We study, both numerically and experimentally, the relative intensity noise (RIN) and timing jitter characteristics of optical parametric generation (OPG) process in MgO-doped periodically poled LiNbO3 (MgO:PPLN) pumped by fiber femtosecond laser. We directly characterize the RIN, and measure timing jitter spectral density of the OPG process based on the balanced optical cross-correlator (BOC) technique for the first time as well, which are both in a fairly good agreement with numerical simulation. Both the numerical and experimental study reveals that OPG can suffer from a smaller intensity fluctuation but a lager temporal jitter when it is driven into saturation. Furthermore, we demonstrate that with a 30 mW CW diode laser injection seeding the OPG output results in superior noise performance compared to the vacuum fluctuations seeded OPG.
© 2017 Optical Society of America
Femtosecond laser sources are of great importance in a variety of applications including multi-photon fluorescence , time-resolved optical spectroscopy , coherent Raman scattering microscopy , as well as light-matter interaction at the nano-scale . Traditionally, femtosecond lasers have been used in time-resolved studies due to its ultrashort pulse duration. Nowadays, a high power, broadband tuning spectral range and excellent noise performance are almost compulsive for applications with femtosecond lasers. There are already lots of technologies which exist to achieve high power and broadband laser spectrum. For the noise of ultrafast laser pulses, there is an increasing concern, no matter where the noise directly comes from, oscillators with cavity or nonlinear process without cavity. Noise characteristics such as relative intensity noise (RIN) and timing jitter must be considered to determine whether the ultrashort pulses are quiet enough for the intended applications. To improve currently existing low-noise applications and further enable new applications, the noise of ultrashort pulse laser must be properly measured and then controlled.
Nonlinear frequency conversion techniques can provide the possibility to realize effectively tunable laser sources in a wide spectral region. The optical parametric processes, consisting of optical parametric generation (OPG), optical parametric amplifiers (OPAs) and optical parametric oscillators (OPOs), have been shown to be attractive laser sources of coherent radiation and broad spectrum. Compared with OPOs, OPG/OPAs are simpler, more robust and economical devices since no synchronization of a cavity to pump laser is required. The scheme for OPAs is less complicated than OPO. However, the OPAs still require an initial seed signal pulse. The seed pulses must be generated by a nonlinear optical process and cover the desired spectral wavelength range, leading to the complexity of the experimental system. As a result, the OPG is more promising for practical applications due to its robustness, flexibility as well as cost-effectiveness.
The combination of high average power femtosecond fiber lasers as pump sources and nonlinear crystal with very high effective nonlinearity allow high parametric gains, enabling high repetition rate as well as high average output power single pass femtosecond OPG [5,6]. In addition, a double pass OPG approach allowing for a highly efficient tunable output in the NIR has also been reported recently . Except for conversion efficiency and spectral tunability property, high pulse-to-pulse energy stability and tight synchronization between two independent sources are essential for time-resolved spectroscopy and nonlinear optics. Therefore, noise characteristics such as RIN and timing jitter have to be considered. In the last few years, C. Manzoni has investigated the temporal jitter characteristics and the carrier-envelope (CEP) relationship between the OPG and the pump pulses. They evaluated the timing jitter and measure the CEPs of the signal pulses based on an f–2f interferometer . A detailed theoretical study as well as a directly experimental measurement of the RIN and timing jitter spectral density of OPG output is still missing. Moreover, the route towards minimum intensity fluctuations and timing jitter is highly desirable.
In this paper, we investigate the RIN and timing jitter characteristics of OPG output pulses. More than 2 W average output power of signal at 1474 nm is generated pumped by a 6 W Yb-fiber laser amplifier system. We build a complete numerical model to calculate the noise performance of the OPG output by solving the Forward Maxwell Equation (FME), with a quantum mechanical initiation mimicked by a noise field. To date, balanced optical cross-correlation method has been proposed as a sensitive technique for measuring timing jitter of mode locked laser rather than that of OPG [9–11]. BOC method  is introduced, for the first time, to the best of our knowledge, to characterize the RIN and the timing jitter spectral density of the OPG output pulses. Both the numerical and experimental study present that driving the OPG process into saturation will lead to a better pulse-to-pulse intensity stability, but a lager temporal jitter when compared with the OPG working below the gain saturation. In order to further suppress the intensity fluctuation as well as to lower the temporal jitter of the OPG output, we adopt the well-known injection seeding method . In this case, with a 30 mW CW diode laser seeding the OPG process exhibits superior noise performance compared with the quantum noise seeded one.
2. Numerical simulations and discussion
A single-wave envelope equation termed the Forward Maxwell Equation (FME) has been commonly used to simulate the pulse dynamics in OPG process . Considering the OPG process is intrinsically quantum based phenomenon, it is commonly described by a two stage semi-classical approach, where the input is quantum noise and the propagation follows classic field nonlinear interaction [15, 16]. Accordingly, we extend FME equation to calculate the RIN and timing jitter spectral density of OPG output by introducing initial quantum noise and pump RIN. For femtosecond OPG process, group-velocity mismatch between the interacting waves must be considered. Following Ref , the FME in a moving coordinate can be derived as17]. Equation (1) can be numerically solved in the frequency domain by the split-step Fourier method with fourth-order Runge-Kutta nonlinear steps.
The semi-classic noise process in OPG can be modeled following Wigner method , which is frequently used to describe noise processes in laser amplifiers. In OPG, vacuum fluctuations are considered to be amplified by parametric gain. The input quantum noise has a random amplitude δE(t) with a autocorrelation of
Next, based on this theory, we have simulated the RIN and timing jitter performance of the OPG output in the numerical model with initial quantum noise. Modeling parameters are selected to be consistent with our experimental conditions. In this case, we use a 25-mm PPLN crystal with a nonlinear coefficient deff = 27 pm/V, as well as poling period Λ = 30 μm (corresponding interacting central wavelength is 1505 nm). In this period, the signal and the idler pulses walk in opposite directions with respect to the pump, in this way the interaction of parametric process could be enhanced . The injected pump pulse duration is set to be a 400 fs FWHM (full width at half maximum) chirped Gaussian pulse centered at 1040 nm with a repetition rate of 53 MHz (the corresponding Fourier transform limited pulse duration is 100 fs). The beam waist is set to be 45 μm inside the nonlinear crystal. The exact dispersion relation as obtained from the Sellmeier equation  is inserted to make sure that the OPG process is accurately modeled. In order to give a full statistical result of the OPG process, we have calculated a sequence of output pulse temporal positions for 10000 independent simulations initiated by random quantum noise field. The pulse properties, such as pulse intensity, temporal position, etc. are recorded after each calculation. Following the method in , the RIN and timing jitter spectral density are evaluated by the timing errors and intensity errors caused by the temporal and intensity deviations between two adjacent pulses, respectively.
Figure 1(a) displays the RIN spectral density of generated signal pulses when the OPG processes are operated below and above gain saturation, respectively. Clearly, the RIN of the OPG working above the gain saturation is 20 dB lower than below the gain saturation. This also explains the well-known fact that the OPG can suffer from a smaller fluctuation only if driven into saturation [7, 8]. The two main factors governing the OPG output intensity fluctuations are the parametric gain and the quantum noise. As is shown in Eq. (3), the parametric gain of OPG process is proportional to the amplitude of pump electric field. Thus, the RIN of OPG output can be determined by the pump power and initial noise. Before saturation, the RIN spectra density shows a white frequency noise property in a wide frequency range due to the quantum-mechanical phenomenon of the OPG process. After saturation, the OPG process reaches the gain saturation, the output intensity noise will be dominated by the pump laser noise. Generally, pump RIN is lower than the white quantum noise. Thus, the OPG output pulses exhibits an excellent stability when driven into saturation (Fig. 2 shows schematic diagram which demonstrate this process).
In contrast, as shown in Fig. 1(b), the timing jitter of OPG pulse presents a totally different behavior. This can be well explained by using Eq. (1). For simplicity, when backward waves are neglected and the coordinate transformation Γ = t-(z/ vg3) is performed, we can correctly obtain the complex electric field of the signal from Eq. (1)
Subsequently, we consider the spatial and the time variation of the intensity associated with each of these waves. Taking
This equation indicates that the group velocity mismatch could be treated as the loss in the OPG process. As a result, the OPG processes have a pump threshold. Above the pump threshold, the quantum noise can be stimulated at certain crystal position and evolved from the fluctuating random fields to the generated pulse situation. The noise seen in OPG system is not shot noise; it is the quantum noise of the light beam itself. The intensity distribution of quantum noise follows a Gaussian distribution. The exact position is also related with the intensity distribution of input quantum noise. Timing jitter of the generated signal pulses is governed by the exact position. Thus the randomness of quantum noise leads to the temporal jitter of generated signal pulses. See Fig. 2 for a schematic diagram of OPG process, when OPG process operated above pump threshold, quantum noise propagated along the nonlinear crystal and evolved into generated pulse situation (the dark solid line exhibit the intensity evolution of input quantum noise). At saturation situation, there is a larger possibility that quantum noise can be amplified into signal pulses. Thus stimulated positions inside nonlinear crystal are larger. Therefore the generated signal pulses present larger temporal jitter.
Consequently, as observed in simulation, timing jitter and the RIN property of the signal pulses are anticorrelated parameters in the OPG process. When the OPG process is operated above saturation, the generated pulses exhibit a good intensity fluctuation property, while suffer from a strong timing jitter. However, the generated signal pulses showed a somewhat different behavior when the OPG process is worked below saturation.
3. Experimental setup and results
Subsequently, with the aim to characterize the OPG’s power scaling and spectral coverage properties, the experimental setup is depicted in Fig. 3. The OPG is pumped by a home-build Yb-fiber laser system, including a 53 MHz Yb-fiber oscillator, an Yb-fiber amplifier and a pulse compressor, providing up to 6 W output power. Its central wavelength is 1040 nm with an FWHM of 34 nm, as well as pulse duration of 100 fs. The nonlinear crystal for OPG is a 25 mm long, 8.5 mm wide, and 1mm thick 5% MgO:PPLN, with seven gratings with periods ranging from 28.5 to 31.5 μm, in step of 0.5 μm. In our experiment the crystal is housed in an oven whose temperature is adjustable from room temperature to 200 °C. A combination of a half-wave plate (HWP) and a polarization beam splitter (PBS) are used here to control the injection pump power into the crystal. Two lenses are used for focusing and collimating the beam through the nonlinear crystal, respectively. The generated signal, idler and the residual pump are separated by a dichroic mirror (DM), which is 99% reflective over 1400 nm ~2100 nm, 95% transmittive for the pump and highly transmittive for the idler wavelength.
The pump pulse is focused to the OPG crystal with a focusing lens (f = 200 mm), making sure the beam waist radius of 60 um at the center of crystal. We obtain the maximum OPG output power by optimizing the transmitting grating pairs first, and the corresponding pump pulse duration are measured to be 400 fs. Figure 4(a) presents the signal spectra and average output power for different poling periods measured at 40 °C and 6 W pump input. Clearly, the signal spectra can be tuned from 1420 to 1560 nm. The filled black circles indicate the average OPG signal output power at each period with 6W incident pump power, and the maximum output power is 2.1 W at 1474 nm. Furthermore, as is demonstrated in Fig. 4(b), the precisely adjustable of the crystal temperature allows for gap-free tuning of the signal wavelength for the 29.5 μm poling period. Figure 4(c) depicts a typical autocorrelation of signal pulses at 1474 nm, with the pulse duration of 350 fs. We also characterize the power scaling of the OPG output as a function of average input pump power. Using the poling period of 29.5 μm and operating at temperature of 40 °C, we are able to extract up to 2.1 W of signal for an average pump power of 6 W, corresponding to a conversion efficiency of nearly 36% (see Fig. 4(d)).
Note that the MgO:PPLN nonlinear crystal used in our experiment is definitely longer in comparison with the crystals reported in other femtosecond OPG processes [5–7]. As expected, this configuration enabling significantly larger spot sizes on the face of nonlinear crystal allows higher pump power and has a higher damage threshold, which can lead to an efficiently single pass OPG output. Our experiment also presents that a higher efficiency is obtained using negatively chirped pulse. Based on theory in , we attribute this phenomenon to the fact that the pump to signal conversion efficiency is determined not only by the duration of incident pump pulse but the dynamic propagation of the pump pulse in the nonlinear crystal. The negatively chirped pulse is compressed first in the front of the crystal due to the dispersion compensation by positive dispersion of the crystal. On the other hand, when the pump pulses propagate in the front of the nonlinear crystal, the phase matched signal pulse slightly amplify from the quantum noise field and the pump deplete slowly under this condition. Subsequently, the huge pump depletion occurs nears the spot point inside the crystal. We choose the 25-mm nonlinear crystal due to this accumulated effect inside the nonlinear crystal. Thus, the high pump depletion occurs in a rather short distance inside nonlinear crystal (the measured pump depletion is shown in inset of Fig. 4(d)) owing to the large nonlinear coefficient of long MgO:PPLN and high incident pump power. This effect could weaken the large temporal walk-off in a long crystal. Therefore, the corresponding signal acceptance bandwidth is still large and the measured signal pulse duration is comparable to the pump pulse. However, for wavelength above 1520 nm, the GVM of the signal and the idler with respect to pump pulse have the same sign and then lead to a large temporal walk-off and short pulse interacting length in the crystal. Meanwhile, the reflectivity of the crystal becomes larger in this wavelength range limited by crystal coating technique. As a result, the average output power decreases significantly for wavelength above 1520 nm.
In what follows, we focus on the experimental characterization of noise performance based on the BOC method. When we measure the timing jitter spectral density of the OPG output, we convert the timing jitter to the photodetector voltage fluctuations. Anticorrelated relationships between the RIN and timing jitter properties have been found in our simulation. Apparently, the intensity fluctuations will influence the temporal jitter measurement results. It is remarkable that BOC could precisely extract the timing information without conversion of intensity noise into timing jitter . To overcome the influence of intensity fluctuations in OPG process, BOC approach is used here to measure timing jitter spectra density directly and accurately. The layout of the system is presented in Fig. 5 (the CW seed unit in the dash rectangle is not used in this part). The pump beam is equally divided into two arms with the help of HWP and PBS. We alter another focus lens (f = 100 mm) to reduce the pump threshold as well as to achieve significant conversion efficiency at lower pump power. Limited by the coating wavelength range of PPKTP (AR, 1500~1600 nm), the poling period is switched to be the 30 μm one (the same poling period as used in the numerical simulation). Additionally, a PBS is used to spatially combine the two arms of signal pulses before sending them into the BOC setup. Similar power scaling and wavelength tunability performance is measured from each branch. When pumped by 0.9 W, OPG process is below saturation, providing 10 mW signal output pulse. Increasing the pump power to 1.8W, the process is at saturation and 410 mW average output power has been measured. The combined OPG signal pulses are then filtered out by high bandpass filter (HBF), and combined into the mentioned BOC system based on PPKTP. We measured the RIN and timing jitter spectral density by a fast Fourier transform (FFT) analyzer (Stanford research systems, SR770) as well as an RF analyzer (Agilent, 8560EC).
Figure 6(a) shows the measured spectral density of relative intensity noise (RIN) of OPG output. The root-mean-square (RMS) RIN is 43.02% and 1.95% integrated from 10 HZ to 5 MHz for the process operated below and above saturation, respectively. The two curves of RIN in Fig. 6(a) clearly indicate that the RIN contribution below 1 MHz is small. Thus, the measured spectral density exhibits good consistent with the numerical simulations. The RIN of OPG is mainly caused by adding quantum noise to the RIN of pump laser (the RIN of pump laser has been recorded in ). As expected, the OPG process suffers from huge intensity fluctuation when working below saturation, the output pulses intensity become stable when the OPG process is driven into saturation. On the other hand, as illustrated in Fig. 6(b), when the OPG is operated below saturation, the integrated RMS timing jitter is 9.3 fs integrated from 10 Hz to 5 MHz confirming nearly synchronize with the pump pulse; the same measurement above the saturation presents that the jitter could be as high as 50 fs. Offset frequencies above 5 MHz could not be detected which is restricted by the bandwidth of our detector. Spectra density of timing jitter is in reasonable agreement with numerical values. As could be observed from Fig. 6, the timing jitter curve follows exactly the same frequency as RIN curves below saturation, implying that the timing jitter is determined by the RIN of pump pulse; however, parametric generation is intrinsically a quantum noise amplifier process, the timing jitter curve begin to flatten out when the OPG process is driven above saturation. Accordingly, the OPG presents antiorrelated RIN and timing jitter properties. Besides, considering that relaxation time of the atmospheric and temperature fluctuations is long, which will affect the pulse power drift and timing drift in a long time period (several minutes, hours or more). However, the intensity and timing jitter are used for describing short-term stability of the generated pulse. The corresponding frequency spectra range in order to illustrate the RIN and timing jitter is ranging from several hertz to Nyquist frequency. In this frequency range, the temperature fluctuation and air currents have a rather small influence on intensity noise and jitter. And hence, the measured spectral density is in reasonable agreement with the numerical simulations. In addition, we have also verified that, except for average output power and spectra position, the RIN and timing jitter properties had negligible differences under our investigation.
Until now, we have found and proved the intensity fluctuation and temporal jitter of the generated signal pulses in OPG process are determined by the randomness of quantum noise. The fixed stimulated position inside nonlinear crystal will lead to a small timing jitter of signal pulses. The seed laser power will be sufficient to overcome the energy fluctuations associated with unseeded OPG [23, 24]. Thus, in the following part, we investigate the possibility to improve the noise performance of the generated signal pulses in the OPG process with the help of CW injection seeding. The CW laser diode generates 30 mW output power at 1470 nm (The full width at half maximum (FWHM) of spectrum is 0.044 nm, as is depicted in inset of Fig. 7(b)). The seed laser is sent into our system via a DM, which was 99% reflective over 1400 nm ~2100 nm, 95% transmittive over 1000 nm ~1100 nm (the set-up is illustrated in Fig. 5). Compared to the case of no seeding, the CW seeding lowers the pump threshold, enhance the maximum output power, while has a similar spectra of signal. Here, we focus on the RIN of the output pulse. The RIN spectra and calculated the RMS RIN of OPG with a CW seeding is plotted in Fig. 7(a). A noteworthy fact is that the RMS RIN is 7.37%, lowered by a factor of near 6 to the case of no seeding OPG when operated under saturation; while at saturation the RMS RIN is reduced from 1.95% to 0.37%. The peak to peak intensity fluctuations are dramatically improved. Unfortunately, limited by the CW seeding wavelength and the coating wavelength range of PPKTP, we are not able to measure the timing jitter spectra here. However, to confirm the high mutual coherence between the two OPG output pulses, we measure spectral interference between them (as is shown in Fig. 7(b)). The larger timing jitter of the signal pulses, the lower is the visibility of the spectral interference fringes. This result clearly indicates that OPG with a CW seeding operating under pump depletion conditions better preserves the phase relationships of the seed than the OPG process working above depletions situations. Since there is no spectral interference between two branches of OPG output pulses without CW injection (not shown here).The measured spectral interference pattern also suggest the timing jitter occurring between two branches of OPG output with CW injection seed exhibiting superior timing jitter properties.
In conclusion, we have investigated, both numerically and experimentally, the RIN and timing jitter characteristics of the OPG output driven by femtosecond pulses. By solving the FME and measuring the RIN and timing jitter spectra of OPG output based on BOC technique, we verify that it is anticorrelation between RIN and timing jitter. When the OPG process is driven into saturation, the generated signal output pulses exhibit a large temporal jitter but a small intensity fluctuation. Meanwhile, we have also demonstrated a high efficient femtosecond OPG based on a 25 mm long MgO:PPLN nonlinear crystal, operating at 53 MHz repetition rate with a signal tuning range from 1420 nm to 1560 nm and up to 2.1 W average power at 1474 nm. Our experiment results also suggest that the RIN of OPG output can be significantly minimized by a CW injection seeding. By employing a CW seed, this system will be more attractive for mid-infrared difference frequency generation, multi-photon fluorescence and many other demanding scientific applications.
National Natural Science Foundation of China (NSFC) (61535009, 11527808, 61605142); Changjiang Scholars and Innovative Research Team in University (IRT13033).
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