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Abstract
We demonstrated a fiber-based synchronously pumped optical parametric oscillator (SPOPO) with flexible repetition rates while retaining the cavity length. In contrast to conventional free-space SPOPO, the repetition rate of output signal pulses was solely determined by the repetition rate of the pump source in harmonic, fractional and rational operations. The relevant mechanism relies on synchronous pumping and intrinsic losses in our fiber resonator. The novel scheme enabled us to flexibly tune the repetition rate from 0.5 to 6.0 MHz without altering the resonator configuration. The resulting pulse properties were systematically analyzed at various operation conditions, and particularly showed that a wavelength tuning range of 157 nm was obtained. Such rational harmonic resonance implemented in our SPOPO provides not only a simple yet effective way to tune the repetition rate, but also a feasible approach to narrow down the spectral bandwidth. The presented SPOPO could be useful in nonlinear biomedical imaging by offering a convenient approach to optimize the pulse repetition rate for different biomedical samples with minimum photodamage.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Over the past years, optical nonlinear microscopy (NLM) has been tremendously developed as a powerful tool in biomedical spectroscopy and imaging [1–5]. In particular, multiphoton fluorescence microscopy (MPM) and coherent anti-Stokes Raman scattering (CARS) microscopy are two prominent representatives to image dynamics of a sample with features of diffraction-limited resolution, fast imaging speeds, and deep penetration [6–11]. Currently, the most widely used light sources for NLM are bulky lasers such as Ti: sapphire laser or optical parametric oscillator (OPO) with performance optimized at repetition rates around 80 MHz. Recent studies have shown that the repetition rate could be an important factor to increase the imaging depth and reduce the damage caused by heating and phototoxicity [12]. For instance, it is required to use high pulse energy to achieve a large tissue penetration depth to compensate the absorption and scattering losses [13]. However, the strong intensity due to high peak power and tight lens focusing might generate plasma through multi-photon processes and destruct the biological sample [14]. To obtain a high penetration depth, it is common to employ pulsed excitation with a low repetition rate. The relative low repetition rates are suitable for standard laser scanning microscopes with pixel dwell times of 1 μs, with an aim to maximize the penetration depth and minimize phototoxic effects [15]. Besides, the ability to generate dual-color laser pulses would also benefit the laser material processing for simultaneously addressing various components. In order to mitigate the heat accumulation effect, the controllable operation repetition rate would be desirable to optimize the performance of micromachining in laser melting, welding and ablation [16].
Compared to bulky laser systems, fiber lasers could provide desirable features like flexible configuration of cavity geometric length and alignment-free operation in addition to advantages of low cost, compactness, long-term stability and higher efficiency [17,18]. In this context, developing suitable fiber lasers to meet the requirement of NLM application has been a hot topic in recent years [19,20]. For instance, fiber OPO (FOPO) based on photonic crystal fibers (PCFs) has been identified as an alternative source for CARS imaging where two synchronized picosecond pulses with tunable wavelength difference are required to address particular vibrational resonances. In 2013, E. Lamb et al. presented seminal work on self-seeding FOPO generating 46-MHz picosecond pulses [21]. The scheme was later modified with a much longer cavity length to lower the operation frequency for exciting dense biomedical samples [22]. Furthermore, an electronically tunable FOPO was demonstrated in a fixed cavity length, albeit with a limited tuning range of 2 kHz [23]. Up to date, synchronized dual-color FOPO with tunable range of repetition rate up to MHz has not been reported, which thus imposes restrictions on the full ability for one CARS microscopy system to examine different samples with minimized photodamage.
The desirable wide tunability of repetition rate can be realized by the so-called harmonic pumping technique in a synchronously pumped OPO (SPOPO) [24]. The concept of harmonic mode-locking has been widely adopted in developing fiber lasers that can operate at harmonic repetition rates in a predefined cavity length. Moreover, a more flexible scheme involving rational harmonic resonance was proposed [25], leading to the generation of laser pulses at a high repetition rate up to 200 GHz [26]. The aforementioned techniques have been naturally extended to the SPOPO. For a given optical parametric cavity, various operation repetition rates of the SPOPO can be realized by simply altering the repetition rate of the pump pulses [27–29].
In this paper, we propose and implement a novel scheme to generate dual-color pulses with a wide tunability of repetition rate based on a fiber SPOPO in a fixed geometrical arrangement. In contrast to previously demonstrated SPOPOs, the repetition rate of output pulses depends only on the pump rate in all three cases of harmonic, fractional and rational operations. The underlying mechanism relies on synchronous pumping and high losses in our fiber resonator. Consequently, only down-converted pulses overlapped with the pump excitation in the nonlinear medium can acquire sufficient gain for constructive interference. As a result, the novel scheme enabled us to flexibly tune the repetition rate from 0.5 to 6.0 MHz without altering the resonator configuration. Moreover, due to the dispersion filtering effect in the OPO cavity, a broad wavelength tuning range of 157 nm was achieved. In combination of intrinsically temporal and spatial overlap, the generated dual-color laser source would constitute a convenient tool for CARS spectroscopy to examine different samples. Additionally, we have systematically investigated the related important figures of merit such as pump threshold, signal power, wavelength tunability and spectral bandwidth. In particular, it has been found that much narrower spectral bandwidth could be achieved by rational harmonic resonant-SPOPO (RHR-SPOPO). Therefore, CARS microscopy with high spectral resolution and low photodamage could be expected by using such compact and flexible fiber laser source.
2. Theoretical analysis of RHR-SPOPO
In the traditional SPOPO, the cavity loss was controlled to less than 1% to make sure every signal pulse could be resonant in the nonlinear gain medium [27]. As a result, the repetition rate of the output pulse train can be expressed as: fout = N × fc = M × fp, where fc is the fundamental repetition rate of the OPO cavity determined by the cavity length and fp is the pump repetition rate. N and M are two integers with no common divisors. In contrast, if the cavity loss become pronounced, only those signal pulses temporally overlapping with the pump pulses can obtain enough gain to be resonant in the cavity. In this case, the repetition rate of the output pulse train can be expressed as: fout = fp = (N/M) × fc.
Depending on the numerical values of N and M, there are three resonant situations. When M = 1, the pump repetition rate is an integral multiple of cavity repetition rate, corresponding to the harmonic resonance. When N = 1, the repetition rate of the cavity is multiple of that for the pump, corresponding to the fractional or sub-harmonic resonance. If neither M nor N equals to 1, the OPO would be in rational harmonical resonance. The two integer numbers are essential for temporal overlap between signal and pump pulses and thus affect the resonance. More specifically, the integer M can be regarded as the number of laps inside the OPO cavity for the signal pulse to be overlapped with every N pump pulses.
Here we use an example with N = 3, M = 4 to show the feasibility of this method. Figure 1 shows the detailed working process of the SPOPO. The repetition rates of the OPO cavity and the pump pulse train are assumed to be 2.0 and 1.5 MHz, corresponding to pulse intervals of 500 and 666.7 ns, respectively. Each of the pump pulse would generate a down-converted signal pulse circulating in the OPO cavity. Due to the high loss of the cavity, the signal pulse attenuates quickly with the increase of roundtrips. After 4 loops (500 × 4 = 2000 ns), the small signal pulse would overlap with the subsequent 3rd pump pulse which has the same temporal interval (666.7 × 3≈2000 ns). Consequently, the signal pulse could obtain sufficient parametric gain in the nonlinear medium, which ultimately renders the signal resonating in the OPO cavity. Therefore, the repetition rate of the OPO pulse train is determined by that of the pump pulse.
Fig. 1 Schematic diagram for illustrating the generation of pulse train with a fourth-order harmonic repetition rate from a rational harmonic resonant OPO. The fundamental repetition rate of the OPO cavity and the repetition rate of the output pulse train satisfies 3 × fc = 4 × fp .
In the following section, we will experimentally present a fiber-integrated RHR-SPOPO to demonstrate the competence for tuning the repetition rate. To this end, we choose a piece of PCF as the parametric gain medium and use a fiber laser with tunable repetition rate as the pump source.
3. Experimental realization of a RHR-SPOPO
3.1 Basic configuration
The experimental setup is shown in Fig. 2, which consists of two parts: the pump source and the OPO cavity. The pump source was a home-made 1030-nm fiber laser which was composed of a fiber oscillator, a pre-amplifier and a pulse picker. The pulse picker was based on a fiber-coupled acoustic optical modulator (FAOM). To control the pulse picker, a photodiode was used to measure the repetition rate of the oscillator. The electronic signal was then fed into a field programmable gate array (FPGA), which was programmed to send out square wave signal at a sub-harmonic repetition rate. After that, the signal with reduced repetition rate was used as amplitude modulation signal for the AOM driver. The division ratio of the repetition rate could be controlled by a software written in LabVIEW, resulting a tunable repetition rate from 0.50 to 20 MHz. The pulse duration and spectral bandwidth of the pump pulses after pulse picker were 30 ps and 0.2 nm, respectively. The pump spectral bandwidth was then broadened to be 1.2 nm due to self-phase modulation in the main amplifier. The detailed information of the pump source has been reported in our previous work [30]. The OPO cavity included a wavelength division multiplex (WDM), a main amplifier, a piece of PCF, an output coupler and a fiber delay line. The WDM was used to couple the generated signal pulse into the PCF again. The main amplifier was pumped by two 9-W diode lasers. The gain fiber was 1.0-m 14/135 double clad Yb-doped fiber. The PCF had a fused silica core of 5 μm surrounded by air holes (NTK photonics, LMA-PM-5). The length of the PCF was 40 cm. The output coupler was composed of a half wave plate and a polarization beam splitter. By rotating the half wave plate, the output coupling ratio of the fiber OPO could be precisely controlled. In our experiment, the output ratio was set to be 90%. The tuning range of the fiber delay line was 15 cm and the total cavity length was about 100 m.
Fig. 2 Experimental setup of synchronously pumped OPO with rational harmonic resonance. LD: laser diode; WDM: wavelength division multiplex; PCF: photonic crystal fiber; HWP: half-wave plate; PBS: polarization beam splitter; Yb: ytterbium-doped fiber; SMF: single mode fiber; Pre-Amp: pre-amplifier; FAOM: fiber-coupled acoustic optical modulator; FPGA: field programmable gate array; PD: photodiode.
3.2 Output characteristics of RHR-SPOPO
Now we turn to characterize the repetition rate tunability of the implemented RHR-SPOPO. The operation repetition rate was firstly set at 2 MHz, which corresponded to the fundamental repetition rate f of the OPO cavity. By carefully tuning the delay line, signal resonance in OPO at 2 MHz could be obtained. Then we changed the pump repetition rate. Rational harmonic resonances at various repetition rates were observed with the help of adapting the average power of the pump. The oscilloscope traces for nine OPO pulse trains are shown in Fig. 3(a). The repetition rates of the OPO are 0.50, 0.67, 1.0, 1.3, 1.5, 2.0, 3.0, 4.0 and 6.0 MHz, corresponding to rational harmonic orders of 1/4, 1/3, 1/2, 2/3, 3/4, 1, 3/2, 2 and 3, respectively. If we zoomed in the temporal trace, a tiny non-resonant OPO signal can still be observed with an intensity ratio of 1:1000 compared to the resonant signal. The strength of the non-resonant OPO signal was affected by the round-trip cavity loss. In our experiment, the feedback ratio was intrinsically low mainly due to the transmission of fiber components and coupling efficiency to the photonic crystal fiber, which was estimated to be 0.3%. As a result, the non-resonant OPO signal would be intensively attenuated while circling in the cavity. Therefore, this non-resonant signal pulse would make a negligible impact on nonlinear biomedical applications.
Fig. 3 (a) Oscilloscope traces of signal pulse trains for various orders of rational harmonic resonance. (b)-(c) Output power at 985 nm as a function of the pump power. (d) Pump peak power range depending on the harmonic orders. (e) Wavelength tuning by changing the delay line inside the OPO cavity.
Depending on the number of laps (indicated by the integer M), the nine rational harmonic orders can be divided into four groups, which are 1, 2, 3 (Group I: one lap); 1/2, 3/2 (Group II: two laps); 1/3, 2/3 (Group III: three laps); and 1/4, 3/4 (Group IV: four laps). In general, higher number of laps would result in higher propagation losses for the resonant signal pulse. Figures 3(b) and 3(c) shows the output signal power at 985-nm as a function of the pump power for various rational harmonic orders. For each group, the slope efficiencies were calculated to be (10%, 9.9%, and 9.8%) for (Group I: 1st, 2nd, and 3rd) harmonics; (8.6% and 8.4%) for (Group II: 1/2 and 3/2) rational harmonics; (7.4% and 7.2%) for (Group III: 1/3 and 2/3) rational harmonics; and (5.1% and 5.0%) for (Group IV: 1/4 and 3/4) rational harmonics, respectively. Inside each group, the slope efficiency of each rational harmonic is almost the same, which implies that the total transmission loss affected by the number of laps (Integer M) has a direct impact on the slope efficiency of the RHR-SPOPO. Between different groups, the slope efficiency drops with the increased number of laps due to higher cavity loss. Figure 3(d) depicts the available pump peak power range at each harmonic. The left dot in each line represents the threshold while the right dot represents the maximum pump peak power. Further increase of pump power at each harmonic would introduce other nonlinear effects such as self-phase modulation (SPM), cross-phase modulation (XPM) and stimulate Raman scattering (SRS), which would result in a supercontinuum spectrum [31]. Inside each group, although the absolute output repetition rates were different, the pump threshold and maximum peak power remained the same, which were mainly determined by the FWM process in PCF. For larger number of the laps, the pump thresholds were higher due to the increased cavity loss. The power stability of the pump and resonant signal at second harmonic resonant case was measured, revealing the root-mean-square (RMS) power fluctuations of 1.24% and 2.11% for the pump and signal lasers, respectively.
Thanks to the dispersion filtering effect, the wavelength of the signal pulse could be continuously tuned by changing the delay line [21]. We defined R as the changing rate of the output signal wavelength relative to the mechanical delay distance of the fiber delay line. This changing rate could be theoretically estimated by the formula R = dλ/dL = D × Lc × c/M, where D is the chromatic dispersion, Lc is the optical length of the OPO cavity, c is the speed of the light, and M is the number of laps for a feedback signal encountered with the pump pulse. For the SPOPO at the fundamental repetition rate, M equals to 1. In this case, the above-mentioned formula would be: R = D × Lc × c, which agreed well with the previous result demonstrated by T. Gottschall [22]. As for the case of rational harmonic, although the optical length equals to the cavity length multiply the number of laps (Lc’ = M × Lc), the changing rate would be maintained. This theoretical prediction has been confirmed by our experimental measurement, as shown in Fig. 3(e). All the nine rational harmonics exhibit the same changing rate, which would be convenient for single-band CARS applications with tunable repetition rate due to the free of calibration for wavelengths determined by the delay position.
Besides of the wavelength tuning rate, the tuning range and output power at each rational harmonic are also crucial for practical CARS applications. Therefore, we measured the output power of signal pulses at each wavelength for each rational harmonic order. The output powers for four groups with the same N and different M values are shown in Fig. 4(a), indicating the impact of lap number on the output power and tuning range. The maximum tuning range is 157 nm at fundamental repetition rate. The available output power and tuning range for the signal pulses decreased with the increase of circuiting laps. Inside each group, the output powers for different N values are shown in Figs. 4(b)-4(d). In general, higher output power could be obtained with larger integer N. More specifically, the signal output power for the N/M harmonic is N times as that for the 1/M harmonic. It is worth noting that the available pulse energy for each rational harmonic within the same group (with a same value of M) maintains unchanged independent from the integer N. Therefore, for a given parametric gain medium and input pump pulse, the maximum signal pulse energy extracted from the OPO cavity is only determined by the cavity loss.
Fig. 4 Average power of the signal versus output center wavelength for various harmonic orders. (a) M = 1, 2, 3, 4, N = 1; (b) Group I, one lap: M = 1, N = 1, 2, 3; (c) Group II, two laps: M = 2, N = 1, 3; (d) Group III, three laps: M = 3, N = 1, 2; and (e) Group IV, four laps: M = 4, N = 1, 3.
Rational harmonic resonance in OPO cavity not only provides the flexibility to tune the repetition rate, but also improves the spectral bandwidth due to dispersion filtering, which would be helpful to increase the spectral resolution for CARS detection. The spectral bandwidth of the OPO signal is mainly determined by the phase-matching condition, the spectral bandwidth of the pump and the dispersion filtering effect. The phase-matching condition and the pump spectral bandwidth would directly define the spectral bandwidth of the spontaneous signal. Then the dispersion filtering effect and the parametric gain would define the final spectral bandwidth of the resonant signal. The output spectra of the signal pulses at 985 nm for harmonic orders of 1, 1/2, 1/3 and 1/4 are shown in Fig. 5(a), revealing a spectral bandwidth of 2.52, 1.26, 0.84 and 0.64 nm, respectively. The spectral bandwidth is found to be scaled with 1/M for each harmonic orders. The spectral bandwidths for the same M but different N values are shown in Figs. 5(b)-5(d). Although the repetition rates inside each group are different, their spectral bandwidths are the same. Therefore, the signal spectral bandwidth is determined by the accumulated dispersion in SPOPO.
Fig. 5 Output spectra of signal pulses at 985 nm for various harmonic orders. (a) M = 1, 2, 3, 4, N = 1; (b) Group I, one lap: M = 1, N = 1, 2, 3; (c) Group II, two laps: M = 2, N = 1, 3; (d) Group III, three laps: M = 3, N = 1, 2; and (e) Group IV, four laps: M = 4, N = 1, 3.
4. Discussions and conclusion
There are two advantages of this concept for RHR-SPOPO. First, it is very flexible to design the length of the OPO cavity. Once the pump repetition rate is fixed, no matter which integers used for N and M, the output OPO pulse train would always have the same repetition rate as the pump pulse. Depending on the values of M and N, the dispersion and cavity loss can be engineered to improve the spectral bandwidth and the pump power threshold of OPO pulse. In our experiment, the net dispersion in the OPO cavity and the total cavity loss was estimated to be 1.95 ps2 and 99.7%. For repetition rates inside the same group depending on the number of laps, their spectral bandwidths are the same. Therefore, the signal spectral bandwidth is determined by the accumulated dispersion in SPOPO. As for the pump power threshold and slope efficiency, they were determined by the intra-cavity losses with a fixed output coupler ratio. In general, higher number of laps would result in higher propagation losses for the resonant signal pulse. Second, OPO output pulses with tunable repetition rate could be obtained with only one set of optics by simply changing the pump repetition rate. Therefore, this method would be useful to develop an integrated and cost-efficient fiber-based CARS microscopy system. The requirement of tunable repetition rates can be fulfilled for addressing various biomedical samples with the minimum photodamage.
The proof-of-principle demonstration was conducted to show the flexibility to achieve various harmonic orders, thus resulting in many possible values of repetition rates. Currently, the repetition rate was changed from 0.5 to 6.0 MHz. This RHR-SPOPO method has the potential to support a wide repetition rate tuning range of 0.1-100 MHz, which would cover almost the whole repetition rate range for biomedical imaging applications. In practice, users could freely choose harmonic operation to obtain larger steps. To do this, the upper limit of the pump repetition rate should be increased to larger than 100 MHz. Then the harmonic order range should be well designed to balance the damage and the nonlinearity of the parametric gain medium. If the harmonic order is too high, the required average power of the pump laser would be very large, which would induce lots of heat and cause thermal damage to the PCF. On the other hand, if the harmonic order is too low, the peak power of the pump pulse would increase accordingly. Consequently, FWM process in the PCF would be overtaken by other nonlinear effects such as SPM, XPM and SRS. To go beyond the trade-off, a feasible solution is to splice a coreless endcap to the fiber or using PCF with a larger mode field diameter. In this case, RHR-SPOPO with a broad tuning range of repetition rate could be expected.
The presented dual-color synchronized FOPO with tunable wavelength difference and flexible repetition rate could find applications in nonlinear biomedical imaging including CARS and SRS. Compared to CARS, there is no non-resonant background noise in SRS signal. The SRS has recently emerged as a promising tool in chemical diagnosis and medical examination due to the extraordinary detection sensitivity and the record-high imaging speed [32]. The SRS signal was measured through modulation-transferred laser intensity from either Stokers or pump beam, which sets stringent requirement for the stability of laser source. By further improving the relative intensity noise performance of FOPO in the MHz range or using balance-detection scheme [1], applications in SRS with our fiber laser source could be expected.
In conclusion, we reported a fiber-based SPOPO operating in a novel regime, which could output two-color synchronized pulses with tunable repetition rates. The tunability was realized by simply adjusting the pump repetition rate without the need of changing the cavity length. Compared to conventional approaches, the presented SPOPO could not only provide flexible repetition rates, but also improve the spectral resolution due to the enhanced dispersion filtering by the multiple round trips in the OPO cavity. Consequently, a repetition rate tunable range of 0.5-6.0 MHz and signal spectral bandwidths of 0.64-2.52 nm have been achieved in the condition of rational harmonic resonance. Benefiting from the convenient change of the repetition rate, this compact and tunable fiber laser source could be envisioned to excite different biomedical samples in nonlinear optical microscopy [13,14], where different optimized repetition rates could be used to minimize the photodamage effect and improve the penetration depth.
Funding
National Natural Science Foundation of China (11727812); Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning, Science and Technology; Innovation Program of Basic Science Foundation of Shanghai (18JC1412000).
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