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Abstract
We characterize the relative intensity noise (RIN) and relative timing jitter (RTJ) between the signal and pump pulses of optical parametric amplifiers (OPAs) seeded by three different seed sources. Compared to a white-light continuum (WLC) seeded- and an optical parametric generator (OPG) seeded OPA, the narrowband CW seeded OPA exhibits the lowest root-mean-square (RMS) RIN and RTJ of 0.79% and 0.32 fs, respectively, integrated from 1 kHz to the Nyquist frequency of 1.25 MHz. An improved numerical model based on a forward Maxwell equation (FME) is built to investigate the transfers of the pump and seed’s noise to the resulting OPAs’ intensity and temporal fluctuation. Both the experimental and numerical study indicate that the low level of noise from the narrowband CW seeded OPA is attributed to the elimination of the RIN and RTJ coupled from the noise of seed source, being one of the important contributions to RIN and timing jitter in the other two OPAs. The approach to achieve lower level of noise from this CW seeded OPA by driving it close to saturation is also discussed with the same numerical model.
© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Femtosecond optical parametric amplifiers (OPAs) have been extensively investigated because they are more compact, more robust, easier to build and operate, and lower-cost ultrafast sources with broader wavelength range, compared to traditional ultrafast sources based on rare earth doped gain media. The research on OPA has been mostly concentrated on basic performance parameters such as pulse energy [1], duration [2] and tunable wavelength range [3], rather than the noise properties, in terms of intensity noise and timing jitter. Recently, it has been shown that generation of ultrafast pulses with low level of noise from OPAs enables a number of applications, such as time-resolved pump–probe spectroscopy [4,5], nonlinear bio-imaging [6,7], and free-electron lasers (FELs) [8]. In particular, for some nonlinear bio-imaging methods, e.g., stimulated Raman scattering (SRS) microscopy, the generation of two synchronized trains of femtosecond pulses with independent tunability over a wide spectral range will be required, which is usually implemented by an OPA system [7]. The high performance of the SRS imaging requires weakening the relative intensity noise (RIN) and timing jitter between these two synchronized pulses trains from OPA.
Generally, OPAs can be seeded by various seed sources, resulting in different kinds of OPAs, such as vacuum noise seeded OPA [9–13], white-light continuum (WLC) seeded OPA [14,15], and narrowband continuous wave (CW) seeded OPA [16,17]. Several groups have characterized the RIN or timing jitter of their OPA systems [10–13,15,17]. Vacuum noise seeded OPA, also known as optical parametric generator (OPG), has the simplest construction but suffers from an inherently large pulse-to-pulse intensity fluctuation due to the fact that OPG is essentially equivalent to the amplification of vacuum noise [10]. It has also been shown, both numerically and experimentally, that the intensity fluctuation can be suppressed by driving the parametric process close to or into saturation [10–13], but result in a larger timing jitter [12,13]. By employing a soliton seeded OPA with two-stage concept, lower pulse-to-pulse intensity fluctuation and higher long-term stability have been demonstrated, compared to the traditional WLC seeded OPA [15]. Most recently, the narrowband CW seeded OPA has exhibited much lower level of intensity noise compared to the OPG seeded OPA [17]. Up to now, a detailed experimental and theoretical study of the intensity and temporal noise from OPAs and how to minimize these noise is still absent.
In this work, we focus on the RIN and relative timing jitter (RTJ) between the signal and pump pulses from OPAs. Fiber-laser pumped OPAs with three different seed sources are used for research. An optical cross-correlation method [18] is employed for timing jitter characterization with sub-femtosecond temporal resolution. The narrowband CW seeded OPA exhibits the lowest root-mean-square (RMS) RIN of 0.79%, compared to the WLC seed OPA (1.74%) and OPG seeded OPA (22.6%), integrated from 1 kHz to the Nyquist frequency of 1.25 MHz. Besides, this narrowband CW seeded OPA also shows the lowest RMS RTJ of 0.32 fs, compared to the WLC seeded OPA (0.63 fs) and OPG seeded OPA (12 fs), in the same integrated frequency range. The experimental results are compared with a numerical model based on a nonlinear envelope equation that goes beyond the traditional slowly varying approximation. The comparison reveals that the RIN and RTJ coupled from the noise of the seed source is mostly suppressed by narrowband CW seeding. For the purpose of further reduction of noise from this narrowband CW seeded OPA, the dynamics of its RIN and RTJ when it is driven into saturation is discussed in simulation.
2. Experimental setup and results
Figure 1 illustrates the experimental setup, which contains a home-built Yb-fiber laser system, three different seed sources, a collinear OPA and a sum frequency generator (SFG) for timing jitter measurement. The OPAs are pumped by the Yb-fiber laser system, including a 50 MHz Yb-fiber oscillator centered at 1035 nm, a pulse picker based on acousto-optic modulation (AOM) device, a dual-stage Yb-fiber amplifier and a pulse compressor, more details are described in our earlier work [19]. The Yb-fiber laser system provides 1 W, sub-100 fs pulses, and the repetition rate is set to 2.5 MHz for sufficient average power and pulse energy. The nonlinear crystal for OPAs is a 25 mm long, 8.5 mm wide, and 1mm thick 5% MgO-doped periodically poled LiNbO3 (MgO:PPLN), with seven gratings with periods ranging from 28.5 to 31.5 μm, in step of 0.5 μm. In order to systematically study the noise characteristics of OPAs, we choose three different seed sources for comparison, which include the WLC generated in a photonic crystal fiber (PCF), a commercial narrowband CW laser and an OPG by using the same type of MgO:PPLN crystal as the OPAs. The narrowband CW laser used in our experiments is a commercial laser module (RIO Orion Laser Module, RIO0074-3-02-3), which delivers CW laser at central wavelength of ~1550 nm with spectral linewidth (Lorentzian) less than 5 kHz. This CW laser also exhibits low frequency noise of ~10 Hz/ and RIN of −150 dB/Hz (equivalent to 10−15 1/Hz), at the offset frequency of 1 MHz. It's worth noting that we cut the length of the PCF (NKT, SC-3.7-975) to 6 mm with the purpose to reduce the extra RIN-coupled noise from the WLC process [20]. The RTJ of the OPAs are characterized by an optical cross-correlation method in a SFG based on a type-II phase-matched beta-barium borate (BBO) crystal. By using this cross-correlation method we can convert the timing jitter to the photodetector voltage fluctuations with high sensitivity, which has been widely used for timing jitter measurements in many kinds of ultrafast lasers [18,21,22].
Fig. 1 Schematic setup to characterize RIN and RTJ of OPAs with three different seed sources. TD: time delay, WP: wave plate, PBS: polarization beam splitter, DM: dichroic mirror, SPF: short pass filter, PD: photodetector, OSC: oscilloscope, SSA: signal source analyzer. (a), (b) and (c) are three different seed sources of OPAs
The output pulses of the Yb-fiber system split into two arms using a half-wave plate and a polarization beam splitter (PBS). One arm is used as the driving pulses for the WLC generation or OPG, the other arm split into two arms again which are respectively used as the pump pulses of the OPAs and the reference pump pulses for the RTJ measurement. By rotating the half-wave plate, we can continuously vary the optical power coupled into the PCF (or the MgO:PPLN crystal for OPG) and, hence, obtain a WLC generation (or an OPG output) with proper central wavelength and average power. At the PCF (or the OPG) output, a dichroic mirror (DM) is used to spatially combine the WLC (or the OPG) pulses and the pump pulses before sending them into the MgO:PPLN crystal for the following OPA stage. In order to ensure the overlap between the seed pulses and pump pulses inside the MgO:PPLN crystal, a time delay line (TDL1) is employed for adjusting the optical distances. An optical spectrum analyzer (YOKOGAWA, AQ6370B) with a resolution of 0.5 nm (0.02 nm for measurement of the narrowband CW laser) is employed to record the optical spectrums. The output pulses durations are characterized by using a commercial optical autocorrelator (APE, PulseCheck).
Due to the fact that the noise properties of WLC generation strongly depend on the soliton number N, we firstly calculate the number N. The soliton number N is determined by both pump pulse and fiber parameters through N2 = LD/LNL. Here LD = T2 0/|β2| and LNL = 1/P0 are the characteristic dispersive and nonlinear length scales, where T0 is the pulse duration, β2 is the 2-order dispersion parameter, and P0 is the peak power. Based on our experiment parameters for WLC generation, the calculated soliton number N is 68. Generally, pulse breakup, decay and decoherence will easily appear with such a high value of N, resulting in a poor noise performance of the WLC seed pulses. However, obvious pulse breakup, decay and decoherence only occur after the pulse propagation over a fission distance, which is defined as Lfiss = LD/N (calculated to be ~19 mm in our experiment) [23]. Because the length of PCF used for WLC generation in our experiment is only 6 mm, the soliton fission would have negligible effect on the noise performance of WLC seed pulses.
With incident pump power of 240 mW, the output power of OPAs are 41 mW (WLC seeded OPA), 45 mW (narrowband CW seeded OPA) and 45 mW (OPG seeded OPA), according to the seed power of 1.5 mW, 5 mW and 3 mW, respectively, which indicate that all the three OPAs are working above saturation. Figure 2 shows both the temporal and spectral characteristics of OPA outputs. The central wavelengths of WLC seeded- (pink line), narrowband CW seeded- (blue line) and OPG seeded OPA (red line) are 1530 nm, 1550 nm and 1525 nm, respectively, as shown in Fig. 2(a)-2(c). The insets show the spectrums of their corresponding seed sources. The autocorrelation traces of the three OPAs are plotted in Fig. 2(d)-2(f), which point out that the full width at half maximum (FWHM) of the autocorrelation traces are 135 fs, 240 fs, 170 fs, in a time span of 5 ps. The insets show their respective autocorrelation traces in a longer time span of 15 ps, implying the absence of sub-pulses. The broader pulse duration of narrowband CW seeded OPA is due to its narrower optical spectral width, as a result of the narrowband CW injection seeding [17].
Fig. 2 The output characteristics of the OPAs. Optical spectrums of (a) WLC seeded-, (b) narrowband CW seeded- and (c) OPG seeded OPA; Autocorrelation traces of (d) WLC seeded-, (e) narrowband CW seeded- and (f) OPG seeded OPA.
At the OPAs outputs, the generated signal, idler and the residual pump are separated by a dichroic mirror (DM), which is also used to spatially combine the OPA output pulses and the reference pump pulses for the following RTJ measurement. A wedge prism (not shown in Fig. 1) is used to split about 1% of the OPA outputs for RIN measurement. The signal source analyzer (SSR) used for the RIN and RTJ characterization contains a fast Fourier transform (FFT) analyzer (Stanford research systems, SR770) and an RF analyzer (Agilent, 8560EC).
Figure 3(a) shows the RIN measurement results, which indicate that the RMS RIN is 1.74%, 0.79% and 22.6% integrated from 10 Hz to 1.25 MHz (the Nyquist frequency) from the WLC seeded- (pink line), narrowband CW seeded- (blue line) and OPG seeded OPA (red line), respectively. The spectral density of RIN from the pump pulses is also plotted in Fig. 3(a) with gray line and its integrated RMS RIN is 0.33%. The integrated RMS RIN of the pump pulses is about half of the lowest integrated RIN from all these three OPAs (0.79% from the narrowband CW seeded OPA), which implies that OPA could exhibit higher intensity fluctuation than the pump pulses. Compared with the OPG seeded OPA, which suffers from strong intensity fluctuations, the OPAs with both the WLC seed and CW seed demonstrates a much lower RIN, which are in accordance with some previous works [16,17].
Fig. 3 Noise measurement results of OPAs. (a) Top: Spectral density of RIN from WLC seeded OPA (pink), narrowband CW seeded OPA (blue), OPG seeded OPA (red) and pump pulses (gray); Bottom: Integrated RMS RIN. (b) Top: Spectral density of RTJ from WLC seeded OPA (pink), narrowband CW seeded OPA (blue) and OPG seeded OPA (red); Bottom: Integrated RMS RTJ.
The spectral density of RTJ from the WLC seeded-, narrowband CW seeded- and OPG seeded OPA are plotted in Fig. 3(b) with pink line, blue line and red line, respectively. The corresponding RMS RTJ is 0.63 fs, 0.32 fs and 12 fs integrated from 10 Hz to 1.25 MHz. The RTJ data show a similar situation as the RIN. The integrated RTJ from narrowband CW seeded OPA is about half of the integrated RTJ from WLC seeded OPA, both these two are much smaller than the OPG seeded OPA’s. As evident from Fig. 3(a), the RTJ curve from the narrowband CW seeded OPA follows exactly the same frequency dependency as the RIN curves from the pump pulses, implying that the RTJ from narrowband CW seeded OPA is mainly coupled from the pump pulses’ RIN. The noise of CW laser has negligible influence on the RIN and timing jitter of OPA output. Besides the RTJ curve from WLC seeded OPA follows the same frequency dependency as its own RIN curves, rather than the pump pulses’ RIN, indicating that the noise of WLC seeded OPA is dominated by the noise of the WLC seeding pulses (e.g., the RIN and timing jitter), instead of the intensity fluctuations of the pump pulses. The strong correlation between the RTJ and its RIN in the case of the WLC seed could be understood as such a process: the pump RIN causes fluctuations of the center frequency of the WLC seed pulse, which then couples to the timing jitter through the fiber dispersion [20].
3. Numerical simulation and discussion
In order to study the noise characteristics of OPAs from a dynamic point of view, an accurate numerical model is required for following research. Generally, the dynamic processes in ultrafast optical parametric phenomena (e.g., OPA, OPG and OPO) are considered as the interaction of three waves (pump, signal and idler), which could be described by coupled nonlinear equations with slowly varying envelope approximation [24]. Since the carrier wave is absent in these coupled nonlinear envelope equations, this theory does not apply to every case, such as considering an ultrafast pulse with few optical cycle [25,26]. Recently, a single-wave envelope equation termed the forward Maxwell equation (FME) has been demonstrated to simulate the super-continuum generation in quadratic nonlinear media [26]. The FME allows treatment of all the harmonics by means of a single equation, which will be very suitable in processing the optical parametric phenomena. Meanwhile, this model provides an easy access to introduce a narrowband CW injection seeding into the OPA simulation. The FME in a moving coordinate can be derived as
where, c is the vacuum velocity of light, ε0 the vacuum dielectric permittivity, vref the group velocity at the referenced frequency, n(ω) the frequency-dependent refractive index, k(ω) = n(ω)ω/c denotes the propagation constant, E(z, ω) and PNL(z, ω) refer to the Fourier transform of the electromagnetic field E(z, t) and the second-order nonlinear polarization PNL(z, t), respectively.Being distinguished from the coupled nonlinear equations with slowly varying envelope approximation, the E(z, t) here refer to the real electromagnetic field. In the case of broadband pulse seeding in an OPA system, the initial E(0, t) could be derived as
where, E0s and E0p are the electromagnetic amplitude of the seed pulse and the pump pulse, τs and τp the corresponding pulse durations considering a Gaussian pulse shape, ωs and ωp the corresponding central angular frequencies. Due to the fact that the linewidth of the CW laser (5 kHz) is much narrower than the linewidth of the pump pulses (~5.5 THz), we consider the CW laser as a single-frequency laser in simulation. So in the case of narrowband CW seeding, the E(0, t) could be simply derived asFor comparison, we numerically solve the FME to simulate the OPAs seeded by the broadband pulse and narrowband CW respectively, by using the split-step Fourier method with fourth-order Runge-Kutta algorithm in processing its nonlinear steps. Modeling parameters are selected to be consistent with our experimental conditions. It's worth noting that the accurate simulation of the dynamics in an OPA system will cost lots of time, especially in calculating the pulse position with the accuracy of few attosecond. For the purpose to save computing time, we shorten the length of PPLN from 25 mm to 5 mm in simulation and ensure that all the two kinds of OPAs are working above saturation. The nonlinear coefficient d33 of PPLN crystal is set to be 27 pm/V [26], as well as the poling period of 29.5 μm. The injected pump pulse duration is set to be a 150 fs FWHM Gaussian pulse centered at 1040 nm with a repetition rate of 2.5 MHz and average power of 250 mW. The beam waist is set to be 90 μm inside the nonlinear crystal. The exact dispersion relation is obtained from the Sellmeier equation [27]. The average powers of the seed sources are set to 1.5 mW and 2.5 mW for broadband pulse seeding and narrowband CW seeding respectively, with central wavelength of 1530 nm.
Figure 4 represents the evolution of signal and idler pulses during their interaction along the PPLN crystal. Figure 4(a) and 4(d) trace the average powers of signal and pump pulses along the crystal, from the broadband pulses seeding or narrowband CW seeding to the saturated propagation, respectively. The trends of the average power indicate that the stimulated and saturated positions of both the broadband pulse seeded- and narrowband CW seeded OPA are similar, which are around z = 1 mm and z = 4 mm respectively. The normalized temporal evolution of signal and idler pulses are shown in Fig. 4 (b), 4(c) and Fig. 4 (e), 4(f) for these two OPAs. The axis “time” is with respect to the pump pulse. Consistent with the average power curves, the formations of signal and idler pulses occur at z = 1 mm, and then the signal and idler pulses remain temporally locked to the pump pulses until saturation takes place at z = 4 mm. At saturation, the energy exchange among pump, signal, and idler is strongly reduced, pulses are no more locked and walk each with its own group velocity. It's worth noting that the signal and idler pulses move away from the pump in the same direction after the saturation, limiting the interaction length, which lead to a lower pump-signal conversion efficiency [24].
Fig. 4 Simulation of signal and idler profiles of (a)-(c) broadband pulse seeded- and (d)-(f) narrowband CW seeded OPA. Upper panels show the energies of pump and signal pulses; lower panels map the normalized pulse intensity as a function of z.
In a broadband pulse seeded OPA, the RIN of pump and seed pulses, and the RTJ between the pump and seed pulses will be converted into the temporal and intensity noise of the OPA signal pulses. Whereas in the narrowband CW seeded OPA, only the RIN of pump and seed will lead to the noise of OPA signal pulses due to absent of the RTJ between the pump and seed. The evolutions of the temporal profiles of OPAs outputs (shown in Fig. 4) exhibit that the signal pulses will lock with the pump pulses before driving into saturation and then the signal and will walk away with its own group velocity, which is linear propagation without nonlinear effects. Since the noise of the pump and seed pulses will result in different positions of saturation, leading to different lengths of the linear propagation regime with a definite length of nonlinear crystal. As a result, different temporal walk-offs between the pump and signal pulses emerge due to these different lengths of the linear propagation regime, which is the mechanism of the relative timing jitter for OPA signal pulses. On the other hand, the noise of the pump and seed pulses will be also converted into intensity fluctuations of OPA signal pulses, exhibiting as the RIN.
In order to further investigate the transfers of the pump and seed’s noise to the resulting OPA signal’s noise, we respectively calculate the output relative fluctuation (ORF) and RTJ of OPA signal pulses coupled from the intensity relative fluctuation (IRF) of pump and seed in these two kinds of OPAs. In addition, the ORF and RTJ coupled from the RTJ between the pump and seed pulses (assuming this RTJ from 1 fs to 5 fs) are taken into account, in the case of broadband pulse seeding (Fig. 5(c)). It's worth noting that we should distinguish the abbreviation “ORF” here from “RIN”, where the latter one is generally presented in the form of power density spectrum [28]. By assuming the IRF from 1% to 5% for the pump and seed, the resulting ORF and RTJ are plotted in Fig. 5(a), 5(b) and Fig. 5(d), 5(e), according to the broadband pulse seeded- and narrowband CW seeded OPA, respectively. It is obvious that these two kinds of OPAs show very different noise characteristics. For the broadband pulse seeded OPA, the seed pulses’ noise makes huge contribution to the signal’s temporal and intensity noise. Seed pulses with 0.5% IRF and 5 fs RTJ between the pump and seed pulses could cause about 4% ORF and 600 as RTJ. Whereas in the narrowband CW seeded OPA, most of the noise of signal are coupled from the intensity noise of the pump pulses. Meanwhile the seed source-coupled noise are suppressed by this narrowband CW injection seeding, which helps explain why the RTJ from this kind of OPA follows exactly the same frequency dependency as the RIN curves of the pump pulses in our previous experiments. Although an identical IRF of pump seems cause more RTJ in a narrowband CW injection seeded OPA than the broadband pulse seeded one, the IRF of pump pulses will lead to a higher intensity and temporal noise during the WLC generation [20], which may cause much more noise of OPA signal pulses in the latter OPA. As a consequence, even with the same noise level of the CW seed and the WLC/OPG seed, the CW seeded OPA still exhibits much lower intensity noise and timing jitter than the pulses (WLC/OPG) seeded one, which is confirmed by our experimental results as well.
Fig. 5 Top: Simulated ORF (pink) and RTJ (blue) of broadband pulse seeded OPA coupled from (a) IRF of pump pulses, (b) IRF of seed pulses and (c) RTJ between pump and seed pulses, respectively. Bottom: Simulated ORF (pink) and RTJ (blue) of narrowband CW seeded OPA coupled from (d) IRF of pump pulses and (e) IRF of seed, respectively.
As described above, the signal pulses will lock with the pump pulses before driving into saturation and then the signal and will walk away with its own group velocity. When the OPAs are driving before saturation, the RTJ between the pump and signal pulses could be suppressed by this locking mechanism. On the other hand, since the signal intensity grows much faster with the crystal length z before saturation, an identical IRF of the pump would cause a higher ORF than the situation of saturation. For purpose of getting an insight into the OPAs’ noise characteristics below and above gain saturation, we calculated the ORF from the narrowband CW seeded OPA at different crystal depths, with a 0.5% initial IRF of the seed and pump, respectively. As we expect, the narrowband CW seeded OPA exhibits a smaller intensity fluctuation but a lager temporal jitter when it is driven into saturation, as shown in Fig. 6. Consequently, the numerical simulation indicates that lower timing jitter and affordable intensity fluctuation can be obtained simultaneously when OPA are operated close to saturation, which could be realized by choosing a proper crystal length, as well as carefully optimizing the optical power of the pump and seed.
Fig. 6 Simulated ORF (pink) and RTJ (blue) of narrowband CW seeded OPA due to (a) a 0.5% IRF of pump pulses and (b) a 0.5% IRF of seed versus the crystal length z, respectively.
4. Conclusion
In conclusion, we have investigated the noise characteristics of OPAs respectively seeded by broadband WLC generation, narrowband CW injection and OPG. The narrowband CW seeded OPA exhibits the lowest RIN and RTJ of 0.79% and 0.32 fs [1 kHz 1.25 MHz], respectively, among the three kinds of OPAs. The experimental results are compared with an improved numerical model, indicating that the narrowband CW injection seeding can suppress most of the RIN and RTJ coupled from the noise of the seed source, being one of the important contributions to RIN and timing jitter in a broadband pulse seeded OPA. We also find that this kind of OPA exhibits a smaller intensity fluctuation but a lager temporal jitter when it is driven into saturation in simulation, which provides an effective approach to the further reduction of noise from this kind of OPA. The low level of noise from a narrowband CW seeded OPA is likely to benefit a number of femtosecond-precision timing and synchronization applications which call for femtosecond sources with tunable wavelength.
Funding
National Natural Science Foundation of China (NSFC) (61535009, 11527808, 61605142); Changjiang Scholars and Innovative Research Team in University (IRT13033); Open Fund of the State Key Laboratory on Integrated Optoelectronics (IOSKL2014KF11).
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