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Conventional (1015 nm) and Raman (1055 nm) dissipative solitons generated in an all-fiber Yb laser are mixed in an external photonic crystal fiber (PCF) at pulse energy of up to 4 nJ at the input. It has been found that red-shifted ~20 ps pulses with energy up to 1 nJ are generated in the parametric process. Their peak wavelength is tunable from 1084 to 1102 nm by means of the delay variation between the input pulses. At that, the parametric pulses are shown to be coherent with the input ones and compressible to ~2 ps that is useful in applications. The performed modeling explains the main features of generated pulses.
© 2015 Optical Society of America
1. Introduction
Recent advances in pulsed fiber lasers offer new opportunities for the development of high-performance tunable laser sources for delicate applications, such as air monitoring [1], gas spectroscopy and sensing [2], and especially biomedical imaging [3]. Though high-intensity pico- and femtosecond fiber lasers are featured by limited tunability (within the gain spectra around 1.05 and 1.55 micron for Yb- and Er-doped fibers, correspondingly), the generated pulses can be efficiently converted to other wavelengths, both blue- (anti-Stokes) and red-shifted (Stokes), e.g. in highly nonlinear photonic crystal fibers (PCFs). The nonlinear optical techniques used in the fiber sources are mainly based on parametric four-wave mixing (FWM) and soliton self-frequency shift (SSFS) processes [3–10].
FWM is usually utilized for nonlinear microscopy based on the coherent anti-Stokes Raman scattering (CARS) of two picosecond pulses with frequency difference being resonant to molecular vibrations thus offering real-time label-free imaging of living tissues. The FMW-based fiber sources can be divided on optical parametric amplifiers (OPA) [4–6] and optical parametric oscillators (OPO) [7–9]. In the OPA scheme [5], 3-nJ 2-ps (i.e. 1.5 kW peak power) pulses are generated being widely tunable around 800 nm. They have been applied together with 1050-nm pulses from Yb-doped fiber laser (YDFL) pump for CARS imaging of mouse ear and brain as well as fibroblast cells. Similar parameters but with greatly reduced relative intensity noise have been obtained by the same group in the OPO scheme [8], where a resonant cavity with spectrally filtered feedback for the idler wave is added. The fiber OPO developed recently [9] is able to generate efficiently 5.6 kW picosecond pulses near 800 nm at 1030 nm YDFL pumping that is used for demonstration of high-resolution imaging of CH2 and CH3 in a tissue. Let us note that the OPO scheme is more practical than OPAs as it eliminates the need for tunable seed laser [3].
Special SSFS-based laser sources are developed for deep-tissue imaging by multiphoton fluorescence microscopy (MPFM) requiring high-energy (>10 nJ) femtosecond pulses in optimal spectral window (e.g. ~1700 nm for brain tissue) [3, 10]. Since the soliton energy is proportional to the mode area, energetic pulses tunable from 1600 to 2200 nm have been achieved in large-core silica fibers having anomalous dispersion in this range [10]. Another interesting opportunity for MPFM is short-wavelength side of the water absorption near 1300 nm, where developments of the SSFS sources with required energy face some difficulties [3]. Since conventional silica fibers have normal dispersion in this range, one needs special fibers with large mode area and anomalous dispersion. In this way, YDFL pumping of a specially designed higher-order-mode fiber resulted in the soliton shift from 1045 to 1085 nm with output energy of 6.3 nJ [11].
One of the alternative opportunities to generate tunable high-energy pulses in 1100-1300 nm range is to realize an efficient parametric conversion of high-energy dissipative solitons (DS) generated around 1030 nm in normal-dispersion YDFLs [12, 13]. Herewith, all-fiber configuration of such a source will be a great advantage in applications.
Environmentally-stable all-fiber configurations of DS YDFL are developed recently on the base of polarization-maintaining (PM) fibers, with mode locking by means of NALM (nonlinear amplifying loop mirror) [14, 15] or NPE (nonlinear polarization evolution) in a short piece of non-PM single-mode fiber [16, 17]. Stable DSs with energies beyond 20 nJ in fibers of normal core diameter (~6 μm) are generated [17]. Further DS energy scaling is found to be limited by the onset of stimulated Raman scattering (SRS), converting the excess energy of DSs to the noisy Raman pulse at Stokes wavelength. To overcome this limitation, a new YDFL cavity design with the feedback for Raman pulse provided by its re-injection into the laser cavity via delay loop with proper timing has been proposed and tested in [18]. As a result, formation of a coherent Raman dissipative soliton (RDS) from the noise has been demonstrated. The DS and RDS form a two-color (1030/1075 nm) complex of coherent solitons with comparable energy and chirp both compressible to ~200 fs duration with a capability of their coherent combination [19] thus offering a way for generation of pulses at new wavelengths, with higher total energy and shorter duration as well.
Here we study a possibility of nonlinear conversion of the DS and RDS generated in single laser source (YDFL) to longer wavelengths by means of parametric four-wave mixing in an external PCF. The concept of generating new color via FWM of two-color dissipative soliton complex is novel and is performed for the first time, to our knowledge. Implementation of single source instead of two synchronized pump and signal sources provides also an attractive performance for such systems.
2. Experimental setup
The experimental scheme is shown in Fig. 1.
Fig. 1 Experimental setup: VDS - variable delay line, PWDM - polarization wavelength division multiplexer (Lyot filter), PBS – polarization beam splitter, PCF - photonic crystal fiber, FROG - frequency-resolved optical gating system, OSA - optical spectrum analyzer.
DS pulses are generated in YDFL with ring normal-dispersion cavity, in which the feedback loop for Stokes-shifted Raman pulse is inserted in all-fiber configuration similar to [18, 19] thus providing synchronous generation of coherent RDS in the same cavity. As a result, linearly chirped pulses with duration of ~40 ps and repetition rate of 4.3 MHz are generated at wavelengths of 1015 nm (DS) and 1055 nm (RDS) and delivered into different PM fiber output ports. The generated wavelengths are set by spectrally selective components (fiber Lyot filters) in the cavity, see [19] for details, in order to fulfill parametric phase matching conditions in the PCF. The mixing of DS and RDS is performed in a 5-m long PCF (LMA5-PM, NKT Photonics) with zero dispersion wavelength inside RDS spectrum. The pulses are launched via a polarization wavelength division multiplexer (PWDM) consisting of a standard polarization beam splitter (PBS) and a small piece of polarization-maintaining (PM) fiber aligned at 45° angle to the main PM fiber axis. The PWDM is analogue of Lyot filter [20]. The radiation of DS and RDS propagate in different fiber axes at the PBS output. Then polarization of the solitons is rotated in the 45°-spliced piece of fiber that depends on the wavelength. As a result, the major part of DS and RDS radiation is launched along the slow axis of the PCF (the estimated fast axis fraction is less than 10%). The PCF has two spliced pigtails of PM980-XP fiber that were accurately aligned to the PCF axes. In the PCF, the DS and RDS pulses interact as the signal and the pump waves of the FWM process, respectively, resulting in generation of new parametric (idler) wave. To optimize the FWM interaction between DS and RDS, a free-space variable delay line (VDL) with 300 ps range is used. It allows to control the time delay Δτ between the pulses. According to the energy conservation law, the idler frequency is
where ωp and ωs are the pump and the signal frequencies, respectively. A 5% PM fiber coupler is used for monitoring the spectral and temporal characteristics of output radiation measured by optical spectrum analyzer (OSA) Yokogawa 6370 and frequency-resolved optical gating (FROG) system (Mesaphotonics) with the extended range (up to 100 ps).3. Experimental results and theoretical calculation
Figure 2(a) shows the measured output spectra when the time delay between the pulses is varied. One can see that both the intensity and wavelength of parametric (idler) wave are changed at such variation. The wavelength (in spectral maximum) of idler wave is tuned from 1084 to 1102 nm. The generated spectrum consists of the main peak and a lower-frequency tail which is strongly modulated in its amplitude. The tail becomes dominating with increasing the parametric shifts while the main peak disappears. The width (FWHM) of the main peak is rather narrow (~2 nm) in comparison with the linewidth of interacting solitons (~15 nm).
Fig. 2 (a) Output spectra depending on the time delay between pump (RDS at 1055 nm) and signal (DS at 1015 nm) pulses. (b) Parametric phase matching diagrams: theory (dashed line), experiment (points), DS wavelength domain in the experiment (solid line).
Figure 2(b) shows the scalar phase matching diagrams (parametric wavelength versus pump wavelength) for the slow polarization axis of the 5-m-long LMA5-PM PCF. The dashed lines correspond to the theoretical estimation obtained from the phase matching condition Δβ = 0. In the case of scalar FWM the phase mismatch Δβ can be rewritten as [21]:
where β3, β4 are the 3-nd and the 4-th order dispersion coefficients of the fiber at zero dispersion frequency ω0, Ω = ωp – ωi = ωs – ωp is the parametric frequency shift, Pp is pump power at the PCF input, γ is the fiber nonlinearity coefficient. The following PCF parameters were used in the calculation [21]: γ = 10 (W*km)−1, β3 = 6,756*10−2 ps3/km, β4 = −1*10−4 ps4/km, λ0slow = 1051.85 nm. The pump power Pp = 50 W is taken in correspondence with the experimental data of Fig. 2(a) bearing in mind that the DS and RDS have nearly rectangular shape [18,19]. The part of the theoretical curve in Fig. 2(b) marked by a solid line shows the DS wavelengths range. Points correspond to the experimental idler wavelengths which are plotted at the same pump wavelengths as the solid line.To understand the limitations of experimental tuning range and the generated spectrum bandwidth the following calculations were performed. Temporal characteristics and coherence properties of pulses from the DS/RDS laser source are investigated in detail in [18, 19]. Since the solitones have a positive chirp, we can consider that their wavelengths λs and λp decrease linearly along the pulses. Figure 3(a) schematically shows the calculated temporal wavelength variation of the solitons when the time delay Δτ between the signal (DS) and pump (RDS) pulses is 15 ps. In the parametric process, each part of the pump pulse (λp) interacts with the corresponding (coinciding in time) part of signal pulse (λs) thus resulting in generation of the idler wave at wavelength λi according to Eq. (1) over the overlap region (see solid line in Fig. 3(a)). One can see that parametric pulse have the positive chirp like that for the DS and RDS pulses.
Fig. 3 (a) Calculated temporal wavelength distribution of signal (dotted line), pump (dashed line) and idler (solid line) pulses at time delay Δτ = 15 ps. Inset: parametric conversion efficiency at the overlap area. (b) Calculated parametric conversion efficiency vs. time delay.
Quasi-CW FWM approximation is quite accurate for time scales in excess of 1 ns [22]. However, we use it also in our case for qualitative analysis of experimental spectra. The conversion efficiency of parametric process in the CW approximation is [23]
where is the parametric gain, L is the PCF length and Δβ is defined by Eq. (2). The integral parametric conversion efficiency over the pulse overlap region can be found by calculating the value of ηc for each interacting pair ωp,s = 2πc/ λp,s with relative frequency shift Ωsp = ωs – ωp. The calculated conversion efficiency for Δτ = 15 ps is presented in the inset of Fig. 3(a). One can see that efficient frequency conversion is performed only for a small overlapping area in the vicinity of the pump (RDS) pulse end. Variation of the time delay leads to variation of the relative parametric shifts Ωsp(Δτ) and therefore to changing the peak wavelength of the integral parametric conversion efficiency.Figure 3(b) shows the map of calculated total parametric conversion efficiencies for all possible values of the time delay. One can see that wavelength of the main idler peak varies from 1084 to 1103 nm, which is in good agreement with the experimental data. Besides, the simulation explains the oscillating tail observed in the experiment. The calculated spectral width of the main peak 1.9 - 2.8 nm is also in good agreement with the experimental data. The parametric pulse duration can be estimated as τi = 0.443/Δνi, where 0.443 is the time-bandwidth product for rectangular pulse (that is correct for dissipative solitons) and Δνi is idler bandwidth. The value of Δνi at 1.1 μm is ~0.62 THz resulting in τi = 0.7 ps.
Figures 4(a) and 4(b) show the autocorrelation function (ACF) for initial and compressed idler pulse correspondingly. The data are obtained at maximum energy of 4 nJ for the pump (RDS) pulse and about 2 nJ for the signal (DS) pulse at the PCF input. At that the energy generated idler pulse at 1096 nm reaches 1 nJ. Note that the input pulse energy was sufficiently reduced in comparison with the laser output because of significant losses at propagation via VDL and PWDM (see Fig. 1). The ACFs were reconstructed from the experimentally measured FROG-traces, which are depicted at the top of each panel in Fig. 4. The ACF of initial pulse has a two-scale structure with narrow central peak and broad background that is typical for pulses with stochastic additions. At the same time, the FROG trace also has a regular internal structure, which characterizes chirped pulses, e.g. similar structure was observed for a highly chirped DS in [17]. The pulse ACF duration is 17 ps.
Fig. 4 The FROG-traces and the ACF of initial (a) and compressed (b) parametric pulse at 1096 nm for 4 nJ pump pulse energy. Inset: The cross-correlation function between RDS and initial parametric pulse.
By compressing the idler pulse in the external diffraction gratings compressor we have obtained a narrow intensity peak with ACF duration of 1.5 ps (see Fig. 4(b)) that corresponds to the compression ratio of ~11. This value is close to the estimated one (0.7 ps). At the same time, the ACF of compressed pulse has a background that similarly may have a stochastic nature. The effect may be associated with the influence of RDS-induced Raman amplification. The cross-correlation function (CCF) between the RDS and initial idler pulse is shown in the inset of Fig. 4(a). It was also reconstructed from the corresponding FROG-traces. The deep modulation demonstrates high mutual coherence of the pulses. So, we have in fact weak seed at the idler wavelength which is coherent with pump (RDS) pulse as a consequence of FWM interaction between coherent DS and RDS pulses. It is then manifold amplified via SRS process. During the SRS the noisy background is added to the parametric pulse resulting in its incomplete compression.
4. Conclusion
Thus, we have explored a four wave mixing of conventional and Raman dissipative solitons (with ~40 ps duration and 2-4 nJ energy in PCF) generated in the same Yb-doped fiber laser. The 15-nm wide pump pulse (RDS) and signal pulse (DS) spectra correspond to the zero dispersion wavelength λ0 ~1052 nm and normal-dispersion region (around 1015 nm) of the LMA5-PM PCF respectively. At the same time they are linearly chirped and coherent. It has been found that ~20 ps parametric pulses with relatively narrow spectrum (~2 nm) and energy up to 1 nJ are generated in the FWM process being tunable from 1084 to 1102 nm by means of the delay variation between the input pulses. At that, the generated pulses are shown to be coherent with the input pulses and compressible to ~2 ps that is useful in various applications. Note that they may be further amplified, if necessary.
The developed model describes the main features of the generated pulses such as shorter (compared with pump) duration and relatively narrow spectrum with oscillating tails, as well as their positive chirp and compressibility. It should be noted that the parametric tuning range can be broaden by increasing the DS spectral width (and/or its central wavelength).
Acknowledgments
The authors acknowledge E. Podivilov for helpful discussions and V. Gonta for technical assistance. This work is supported by Russian Science Foundation (grant No. 14-22-00118).
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