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Abstract
To the best of our knowledge, this study is the first demonstration of a mode-locked polarization-maintaining Yb fiber laser that incorporates a liquid-crystal-on-silicon-based electrically programmable filter into the cavity. The intracavity filter continuously tunes pulse characteristics, such as a wavelength tunable range of 1018–1065 nm and pulse width tunable range of 0.3–2.6 ps. Further, numerical simulations of the laser oscillator results were consistent with the experimental results and confirmed the mode-locked pulse generation regime. The proposed technique is expected to have great potential as a seed laser for multifunctional ultrashort-pulse lasers.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Compact and robust ultrashort pulse Yb fiber lasers are employed in advanced various applications such as laser micromachining, optical imaging, and metrology. These applications require wavelength and pulse width tunability. Multiphoton microscopy requires pre-chirp pulses, which are adjusted using a tunable pulse compressor or a combination of a pulse tunable laser and a fixed pulse compressor, for high-contrast imaging. In addition, wavelength tunability expands target samples, such as semiconductor crystals [1]. Laser micromachining systems that contain a wavelength tunable seed laser and switchable amplifiers, such as a Yb doped fiber amplifier for high average power pulses and Yb doped solid state amplifiers for high energy pulses, facilitate various types of processing. These wavelength- and pulse-width-tunable ultrashort pulse lasers, comprising a mode-locked fiber laser oscillator, amplifiers, and a pulse compressor, require a tunable filter technique, a dispersion control technique, and a saturable absorber in the cavity.
Tunable filter techniques, which require mechanical or electrical control, enable mode-locked fiber laser oscillators to tune the wavelength. Mechanical tunable filter techniques, such as rotating (tilting) a grating [2–6], rotating a free-space bandpass filter (BPF) [7], adjusting the fiber polarization controller [8–16], adjusting an optical mirror [17,18], adjusting an inline tunable filter [19,20], sliding the position of the fiber pigtailed collimator lens [21], sliding a filter slit [22,23], and controlling a digital micromirror device (DMD) [24], require fine tuning. In addition, they are plagued by challenges such as large size, low repeatability, and low long-term reliability. An electrically tunable filter requires continuous signal inputs, such as radio-frequency signals generated by a direct digital synthesizer for an acousto-optic tunable filter [25] and modulation pattern signals generated by a pulse (pattern) generator for a Mach-Zehnder intensity modulator [26], which also acts as an active mode-locking device [19,26]. These electrical filter techniques, which require large, heavy, complicated, and expensive signal generators, are unacceptable for practical use. Further, sliding the position of gratings [21,22,24] allows intracavity dispersion tuning; however, they suffer from the same challenges as mechanically tunable filter techniques. Finally, inline dispersion control techniques, such as tunable chirped fiber Bragg gratings and chirped volume Bragg gratings, overcome the challenges of mechanical tuning techniques; however, support a narrower wavelength range than the other techniques.
Saturable absorbers can be categorized into two groups: material and artificial [27]. Material saturable absorbers, such as semiconductor saturable absorber mirrors (SESAMs) [2,3,8,9,14,20,25] and CNT [4,10], have poor long-term reliability and power degradation [28]. By contrast, artificial saturable absorbers, such as nonlinear polarization rotation (NPR) [6,29,30], nonlinear multimodal interference (NL-MMI) [15,16], nonlinear optical loop mirror (NOLM) [31,32], and nonlinear amplifying loop mirror (NALM) [33,34], ensures a high damage threshold and excellent long-term reliability. Moreover, NALM-based mode-locked fiber lasers, which have lower self-staring threshold than NOLM and higher long-term reliability than both NPR and NL-MMI, produce high-energy picosecond pulses with a strong positive chirp referred to as dissipative soliton (DS) and amplifier similariton (AS) [35–37].
The tunable mode-locked fiber laser employed in this study used a NALM and a programmable phase and amplitude filter comprising a liquid crystal on silicon (LCoS) and other fixed optical components. This type of programmable filter is particularly popular in optical-communication research, and has been used in mode-locked Er fiber lasers [38–40] having poor long-term reliability. To the best of our knowledge, this study presents the first fully electrically tunable fiber laser comprising a wavelength- and pulse-width tunable oscillator, core-pumped Yb-doped fiber amplifier (YDFA), and fixed pulse compressor. The oscillator produced ultrashort pulse wavelengths of 1018–1065 nm at a 6.1 MHz repetition rate, and the YDFA amplified the pulses to 11 nJ. Further, compressed pulse-width tunable range was 0.3–2.6 ps. The accurate numerical simulation revealed the mode-locking dynamics. Further, experimental and numerical investigations demonstrated the high flexibility and robustness of NALM-based fiber lasers. Table 1 lists various wavelength-tunable Yb fiber lasers with a tuning range greater than 20 nm.
Table 1. Widely wavelength tunable Yb fiber lasersa
2. Laser configuration and numerical model
2.1 Laser configuration
Figure 1(a) shows a schematic of tunable Yb fiber laser oscillator and Fig. 1(b) shows the corresponding photograph. A dual-gain NALM-based Figure-of-eight (F8) cavity, comprising two gain sections each for the cavity loop (on the left loop) and the NALM loop (on the right loop) [41], compensated for the large insertion loss of the programmable filter and provided better control to achieve mode-locking operation. The cavity consists of polarization-maintaining (PM) fibers, which exhibit excellent stability against mechanical and temperature perturbations, and commercially available PM components, which are optimized at a wavelength of 1064 nm. The two loops were connected by a 2 $\times$ 2 fused coupler with a splitting ratio of 50:50 at 1064 nm. This coupler, which exhibited a sinusoidal dependence of power transmission versus wavelength, enhanced the self-starting mode-locking ability at approximately 1030 nm and wavelength tunability toward longer wavelengths. Each Yb-doped fiber: a 3 m lowly Yb-doped fiber (Coherent, PM-YSF-LO) in the cavity loop and a 1.1 m highly Yb-doped fiber (Coherent, PM-YSF-HI) in the NALM loop, was pumped by a single-mode diode laser (LD) emitting at 976 nm through a 980/1064 WDM. The laser outputs 10% of its optical power through a 10:90 fused coupler. Further, the programmable phase and amplitude filter (Coherent, WaveShaper1000A/SP; WaveShaper) [42] provided a high degree of flexibility, such as changing the pulse regime, tuning the center wavelength, and changing the net cavity dispersion, in the operating range of 1015–1065 nm. Uniform insertion loss over wavelength in the WaveShaper was 4.9 dB. A laptop computer was used to control the LDs and WaveShaper via USB cables. At certain instances, Q-switched mode-locking pulses destroy the FC/APC fiber connectors of the WaveShaper, thus limiting the maximum pump power near the self-starting mode-locking threshold. A dual-stage fiber isolator located behind the Yb-doped fiber ensures unidirectional oscillation operation over a wide wavelength range, and another single-stage isolator blocks $-$25 dB back-reflected light from the WaveShaper to the NALM loop. The total length of the fibers in the cavity and NALM loops were 25 and 8 m, respectively. When WaveShaper provides no dispersion to the cavity, which is dispersion compensation-free [43,44], the estimated net cavity dispersion is 0.72 $\mathrm {ps^2}$ at 1030 nm.
Fig. 1. (a) Schematic and (b) photograph of the proposed tunable mode-locked Yb fiber laser incorporating a programmable optical filter. Each fiber is an all-polarization-maintaining fiber: cavity on the left loop, NALM: nonlinear amplifying loop mirror on the right loop, LD: laser diode, YDF: Yb-doped fiber, and WDM: wavelength division multiplexer.
The output spectra were measured using an optical spectrum analyzer (Yokogawa, AQ6370D). Autocorrelation traces were measured using an auto-correlator (APE, pulseCheck150). The mode-locked pulse trains were measured using a fast InGaAs photodetector (Thorlabs, DET08CFC/M) connected to a 1 GHz oscilloscope (Agilent, Infinium), and radio frequency (RF) spectra were measured using an RF spectrum analyzer (Anritsu, MS2667C). Furthermore, the average power and stability of the laser were measured using a power meter (Thorlabs, S132C and PD100).
2.2 Numerical model
The proposed simulation program was based on an accurate model of the fiber laser, as shown in Fig. 1. Each PM fiber segment was modelled using the generalized nonlinear Schrödinger equation (GNLSE), including the saturated gain width, finite bandwidth, stimulated Raman scattering, and self-steepening according to:
Table 2. Fiber parameters in the simulationa
Equation (1) was numerically solved by utilizing a fourth-order Runge-Kutta method in the interaction picture method [48] in the frequency domain [49]. To accelerate the calculation process, the simulation utilizes a conservation quantity error algorithm with an adaptive step size method [50]. The numerical model of the NALM is presented in Ref. [51]. The incident electric field to the NALM loop was divided by a 2 $\times$ 2 coupler into clockwise and counter-clockwise electric fields and recombined at the same coupler after passing through the four-segment fibers in the NALM. The simulations began with random noise, and the pulses stabilized after several tens of roundtrips. However, the transition process and time of each filter change were unknown, and the simulation cannot reveal the transition process of the pulses in response to the change.
3. Numerical and experimental results
3.1 Self-starting mode-locking
When the WaveShaper was a flat-top BPF centered at 1032 nm with a bandwidth of 1.5 nm and provided a group velocity dispersion (GVD) $\beta _{2}$ of 0 $\mathrm {ps^2}$, the oscillator started multi-pulse mode-locking with the pump power of the cavity loop increased to 110 mW and the NALM loop to 90 mW. No mechanical perturbations were required to initiate mode locking. Further, the oscillator requires a flat-top BPF for self-starting. The oscillator produces only Q-switched mode-locking pulses with a Gaussian filter. Various flat-top BPFs, which are centered at 1030–1035 nm, a FWHM bandwidth of 1.6–2.2 nm, and a GVD $\beta _{2}$ of 0–0.29 $\mathrm {ps^2}$, are functional as well. By slowly decreasing the pump power in the cavity loop from 110 to 67 mW and in the NALM loop from 90 to 77 mW, the laser produced a continuous-wave (CW) mode-locked pulse. Consequently, the output pulses were DS pulses and a pulse energy of 0.15 nJ at a repetition rate of 6.12 MHz. Details of the pulse characteristics presented in Section 3.2.
When the WaveShaper was a flat-top BPF centered at 1035 nm with a bandwidth of 20 nm and provided a GVD $\beta _{2}$ of $-$0.75 $\mathrm {ps^2}$, the laser produced noise-like pulses, and the total pulse energy was 0.21 nJ. Figure 2(a) shows the simulated output spectra of 600 pulses generated from the oscillator. Figures 2(b) and (c) show the simulated output spectra and temporal shapes of the output pulses, respectively, with round trips (output pulses) of 598–600th in Fig. 2(a). The simulated pulses exhibited a lower complexity than typical noise-like pulses, comprising many femtosecond pulses. Figure 2(d) shows the measured output spectrum (purple curve) and the simulated output spectrum (green curve) averaged of the 101–600th output pulses in Fig. 2(a). These simulation results were consistent with the experimental results. Figure 2(e) shows a measured autocorrelation trace, wherein an unclear coherence spike was observed. Moreover, it indicated that the pulses were in noise-like pulse regime that had low complexity of the pulse structure [52,53].
Fig. 2. Characteristics of noise-like mode-locking operation. (a) Simulated pulse evolution process with round trip. Output characteristics of the simulated pulses: (b) spectrum intensity and (c) temporal pulse profile for the 598–600th round trips. (d) Experimental (purple curve) and simulated (green curve) output spectra averaged from 101 to 600th. (e) Measured autocorrelation trace.
3.2 Filter shape control
The mode-locked pulse state is dependent on the intracavity filter shape. Figure 3 shows the simulated spectra evolution of 100 output pulses with each filter; the one centered at 1032 nm with a FWHM bandwidth of 1.5 nm provided no GVD. The oscillator with a flat-top BPF produced unstable pulses, whose output spectra alternated for each round trip (as shown in Fig. 3(a)). Whereas, with a Gaussian filter, it produced stable pulses (as shown in Fig. 3(b)). The following is one of the reasons for the instability of the pulse trains with the flat-top filter. Flat-top spectral filter shape corresponds to sinc-shaped temporal response. The sinc-shaped response generates satellite pulses, which are weak and equidistant from each other, around the central (main) peak pulse. The central peak pulse is spectrally and temporally broadened by self-phase modulation (SPM), and partially overlapped with satellite pulses. Overlapped pulse components affect the nonlinear optical effects, and the pulse evolution during cavity round-trip becomes complex. This sequence occurs at every round-trip; therefore, the pulse trains become unstable. Furthermore, for self-starting, the sinc-shaped temporal response probably possibly aids in the generation of large intensity noise and the survival of the pulses.
Fig. 3. Simulated spectral evolution of output pulses with (a) flat-top bandpass and (b) Gaussian filtering centered at 1030 nm and a bandwidth of 1.5 nm.
The oscillator produces stable mode-locked pulses by changing the filter shape from a flat-top BPF to a Gaussian shape. Figures 4(a) and (b) show the measured (purple curves) and simulated output spectra (green curves) with the same BPF settings as in Fig. 3, respectively. The simulated spectra were averaged over 100 round trips. The simulation results were consistent with the experimental results. Further, the output spectral shape was changed from M-shaped with several valleys to a smooth one through a change in the BPF shape. Many sidelobes are shown in Fig. 4(a) indicating approximate wave-breaking [52]. The oscillator lost its mode-locked state by increasing the bandwidth above 1.5 nm. Figures 4(c) and (d) show the pulse train with a pulse repetition rate of 6.12 MHz, corresponding to a pulse interval of 163 ns. The oscillator produced unstable pulses with a flat-top BPF whereas the Gaussian filter produced stable pulses. These states were consistent with the numerical simulation results shown in Fig. 3.
Fig. 4. Dependance of bandpass filter shape on output pulse characteristics. Comparison of spectra obtained from experiments (purple curves) and simulations (green curves). Spectra of pulses with (a) flat-top bandpass and (b) Gaussian filtering with a bandwidth of 1.5 nm. Oscilloscope traces of the output pulse train of (c) flat-top bandpass and (d) Gaussian filtering.
3.3 Bandwidth control
The bandwidth of intracavity BPF affected the mode-locked pulse state. Figure 5 shows the measured (purple curves) and simulated (green curves) pulse characteristics depending on a Gaussian filter bandwidth. When the bandwidth of the Gaussian filter was in the range of 0.5–3.3 nm, the oscillator output mode-locked pulses. Beyond the bandwidth range, the oscillator output amplified spontaneous emission light, unstable CW laser, and Q-switched mode-locking laser pulses. Figures 5(a), (c), and (e) show the output spectra, temporal shape, and autocorrelation trace, respectively, with the Gaussian filter bandwidth of 1.1 nm. Figures 5(b), (d), and (f) show the same characteristics for the bandwidth of 3.3 nm, respectively. As shown in Figs. 5(c) and (d), the pulse shape was rectangular with a triangular autocorrelation function. At a BPF bandwidth of 1.1 nm, simulated output pulse characteristics, such as depressed temporal shape, sharp slopes, and tangent phase chirp, indicated that the oscillator was an intermediate state in the switching process between AS and DS [54]. Whereas, at a bandwidth of 3.3 nm, the arctangent phase chirp indicated that the pulse was a DS. The simulation results were consistent with the experimental results.
Fig. 5. Characteristics of output pulses for Gaussian shape filters with different bandwidths. The spectra of the pulses with bandwidths of (a) 1.1 and (b) 3.3 nm; temporal shapes of the pulses with bandwidths of (c) 1.1 and (d) 3.3 nm; autocorrelation traces of the pulses with bandwidths of (e) 1.1 and (f) 3.3 nm.
Figure 6 shows the simulated intracavity pulse evolution dynamics in the spectral and temporal domain, with a Gaussian filter having a bandwidth of 1.1 or 3.3 nm. The pulse profile with a BPF bandwidth of 1.1 nm changed dynamically compared to that of 3.3 nm. At a BPF bandwidth of 1.1 nm, SPM greatly affected the output spectral width; thus, the output spectrum (location (G) in Fig. 6(a)) became slightly wider than that at 3.3 nm bandwidth, as shown in location (G) in Fig. 6(b). At a BPF bandwidth of 3.3 nm, the spectral breathing ratio, which is defined as the ratio of the maximum and minimum spectral widths in the cavity, was 2.5 (shown in Fig. 6(b)) and the temporal breathing ratio was 2 (shown in Fig. 6(d)). A stable mode-locked state requires a large breathing ratio, and the simulation results were consistent with the experimental results wherein the oscillator loses a mode-locked state with BPF bandwidths of 3.4 nm and above.
Fig. 6. Numerical results of spectral and temporal evolution during cavity round-trip. Spectral evolution with Gaussian filter bandwidths of (a) 1.1 and (b) 3.3 nm. Temporal evolution with the bandwidths of (c) 1.1 and (d) 3.3 nm: NALM, nonlinear amplifying loop mirror loop; (A) YDF-LO, lowly Yb-doped fiber in the cavity loop; (B) dual-stage optical isolator; (C) and (F) 2 $\times$ 2 coupler; (D) YDF-HI, highly Yb-doped fiber in the NALM loop; (E) WDM, wavelength division multiplexer in the NALM loop; (G) 1 $\times$ 2 coupler; (H) single stage optical isolator; (I) optical fiber facet after filtering in a WaveShaper; (J) WDM in the cavity loop.
Figure 7 shows the dependence of the output pulse characteristics on the Gaussian filter bandwidth. Figure 7(a) shows output spectra at different filter bandwidths. Figures 7(b), (c) and (d) show the characteristics of the output pulses as the function of the Gaussian filter bandwidths. The wider the filter bandwidth is, the smaller the losses is in the cavity. Thus, the oscillator produced higher-energy pulses, as shown in Fig. 7(b). Further, the wider the pulse width was, the weaker the SPM occurred; thus, the pulse spectral width saturated, as shown in Fig. 7(c). The simulation results were consistent with the experimental results.
Fig. 7. Dependence of the output pulse characteristics on the Gaussian filter bandwidth. (a) Experimentally measured output spectra with Gaussian filter bandwidths of 0.5–3.3 nm. Characteristics of output pulses as a function of Gaussian filter bandwidth: (b) pulse energy, (c) spectral width, and (d) autocorrelation trace width. The purple circles denote the experimental results and the green squares denote the simulation results.
3.4 Center wavelength control
After the oscillator produced CW mode-locked pulses at 1032 nm with a Gaussian filter, the center wavelength of the filter was successfully tuned, maintaining a mode-locked state from 1018 to 1062 nm with a step-size of 0.2 nm. However, the oscillator required greater pump power as the center wavelength moved away from 1030 nm. Figure 8(a) shows the entire tunable spectra. The spectrum range of 1018–1065 nm covers various gain media other than Yb-doped fiber, such as Yb:YAG, Yb:KGW, Yb:YLF, Yb:KYW, $\mathrm {Yb:CaF_2}$, Yb:CALGO, and Nd:YAG.
Fig. 8. Dependence of output pulse characteristics on the center wavelength of the Gaussian filter. (a) Experimentally measured output spectra with a filter center wavelength of 1018–1062 nm. Characteristics of output pulses as a function of center wavelength, (b) pulse energy, (c) spectral width, and (d) autocorrelation trace width.
Figure 9 shows short and long-term stability of output pulses with the Gaussian filter centered at 1040 nm with the bandwidth of 3.0 nm. Figure 9(a) shows the RF spectra around at the fundamental and harmonic repetition rate. The RF spectrum yielded a signal-to-noise ratio (SNR) higher than 75 dB at a resolution bandwidth (RBW) of 100 Hz, indicating the high quality of the mode-locked pulses without any sign of modulation. Figure 9(b) shows the power stability at room temperature. The power fluctuation was 0.48% root mean square (RMS) over 10 h. This stability was benefited from the all-fiber configuration, which was affected only by temperature and pump power.
Fig. 9. Short- and long-term stability of the mode-locked fiber laser. (a) Radio frequency (RF) spectrum of output pulses from the oscillator at the fundamental frequency with a span of 1 MHz at a resolution bandwidth of 100 Hz, inset: span of 300 MHz at a resolution bandwidth of 3 kHz. (b) Average output power stability of fiber laser over 10 h at room temperature.
3.5 Dispersion control
An intracavity WaveShaper acting as a phase filter provided GVD to enable control of the net cavity dispersion. Figure 10 shows the dependence of the output pulse characteristics on the net cavity dispersion. WaveShaper also acts as a Gaussian spectral filter centered at 1040 nm with a bandwidth of 3.0 nm. This central wavelength of 1040 nm, away from the gain peak of the Yb-doped fiber at approximately 1030 nm, reduced the gain-narrowing effect [55]. Figure 10(a) shows the output spectra with the different net cavity dispersion. Figures 10(b), (c) and (d) show characteristics of the output pulses as the function of the net cavity dispersion. The WaveShaper, acting as a Gaussian filter, provided GVD independent of the cavity loss. Consequently, thus the pulse energy was constant, as shown in Fig. 10(b). However, when the WaveShaper provided normal (anomalous) dispersion, the peak power of pulses behind the WaveShaper decreased (increased). This stimulated weak SPM, and thus yielded narrower output spectrum. Therefore, the balance between the net cavity dispersion and the SPM effect maintained the nearly constant pulse widths.
Fig. 10. Dependence of the output pulse characteristics on the net cavity dispersion. (a) Experimentally measured output spectra with net cavity dispersion of 0.49–0.95 $\mathrm {ps^2}$. Characteristics of output pulses as a function of net cavity dispersion, (b) pulse energy, (c) spectral width, and (d) autocorrelation trace width.
The output pulses from the oscillator were amplified to a pulse energy of 10.8 nJ using a homemade YDFA, and a pair of transmission gratings (LightSmyth Technologies, 1000 lines/mm) compressed the pulses. The distance between the parallel gratings was fixed at 152 mm at $31^\circ$ angle of incidence, which allowed the shortest pulse at a net cavity dispersion of 0.49 $\mathrm {ps^2}$. Consequently, the compressed output pulse energy was 8.7 nJ, corresponding to an efficiency of 80%. Figure 11(a) shows the autocorrelation traces of the shortest and longest pulses. Assuming Gaussian temporal shapes, the shortest and longest pulse widths were estimated to be 0.3 and 2.6 ps, respectively. Figure 11(b) shows the characteristics of the compressed pulses as a function of the net cavity dispersion.
Fig. 11. Tunable pulse characteristics. (a) Measured autocorrelation traces of compressed pulses and their Gaussian fit function (green dashed curve). The laser produced the shortest pulse at a net cavity dispersion of 0.49 $\mathrm {ps^2}$ (purple solid curve), and the longest pulse at a net cavity dispersion of 0.95 $\mathrm {ps^2}$ (orange solid curve). (b) Pulse width as a function of net cavity dispersion.
4. Discussion
An intracavity programmable filter provides many functions, such as center wavelength, pulse shape, and pulse width tunability, for a NALM-based mode-locked fiber laser. These tunabilities indicate the flexibility and robustness of the fiber laser and are feasible at other wavelength ranges that are covered by programmable filters. The filter also provides a degree of freedom for self-starting mode-locking, and thus seemingly reduces the lasing threshold of the pump power. Moreover, increasing the pump power, which was limited in this work to prevent fiber connector damage, probably enabled the laser to self-start with a Gaussian filter centered over a wider wavelength range and thus produce higher pulse energy in the AS regime.
The combination of a higher pump power and multi-wavelength bandpass filtering possibly enables multi-wavelength lasing [12,15,56], which is useful for dual-comb applications, such as spectroscopy and metrology. The combination of the proposed simulation and machine-learning algorithms, which were designed for our cavity design, as developed by Kokhanovskiy et al. [57], is expected to enable self-tuning and aid in determining new sciences and technologies.
5. Conclusion
This study successfully developed a tunable mode-locked Yb fiber laser comprising a liquid-crystal-on-silicon-based electrically programmable filter and a nonlinear amplifying loop mirror in the cavity. The intracavity filter provides a laser with many functions, such as producing several types of mode-locked pulses, wavelength tuning, and pulse width tuning. This laser produced noise-like pulses, which had a broad spectrum and time complexity, and dissipative soliton pulses, which covered a spectrum range of 1018–1065 nm. The proposed tunable fiber laser system, comprising the Yb fiber laser oscillator, a YDFA, and a pulse compressor, produced 0.3–2.6 ps pulses without any mechanical moving parts. The architecture of the laser can be applied to high-power ultrashort pulse lasers for many applications, such as metrology, pulse width adjustment in laser micromachining, and high-contrast multiphoton microscopy. Moreover, the numerical simulation model, which was consistent with the experimental results, contributes to a better understanding of pulse evolution in a complicated fiber laser cavity. In the future, we plan to produce higher-energy and broader spectrum pulses from the oscillator using simulations.
Acknowledgments
We gratefully acknowledge Dr. R. Stolte from Coherent Corp. for his support including the loan of a programmable filter.
Disclosures
Masanori Nishiura: Sevensix Inc. (F,E,P).
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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