Abstract

Optical parametric oscillators (OPOs) are uniquely versatile—albeit complex—platforms for the generation of tunable coherent light in difficult-to-access spectral regions. A synchronously pumped ${\chi ^{(2)}}$ femtosecond OPO producing sub-100-fs pulses, by means of optical soliton formation in a single-mode fiber-feedback cavity, is presented for the first time. This approach removes the requirement for active stabilization and bulk dispersion compensation elements associated with traditional OPOs, while reducing the physical footprint by a factor of 3. Transform-limited pulses of 80–120 fs are generated for both normal and anomalous dispersion, while a new type of spectral sideband formation is observed and studied. Experimental results are supported by detailed simulations based on nonlinear pulse propagation theory, which serve to enrich the understanding of femtosecond pulse evolution in OPOs perturbed by strong Kerr nonlinearity. The OPO provides a unique platform for the study of intracavity soliton phenomena across a wide wavelength range.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. INTRODUCTION

Nonlinear frequency conversion techniques based on ${\chi ^{(2)}}$ processes are extensively exploited in photonics to generate coherent radiation in spectral regions inaccessible to conventional lasers [1,2]. Synchronously pumped optical parametric oscillators (OPOs) based on nonlinear crystals, such as MgO-doped periodically poled ${{\rm LiNbO}_3}$ (MgO:PPLN), ${{\rm BiB}_3}{{\rm O}_6}$, and the new generation of nonoxide materials such as ${{\rm CdSiP}_2}$, orientation-patterned gallium arsenide (OP-GaAs) and phosphide (OP-GaP), have enabled complete wavelength generation from the ultraviolet to ${\sim}{12}\;\unicode{x00B5}{\rm m}$ in the mid-infrared (mid-IR), providing picosecond and femtosecond pulses at MHz repetition rates with kilowatt-level peak power [38]. Such ultrafast OPOs are now firmly established as the gold-standard laser light sources for applications requiring broadly tunable ultrashort pulses at high repetition rates, including molecular fingerprint spectroscopy, coherent anti-Stokes Raman scattering (CARS), stimulated Raman scattering (SRS), and high-resolution multiphoton microscopy [911]. Furthermore, the intrinsic phase-locked nature of degenerate synchronously pumped femtosecond OPOs has enabled them to become a driving force in the development of mid-IR frequency combs for applications in dual-comb spectroscopy [1214]. From a quantum standpoint, OPOs play host to a rich variety of nonlinear effects, which have been exploited to develop coherent networks capable of advanced computation [15,16]. Pulse dynamics in such devices are a complex interplay of ${\chi ^{(2)}}$ nonlinearity, dispersion, and Kerr nonlinearity, and remain an intensely studied field of research [1719].

Despite outstanding performance characteristics, stable long-term operation of femtosecond OPOs requires careful control of intracavity dispersion and cavity length, which is generally achieved by deploying prism pairs together with piezoelectric actuators and feedback electronics, resulting in a relatively costly and complex system design. With understandable reluctance to invest in such an elaborate scheme, single-pass supercontinuum generation has been explored as a more simple and cost-effective alternative for wavelength generation in the near-IR to mid-IR [20,21]. However, supercontinuum sources also require specialist fiber designs, offer much lower spectral brightness, and suffer from intrinsically higher background noise [22]. Another strategy is the generation of frequency-shifted solitons in a single pass through a highly nonlinear fiber. However, since the available tunability is dependent on the input peak power, powerful pump sources at $\gt 1.5\; \unicode{x00B5}{\rm m}$ are required to match the tuning range of an OPO [23,24]. In many cases, particularly at high repetition rates, the only source able to satisfy this condition is an OPO itself [25]. Since ultrafast OPOs reached technological maturity in the late 1990s, efforts to reduce their complexity and cost have been hampered by fundamental limitations imposed by long free-space cavities and synchronization tolerances of ${\sim}{100}\;\unicode{x00B5}{\rm m}$. One promising template for synchronously pumped OPOs is a fiber-feedback resonator, which has a dramatically reduced footprint, as most of the cavity length is confined inside a passive optical fiber [26]. Moreover, compared to a free-space resonator, increased intracavity group velocity dispersion (GVD) leads to remarkable insensitivity of the output power and wavelength to cavity length fluctuations, negating the requirement for active stabilization. This cavity configuration is especially effective when using the combination of a powerful pump laser and a relatively long nonlinear crystal, yielding a large parametric gain, and requiring only a small feedback signal to sustain oscillation [2729]. As pump pulse durations decrease toward ${\sim}{100}\;{\rm fs}$, the use of long nonlinear crystals becomes increasingly precluded by enhanced temporal walk-off, and nonlinear as well as dispersive effects become more dominant, leading to spectral and temporal broadening. Period-doubling and chaotic pulsing may also be observed as the circulating peak power increases [30]. Subsequently, the fiber-feedback concept has not been demonstrated at such a short time scale in a tunable OPO, with sub-100-fs pulses only achieved by precise dispersion control in a 1.03 µm pumped degenerate doubly resonant oscillator [31].

On the other hand, self-similar pulse evolution, in the form of solitons, dissipative solitons, and similaritons, is a well-established method of ultrashort pulse generation in mode-locked lasers. Early fiber lasers operating near ${\sim}{1.5}\;\unicode{x00B5}{\rm m}$ exploited the anomalous dispersion of standard silica fibers at this wavelength to generate solitons with durations as short as ${\sim}{200}\;{\rm fs}$, although maximum pulse energies were limited to ${\sim}{100}\;{\rm pJ}$ as a direct result of the soliton area theorem [32,33]. In addition, when solitonic pulses encounter periodic perturbations from gain and output coupling elements, energy is shed in the form of dispersive waves, which copropagate in the cavity with a different group velocity and lead to the dissipation of power into Kelly sidebands at phase-matched wavelengths [34,35]. Contemporary devices circumvent these issues by generating linearly chirped pulses in normal dispersion fibers, with a grating compressor used to restore transform-limited pulses outside the cavity [36]. Conversely, bulk lasers and synchronously pumped OPOs often deploy intracavity elements, such as prism pairs, to dechirp the pulse on each round trip. Soliton formation has been observed in such OPOs near the zero-dispersion wavelength (ZDW), but competition between synchronization of the dispersive and solitonic spectral components results in significant instability [37]. Due to the wavelength dependence of crystal dispersion, the prism pair needs to be continually translated as the wavelength is tuned, in order to maintain chirp-free pulses.

Here, we report a synchronously pumped fiber-feedback OPO providing widely tunable ${\lt} 100 \;{\rm fs}$ pulses at 80 MHz repetition rate in the near-IR. Pumping with a femtosecond Ti:sapphire laser at 803 nm, up to 110 mW of output power is generated with a total tuning range of 1051–1700 nm, which can be rapidly covered by a combination of cavity length variation and changing the crystal quasi-phased-matched (QPM) grating period. In the anomalous dispersion regime ($\lambda \gt {1310}\;{\rm nm}$), we observe transform-limited pulses, power scaling, and hysteresis associated with soliton formation, whereas in the normal dispersion regime ($\lambda \lt {1310}\;{\rm nm}$), chirped pulses of 80–100 fs are accompanied by Kelly-like sideband spectral features. A theoretical model based on the generalized nonlinear Schrödinger equation (GNLSE) is used to simulate the pulse dynamics, and provides excellent agreement with experimental results. To the best of our knowledge, this work represents the first report of soliton formation in a fiber-feedback OPO, and the first observation of sideband formation in a synchronously pumped OPO. Compared to traditional femtosecond OPOs, this system offers improved stability and small footprint, as well as reduced complexity and cost, making it an attractive source for coherent spectroscopy and microscopy. The combination of high parametric gain with a passive waveguide element also offers a unique platform to study soliton behavior, in presence of both ${\chi ^{(2)}}$ and ${\chi ^{(3)}}$ nonlinear processes, paving the way for future advances in tunable ultrafast sources.

2. RESULTS

A. Experimental Setup and Tuning

The experimental setup for the soliton fiber-feedback OPO is shown in Fig. 1. In order to obtain the highest performance of the fiber-feedback OPO, we first undertook optimization of coupling efficiency into the fiber retroreflector by using an input beam from an external near-IR OPO, and measuring the power reflected from a pellicle beam splitter. We found that ${\sim}{96}\%$ of the reflected beam remained in the same linear polarization as the incident beam, implying that use of polarization maintaining fiber would not substantially improve the device efficiency. The maximum aggregate in/outcoupling efficiency from the retroreflector was measured to be ${\sim}{70}\%$. Wavelength tuning of the OPO was accomplished by variation of the QPM grating period, and adjustment of the cavity length. Optical spectra were recorded using a spectrum analyzer with resolution of ${\sim}{0.7}\;{\rm nm}$, with the data shown in Figs. 2(a) and 2(b). For each spectrum, the central signal wavelength was extracted using a center-of-mass averaging algorithm. White data points in Fig. 2(a) represent the signal wavelengths generated at selected QPM grating periods, superimposed on the parametric gain map for a 1-mm-long MgO:PPLN crystal, calculated using the Sellmeier equations [38]. For each grating period, the broad signal gain bandwidth enables ${\sim}{100}\;{\rm nm}$ of additional tuning by varying the cavity length. In Fig. 2(b), the data points for all grating periods are plotted against the relative change in cavity length. Here, it becomes evident that dispersion shifts from the normal to anomalous regime (positive to negative) at a signal wavelength of $\lambda _s {\sim}\;{1310}\;{\rm nm}$, consistent with the expected ZDW of single-mode silica fibers. The choice of shorter or longer grating periods determines OPO operation in the anomalous and normal dispersion regime, respectively. Close to the ZDW, the signal spectra are instantaneously broad and unstable, characteristic of synchronously pumped OPOs with negligible GVD [39]. The total tuning range was recorded to be 1051–1700 nm, which included a transition through degeneracy at ${\lambda _{s}}\sim\;{1606}\;{\rm nm}$ (${\lambda _p} = {803}\;{\rm nm}$), and the group delay dispersion (GDD) was calculated to vary from ${\rm GDD} = {3.46} \times {{10}^4}\;{{\rm fs}^2}$ at 1051 nm to ${\rm GDD} = - {6.69} \times {{10}^4}\;{{\rm fs}^2}$ at 1700 nm (see Supplement 1 for details of dispersion calculation). The operating behavior and output characteristics in each dispersion regime are discussed separately in the following sections.

 

Fig. 1. Schematic of the experimental setup for the Ti:sapphire-pumped soliton fiber-feedback OPO. HWPs, half-wave plates; PBS, polarizing beam splitter; L, lenses; M, mirrors; OC, output coupler; SMF-28, single-mode fiber retroreflector.

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Fig. 2. (a) Measured signal data points (white), superimposed on the parametric gain bandwidth for 1-mm-long MgO:PPLN crystal with QPM grating periods varying over $\Lambda = {19.0 - 22}\;\unicode{x00B5}{\rm m}$, calculated using the Sellmeier equations in [38]. (b) Cavity delay tuning of the OPO, with measured signal data points plotted against relative change in cavity length, normalized to the shortest possible cavity for operation; inset, calculated net cavity GDD across the tuning range.

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B. Anomalous Dispersion

The anomalous dispersion regime refers to all wavelengths above ${\lambda _{s}}\sim\;{1310}\;{\rm nm}$, and wavelength tuning in this region is achieved using QPM grating of $\Lambda \lt {20.3}\;\unicode{x00B5}{\rm m}$. Here, the net negative dispersion acts to oppose nonlinear effects, primarily self-phase modulation (SPM) and Raman scattering, which are associated with ultrashort pulse propagation in optical fibers, and are also in the nonlinear crystal in the presence of high intracavity signal intensities. Figure 3(a) shows that, across this region, spectra exhibit a symmetric profile. With the 30% output coupler in place and the grating period set to $\Lambda = {20.2}\;\unicode{x00B5}{\rm m}$, the output power steadily increases with cavity delay, from 40 mW at 1330 nm to a maximum of 110 mW at 1460 nm. Beyond this wavelength, oscillation abruptly ceases, and can only be achieved at ${\lambda _s} \gt {1460}\;{\rm nm}$ if the output coupling is reduced, and the grating period is decreased to $\Lambda = {20.0}\;\unicode{x00B5}{\rm m}$. Interestingly, once the OPO ceases operation, it is observed that in order to recover the maximum power at 1460 nm, the cavity length must first be positively detuned to the mirror position equivalent to ${\lambda _{s}}\sim {1350}\;{\rm nm}$ to restart oscillation, and then negatively detuned to its original position, thus indicating that the cavity length tuning displays hysteresis behavior. It is also found that while the oscillation threshold is ${\sim}{700}\;{\rm mW}$ at 1330 nm, it increases to ${\sim}{900}\;{\rm mW}$ at 1460 nm. Using a 5% output coupler, the OPO could be freely tuned across 1460–1700 nm using the $\Lambda = {20.0}\;\unicode{x00B5}{\rm m}$ grating period, delivering output powers of 10–40 mW. At 1606 nm, corresponding to degeneracy, the spectrum and power were observed to rapidly fluctuate, as the OPO alternated between singly and doubly resonant oscillation. Beyond degeneracy, singly resonant operation is resumed, albeit with the OPO cavity providing resonance at the idler wavelength. Due to the limited range of the spectrum analyzer, no idler spectra could be recorded beyond 1650 nm, but the signal at ${\lambda _s} \lt {1606}\;{\rm nm}$ could be measured. Using interferometric autocorrelation, signal pulses were measured to have typical duration of ${\sim}{106}\;{\rm fs}$ (assuming a ${sech}^{2}$ profile), as shown in Fig. 3(b), with the corresponding spectrum presented in Fig. 3(c). The spectral full-width at half-maximum (FWHM) of $\Delta \lambda \sim {21}\;{\rm nm}$ yields a time-bandwidth product of $\Delta \nu \Delta \tau \sim {0.316}$, very close to the transform limit. Across the range of 1330–1460 nm, repeated measurements confirmed 95–110 fs pulses with pedestal-free autocorrelation traces, indicating minimal chirp. Figure 3(d) and the inset show the excellent passive power and wavelength stability, recorded over periods of 30 min and 20 min, respectively. During this time, power fluctuations were measured to be 0.26% rms, and central wavelength fluctuations to be 0.016% rms, in strong agreement with previous reports [26,29]. For clarity, the central wavelength and FWHM bandwidth stability are also presented separately in Fig. 3(e).

 

Fig. 3. (a) Measured signal spectra and output average power across the anomalous dispersion regime. (b) Typical interferometric autocorrelation at 1460 nm. (c) Simultaneous signal spectrum. (d) Power stability measurement at 1455 nm over a period of 30 min; inset, spectral stability measurement over a period of 20 min. (e) Central wavelength and FWHM bandwidth stability over the same time period.

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C. Normal Dispersion

When operating in the normal dispersion regime (${\lambda _s} \lt {1310}\;{\rm nm}$), interaction between positive GVD and nonlinear effects, primarily SPM, act to enhance spectral and temporal broadening effects experienced by the intracavity pulses. A measure of the relative importance of dispersion and nonlinearity across the operating bandwidth is given by [40]

$${N^2} = {L_d}/{L_n} = \gamma (\omega ){P_0}T_0^2/|{{\beta _2}(\omega )} |,$$
where ${L_d} = T_0^2/| {{\beta _2}(\omega)} |$ is the dispersion length and ${L_n} = 1/\gamma (\omega){P_0}$ is the nonlinear length, with $\gamma (\omega) = {\omega _0}{n_2}/{\textit{cA}_{\rm eff}}$ the nonlinear coefficient, where ${n_2} = {2.6} \times {{10}^{- 20}}\;{{\rm m}^2}/{\rm W}$ is the nonlinear refractive index of single-mode fiber, ${A_{\rm eff}} = {75}\;\unicode{x00B5}{\rm m}^2$ is the effective mode area, ${P_0}$ is the peak power, ${T_0}$ is related to the pulse FWHM by $\Delta {\tau _{\rm FWHM}} = {1.763}{T_0}$, and ${\beta _2}(\omega)$ is the GVD. Using these values, together with an average power in the fiber of 100 mW, $\Delta {\tau _{\rm FWHM}} = {100}\;{\rm fs}$, and ${\beta _2}(\omega)$ determined from Fig. 2(b), we obtain a ratio ${L_d}/{L_n}$ varying from ${\sim}{8}$ at 1050 nm to ${\sim}{40}$ at 1270 nm. This suggests that the cavity is heavily dominated by SPM, in particular when operating close to the ZDW, where spectral bandwidths of up to 60 nm (FWHM) are measured. By tuning to shorter wavelengths, corresponding to increasing ${\beta _2}$, we observe the spectrum evolving through distinct phases, shown in Fig. 4(a). Also plotted is the extracted power across the tuning range with the 30% output coupler, which remains in the range of 60–70 mW over 1150–1300 nm, before trailing off with increasing dispersion. Beginning at ${\lambda _{s}}\sim {1230}\;{\rm nm}$, and going toward shorter wavelengths, well-defined spectral sidebands emerge in the wings of the pulse. These resemble Kelly sidebands often produced in mode-locked lasers operating in the anomalous dispersion regime, in that their wavelength offset is proportional to ${m^{0.5}}$, where $m$ is the order of the sideband. Finally, at the shortest wavelengths, the main spectral lobe acquires steep square sides and deep modulation across the central part. This is consistent with the phenomenon of optical wave breaking, where normal dispersion causes the redshifted spectral components of a chirped pulse to overtake the slower traveling blueshifted components, leading to the formation of an oscillatory interference structure [41]. A typical interferometric autocorrelation at 1215 nm and its corresponding spectrum are shown in Figs. 4(b) and 4(c), respectively, revealing a pulse duration of 89 fs, shorter than that of the pump. However, the time-bandwidth product of $\Delta \nu \Delta \tau \sim {0.38}$ is 1.2 times the ${sech}^{2}$ transform limit, confirming the slightly chirped nature of the pulses. A typical power scaling measurement, plotted in Fig. 4(d), shows an oscillation threshold of ${\sim}{800}\;{\rm mW}$ and a slope efficiency of $\eta \sim {13}\%$, with no evidence of saturation, indicating that the use of stronger output coupling could further increase output power. This threshold of 800 mW is slightly higher than the 700 mW measured in the anomalous dispersion regime. We attribute the small increase in threshold in the normal dispersion operation to the chirp on signal pulses, which leads to a reduced pump–signal interaction. The signal pulses in the normal dispersion regime are significantly broadened after exiting the fiber, and so their peak power is lower when returned through the crystal. Only the central part is amplified, leading to increased OPO threshold.
 

Fig. 4. (a) Measured signal spectra and output average power across the normal dispersion regime. (b) Typical interferometric autocorrelation at 1215 nm. (c) Simultaneous signal spectrum. (d) Power scaling measurement at 1220 nm; inset, signal beam profile. (e) Spectral stability measurement at 1171 nm over a period of 20 min.

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The excellent ${{\rm TEM}_{00}}$ spatial quality exhibited by the output signal beam with a circularity of $\gt 90 \%$, recorded using a pyroelectric camera, is displayed in the inset of Fig. 4(d). Finally, the spectral stability measurement at 1171 nm, shown in Fig. 4(e), reveals similarly low fluctuation of the central wavelength, and indicates that the sidebands remain invariant in position.

3. SIMULATIONS

Certain behavior, including spectral sidebands in the presence of normal dispersion, and cavity delay hysteresis in the anomalous dispersion regime, are not characteristic of standard femtosecond OPOs and hint at alternative pulse dynamics. Since intracavity powers are many times higher than the soliton energy, it is expected that soliton effects are heavily influential. In order to study pulse evolution inside the OPO, we performed numerical simulations considering the interplay between dispersion, nonlinearity, and parametric gain.

The simulation was first performed for an initial signal wavelength of ${\lambda _s} = {1350}\;{\rm nm}$ (anomalous dispersion regime) and a grating period of $\Lambda = {20.2}\;\unicode{x00B5}{\rm m}$. It was observed that once the fiber-coupled power surpassed a critical value, the spectrum broadened significantly, and a fundamental soliton was emitted on the trailing edge of the pulse. The critical power was found to be that which exceeds the value for an ${N^2} = {L_d}/{L_n} = {4}$ at the given wavelength. The soliton is redshifted to a longer wavelength, ${\lambda _s^\prime}$, and propagates in the fiber at a slower group velocity relative to the “cold-cavity” wavelength, ${\lambda _s}$, subsequently falling out of synchronization with the pump. If the cavity length is slightly shortened, by increasing the offset parameter, $\Delta {T_s}$, from zero, the pump pulse can resume synchronization to this soliton at ${\lambda _s^\prime}$. Steady state is reached when $\Delta {T_s}$ is such that ${\lambda _s^\prime}$ and the intracavity power remain constant on consecutive round trips. The magnitude of $\Delta {T_s}$ required for a steady-state solution was found by initiating the simulation with $\Delta {T_s}$ as a free parameter, with the resultant temporal and spectral evolution profiles shown in Figs. 5(a) and 5(b), respectively. The inset of Fig. 5(a) shows a detailed view of the steady-state temporal evolution, resulting in a soliton pulse duration of 95 fs estimated at the output coupler, well matched with the experimental measurements presented in Fig. 3(b), indicating stable soliton formation, owing to the nearly identical pulse durations of the pump and the soliton [42]. When the intracavity power surpasses the soliton threshold after 10 round trips, $\Delta {T_s}$ adjusts to match the new round trip time, converging on a value of $\Delta {T_{s}}\sim\;{120}\;{\rm fs}$, which corresponds to a wavelength shift from 1350 nm to 1364 nm. Repeating the simulation at various wavelengths across ${\lambda _{s}}\sim {1300 {-} 1380}\;{\rm nm}$ yields values of $\Delta {T_s} = {118 {-} 125}\;{\rm fs}$. The final field exhibits a ${sech}^{2}$ shape in both the temporal and spectral domain. A temporal delay of $\Delta {T_s} = {120}$ fs indicates an offset of $\Delta z \sim{36}\;\unicode{x00B5}{\rm m}$ from the cold-cavity length, or a translation of ${{\rm M}_3}$ by 18 µm. A schematic of the pulse evolution is shown in Fig. 5(c). As the cavity is further shortened, the signal wavelength increases in accordance with increasing anomalous dispersion, suggesting that the offset from the cold-cavity wavelength remains constant. Since ${\beta _2}$ increases almost linearly with wavelength, the power contained within a fundamental soliton also increases linearly with wavelength. Furthermore, the soliton redshift and resultant temporal delay are known to be approximately proportional to the fiber-coupled power, for given dispersion and nonlinearity [40]. In order to determine the expected intracavity power as a function of wavelength, simulations were performed using initial pulses corresponding to intracavity peak powers between 0 and 40 kW for wavelengths across 1300–1500 nm, and the steady-state spectral and temporal shifts identified. The resultant soliton central wavelength, ${\lambda _s^\prime}$, and physical cavity length offset, $\Delta z$, are plotted in Fig. 5(d). The plot shows that, for a fixed intracavity power, the soliton temporal delay and the required $\Delta z$ rapidly decrease toward zero as we approach longer wavelengths. Alternatively, for a fixed $\Delta z$, the intracavity power must increase in order to maintain synchronization. The dots represent the experimental limits of tuning and the positions at which 2 kW intervals are crossed for a constant $\Delta z \sim {36}\;\unicode{x00B5}{\rm m}$. Using the known losses for the output coupler and the fiber input, these data points are compared to the experimentally measured peak power, as shown in Fig. 5(e). Strong quantitative agreement is seen at shorter wavelengths, including the increase in power beyond ${\lambda _{s}}\sim {1380}\;{\rm nm}$. The discrepancy at longer wavelengths could be explained by an increase in output coupler transmission, or reduced fiber attenuation. Also displayed is the experimentally observed hysteresis loop, with the blue shaded area representing wavelengths at which oscillation could be recovered. From Fig. 2(a), it is seen that for a grating period of $\Lambda = {20.2}\;\unicode{x00B5}{\rm m}$, peak parametric efficiency occurs for wavelengths close to ${\lambda _s} = {1350}\;{\rm nm}$ and falls to ${\sim}{0.6}$ at ${\lambda _s} = {1460}\;{\rm nm}$. Therefore, the loss of oscillation beyond ${\lambda _s} = {1460}\;{\rm nm}$ is attributed to insufficient gain to sustain the required intracavity power for synchronization at $\Delta z = {36}\;\unicode{x00B5}{\rm m}$. Once interrupted, the lower parametric efficiency and higher soliton threshold prevent the signal pulse train from recovering its previous power without first tuning the cavity length to synchronize to a wavelength in the blue zone. It is to be noted that oscillation is achieved without hysteresis across 1400–1700 nm for $\Lambda = {20.0}\;\unicode{x00B5}{\rm m}$, albeit with significantly reduced powers, suggesting that the offset from the cold-cavity length is negligible when oscillation is achieved on this grating period.

 

Fig. 5. (a) Simulation of a soliton pulse evolving from noise at an initial wavelength of ${\lambda _s} = {1350}\;{\rm nm}$, with $\Delta {T_s}$ free to adapt to the changing group velocity. Inset, close-up of the final two round trips in steady state, showing a pulse duration of 95 fs. (b) Corresponding spectral evolution showing the soliton self-frequency shift after 10 round trips. (c) Schematic of stable soliton formation: (1) pulse builds up from noise, (2) pulse undergoes self-frequency shift (arrow indicates deceleration), (3) cavity is delayed to resume synchronization, (4) synchronization at ${\lambda _s^\prime}$ with a temporal offset, $\Delta {T_s}$, from the cold-cavity round trip time. (d) Cavity length offset, $\Delta z$, from the cold-cavity length as a function of the shifted soliton wavelength, ${\lambda _s^\prime}$, as a function of intracavity peak power between 0 and 32 kW. Yellow dots represent points at which the 2 kW contours are crossed for $\Delta z = {36}\;\unicode{x00B5}{\rm m}$. (e) Experimentally measured intracavity peak power vs wavelength when tuning by cavity delay for a grating period of $\Lambda = {20.2}\;\unicode{x00B5}{\rm m}$, compared to the values taken from (d). Arrows represent observed power hysteresis loop; blue zones are wavelengths at which oscillation is recovered.

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Close to degeneracy, the cavity optical coatings ensure that both the signal and idler are coupled into the fiber, although only the signal wave is synchronized to the cavity length. Simultaneously viewing both signal and idler spectra on a spectrum analyzer revealed deep modulations in the idler spectrum, with the modulation period decreasing as the signal and idler separate from degeneracy. Two examples of this are shown in Fig. 6(a), recorded beyond the degeneracy point, where the idler now corresponds to the shorter-wavelength pulse. This is a result of group velocity mismatch between the signal and idler, leading to a temporal delay between the two pulses upon exiting the fiber. The Fourier transform of two closely spaced coherent pulses contains an interference term proportional to ${\cos}({2}\pi \nu t)$, where the modulation frequency $\nu$ is related to the pulse separation, ${\tau _{\rm del}}$, by $\nu = {1/}{\tau _{\rm del}}$. Such modulations are often observed in mode-locked fiber lasers supporting soliton molecules [43,44]. For two identical pulses with a well-defined phase relationship, the modulation depth is expected to be 100%. However, the position of the spectrum analyser (after the OC) allowed the detection of both a single-pass idler and a double-pass fiber-coupled contribution.

 

Fig. 6. (a) Idler spectra recorded at ${\lambda _i}\;\sim\;{1527}\;{\rm nm}$ to degeneracy at ${\sim}{1606}\;{\rm nm}$, showing the increase in modulation period, $\Delta \lambda$. The signal spectrum also becomes visible as degeneracy is approached. (b) Comparison of experimentally determined, $\Delta \lambda$, and relative signal/idler group delay, with the theoretical predictions.

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By measuring the modulation period, $\Delta \lambda$, we were able to calculate the group delay between the two pulses and compare to that predicted by the dispersion relation of the fiber. In the absence of a full Sellmeier equation for SMF-28, we calculated the effective group index as a function of wavelength using data from the Fig. 2(b) inset, and considering the known fiber length of 86 cm, a cavity round trip time of 12.4998 ns, and quoted values of group index, ${n_g}({1310}\;{\rm nm}) = {1.4676}$ and ${n_g}({1550}\;{\rm nm}) = {1.4682}$. The experimental data for group delay and the modulation period as a function of wavelength is plotted against the theoretical prediction in Fig. 6(b), where the additional delay due to ${{ L}_2}$, the output coupler, and three crystal passes was also considered. Dispersion causes $\Delta \lambda$ to vary over the bandwidth of one pulse. So, the average value was extracted from the peak oscillation in the Fourier transform of each spectrum. The signal spectrum was not observed to be modulated, which we attribute to the washing out of fringes by parametric gain. In addition to the spectral interference, two copropagating pulses of different wavelengths are also predicted to induce temporal modulation; however, we were unable to make autocorrelation measurements at such low powers.

Finally, we performed simulations of pulse evolution at wavelengths in the normal dispersion region, with an example at $\lambda \sim {1104}\;{\rm nm}$ shown in Figs. 7(a) and 7(b). Steady state is obtained within ${\sim}{25}$ round trips of the cavity, and spectral sidebands are immediately evident after the first round trip. By comparing the simulated spectrum at the output coupler to an experimentally measured spectrum at the same wavelength, it can be seen in Fig. 7(c) that the main features are accurately reproduced, including the wavelength offset of each sideband and the dip in the center of the main lobe. While the Kelly sidebands are produced by a phase-matched four-wave mixing process between copropagating dispersive radiation and a periodically amplified soliton, here the finite temporal duration of each input pump pulse selectively amplifies certain spectral components of the resonating signal via a similar phase-matching effect [34,35]. Although Kelly sidebands are typically observed while operating in the anomalous dispersion regime, it has been shown that the soliton chirp can lead to spectral sidebands even in the normal dispersion regime [45]. With fiber-coupled peak powers up to 18 kW across the normal dispersion region, the signal experiences nonlinear phase shifts of up to ${20}\pi$ in each round trip, inducing a large chirp, which in turn leads to temporal broadening of the pulse from ${\sim}{100}\; {\rm fs}$ to ${\sim}{500 - 700}\;{\rm fs}$. Since only the central part of the broadened signal pulse experiences gain, the wavelengths contained within the central section of the pulse are selectively amplified.

 

Fig. 7. (a) Simulated temporal and (b) spectral evolution of a femtosecond pulse from noise in the OPO at a central wavelength of 1104 nm, (c) comparison of the steady-state simulated spectrum with an experimentally measured spectrum at the same wavelength, (d) experimentally measured autocorrelation, and (e) simulated autocorrelation at the same wavelength.

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Therefore, the sideband separation is dependent on the pump pulse duration and the accumulated round trip dispersive and nonlinear phase shifts, which both increase at shorter wavelengths. After amplification, the signal pulse resembles a narrow peak superimposed on a weak background of dispersive radiation. Comparison of experimental and simulated autocorrelation traces shown in Figs. 7(d) and 7(e) reveal a similar structure with estimated pulse durations of ${\sim}{77}\;{\rm fs}$ and ${\sim}{85}\;{\rm fs}$, respectively. The slight discrepancy can be attributed to the uncertainty of the experimental pulse shape, for which a ${sech}^{2}$ fit was applied.

4. SUMMARY

We have demonstrated a viable and stable femtosecond laser source in a compact, practical, and simplified design, by exploiting fiber-based soliton formation in a ${\chi ^{(2)}}$ OPO, for the first time, generating tunable near-IR sub-100-fs pulses of up to 110 mW average power at 80 MHz repetition rate. Using rapid tuning methods based on the QPM grating period and OPO cavity length variation, we have achieved spectral coverage across 1051–1700 nm, enabling device characterization in the presence of continually varying dispersion and nonlinearity. In the anomalous dispersion regime, transform-limited ${\sim}{100}\;{\rm fs}$ ${sech}^{2}$ pulses have been generated, while in the normal dispersion regime, chirped pulses of ${\sim}{80}\;{\rm fs}$ were measured, and accompanied by rich spectral features. The use of a readily available single-mode fiber with an integrated mirror has reduced the required optics, enabled a footprint of only ${30} \times {40}\;{\rm cm}$, and led to passive power and wavelength fluctuations better than 0.3% rms and 0.015% rms, respectively. Using a suitable dichroic mirror in place of ${{\rm M}_2}$, mid-IR idler pulses could also be extracted across 1.6–3.4 µm, which could be extended to even longer wavelengths using nonoxide nonlinear crystals such as ${\rm CdSiP}_2$ and OP-GaP. The demonstrated OPO represents an attractive and practical source for tabletop spectroscopy, nonlinear microscopy, and seeding of optical parametric amplifiers, given its high stability together with a compact and simplified design. Compared to a single-pass soliton generation setup, there is also no need for a delay line to compensate for varying pulse delay with wavelength. In principle, the output power can be scaled arbitrarily by using looser crystal focusing, combined with stronger pumping and output coupling to ensure relatively low powers are returned through the fiber. We have performed simulations based on the GNLSE and have successfully validated the experimental observations in both dispersion regimes. Future work will exploit fibers with varying dispersion profiles and higher nonlinearity, in order to further investigate power and hysteresis effects in the soliton regime, and even the possibility of intracavity supercontinuum generation. Moreover, the fiber-feedback femtosecond OPO presented in this work could be reconfigured to study other pulse formation mechanisms including simultons [19]. It is expected that a more rigorous theoretical analysis considering additional effects, such as pump depletion and group velocity mismatch, will yield even closer quantitative agreement with spectral features, and enable analytical expressions for pulse duration and sideband positions to be derived in the normal dispersion regime.

Funding

Ministerio de Ciencia, Innovación y Universidades (nuOPO, TEC2015-68234-R); European Commission (Mid-Tech, H2020-MSCA-ITN-2014); Generalitat de Catalunya (CERCA Programme); Generalitat de Catalunya, Severo Ochoa Programme for Centres of Excellence in RD (SEV-2015-0522-16-1); Fundación Cellex.

Disclosures

The authors declare no conflicts of interest.

 

See Supplement 1 for supporting content.

REFERENCES

1. M. H. Dunn and M. Ebrahim-Zadeh, “Parametric generation of tunable light from continuous-wave to femtosecond pulses,” Science 286, 1513–1517 (1999). [CrossRef]  

2. M. Ebrahim-Zadeh and I. T. Sorokina, Mid-Infrared Coherent Sources and Applications (Springer, 2008).

3. M. Ebrahim-Zadeh, “Efficient ultrafast frequency conversion sources for the visible and ultraviolet based on BiB3O6,” IEEE J. Sel. Top. Quantum Electron. 13, 679–691 (2007). [CrossRef]  

4. C. F. O’Donnell, S. C. Kumar, and M. Ebrahim-Zadeh, “Enhancement of efficiency in femtosecond optical parametric oscillators using group-velocity-matching in long nonlinear crystals,” APL Photon. 4, 050801 (2019). [CrossRef]  

5. N. Leindecker, A. Marandi, R. L. Byer, K. L. Vodopyanov, J. Jiang, I. Hartl, M. Fermann, and P. G. Schunemann, “Octave-spanning ultrafast OPO with 2.6-6.1 µm instantaneous bandwidth pumped by femtosecond Tm-fiber laser,” Opt. Express 20, 7046–7053 (2012). [CrossRef]  

6. S. C. Kumar, P. G. Schunemann, K. T. Zawilski, and M. Ebrahim-Zadeh, “Advances in ultrafast optical parametric sources for the mid-infrared based on CdSiP2,” J. Opt. Soc. Am. B 33, D44–D56 (2016). [CrossRef]  

7. L. Maidment, P. G. Schunemann, and D. T. Reid, “Molecular fingerprint-region spectroscopy from 5 to 12 µm using an orientation-patterned gallium phosphide optical parametric oscillator,” Opt. Lett. 41, 4261–4264 (2016). [CrossRef]  

8. C. F. O’Donnell, S. C. Kumar, P. G. Schunemann, and M. Ebrahim-Zadeh, “Femtosecond optical parametric oscillator continuously tunable across 3.6–8 µm based on orientation-patterned gallium phosphide,” Opt. Lett. 44, 4570–4573 (2019). [CrossRef]  

9. I. Rocha-Mendoza, W. Langbein, P. Watson, and P. Borri, “Differential coherent anti-Stokes Raman scattering microscopy with linearly chirped femtosecond laser pulses,” Opt. Lett. 34, 2258–2260 (2009). [CrossRef]  

10. V. Andresen, S. Alexander, W. M. Heupel, M. Hirschberg, R. M. Hoffman, and P. Friedl, “Infrared multiphoton microscopy: sub-cellular-resolved deep tissue imaging,” Curr. Opin. Biotech. 20, 54–62 (2009). [CrossRef]  

11. J. Herz, V. Siffrin, A. E. Hauser, A. U. Brandt, T. Leuenberger, H. Radbruch, F. Zipp, and R. A. Niesner, “Expanding two-photon intravital microscopy to the infrared by means of optical parametric oscillator,” Biophys. J. 98, 715–723 (2010). [CrossRef]  

12. Y. Kobayashi, K. Torizuka, A. Marandi, R. L. Byer, R. A. McCracken, Z. Zhang, and D. T. Reid, “Femtosecond optical parametric oscillator frequency combs,” J. Opt. 17, 094010 (2015). [CrossRef]  

13. I. Coddington, N. Newbury, and W. Swann, “Dual-comb spectroscopy,” Optica 3, 414–426 (2016). [CrossRef]  

14. Y. Jin, S. M. Cristescu, F. J. M. Harren, and J. Mandon, “Femtosecond optical parametric oscillators toward real-time dual-comb spectroscopy,” Appl. Phys. B 119, 65–74 (2015). [CrossRef]  

15. A. Marandi, Z. Wang, K. Takata, R. L. Byer, and Y. Yamamoto, “Network of time-multiplexed optical parametric oscillators as a coherent Ising machine,” Nat. Photonics 8, 937–942 (2014). [CrossRef]  

16. P. L. McMahon, A. Marandi, Y. Haribara, R. Hamerly, C. Langrock, S. Tamate, T. Inagaki, H. Takesue, S. Utsunomiya, K. Aihara, and R. L. Byer, “A fully programmable 100-spin coherent Ising machine with all-to-all connections,” Science 354, 614–617 (2016). [CrossRef]  

17. M. Conforti, F. Baronio, and C. De Angelis, “Nonlinear envelope equation for broadband optical pulses in quadratic media,” Phys. Rev. A 81, 053841 (2010). [CrossRef]  

18. R. Hamerly, A. Marandi, M. Jankowski, M. M. Fejer, Y. Yamamoto, and H. Mabuchi, “Reduced models and design principles for half-harmonic generation in synchronously pumped optical parametric oscillators,” Phys. Rev. A 94, 063809 (2016). [CrossRef]  

19. M. Jankowski, A. Marandi, C. R. Phillips, R. Hamerly, K. A. Ingold, R. L. Byer, and M. M. Fejer, “Temporal simultons in optical parametric oscillators,” Phys. Rev. Lett. 120, 053904 (2018). [CrossRef]  

20. C. Xu and F. W. Wise, “Recent advances in fibre lasers for nonlinear microscopy,” Nat. Photonics 7, 875–882 (2013). [CrossRef]  

21. C. F. Kaminski, R. S. Watt, A. D. Elder, J. H. Frank, and J. Hult, “Supercontinuum radiation for applications in chemical sensing and microscopy,” Appl. Phys. B 92, 367 (2008). [CrossRef]  

22. S. Lefrancois, D. Fu, G. R. Holtom, L. Kong, W. J. Wadsworth, P. Schneider, R. Herda, A. Zach, X. Sunney Xie, and F. W. Wise, “Fiber four-wave mixing source for coherent anti-Stokes Raman scattering microscopy,” Opt. Lett. 37, 1652–1654 (2012). [CrossRef]  

23. F. M. Mitschke and L. F. Mollenauer, “Discovery of the soliton self-frequency shift,” Opt. Lett. 11, 659–661 (1986). [CrossRef]  

24. Y. Tang, L. G. Wright, K. Charan, T. Wang, C. Xu, and F. W. Wise, “Generation of intense 100 fs solitons tunable from 2 to 4.3 µm in fluoride fiber,” Optica 3, 948–951 (2016). [CrossRef]  

25. T. Cheng, Y. Kanou, K. Asano, D. Deng, M. Liao, M. Matsumoto, T. Misumi, T. Suzuki, and Y. Ohishi, “Soliton self-frequency shift and dispersive wave in a hybrid four-hole AsSe2-As2S5 microstructured optical fiber,” Appl. Phys. Lett. 104, 121911 (2014). [CrossRef]  

26. T. Südmeyer, J. Aus der Au, R. Paschotta, U. Keller, P. G. R. Smith, G. W. Ross, and D. C. Hanna, “Femtosecond fiber-feedback optical parametric oscillator,” Opt. Lett. 26, 304–306 (2001). [CrossRef]  

27. T. Südmeyer, E. Innerhofer, F. Brunner, R. Paschotta, T. Usami, H. Ito, S. Kurimura, K. Kitamura, D. C. Hanna, and U. Keller, “High-power femtosecond fiber-feedback optical parametric oscillator based on periodically poled stoichiometric LiTaO3,” Opt. Lett. 29, 1111–1113 (2004). [CrossRef]  

28. F. Kienle, P. S. Teh, S.-U. Alam, C. B. E. Gawith, D. C. Hanna, D. J. Richardson, and D. P. Shepherd, “Compact, high-pulse-energy, picosecond optical parametric oscillator,” Opt. Lett. 35, 3580–3582 (2010). [CrossRef]  

29. T. Steinle, F. Neubrech, A. Steinmann, X. Yin, and H. Giessen, “Mid-infrared Fourier-transform spectroscopy with a high-brilliance tunable laser source: investigating sample areas down to 5 µm diameter,” Opt. Express 23, 11105–11113 (2015). [CrossRef]  

30. T. Steinle, J. N. Greiner, J. Wrachtrup, H. Giessen, and I. Gerhardt, “Unbiased all-optical random-number generator,” Phys. Rev. X 7, 041050 (2017). [CrossRef]  

31. K. A. Ingold, A. Marandi, M. J. F. Digonnet, and R. L. Byer, “Fiber-feedback optical parametric oscillator for half-harmonic generation of sub-100-fs frequency combs around 2 µm,” Opt. Lett. 40, 4368–4371 (2015). [CrossRef]  

32. L. F. Mollenauer and R. H. Stolen, “The soliton laser,” Opt. Lett. 9, 13–15 (1984). [CrossRef]  

33. I. N. Duling, “All-fiber ring soliton laser mode locked with a nonlinear mirror,” Opt. Lett. 16, 539–541 (1991). [CrossRef]  

34. S. M. J. Kelly, “Characteristic sideband instability of periodically amplified average soliton,” Electron. Lett. 28, 806–807 (1992). [CrossRef]  

35. N. J. Smith, K. J. Blow, and I. Andonovic, “Sideband generation through perturbations to the average soliton model,” J. Lightwave Technol. 10, 1329–1333 (1992). [CrossRef]  

36. F. W. Wise, A. Chong, and W. H. Renninger, “High-energy femtosecond fiber lasers based on pulse propagation at normal dispersion,” Laser Photon. Rev. 2, 58–73 (2008). [CrossRef]  

37. D. T. Reid, J. M. Dudley, M. Ebrahim-Zadeh, and W. Sibbett, “Soliton formation in a femtosecond optical parametric oscillator,” Opt. Lett. 19, 825–827 (1994). [CrossRef]  

38. O. Paul, A. Quosig, T. Bauer, M. Nittmann, J. Bartschke, G. Anstett, and J. A. L’huillier, “Temperature-dependent Sellmeier equation in the MIR for the extraordinary refractive index of 5% MgO doped congruent LiNbO3,” Appl. Phys. B 86, 111–115 (2007). [CrossRef]  

39. T. J. Driscoll, G. M. Gale, and F. Hache, “Ti:sapphire second-harmonic-pumped visible range femtosecond optical parametric oscillator,” Opt. Commun. 110, 638–644 (1994). [CrossRef]  

40. G. P. Agrawal, Nonlinear Fiber Optics (Springer, 2000).

41. W. J. Tomlinson, R. H. Stolen, and A. M. Johnson, “Optical wave breaking of pulses in nonlinear optical fibers,” Opt. Lett. 10, 457–459 (1985). [CrossRef]  

42. P. Jian, W. E. Torruellas, M. Haelterman, S. Trillo, U. Peschel, and F. Lederer, “Solitons of singly resonant optical parametric oscillators,” Opt. Lett. 24, 400–402 (1999). [CrossRef]  

43. P. Grelu and N. Akhmediev, “Dissipative solitons for mode-locked lasers,” Nat. Photonics 6, 84–92 (2012). [CrossRef]  

44. J. Peng and H. Zeng, “Ultrafast fibre lasers: build-up of dissipative optical soliton molecules via diverse soliton interactions,” Laser Photon. Rev. 12, 1870037 (2018). [CrossRef]  

45. L. W. Liou and G. P. Agrawal, “Effect of frequency chirp on soliton spectral sidebands in fiber lasers,” Opt. Lett. 20, 1286–1288 (1995). [CrossRef]  

References

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  • |

  1. M. H. Dunn and M. Ebrahim-Zadeh, “Parametric generation of tunable light from continuous-wave to femtosecond pulses,” Science 286, 1513–1517 (1999).
    [Crossref]
  2. M. Ebrahim-Zadeh and I. T. Sorokina, Mid-Infrared Coherent Sources and Applications (Springer, 2008).
  3. M. Ebrahim-Zadeh, “Efficient ultrafast frequency conversion sources for the visible and ultraviolet based on BiB3O6,” IEEE J. Sel. Top. Quantum Electron. 13, 679–691 (2007).
    [Crossref]
  4. C. F. O’Donnell, S. C. Kumar, and M. Ebrahim-Zadeh, “Enhancement of efficiency in femtosecond optical parametric oscillators using group-velocity-matching in long nonlinear crystals,” APL Photon. 4, 050801 (2019).
    [Crossref]
  5. N. Leindecker, A. Marandi, R. L. Byer, K. L. Vodopyanov, J. Jiang, I. Hartl, M. Fermann, and P. G. Schunemann, “Octave-spanning ultrafast OPO with 2.6-6.1 µm instantaneous bandwidth pumped by femtosecond Tm-fiber laser,” Opt. Express 20, 7046–7053 (2012).
    [Crossref]
  6. S. C. Kumar, P. G. Schunemann, K. T. Zawilski, and M. Ebrahim-Zadeh, “Advances in ultrafast optical parametric sources for the mid-infrared based on CdSiP2,” J. Opt. Soc. Am. B 33, D44–D56 (2016).
    [Crossref]
  7. L. Maidment, P. G. Schunemann, and D. T. Reid, “Molecular fingerprint-region spectroscopy from 5 to 12 µm using an orientation-patterned gallium phosphide optical parametric oscillator,” Opt. Lett. 41, 4261–4264 (2016).
    [Crossref]
  8. C. F. O’Donnell, S. C. Kumar, P. G. Schunemann, and M. Ebrahim-Zadeh, “Femtosecond optical parametric oscillator continuously tunable across 3.6–8 µm based on orientation-patterned gallium phosphide,” Opt. Lett. 44, 4570–4573 (2019).
    [Crossref]
  9. I. Rocha-Mendoza, W. Langbein, P. Watson, and P. Borri, “Differential coherent anti-Stokes Raman scattering microscopy with linearly chirped femtosecond laser pulses,” Opt. Lett. 34, 2258–2260 (2009).
    [Crossref]
  10. V. Andresen, S. Alexander, W. M. Heupel, M. Hirschberg, R. M. Hoffman, and P. Friedl, “Infrared multiphoton microscopy: sub-cellular-resolved deep tissue imaging,” Curr. Opin. Biotech. 20, 54–62 (2009).
    [Crossref]
  11. J. Herz, V. Siffrin, A. E. Hauser, A. U. Brandt, T. Leuenberger, H. Radbruch, F. Zipp, and R. A. Niesner, “Expanding two-photon intravital microscopy to the infrared by means of optical parametric oscillator,” Biophys. J. 98, 715–723 (2010).
    [Crossref]
  12. Y. Kobayashi, K. Torizuka, A. Marandi, R. L. Byer, R. A. McCracken, Z. Zhang, and D. T. Reid, “Femtosecond optical parametric oscillator frequency combs,” J. Opt. 17, 094010 (2015).
    [Crossref]
  13. I. Coddington, N. Newbury, and W. Swann, “Dual-comb spectroscopy,” Optica 3, 414–426 (2016).
    [Crossref]
  14. Y. Jin, S. M. Cristescu, F. J. M. Harren, and J. Mandon, “Femtosecond optical parametric oscillators toward real-time dual-comb spectroscopy,” Appl. Phys. B 119, 65–74 (2015).
    [Crossref]
  15. A. Marandi, Z. Wang, K. Takata, R. L. Byer, and Y. Yamamoto, “Network of time-multiplexed optical parametric oscillators as a coherent Ising machine,” Nat. Photonics 8, 937–942 (2014).
    [Crossref]
  16. P. L. McMahon, A. Marandi, Y. Haribara, R. Hamerly, C. Langrock, S. Tamate, T. Inagaki, H. Takesue, S. Utsunomiya, K. Aihara, and R. L. Byer, “A fully programmable 100-spin coherent Ising machine with all-to-all connections,” Science 354, 614–617 (2016).
    [Crossref]
  17. M. Conforti, F. Baronio, and C. De Angelis, “Nonlinear envelope equation for broadband optical pulses in quadratic media,” Phys. Rev. A 81, 053841 (2010).
    [Crossref]
  18. R. Hamerly, A. Marandi, M. Jankowski, M. M. Fejer, Y. Yamamoto, and H. Mabuchi, “Reduced models and design principles for half-harmonic generation in synchronously pumped optical parametric oscillators,” Phys. Rev. A 94, 063809 (2016).
    [Crossref]
  19. M. Jankowski, A. Marandi, C. R. Phillips, R. Hamerly, K. A. Ingold, R. L. Byer, and M. M. Fejer, “Temporal simultons in optical parametric oscillators,” Phys. Rev. Lett. 120, 053904 (2018).
    [Crossref]
  20. C. Xu and F. W. Wise, “Recent advances in fibre lasers for nonlinear microscopy,” Nat. Photonics 7, 875–882 (2013).
    [Crossref]
  21. C. F. Kaminski, R. S. Watt, A. D. Elder, J. H. Frank, and J. Hult, “Supercontinuum radiation for applications in chemical sensing and microscopy,” Appl. Phys. B 92, 367 (2008).
    [Crossref]
  22. S. Lefrancois, D. Fu, G. R. Holtom, L. Kong, W. J. Wadsworth, P. Schneider, R. Herda, A. Zach, X. Sunney Xie, and F. W. Wise, “Fiber four-wave mixing source for coherent anti-Stokes Raman scattering microscopy,” Opt. Lett. 37, 1652–1654 (2012).
    [Crossref]
  23. F. M. Mitschke and L. F. Mollenauer, “Discovery of the soliton self-frequency shift,” Opt. Lett. 11, 659–661 (1986).
    [Crossref]
  24. Y. Tang, L. G. Wright, K. Charan, T. Wang, C. Xu, and F. W. Wise, “Generation of intense 100 fs solitons tunable from 2 to 4.3 µm in fluoride fiber,” Optica 3, 948–951 (2016).
    [Crossref]
  25. T. Cheng, Y. Kanou, K. Asano, D. Deng, M. Liao, M. Matsumoto, T. Misumi, T. Suzuki, and Y. Ohishi, “Soliton self-frequency shift and dispersive wave in a hybrid four-hole AsSe2-As2S5 microstructured optical fiber,” Appl. Phys. Lett. 104, 121911 (2014).
    [Crossref]
  26. T. Südmeyer, J. Aus der Au, R. Paschotta, U. Keller, P. G. R. Smith, G. W. Ross, and D. C. Hanna, “Femtosecond fiber-feedback optical parametric oscillator,” Opt. Lett. 26, 304–306 (2001).
    [Crossref]
  27. T. Südmeyer, E. Innerhofer, F. Brunner, R. Paschotta, T. Usami, H. Ito, S. Kurimura, K. Kitamura, D. C. Hanna, and U. Keller, “High-power femtosecond fiber-feedback optical parametric oscillator based on periodically poled stoichiometric LiTaO3,” Opt. Lett. 29, 1111–1113 (2004).
    [Crossref]
  28. F. Kienle, P. S. Teh, S.-U. Alam, C. B. E. Gawith, D. C. Hanna, D. J. Richardson, and D. P. Shepherd, “Compact, high-pulse-energy, picosecond optical parametric oscillator,” Opt. Lett. 35, 3580–3582 (2010).
    [Crossref]
  29. T. Steinle, F. Neubrech, A. Steinmann, X. Yin, and H. Giessen, “Mid-infrared Fourier-transform spectroscopy with a high-brilliance tunable laser source: investigating sample areas down to 5 µm diameter,” Opt. Express 23, 11105–11113 (2015).
    [Crossref]
  30. T. Steinle, J. N. Greiner, J. Wrachtrup, H. Giessen, and I. Gerhardt, “Unbiased all-optical random-number generator,” Phys. Rev. X 7, 041050 (2017).
    [Crossref]
  31. K. A. Ingold, A. Marandi, M. J. F. Digonnet, and R. L. Byer, “Fiber-feedback optical parametric oscillator for half-harmonic generation of sub-100-fs frequency combs around 2 µm,” Opt. Lett. 40, 4368–4371 (2015).
    [Crossref]
  32. L. F. Mollenauer and R. H. Stolen, “The soliton laser,” Opt. Lett. 9, 13–15 (1984).
    [Crossref]
  33. I. N. Duling, “All-fiber ring soliton laser mode locked with a nonlinear mirror,” Opt. Lett. 16, 539–541 (1991).
    [Crossref]
  34. S. M. J. Kelly, “Characteristic sideband instability of periodically amplified average soliton,” Electron. Lett. 28, 806–807 (1992).
    [Crossref]
  35. N. J. Smith, K. J. Blow, and I. Andonovic, “Sideband generation through perturbations to the average soliton model,” J. Lightwave Technol. 10, 1329–1333 (1992).
    [Crossref]
  36. F. W. Wise, A. Chong, and W. H. Renninger, “High-energy femtosecond fiber lasers based on pulse propagation at normal dispersion,” Laser Photon. Rev. 2, 58–73 (2008).
    [Crossref]
  37. D. T. Reid, J. M. Dudley, M. Ebrahim-Zadeh, and W. Sibbett, “Soliton formation in a femtosecond optical parametric oscillator,” Opt. Lett. 19, 825–827 (1994).
    [Crossref]
  38. O. Paul, A. Quosig, T. Bauer, M. Nittmann, J. Bartschke, G. Anstett, and J. A. L’huillier, “Temperature-dependent Sellmeier equation in the MIR for the extraordinary refractive index of 5% MgO doped congruent LiNbO3,” Appl. Phys. B 86, 111–115 (2007).
    [Crossref]
  39. T. J. Driscoll, G. M. Gale, and F. Hache, “Ti:sapphire second-harmonic-pumped visible range femtosecond optical parametric oscillator,” Opt. Commun. 110, 638–644 (1994).
    [Crossref]
  40. G. P. Agrawal, Nonlinear Fiber Optics (Springer, 2000).
  41. W. J. Tomlinson, R. H. Stolen, and A. M. Johnson, “Optical wave breaking of pulses in nonlinear optical fibers,” Opt. Lett. 10, 457–459 (1985).
    [Crossref]
  42. P. Jian, W. E. Torruellas, M. Haelterman, S. Trillo, U. Peschel, and F. Lederer, “Solitons of singly resonant optical parametric oscillators,” Opt. Lett. 24, 400–402 (1999).
    [Crossref]
  43. P. Grelu and N. Akhmediev, “Dissipative solitons for mode-locked lasers,” Nat. Photonics 6, 84–92 (2012).
    [Crossref]
  44. J. Peng and H. Zeng, “Ultrafast fibre lasers: build-up of dissipative optical soliton molecules via diverse soliton interactions,” Laser Photon. Rev. 12, 1870037 (2018).
    [Crossref]
  45. L. W. Liou and G. P. Agrawal, “Effect of frequency chirp on soliton spectral sidebands in fiber lasers,” Opt. Lett. 20, 1286–1288 (1995).
    [Crossref]

2019 (2)

C. F. O’Donnell, S. C. Kumar, and M. Ebrahim-Zadeh, “Enhancement of efficiency in femtosecond optical parametric oscillators using group-velocity-matching in long nonlinear crystals,” APL Photon. 4, 050801 (2019).
[Crossref]

C. F. O’Donnell, S. C. Kumar, P. G. Schunemann, and M. Ebrahim-Zadeh, “Femtosecond optical parametric oscillator continuously tunable across 3.6–8 µm based on orientation-patterned gallium phosphide,” Opt. Lett. 44, 4570–4573 (2019).
[Crossref]

2018 (2)

M. Jankowski, A. Marandi, C. R. Phillips, R. Hamerly, K. A. Ingold, R. L. Byer, and M. M. Fejer, “Temporal simultons in optical parametric oscillators,” Phys. Rev. Lett. 120, 053904 (2018).
[Crossref]

J. Peng and H. Zeng, “Ultrafast fibre lasers: build-up of dissipative optical soliton molecules via diverse soliton interactions,” Laser Photon. Rev. 12, 1870037 (2018).
[Crossref]

2017 (1)

T. Steinle, J. N. Greiner, J. Wrachtrup, H. Giessen, and I. Gerhardt, “Unbiased all-optical random-number generator,” Phys. Rev. X 7, 041050 (2017).
[Crossref]

2016 (6)

2015 (4)

Y. Jin, S. M. Cristescu, F. J. M. Harren, and J. Mandon, “Femtosecond optical parametric oscillators toward real-time dual-comb spectroscopy,” Appl. Phys. B 119, 65–74 (2015).
[Crossref]

Y. Kobayashi, K. Torizuka, A. Marandi, R. L. Byer, R. A. McCracken, Z. Zhang, and D. T. Reid, “Femtosecond optical parametric oscillator frequency combs,” J. Opt. 17, 094010 (2015).
[Crossref]

T. Steinle, F. Neubrech, A. Steinmann, X. Yin, and H. Giessen, “Mid-infrared Fourier-transform spectroscopy with a high-brilliance tunable laser source: investigating sample areas down to 5 µm diameter,” Opt. Express 23, 11105–11113 (2015).
[Crossref]

K. A. Ingold, A. Marandi, M. J. F. Digonnet, and R. L. Byer, “Fiber-feedback optical parametric oscillator for half-harmonic generation of sub-100-fs frequency combs around 2 µm,” Opt. Lett. 40, 4368–4371 (2015).
[Crossref]

2014 (2)

T. Cheng, Y. Kanou, K. Asano, D. Deng, M. Liao, M. Matsumoto, T. Misumi, T. Suzuki, and Y. Ohishi, “Soliton self-frequency shift and dispersive wave in a hybrid four-hole AsSe2-As2S5 microstructured optical fiber,” Appl. Phys. Lett. 104, 121911 (2014).
[Crossref]

A. Marandi, Z. Wang, K. Takata, R. L. Byer, and Y. Yamamoto, “Network of time-multiplexed optical parametric oscillators as a coherent Ising machine,” Nat. Photonics 8, 937–942 (2014).
[Crossref]

2013 (1)

C. Xu and F. W. Wise, “Recent advances in fibre lasers for nonlinear microscopy,” Nat. Photonics 7, 875–882 (2013).
[Crossref]

2012 (3)

2010 (3)

F. Kienle, P. S. Teh, S.-U. Alam, C. B. E. Gawith, D. C. Hanna, D. J. Richardson, and D. P. Shepherd, “Compact, high-pulse-energy, picosecond optical parametric oscillator,” Opt. Lett. 35, 3580–3582 (2010).
[Crossref]

M. Conforti, F. Baronio, and C. De Angelis, “Nonlinear envelope equation for broadband optical pulses in quadratic media,” Phys. Rev. A 81, 053841 (2010).
[Crossref]

J. Herz, V. Siffrin, A. E. Hauser, A. U. Brandt, T. Leuenberger, H. Radbruch, F. Zipp, and R. A. Niesner, “Expanding two-photon intravital microscopy to the infrared by means of optical parametric oscillator,” Biophys. J. 98, 715–723 (2010).
[Crossref]

2009 (2)

I. Rocha-Mendoza, W. Langbein, P. Watson, and P. Borri, “Differential coherent anti-Stokes Raman scattering microscopy with linearly chirped femtosecond laser pulses,” Opt. Lett. 34, 2258–2260 (2009).
[Crossref]

V. Andresen, S. Alexander, W. M. Heupel, M. Hirschberg, R. M. Hoffman, and P. Friedl, “Infrared multiphoton microscopy: sub-cellular-resolved deep tissue imaging,” Curr. Opin. Biotech. 20, 54–62 (2009).
[Crossref]

2008 (2)

C. F. Kaminski, R. S. Watt, A. D. Elder, J. H. Frank, and J. Hult, “Supercontinuum radiation for applications in chemical sensing and microscopy,” Appl. Phys. B 92, 367 (2008).
[Crossref]

F. W. Wise, A. Chong, and W. H. Renninger, “High-energy femtosecond fiber lasers based on pulse propagation at normal dispersion,” Laser Photon. Rev. 2, 58–73 (2008).
[Crossref]

2007 (2)

O. Paul, A. Quosig, T. Bauer, M. Nittmann, J. Bartschke, G. Anstett, and J. A. L’huillier, “Temperature-dependent Sellmeier equation in the MIR for the extraordinary refractive index of 5% MgO doped congruent LiNbO3,” Appl. Phys. B 86, 111–115 (2007).
[Crossref]

M. Ebrahim-Zadeh, “Efficient ultrafast frequency conversion sources for the visible and ultraviolet based on BiB3O6,” IEEE J. Sel. Top. Quantum Electron. 13, 679–691 (2007).
[Crossref]

2004 (1)

2001 (1)

1999 (2)

M. H. Dunn and M. Ebrahim-Zadeh, “Parametric generation of tunable light from continuous-wave to femtosecond pulses,” Science 286, 1513–1517 (1999).
[Crossref]

P. Jian, W. E. Torruellas, M. Haelterman, S. Trillo, U. Peschel, and F. Lederer, “Solitons of singly resonant optical parametric oscillators,” Opt. Lett. 24, 400–402 (1999).
[Crossref]

1995 (1)

1994 (2)

T. J. Driscoll, G. M. Gale, and F. Hache, “Ti:sapphire second-harmonic-pumped visible range femtosecond optical parametric oscillator,” Opt. Commun. 110, 638–644 (1994).
[Crossref]

D. T. Reid, J. M. Dudley, M. Ebrahim-Zadeh, and W. Sibbett, “Soliton formation in a femtosecond optical parametric oscillator,” Opt. Lett. 19, 825–827 (1994).
[Crossref]

1992 (2)

S. M. J. Kelly, “Characteristic sideband instability of periodically amplified average soliton,” Electron. Lett. 28, 806–807 (1992).
[Crossref]

N. J. Smith, K. J. Blow, and I. Andonovic, “Sideband generation through perturbations to the average soliton model,” J. Lightwave Technol. 10, 1329–1333 (1992).
[Crossref]

1991 (1)

1986 (1)

1985 (1)

1984 (1)

Agrawal, G. P.

Aihara, K.

P. L. McMahon, A. Marandi, Y. Haribara, R. Hamerly, C. Langrock, S. Tamate, T. Inagaki, H. Takesue, S. Utsunomiya, K. Aihara, and R. L. Byer, “A fully programmable 100-spin coherent Ising machine with all-to-all connections,” Science 354, 614–617 (2016).
[Crossref]

Akhmediev, N.

P. Grelu and N. Akhmediev, “Dissipative solitons for mode-locked lasers,” Nat. Photonics 6, 84–92 (2012).
[Crossref]

Alam, S.-U.

Alexander, S.

V. Andresen, S. Alexander, W. M. Heupel, M. Hirschberg, R. M. Hoffman, and P. Friedl, “Infrared multiphoton microscopy: sub-cellular-resolved deep tissue imaging,” Curr. Opin. Biotech. 20, 54–62 (2009).
[Crossref]

Andonovic, I.

N. J. Smith, K. J. Blow, and I. Andonovic, “Sideband generation through perturbations to the average soliton model,” J. Lightwave Technol. 10, 1329–1333 (1992).
[Crossref]

Andresen, V.

V. Andresen, S. Alexander, W. M. Heupel, M. Hirschberg, R. M. Hoffman, and P. Friedl, “Infrared multiphoton microscopy: sub-cellular-resolved deep tissue imaging,” Curr. Opin. Biotech. 20, 54–62 (2009).
[Crossref]

Anstett, G.

O. Paul, A. Quosig, T. Bauer, M. Nittmann, J. Bartschke, G. Anstett, and J. A. L’huillier, “Temperature-dependent Sellmeier equation in the MIR for the extraordinary refractive index of 5% MgO doped congruent LiNbO3,” Appl. Phys. B 86, 111–115 (2007).
[Crossref]

Asano, K.

T. Cheng, Y. Kanou, K. Asano, D. Deng, M. Liao, M. Matsumoto, T. Misumi, T. Suzuki, and Y. Ohishi, “Soliton self-frequency shift and dispersive wave in a hybrid four-hole AsSe2-As2S5 microstructured optical fiber,” Appl. Phys. Lett. 104, 121911 (2014).
[Crossref]

Aus der Au, J.

Baronio, F.

M. Conforti, F. Baronio, and C. De Angelis, “Nonlinear envelope equation for broadband optical pulses in quadratic media,” Phys. Rev. A 81, 053841 (2010).
[Crossref]

Bartschke, J.

O. Paul, A. Quosig, T. Bauer, M. Nittmann, J. Bartschke, G. Anstett, and J. A. L’huillier, “Temperature-dependent Sellmeier equation in the MIR for the extraordinary refractive index of 5% MgO doped congruent LiNbO3,” Appl. Phys. B 86, 111–115 (2007).
[Crossref]

Bauer, T.

O. Paul, A. Quosig, T. Bauer, M. Nittmann, J. Bartschke, G. Anstett, and J. A. L’huillier, “Temperature-dependent Sellmeier equation in the MIR for the extraordinary refractive index of 5% MgO doped congruent LiNbO3,” Appl. Phys. B 86, 111–115 (2007).
[Crossref]

Blow, K. J.

N. J. Smith, K. J. Blow, and I. Andonovic, “Sideband generation through perturbations to the average soliton model,” J. Lightwave Technol. 10, 1329–1333 (1992).
[Crossref]

Borri, P.

Brandt, A. U.

J. Herz, V. Siffrin, A. E. Hauser, A. U. Brandt, T. Leuenberger, H. Radbruch, F. Zipp, and R. A. Niesner, “Expanding two-photon intravital microscopy to the infrared by means of optical parametric oscillator,” Biophys. J. 98, 715–723 (2010).
[Crossref]

Brunner, F.

Byer, R. L.

M. Jankowski, A. Marandi, C. R. Phillips, R. Hamerly, K. A. Ingold, R. L. Byer, and M. M. Fejer, “Temporal simultons in optical parametric oscillators,” Phys. Rev. Lett. 120, 053904 (2018).
[Crossref]

P. L. McMahon, A. Marandi, Y. Haribara, R. Hamerly, C. Langrock, S. Tamate, T. Inagaki, H. Takesue, S. Utsunomiya, K. Aihara, and R. L. Byer, “A fully programmable 100-spin coherent Ising machine with all-to-all connections,” Science 354, 614–617 (2016).
[Crossref]

Y. Kobayashi, K. Torizuka, A. Marandi, R. L. Byer, R. A. McCracken, Z. Zhang, and D. T. Reid, “Femtosecond optical parametric oscillator frequency combs,” J. Opt. 17, 094010 (2015).
[Crossref]

K. A. Ingold, A. Marandi, M. J. F. Digonnet, and R. L. Byer, “Fiber-feedback optical parametric oscillator for half-harmonic generation of sub-100-fs frequency combs around 2 µm,” Opt. Lett. 40, 4368–4371 (2015).
[Crossref]

A. Marandi, Z. Wang, K. Takata, R. L. Byer, and Y. Yamamoto, “Network of time-multiplexed optical parametric oscillators as a coherent Ising machine,” Nat. Photonics 8, 937–942 (2014).
[Crossref]

N. Leindecker, A. Marandi, R. L. Byer, K. L. Vodopyanov, J. Jiang, I. Hartl, M. Fermann, and P. G. Schunemann, “Octave-spanning ultrafast OPO with 2.6-6.1 µm instantaneous bandwidth pumped by femtosecond Tm-fiber laser,” Opt. Express 20, 7046–7053 (2012).
[Crossref]

Charan, K.

Cheng, T.

T. Cheng, Y. Kanou, K. Asano, D. Deng, M. Liao, M. Matsumoto, T. Misumi, T. Suzuki, and Y. Ohishi, “Soliton self-frequency shift and dispersive wave in a hybrid four-hole AsSe2-As2S5 microstructured optical fiber,” Appl. Phys. Lett. 104, 121911 (2014).
[Crossref]

Chong, A.

F. W. Wise, A. Chong, and W. H. Renninger, “High-energy femtosecond fiber lasers based on pulse propagation at normal dispersion,” Laser Photon. Rev. 2, 58–73 (2008).
[Crossref]

Coddington, I.

Conforti, M.

M. Conforti, F. Baronio, and C. De Angelis, “Nonlinear envelope equation for broadband optical pulses in quadratic media,” Phys. Rev. A 81, 053841 (2010).
[Crossref]

Cristescu, S. M.

Y. Jin, S. M. Cristescu, F. J. M. Harren, and J. Mandon, “Femtosecond optical parametric oscillators toward real-time dual-comb spectroscopy,” Appl. Phys. B 119, 65–74 (2015).
[Crossref]

De Angelis, C.

M. Conforti, F. Baronio, and C. De Angelis, “Nonlinear envelope equation for broadband optical pulses in quadratic media,” Phys. Rev. A 81, 053841 (2010).
[Crossref]

Deng, D.

T. Cheng, Y. Kanou, K. Asano, D. Deng, M. Liao, M. Matsumoto, T. Misumi, T. Suzuki, and Y. Ohishi, “Soliton self-frequency shift and dispersive wave in a hybrid four-hole AsSe2-As2S5 microstructured optical fiber,” Appl. Phys. Lett. 104, 121911 (2014).
[Crossref]

Digonnet, M. J. F.

Driscoll, T. J.

T. J. Driscoll, G. M. Gale, and F. Hache, “Ti:sapphire second-harmonic-pumped visible range femtosecond optical parametric oscillator,” Opt. Commun. 110, 638–644 (1994).
[Crossref]

Dudley, J. M.

Duling, I. N.

Dunn, M. H.

M. H. Dunn and M. Ebrahim-Zadeh, “Parametric generation of tunable light from continuous-wave to femtosecond pulses,” Science 286, 1513–1517 (1999).
[Crossref]

Ebrahim-Zadeh, M.

C. F. O’Donnell, S. C. Kumar, and M. Ebrahim-Zadeh, “Enhancement of efficiency in femtosecond optical parametric oscillators using group-velocity-matching in long nonlinear crystals,” APL Photon. 4, 050801 (2019).
[Crossref]

C. F. O’Donnell, S. C. Kumar, P. G. Schunemann, and M. Ebrahim-Zadeh, “Femtosecond optical parametric oscillator continuously tunable across 3.6–8 µm based on orientation-patterned gallium phosphide,” Opt. Lett. 44, 4570–4573 (2019).
[Crossref]

S. C. Kumar, P. G. Schunemann, K. T. Zawilski, and M. Ebrahim-Zadeh, “Advances in ultrafast optical parametric sources for the mid-infrared based on CdSiP2,” J. Opt. Soc. Am. B 33, D44–D56 (2016).
[Crossref]

M. Ebrahim-Zadeh, “Efficient ultrafast frequency conversion sources for the visible and ultraviolet based on BiB3O6,” IEEE J. Sel. Top. Quantum Electron. 13, 679–691 (2007).
[Crossref]

M. H. Dunn and M. Ebrahim-Zadeh, “Parametric generation of tunable light from continuous-wave to femtosecond pulses,” Science 286, 1513–1517 (1999).
[Crossref]

D. T. Reid, J. M. Dudley, M. Ebrahim-Zadeh, and W. Sibbett, “Soliton formation in a femtosecond optical parametric oscillator,” Opt. Lett. 19, 825–827 (1994).
[Crossref]

M. Ebrahim-Zadeh and I. T. Sorokina, Mid-Infrared Coherent Sources and Applications (Springer, 2008).

Elder, A. D.

C. F. Kaminski, R. S. Watt, A. D. Elder, J. H. Frank, and J. Hult, “Supercontinuum radiation for applications in chemical sensing and microscopy,” Appl. Phys. B 92, 367 (2008).
[Crossref]

Fejer, M. M.

M. Jankowski, A. Marandi, C. R. Phillips, R. Hamerly, K. A. Ingold, R. L. Byer, and M. M. Fejer, “Temporal simultons in optical parametric oscillators,” Phys. Rev. Lett. 120, 053904 (2018).
[Crossref]

R. Hamerly, A. Marandi, M. Jankowski, M. M. Fejer, Y. Yamamoto, and H. Mabuchi, “Reduced models and design principles for half-harmonic generation in synchronously pumped optical parametric oscillators,” Phys. Rev. A 94, 063809 (2016).
[Crossref]

Fermann, M.

Frank, J. H.

C. F. Kaminski, R. S. Watt, A. D. Elder, J. H. Frank, and J. Hult, “Supercontinuum radiation for applications in chemical sensing and microscopy,” Appl. Phys. B 92, 367 (2008).
[Crossref]

Friedl, P.

V. Andresen, S. Alexander, W. M. Heupel, M. Hirschberg, R. M. Hoffman, and P. Friedl, “Infrared multiphoton microscopy: sub-cellular-resolved deep tissue imaging,” Curr. Opin. Biotech. 20, 54–62 (2009).
[Crossref]

Fu, D.

Gale, G. M.

T. J. Driscoll, G. M. Gale, and F. Hache, “Ti:sapphire second-harmonic-pumped visible range femtosecond optical parametric oscillator,” Opt. Commun. 110, 638–644 (1994).
[Crossref]

Gawith, C. B. E.

Gerhardt, I.

T. Steinle, J. N. Greiner, J. Wrachtrup, H. Giessen, and I. Gerhardt, “Unbiased all-optical random-number generator,” Phys. Rev. X 7, 041050 (2017).
[Crossref]

Giessen, H.

Greiner, J. N.

T. Steinle, J. N. Greiner, J. Wrachtrup, H. Giessen, and I. Gerhardt, “Unbiased all-optical random-number generator,” Phys. Rev. X 7, 041050 (2017).
[Crossref]

Grelu, P.

P. Grelu and N. Akhmediev, “Dissipative solitons for mode-locked lasers,” Nat. Photonics 6, 84–92 (2012).
[Crossref]

Hache, F.

T. J. Driscoll, G. M. Gale, and F. Hache, “Ti:sapphire second-harmonic-pumped visible range femtosecond optical parametric oscillator,” Opt. Commun. 110, 638–644 (1994).
[Crossref]

Haelterman, M.

Hamerly, R.

M. Jankowski, A. Marandi, C. R. Phillips, R. Hamerly, K. A. Ingold, R. L. Byer, and M. M. Fejer, “Temporal simultons in optical parametric oscillators,” Phys. Rev. Lett. 120, 053904 (2018).
[Crossref]

R. Hamerly, A. Marandi, M. Jankowski, M. M. Fejer, Y. Yamamoto, and H. Mabuchi, “Reduced models and design principles for half-harmonic generation in synchronously pumped optical parametric oscillators,” Phys. Rev. A 94, 063809 (2016).
[Crossref]

P. L. McMahon, A. Marandi, Y. Haribara, R. Hamerly, C. Langrock, S. Tamate, T. Inagaki, H. Takesue, S. Utsunomiya, K. Aihara, and R. L. Byer, “A fully programmable 100-spin coherent Ising machine with all-to-all connections,” Science 354, 614–617 (2016).
[Crossref]

Hanna, D. C.

Haribara, Y.

P. L. McMahon, A. Marandi, Y. Haribara, R. Hamerly, C. Langrock, S. Tamate, T. Inagaki, H. Takesue, S. Utsunomiya, K. Aihara, and R. L. Byer, “A fully programmable 100-spin coherent Ising machine with all-to-all connections,” Science 354, 614–617 (2016).
[Crossref]

Harren, F. J. M.

Y. Jin, S. M. Cristescu, F. J. M. Harren, and J. Mandon, “Femtosecond optical parametric oscillators toward real-time dual-comb spectroscopy,” Appl. Phys. B 119, 65–74 (2015).
[Crossref]

Hartl, I.

Hauser, A. E.

J. Herz, V. Siffrin, A. E. Hauser, A. U. Brandt, T. Leuenberger, H. Radbruch, F. Zipp, and R. A. Niesner, “Expanding two-photon intravital microscopy to the infrared by means of optical parametric oscillator,” Biophys. J. 98, 715–723 (2010).
[Crossref]

Herda, R.

Herz, J.

J. Herz, V. Siffrin, A. E. Hauser, A. U. Brandt, T. Leuenberger, H. Radbruch, F. Zipp, and R. A. Niesner, “Expanding two-photon intravital microscopy to the infrared by means of optical parametric oscillator,” Biophys. J. 98, 715–723 (2010).
[Crossref]

Heupel, W. M.

V. Andresen, S. Alexander, W. M. Heupel, M. Hirschberg, R. M. Hoffman, and P. Friedl, “Infrared multiphoton microscopy: sub-cellular-resolved deep tissue imaging,” Curr. Opin. Biotech. 20, 54–62 (2009).
[Crossref]

Hirschberg, M.

V. Andresen, S. Alexander, W. M. Heupel, M. Hirschberg, R. M. Hoffman, and P. Friedl, “Infrared multiphoton microscopy: sub-cellular-resolved deep tissue imaging,” Curr. Opin. Biotech. 20, 54–62 (2009).
[Crossref]

Hoffman, R. M.

V. Andresen, S. Alexander, W. M. Heupel, M. Hirschberg, R. M. Hoffman, and P. Friedl, “Infrared multiphoton microscopy: sub-cellular-resolved deep tissue imaging,” Curr. Opin. Biotech. 20, 54–62 (2009).
[Crossref]

Holtom, G. R.

Hult, J.

C. F. Kaminski, R. S. Watt, A. D. Elder, J. H. Frank, and J. Hult, “Supercontinuum radiation for applications in chemical sensing and microscopy,” Appl. Phys. B 92, 367 (2008).
[Crossref]

Inagaki, T.

P. L. McMahon, A. Marandi, Y. Haribara, R. Hamerly, C. Langrock, S. Tamate, T. Inagaki, H. Takesue, S. Utsunomiya, K. Aihara, and R. L. Byer, “A fully programmable 100-spin coherent Ising machine with all-to-all connections,” Science 354, 614–617 (2016).
[Crossref]

Ingold, K. A.

M. Jankowski, A. Marandi, C. R. Phillips, R. Hamerly, K. A. Ingold, R. L. Byer, and M. M. Fejer, “Temporal simultons in optical parametric oscillators,” Phys. Rev. Lett. 120, 053904 (2018).
[Crossref]

K. A. Ingold, A. Marandi, M. J. F. Digonnet, and R. L. Byer, “Fiber-feedback optical parametric oscillator for half-harmonic generation of sub-100-fs frequency combs around 2 µm,” Opt. Lett. 40, 4368–4371 (2015).
[Crossref]

Innerhofer, E.

Ito, H.

Jankowski, M.

M. Jankowski, A. Marandi, C. R. Phillips, R. Hamerly, K. A. Ingold, R. L. Byer, and M. M. Fejer, “Temporal simultons in optical parametric oscillators,” Phys. Rev. Lett. 120, 053904 (2018).
[Crossref]

R. Hamerly, A. Marandi, M. Jankowski, M. M. Fejer, Y. Yamamoto, and H. Mabuchi, “Reduced models and design principles for half-harmonic generation in synchronously pumped optical parametric oscillators,” Phys. Rev. A 94, 063809 (2016).
[Crossref]

Jian, P.

Jiang, J.

Jin, Y.

Y. Jin, S. M. Cristescu, F. J. M. Harren, and J. Mandon, “Femtosecond optical parametric oscillators toward real-time dual-comb spectroscopy,” Appl. Phys. B 119, 65–74 (2015).
[Crossref]

Johnson, A. M.

Kaminski, C. F.

C. F. Kaminski, R. S. Watt, A. D. Elder, J. H. Frank, and J. Hult, “Supercontinuum radiation for applications in chemical sensing and microscopy,” Appl. Phys. B 92, 367 (2008).
[Crossref]

Kanou, Y.

T. Cheng, Y. Kanou, K. Asano, D. Deng, M. Liao, M. Matsumoto, T. Misumi, T. Suzuki, and Y. Ohishi, “Soliton self-frequency shift and dispersive wave in a hybrid four-hole AsSe2-As2S5 microstructured optical fiber,” Appl. Phys. Lett. 104, 121911 (2014).
[Crossref]

Keller, U.

Kelly, S. M. J.

S. M. J. Kelly, “Characteristic sideband instability of periodically amplified average soliton,” Electron. Lett. 28, 806–807 (1992).
[Crossref]

Kienle, F.

Kitamura, K.

Kobayashi, Y.

Y. Kobayashi, K. Torizuka, A. Marandi, R. L. Byer, R. A. McCracken, Z. Zhang, and D. T. Reid, “Femtosecond optical parametric oscillator frequency combs,” J. Opt. 17, 094010 (2015).
[Crossref]

Kong, L.

Kumar, S. C.

Kurimura, S.

L’huillier, J. A.

O. Paul, A. Quosig, T. Bauer, M. Nittmann, J. Bartschke, G. Anstett, and J. A. L’huillier, “Temperature-dependent Sellmeier equation in the MIR for the extraordinary refractive index of 5% MgO doped congruent LiNbO3,” Appl. Phys. B 86, 111–115 (2007).
[Crossref]

Langbein, W.

Langrock, C.

P. L. McMahon, A. Marandi, Y. Haribara, R. Hamerly, C. Langrock, S. Tamate, T. Inagaki, H. Takesue, S. Utsunomiya, K. Aihara, and R. L. Byer, “A fully programmable 100-spin coherent Ising machine with all-to-all connections,” Science 354, 614–617 (2016).
[Crossref]

Lederer, F.

Lefrancois, S.

Leindecker, N.

Leuenberger, T.

J. Herz, V. Siffrin, A. E. Hauser, A. U. Brandt, T. Leuenberger, H. Radbruch, F. Zipp, and R. A. Niesner, “Expanding two-photon intravital microscopy to the infrared by means of optical parametric oscillator,” Biophys. J. 98, 715–723 (2010).
[Crossref]

Liao, M.

T. Cheng, Y. Kanou, K. Asano, D. Deng, M. Liao, M. Matsumoto, T. Misumi, T. Suzuki, and Y. Ohishi, “Soliton self-frequency shift and dispersive wave in a hybrid four-hole AsSe2-As2S5 microstructured optical fiber,” Appl. Phys. Lett. 104, 121911 (2014).
[Crossref]

Liou, L. W.

Mabuchi, H.

R. Hamerly, A. Marandi, M. Jankowski, M. M. Fejer, Y. Yamamoto, and H. Mabuchi, “Reduced models and design principles for half-harmonic generation in synchronously pumped optical parametric oscillators,” Phys. Rev. A 94, 063809 (2016).
[Crossref]

Maidment, L.

Mandon, J.

Y. Jin, S. M. Cristescu, F. J. M. Harren, and J. Mandon, “Femtosecond optical parametric oscillators toward real-time dual-comb spectroscopy,” Appl. Phys. B 119, 65–74 (2015).
[Crossref]

Marandi, A.

M. Jankowski, A. Marandi, C. R. Phillips, R. Hamerly, K. A. Ingold, R. L. Byer, and M. M. Fejer, “Temporal simultons in optical parametric oscillators,” Phys. Rev. Lett. 120, 053904 (2018).
[Crossref]

R. Hamerly, A. Marandi, M. Jankowski, M. M. Fejer, Y. Yamamoto, and H. Mabuchi, “Reduced models and design principles for half-harmonic generation in synchronously pumped optical parametric oscillators,” Phys. Rev. A 94, 063809 (2016).
[Crossref]

P. L. McMahon, A. Marandi, Y. Haribara, R. Hamerly, C. Langrock, S. Tamate, T. Inagaki, H. Takesue, S. Utsunomiya, K. Aihara, and R. L. Byer, “A fully programmable 100-spin coherent Ising machine with all-to-all connections,” Science 354, 614–617 (2016).
[Crossref]

Y. Kobayashi, K. Torizuka, A. Marandi, R. L. Byer, R. A. McCracken, Z. Zhang, and D. T. Reid, “Femtosecond optical parametric oscillator frequency combs,” J. Opt. 17, 094010 (2015).
[Crossref]

K. A. Ingold, A. Marandi, M. J. F. Digonnet, and R. L. Byer, “Fiber-feedback optical parametric oscillator for half-harmonic generation of sub-100-fs frequency combs around 2 µm,” Opt. Lett. 40, 4368–4371 (2015).
[Crossref]

A. Marandi, Z. Wang, K. Takata, R. L. Byer, and Y. Yamamoto, “Network of time-multiplexed optical parametric oscillators as a coherent Ising machine,” Nat. Photonics 8, 937–942 (2014).
[Crossref]

N. Leindecker, A. Marandi, R. L. Byer, K. L. Vodopyanov, J. Jiang, I. Hartl, M. Fermann, and P. G. Schunemann, “Octave-spanning ultrafast OPO with 2.6-6.1 µm instantaneous bandwidth pumped by femtosecond Tm-fiber laser,” Opt. Express 20, 7046–7053 (2012).
[Crossref]

Matsumoto, M.

T. Cheng, Y. Kanou, K. Asano, D. Deng, M. Liao, M. Matsumoto, T. Misumi, T. Suzuki, and Y. Ohishi, “Soliton self-frequency shift and dispersive wave in a hybrid four-hole AsSe2-As2S5 microstructured optical fiber,” Appl. Phys. Lett. 104, 121911 (2014).
[Crossref]

McCracken, R. A.

Y. Kobayashi, K. Torizuka, A. Marandi, R. L. Byer, R. A. McCracken, Z. Zhang, and D. T. Reid, “Femtosecond optical parametric oscillator frequency combs,” J. Opt. 17, 094010 (2015).
[Crossref]

McMahon, P. L.

P. L. McMahon, A. Marandi, Y. Haribara, R. Hamerly, C. Langrock, S. Tamate, T. Inagaki, H. Takesue, S. Utsunomiya, K. Aihara, and R. L. Byer, “A fully programmable 100-spin coherent Ising machine with all-to-all connections,” Science 354, 614–617 (2016).
[Crossref]

Misumi, T.

T. Cheng, Y. Kanou, K. Asano, D. Deng, M. Liao, M. Matsumoto, T. Misumi, T. Suzuki, and Y. Ohishi, “Soliton self-frequency shift and dispersive wave in a hybrid four-hole AsSe2-As2S5 microstructured optical fiber,” Appl. Phys. Lett. 104, 121911 (2014).
[Crossref]

Mitschke, F. M.

Mollenauer, L. F.

Neubrech, F.

Newbury, N.

Niesner, R. A.

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Y. Kobayashi, K. Torizuka, A. Marandi, R. L. Byer, R. A. McCracken, Z. Zhang, and D. T. Reid, “Femtosecond optical parametric oscillator frequency combs,” J. Opt. 17, 094010 (2015).
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M. Jankowski, A. Marandi, C. R. Phillips, R. Hamerly, K. A. Ingold, R. L. Byer, and M. M. Fejer, “Temporal simultons in optical parametric oscillators,” Phys. Rev. Lett. 120, 053904 (2018).
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Supplementary Material (1)

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Figures (7)

Fig. 1.
Fig. 1. Schematic of the experimental setup for the Ti:sapphire-pumped soliton fiber-feedback OPO. HWPs, half-wave plates; PBS, polarizing beam splitter; L, lenses; M, mirrors; OC, output coupler; SMF-28, single-mode fiber retroreflector.
Fig. 2.
Fig. 2. (a) Measured signal data points (white), superimposed on the parametric gain bandwidth for 1-mm-long MgO:PPLN crystal with QPM grating periods varying over $\Lambda = {19.0 - 22}\;\unicode{x00B5}{\rm m}$, calculated using the Sellmeier equations in [38]. (b) Cavity delay tuning of the OPO, with measured signal data points plotted against relative change in cavity length, normalized to the shortest possible cavity for operation; inset, calculated net cavity GDD across the tuning range.
Fig. 3.
Fig. 3. (a) Measured signal spectra and output average power across the anomalous dispersion regime. (b) Typical interferometric autocorrelation at 1460 nm. (c) Simultaneous signal spectrum. (d) Power stability measurement at 1455 nm over a period of 30 min; inset, spectral stability measurement over a period of 20 min. (e) Central wavelength and FWHM bandwidth stability over the same time period.
Fig. 4.
Fig. 4. (a) Measured signal spectra and output average power across the normal dispersion regime. (b) Typical interferometric autocorrelation at 1215 nm. (c) Simultaneous signal spectrum. (d) Power scaling measurement at 1220 nm; inset, signal beam profile. (e) Spectral stability measurement at 1171 nm over a period of 20 min.
Fig. 5.
Fig. 5. (a) Simulation of a soliton pulse evolving from noise at an initial wavelength of ${\lambda _s} = {1350}\;{\rm nm}$, with $\Delta {T_s}$ free to adapt to the changing group velocity. Inset, close-up of the final two round trips in steady state, showing a pulse duration of 95 fs. (b) Corresponding spectral evolution showing the soliton self-frequency shift after 10 round trips. (c) Schematic of stable soliton formation: (1) pulse builds up from noise, (2) pulse undergoes self-frequency shift (arrow indicates deceleration), (3) cavity is delayed to resume synchronization, (4) synchronization at ${\lambda _s^\prime}$ with a temporal offset, $\Delta {T_s}$, from the cold-cavity round trip time. (d) Cavity length offset, $\Delta z$, from the cold-cavity length as a function of the shifted soliton wavelength, ${\lambda _s^\prime}$, as a function of intracavity peak power between 0 and 32 kW. Yellow dots represent points at which the 2 kW contours are crossed for $\Delta z = {36}\;\unicode{x00B5}{\rm m}$. (e) Experimentally measured intracavity peak power vs wavelength when tuning by cavity delay for a grating period of $\Lambda = {20.2}\;\unicode{x00B5}{\rm m}$, compared to the values taken from (d). Arrows represent observed power hysteresis loop; blue zones are wavelengths at which oscillation is recovered.
Fig. 6.
Fig. 6. (a) Idler spectra recorded at ${\lambda _i}\;\sim\;{1527}\;{\rm nm}$ to degeneracy at ${\sim}{1606}\;{\rm nm}$, showing the increase in modulation period, $\Delta \lambda$. The signal spectrum also becomes visible as degeneracy is approached. (b) Comparison of experimentally determined, $\Delta \lambda$, and relative signal/idler group delay, with the theoretical predictions.
Fig. 7.
Fig. 7. (a) Simulated temporal and (b) spectral evolution of a femtosecond pulse from noise in the OPO at a central wavelength of 1104 nm, (c) comparison of the steady-state simulated spectrum with an experimentally measured spectrum at the same wavelength, (d) experimentally measured autocorrelation, and (e) simulated autocorrelation at the same wavelength.

Equations (1)

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N 2 = L d / L n = γ ( ω ) P 0 T 0 2 / | β 2 ( ω ) | ,

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