency ν0,s, as well as into spectrally downshifted idler pulses with center frequency ν0,i. As discussed in reference [20] efficient FWM occurs, if energy is conserved (2ν0,p = ν0,i + ν0,s) and if the phase mismatch between the three pulses nearly vanishes:
with P0 being the pump peak power, γ the nonlinear coefficient of the fiber, and β(ν0,p), β(ν0,s) and β(ν0,i) the propagation constants of the pump, signal and idler pulses, respectively. The resulting gain experienced by the signal and idler pulses is defined by with Ω = ν0,p − ν0,s = ν0,i − ν0,p denoting the spectral difference between the pump, signal and idler pulses. As can be seen from Eq. (1) and Eq. (2), the problem of phase matching can be solved by an appropriate choice of the pump peak power and the dispersion of the PCF. Specifically, pumping a PCF near its zero-dispersion wavelength results in a phase-matched, spectrally broad gain bandwidth [10] without the need of an additional temperature control or pump wavelength detuning [21,22]. The spectrum of the signal pulses generated by spontaneous FWM in the first round trip of an oscillation in the FOPO resembled this broad gain curve nearly independent of the chirp of the pump pulses.
Fig. 1 Schematic setup of a dispersion-tuned FOPO. WDM: wavelength-division multiplexer, PCF: photonic crystal fiber, SMF: single-mode fiber.
Second, the FOPO encompassed a single-mode fiber (SMF) to feed back and temporally stretch the signal pulses by GVD as a means to select the resonant spectral component: considering a long duration of the chirped signal pulses compared to the duration of the pump pulses, only a narrow spectral part of the stretched signal pulses was temporally overlapping with the successive pump pulses and was therewith amplified, meaning that the initial spectrally broad gain bandwidth was narrowed down to an effective gain bandwidth. In order to explain the formation of the output idler pulses, Fig. 2(a) illustrates the signal, pump and idler pulses, interacting in the FWM process during one single pass through the PCF, in a spectrogram (spectral distribution versus time). The pump pulses (green color) exhibit no chirp, i.e., the pump pulses are represented by a vertical ellipse. The resonant signal pulses (blue color), on the other hand, are represented by a tilted ellipse, indicating a significant chirp, accumulated due to GVD in the SMF. In order to highlight the chirp of the signal pulses, the duration of the signal pulses is exaggerated in the illustration. By the interaction of the pump and signal pulses in the FWM process, the output idler pulses (red color) are generated with a center frequency ν0,i, given by the difference of the center frequencies of the pump (ν0,p) and signal pulses (ν0,s):
Fig. 2 Illustration of the spectral distributions of the resonant signal (blue), pump (green) and output idler (red) pulses, interacting in a FWM process. The distribution of each pulse is normalized to the maximum spectral power of the pulse. The illustrations do not resemble numerical results, but should give an idea of the principal functionality of OPCPO. (a) In case of unchirped pump pulses, the spectral bandwidth ∆νi of the idler pulses is given by the combination of the pump and overlapped signal spectrum. (b) Oppositely chirped signal and pump pulses generate idler pulses with a broad spectral bandwidth. (c) Pump and signal pulses with chirp parameters in the ratio of 1:2 generate idler pulses with a narrow spectral bandwidth.
The spectral bandwidth of the idler pulses is thereby formed and set fixed by each frequency component of the pump pulses mixing with each temporally overlapping frequency component of the signal pulses. However, this constraint can be bypassed by adjusting the chirp of the pump pulses: figure 2(b) shows the case of pump pulses with the same spectral bandwidth as in Fig. 2(a), but with a negative chirp. The instantaneous frequencies νj(t) of both the linearly chirped signal (index s) and the pump pulses (index p) can be described by νj(t) = ν0,j + bj · t, with the center frequency ν0,j, and the chirp parameter bj = ∆νj/∆tj determined by the bandwidth ∆νj (≷ 0) and temporal duration ∆tj (> 0) of the respective pulses. A positive (negative) bj corresponds to positively (negatively) chirped pulses. With this definition, the electric field of a pulse with envelope Aj is given by Ej(t) = Aj exp(i2πνj(t)·t) = Aj exp(i2πν0,j·t +i2πbj·t2) [23]. When considering chirped pulses, Eq. (3) can be written in terms of instantaneous frequencies: νi(t) = 2νp(t) − νs(t), meaning that at each instant of time t the instantaneous frequency of the output idler pulses is directly given by the difference of the instantaneous frequencies of the pump and signal pulses. Therewith, the instantaneous frequency νi(t) of the output idler pulses in Fig. 2(b) reads:
Thus, FWM of pump and signal pulses with oppositely signed chirp parameters results in a chirp enhancement (bi = 2bp − bs) and therewith in idler pulses with a spectral bandwidth wider than in the case of unchirped pump pulses (Fig. 2(a)).
Equation (4) furthermore states, that equally signed chirp parameters with 0 < bp < bs in contrast result in a chirp reduction, and that the special case of bp = 1/2 bs (Fig. 2(c)) even results in a chirp cancellation (bi = 0) and, thus, in idler pulses, which are spectrally narrower than the pump pulses.
The comparison of Figs. 2(b) and 2(c) clearly highlights the chirp of the pump pulses as a control parameter, which should allow to adjust the idler spectral bandwidth simply via an appropriate dispersion management of the pump pulses. Nevertheless, the illustrations in Fig. 2 only visualize FWM during one single pass through the FOPO and do not include all linear and nonlinear effects contributing to the pulse dynamics. We identified self-phase modulation (SPM) in the PCF and SMF, distorting the chirp of the pump and signal pulses, as an antagonist of the illustrated concept. However, as will be presented in the next section, the impact of SPM can be minimized by an appropriate choice of SMF and feedback efficiency in order to enable an OPCPO. Furthermore, we identified the strength of the FWM gain changing with the idler center wavelength to affect OPCPO operation and will consider its impact in section 4.
3. Optical parametric chirped pulse oscillator with adaptive output bandwidth
In order to verify the concept of OPCPO, we simulated the pulse dynamics of a FOPO by means of a numerical model, which was based on the generalized scalar nonlinear Schrödinger equation (GNLSE), including higher-order dispersion, Raman scattering, self-steepening, and quantum noise [24], and which was previously proven to accurately represent nonlinear pulse propagation in fibers [25,26]. A simulation of an experimentally realized FOPO pumped with unchirped pump pulses [10] revealed a very good agreement between the numerical model and the experiment within the error margins of the experimental parameters. The FOPO within this publication, which was in accordance with the scheme in Fig. 1, comprised 10 cm of PCF (modeled to represent the PCF SC-5.0-1040 from NKT Photonics with a ZDW at 1040 nm) and 10 m of SMF (modeled to represent the fiber LMA-15 from NKT Photonics), with the latter one exhibiting a large effective mode diameter of 12.8 µm in order to reduce nonlinear effects (see appendix for specific fiber parameters). The Gaussian-shaped pump pulses were chosen to have a constant spectral full width at half maximum (FWHM) of 3.3 nm (2 nm half-width at 1/e intensity point), a center wavelength of 1040 nm and a constant peak power of 5 kW. During each round trip, the spectral content above 1000 nm (i.e. pump and idler pulses) was coupled out of the resonator behind the PCF. The spectral content below 1000 nm was fed into the SMF with a low coupling efficiency of 0.5 % and behind the SMF back into the PCF with a coupling efficiency of 80 %. The coupling efficiency into the SMF was specifically chosen to 0.5 % because this coupling efficiency resulted in an appropriate compromise between a high output pulse energy and a wide wavelength tuning range on the one side and a low impact of SPM on the other side, as will be shown throughout this publication. A higher coupling efficiency resulted in significant temporal and spectral distortions of the signal as well as the idler pulses due to SPM in the SMF. In case of a coupling efficiency above 4 % no steady state of the FOPO operation within the numerical simulation was reached due to interfering nonlinearity.
In order to highlight the impact of the chirp of the pump pulses, Fig. 3(a) shows the spectral FWHM of the output idler pulses in steady state of the FOPO as a function of the duration of the pump pulses (0 to 150 ps, i.e, 0 to 800 nJ pulse energy) times the sign of the chirp of the pump pulses. The idler pulses were centered around a wavelength of 1260 nm, which coincided with the maximum of the FWM gain. Based on the evolution of the spectral bandwidth, the diagram is divided into 4 color-coded segments. In the yellow and red shaded areas, the OPCPO operation was strongly influenced by SPM, due to the relatively short pump pulse duration below 20 ps in this regime, which resulted in an increased impact of SPM rendering FWM out as the predominant nonlinear effect in the PCF. Simulations without feedback (i.e. only spontaneous FWM occurred) showed that in this regime the spectral bandwidth of the pump pulses was altered by SPM by more than 30 %. In this way, SPM contributed to an excessive decrease, respectively increase of the idler bandwidth for negatively or positively chirped pump pulses, resulting in the vertical shear between the curves in the two parts of the yellow shaded area. For pump pulse durations below 3 ps (red shaded area), the impact of SPM altered the pulse dynamics so massively, that no steady state of the FOPO operation within the numerical simulation was reached.
Fig. 3 (a) Bandwidth (FWHM) of the output idler pulses as a function of the duration of the pump pulses with a bandwidth of 3.3 nm (FWHM). The simulated data points are connected by the solid lines to guide the eye. The x-axis shows the temporal duration times the sign of the chirp of the pump pulses. Corresponding spectrograms of the signal and pump pulses in front of the PCF and the generated idler pulses after the PCF are shown in (b), (c), (d) for negatively chirped pump pulses with a duration of 150 ps, and in in (e), (f), (g) for positively chirped pump pulses with a duration of 150 ps.
The blue shaded area highlights a regime of pump pulses with a negative chirp and durations above 20 ps, which interacted by FWM with the positively chirped signal pulses. Because the pump and signal pulses exhibited contrary chirp parameters, idler pulses with a broad spectral bandwidth of up to 9.1 nm (1.72 THz) were generated, in accordance with the conception in Fig. 2(b). In general, the idler bandwidth increased with increasing pump pulse duration in this regime, as the temporal overlap of the pump and signal pulses increased with increasing pump pulse duration. Figures. 3(b) and 3(c) show the spectrograms of the pump and signal pulses, respectively, in front of the PCF for the case of a pump pulse duration of 150 ps. The resulting spectrogram of the generated idler pulses behind the PCF is shown in Fig. 3(d), indicating negatively chirped pulses with a broad spectral FWHM of 9.1 nm (1.72 THz), a duration of 70 ps and a pulse energy of 88 nJ (conversion efficiency of 22 % into signal and idler pulses). The generation of such a high pulse energy in a fiber is only possible by avoiding interfering nonlinearity via the utilization of long pump pulse durations above 100 ps and is thus a beneficial side effect of the OPCPO concept. Accordingly, after a temporal compression of the output idler pulses with a spectral bandwidth of 9.1 nm (1.72 THz), the pulses should exhibit a peak power above 190 kW with a duration of 427 fs. As will be shown in the next section, such a temporal compression could simply be accomplished by applying only positive GVD, e.g., via a normal dispersive fiber, a block of normal dispersive material or a grating-based pulse compressor. The green shaded area highlights the regime of pump and signal pulses with equally signed chirp parameters and pump pulse durations above 20 ps. In case of a pump pulse duration of 150 ps (corresponding spectrograms in Figs. 3(e)–3(g)), the pump pulses exhibited a chirp parameter of ∆νp/∆tp = 0.92 THz/150 ps = 0.0061 THz/ps, while the signal pulses exhibited a chirp parameter of 0.92 THz/72 ps = 0.0128 THz/ps. These chirp parameters with a ratio of about 1 to 2 did really zero out in the FWM process, resulting in an idler pulse with a low spectral bandwidth of 0.05 nm (0.01 THz), a duration of 72 ps and a pulse energy of 88 nJ.
The apparent saturation of the depicted curve towards long pump pulse durations (for positive and negative chirps), which seems inconsistent with the concept, is due to the form of presentation: although the pump pulse duration ∆tp is incrementing equidistantly along the x axis, the change of the chirp parameter bp = ∆νp/∆tp of the pump pulses is ceasing related to the fixed pump bandwidth of 3.3 nm (0.92 THz), which results in an obvious saturation of the idler bandwidth.
In summary, despite the action of SPM, the chirp of the pump pulses can be used to alter the bandwidth of the output idler pulses in a defined way. Spectral bandwidths adjustable between 9.1 and 0.05 nm (1.72 and 0.01 THz) at a center wavelength of 1260 nm, corresponding to bandwidth-limited output pulse durations between 427 fs and 47 ps, were reached only by dispersion management of the pump pulses. Therewith, the concept of OPCPO does not only enable a novel flexibility in spectral bandwidth, but additionally the generation of output spectra wider (+40%) or narrower (−44%) than shown with the standard approach using unchirped pump pulses [3,4]. A broader output pulse bandwidth (~ 2.3 THz) has only been accomplished by means of a FOPO resonator with specifically engineered dispersion parameters and by the incorporation of an additional Erbium-doped fiber amplifier directly into the FOPO resonator [27].
4. Tunability of the output pulse wavelength
In order to combine OPCPO with the wavelength tunability of a FOPO, the change of the strength of the FWM gain with the idler center wavelength can be counteracted via an appropriate choice of pump power and feedback efficiency. Simulations were conducted as a function of the resonant wavelength, while the pump pulse duration was kept constant at 150 ps with a positive, respectively negative chirp for the generation of narrow- or broadband pulses.
4.1. Broadband output pulses
Figure 4(a) shows the evolution of the spectral bandwidth (FWHM, blue circles) of the broadband output idler pulses as a function of their center wavelength, as well as the FWM gain curve. Corresponding to the gain curve, the center wavelength of the idler pulses could be tuned between 1200 and 1300 nm with the spectral bandwidth exhibiting a maximum of 1.73 THz (9.2 nm) at 1257 nm. The signal pulses (not shown), which could additionally be coupled out of the resonator with an outcoupling degree of 99.5 % (at a required feedback efficiency of 0.5 %), were simultaneously tuned between 917 and 866 nm. The decrease of the idler bandwidth to about 0.41 THz towards the boundaries of the tuning bandwidth can be explained by the decreasing gain, analogous to the effect of gain narrowing: the Gaussian temporal intensity profile of the pump pulses in combination with the chirped signal pulses leads to an effectively reduced gain bandwidth, as only those spectral components are amplified, which are temporally overlapping with the temporally central, intense part of the pump pulses. When the FWM gain decreases as a function of the idler wavelength, while the resonator losses are kept constant, the resulting effective gain bandwidth decreases. However, we were able to verify within our numerical experiment, that this functional wavelength-dependence of the effective gain bandwidth can be balanced out by gain flattening [28], in order to retain a fixed idler bandwidth when tuning the idler center wavelength without the need to re-adjust the chirp of the pump pulses. Especially an adjustment of the pump peak power and/or the feedback efficiency with the idler center wavelength allows to keep the effective gain bandwidth constant in a simple and fiber-compatible manner. As an example, Figs. 5(a) and 5(b) show, how the idler bandwidth could be adjusted via the pump peak power for idler center wavelengths of 1210 and 1300 nm, respectively. As marked by the red-plotted spectra in Fig. 5 and by the red circles in Fig. 4(a), a spectral bandwidth of 1.73 THz, equal to the maximum spectral bandwidth at an idler center wavelength of 1257 nm, was reached by increasing the pump peak power from 5 to about 6 kW for an idler center wavelength of 1210 nm, and to 5.8 kW for an idler center wavelength of 1300 nm. In this way, the idler pulse bandwidth could be leveled, e.g., to the dashed lines in Fig. 4(a), independent of the idler center wavelength within the tuning range. The apparent change of the spectral profile with the pump peak power did not impair the possibility of a temporal compression of the idler pulses only via positive GVD (see Fig. 4(b)). These opportunities to simply accomplish gain flattening will allow to chirp the pump pulses by adjustment-free means, e.g., by chirped fiber Bragg gratings (CFBG).
Fig. 4 (a) Spectral bandwidth (FWHM, blue circles) of the output idler pulses and FWM gain (green line) as a function of the idler center wavelength. The chirp of the pump pulses was optimized and kept constant for the generation of idler pulses with a large bandwidth of 1.72 THz (9.1 nm) at a center wavelength of 1260 nm. The black arrows and red circles exemplify, how the spectral bandwidth can be increased by increasing the pump power as depicted in detail in Fig. 5. (b) Potential bandwidth-limited durations (dark-red circles) of the idler pulses and the minimal durations (blue crosses) reachable by applying only GVD to the idler pulses. The black arrows and red symbols exemplify, how the idler pulse duration can be decreased by increasing the pump power. The green diamonds show the idler pulse energy.
Fig. 5 Evolution of the idler spectrum as a function of the pump peak power for idler center wavelengths of (a) 1210 nm and (b) 1300 nm; in (a) the pump peak power was incremented from 5.25 to 7 kW in steps of 0.25 kW and in (b) from 5.2 to 6.0 kW in steps of 0.1 kW. The spectra drawn in red exhibited a FWHM bandwidth of 1.73 THz (9.2 nm). The individual spectra are shifted vertically against each other for better visibility; the chirp and the duration of 150 ps of the pump pulses was kept fixed.
The pulse energy of the broadband idler pulses is shown in Fig. 4(b) (green diamonds) as a function of their center wavelength. The maximum of 102 nJ (max. conversion efficiency of 25.5 %) at a center wavelength of 1243 nm was not co-localized with the maximum of the gain curve at 1260 nm (green curve in Fig. 4(a)), as the depletion of the pump pulses resulted in a change of the phase mismatch between the mixing pulses in the FWM process along the PCF and therewith in a shift of the gain maximum to shorter wavelengths [20,29].
Furthermore, the possibility of an adjustment-free temporal compression of the broadband idler pulses was investigated. The spectral phase of these pulses was predominated by negative GVD, because the positive chirp of the signal pulses was inversely transferred onto the broadband idler pulses during the FWM process (compare Figs. 3(b)–3(d)). Corresponding to the spectral bandwidth plotted in Fig. 4(a), Fig. 4(b) shows the potential bandwidth-limited durations (dark-red circles) of the idler pulses and the minimal pulse durations (blue crosses), reachable by a compression of the idler pulses, e.g., via a Martinez compressor [30]. For the pulse compression a GVD of β2 = 3.177 ps2 at a wavelength of 1260 nm was assumed. Although this dispersion value was kept fixed when tuning the idler center wavelength, high compression efficiencies between 82 and 99 % were reached, which enabled almost bandwidth-limited output idler pulse durations between 873 and 429 fs. The variance of 444 fs was due to the change of the spectral bandwidth with the idler center wavelength and can in case be minimized via the above mentioned gain-flattening. Corresponding to the idler bandwidths (red symbols) in Fig. 4(a), the red crosses in Fig. 4(b) show the decreased compressed durations of 426 fs at 1210 nm (compression efficiency of 97% with β2 = 3.04 ps2) and 465 fs at 1300 nm (compression efficiency of 89% with β2 = 3.11 ps2), which were reached by the mentioned increase of pump peak power and an adjustment of the applied dispersion. In case of a grating-based Martinez compressor [30], the required adjustment of the dispersion could be accomplished by translating the grating (1200 lines per mm) by less than 8 mm.
4.2. Narrowband output pulses
Figure 6 shows the evolution of the spectral bandwidth (FWHM, blue circles) of the narrowband idler pulses as a function of their center wavelength, and the idler pulse energy (green crosses), which did not change compared to the energy of the broadband output pulses. The idler bandwidth increased up to 0.03 THz towards the edges of the tuning bandwidth, but stayed otherwise remarkably flat between 0.01 and 0.014 THz (0.05 and 0.07 nm) in the tuning range between 1220 and 1280 nm. The increase of the spectral bandwidth towards the edges of the tuning range was due to the change of the effective gain bandwidth as already discussed for the case of broadband pulses. When the effective gain bandwidth decreased, the bandwidth of the signal pulses decreased, such that the chirp ratio was turned away from the optimal value of 1:2, which resulted in spectrally broader idler pulses. According to the gain curve, one would expect an even stronger change of the idler bandwidth, especially in the range between 1230 and 1260 nm. However, we were able to verify, that in this spectral range the gain narrowing effect was partially compensated by SPM acting on the signal pulses due to the high pulse energy in this range (green crosses). If the feedback efficiency of the FOPO was set different from 0.5 %, which resulted in a different impact of SPM in the SMF, a stronger change of the idler bandwidth with the idler center wavelength was observed. In case that the increase of the idler bandwidth towards the edges of the tuning bandwidth should not be tolerable, a gain flattening can be applied, e.g., for an idler center wavelength of 1295 nm a spectral bandwidth of 0.01 THz was reached with an increased coupling efficiency of 2.1% into the SMF.
Fig. 6 Spectral bandwidth (FWHM, blue circles) and pulse energy (green crosses) of the idler pulses as a function of the idler center wavelength. The chirp of the pump pulses was optimized for the generation of idler pulses with a narrow bandwidth of 0.01 THz (0.05 nm) at a center wavelength of 1260 nm and kept fixed for the calculated tuning process.
5. Conclusion
We have presented a concept for optical parametric chirped pulse oscillation, which enables to adjust the spectral bandwidth of the output pulses of a fiber optical parametric oscillator by adjusting the chirp of the pump pulses only. The envisaged concept provides a novel degree of flexibility to fiber optical parametric oscillators without compromising their fiber-integrability and should therewith allow to adapt a fiber optical parametric oscillator to a variety of different applications, almost independent of the available bandwidth of the pump pulses.
Based on this concept, we have numerically modeled a FOPO, which is able to convert pump pulses with a spectral bandwidth of 3.3 nm into output pulses with a variable spectral bandwidth ranging continuously between more than 9 and about 0.05 nm (1.72 and 0.01 THz). Narrowband spectra were accomplished with a specific chirp ratio of 1:2 between the pump and signal pulses. Broadband spectra with bandwidths larger than the bandwidth of the pump pulses were accomplished with opposing chirp parameters. A calculated external compression of such broadband pulses yielded a minimal duration as low as 427 fs with a peak power of up to 190 kW. We have shown, that the spectral bandwidth of the output pulses can be retained while tuning the center wavelength of the output pulses between 1200 and 1300 nm without re-adjustments of the pump pulse chirp, but by simply adjusting the pump peak power or the feedback efficiency. Based on this opportunity, stretching the pump pulses could be implemented by alignment-free, fiber-based means, e.g., by exchangeable, switchable or even tunable CFBGs [31], such that an optical parametric chirped pulse oscillator should even allow the fastly alternating application of narrow- and broadband pulses, e.g., in multimodal nonlinear microscopy. The OPCPO concept is thereby not limited to the here modeled length of the SMF of 10 m. As only the ratio between the chirp parameters of the pump and signal pulses defines the bandwidth of the output idler pulses, a change of the length of the SMF can theoretically be compensated by an appropriate change of the pump pulse chirp.
Especially due to the combination of flexibility in spectral bandwidth and tunability in wavelength, our OPCPO concept will push fiber-based light sources to become reliable workhorses, providing highly adaptive pulses.
A. Simulation parameters
The dispersion parameters βn and nonlinear coefficients γ of the SMF and PCF, used for solving the nonlinear Schrödinger equations, are given in table 1.
Table 1. Fiber parameters. All values are given in SI-units: γ in 1/Wm, βn in sn/m.
Funding
Deutsche Forschungsgemeinschaft Open Access Publication Fund of the University of Münster, Cells-in-Motion Cluster of Excellence (EXC 1003 - CiM) flexible fund project FF-2013-09.
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