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Abstract
An inertial-free, ultrafast frequency comb source based on two chirped optical frequency combs (OFCs) is proposed and experimentally demonstrated. The high linearity frequency sweeping is realized by the Vernier effect between the two OFCs rather than any mechanical motion component, so that good stability and reliability are ensured and no recalibration or resampling process is required. Swept rate up to 1 MHz is realized while keeping a narrow instantaneous linewidth of 0.03 nm, thanks to the extra-cavity frequency sweeping method. The wavelength step is proportional to the swept rate (3.8 pm at 10 kHz), and can be tuned by changing the repetition rate difference between the two OFCs. This swept source is applied for high-speed wavelength encoded imaging and achieves 4.4-μm spatial resolution at a 329-kHz frame rate. Compared with the traditional time-stretch microscopy, the signal acquisition bandwidth decreased from 3.8 GHz to below 90 MHz to achieve the same spatial resolution. Furthermore, the exposure time for a specific wavelength is much longer due to the discrete sweeping feature, which is a benefit for higher sensitivity. This discrete swept source provided a promising low-cost option for high-speed biomedical imaging systems and high-accuracy spectroscopy.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
A frequency swept light source establishes a mapping relation between the frequency domain and the time domain through emitting different wavelengths at different times, so that the spectrally resolved information can be rapidly and serially detected on the time axis by a single-pixel photo-detector (PD). In the last few decades, frequency swept sources have been extensively used in the field of biomedical imaging like optical coherence tomography (OCT) [1–9] and wavelength encoded microscopy [10–14], and dramatically improved the imaging speed. In addition, other fields like absorption spectroscopy [15,16] and fiber sensor [17,18] also have demands for frequency swept source.
Driving by the continually expanding applications, many types of frequency swept source have emerged to date. The most straightforward scheme among them is introducing a wavelength scanning filter into a laser cavity with broadband gain medium. Early studies mainly focus on raising up the swept speed of the filter by different designs, e.g., tunable fiber Fabry-Perot (FFP) filter [3,19], galvo driven grating [4], and the combination of diffraction grating with rotating mirror [2,20] or polygon mirror scanner [5,21–23]. Although the polygon mirror scanner method can achieve swept rate of hundreds of kilohertz by clever structure [5], the bulk optics design make the system complex and costly. The dispersion tuning technique provided a simple and non-mechanical approach for wavelength sweeping [24]. However, the instantaneous linewidths are normally around 1 nm at high swept rates [7,18,25,26], which limited its application for long range OCT and high-resolution spectroscopy or microscopy. Actually, there exist a trade-off between the swept speed and instantaneous linewidth of all the above mentioned approaches, since it requires enough roundtrips to build up lasing from the amplified stimulated emission background at a given wavelength [3]. This problem was circumvented by the Fourier domain mode locking (FDML) technique by using a long fiber delay line in the laser cavity to store the entire frequency sweep. Simultaneously, an FFP filter is synchronously swept with the round-trip time of the cavity to achieve a quasi-stationary operation [6]. Therefore, swept rates as high as hundreds of kilohertz can be realized while keeping moderate instantaneous linewidth [15,27–30]. Although the swept rate can be promoted to megahertz magnitude with the help of time-interleaving technique, the setup become slightly complicated [31–33]. It should be noted that an extra recalibration channel is normally required as a reference for resampling in the post processing, since the frequency sweeping is nonlinear and unstable for FFP filter operating at high swept rate [27,29,31–33]. Otherwise, a lot of efforts should be made to design a complex drive waveform for the filter to achieve k-space linear sweeping [28]. In addition, reliability and stability issues may also occur due to the internal mechanical motion of the filters. Recently, the short-cavity micro-electro-mechanical systems (MEMS) tunable lasers are emerging as powerful light sources for biomedical imaging; however, inertial components are still required [8,34,35]. The time stretch based ultrafast swept source provided an inertial-free solution for biomedical imaging, but the imaging sensitivity is not so good since the power is dissipative in the dispersive element [9,36–41]. Furthermore, large bandwidth PD and real-time oscilloscope are essential for capturing the wavelength-to-time mapped information to achieve high spectral accuracy [42], which brings great expense to the imaging system.
In recent years, discrete swept sources, also known as wavelength-stepped or frequency comb sources, have received much attention for their advantages over conventional continuously swept sources in terms of instantaneous linewidth, signal acquisition bandwidth and detection sensitivity [43–50]. The commonly used method is introducing a static comb like filter with high finesse into the laser cavity of a broadband swept source to discretely sample the spectrum [44–47,50]. Linewidth narrowing can be observed because the multiple longitudinal modes in the cavity are partially suppressed by the narrow bandwidth filter. In combination with the subsampling concept, large depth OCT imaging is demonstrated with low signal acquisition bandwidth [50]. Furthermore, the pulse modulated temporal intensity provided higher peak power at the same average power compared to the continuously swept source, thus enabling higher detection sensitivity [49]. However, it is also necessary to consider that the wavelength steps of these existing discrete swept sources are normally at 0.2-nm level [44,48,49] and even up to 1.6 nm [47,50]. Therefore, the principal measurement range for OCT application is very limited and aliasing occurs at deeper depths, although this problem can be mitigated through subsamping and circular coherent ranging in the context of sparse scattering [50]. Moreover, a finer wavelength step is required for some high resolution spectroscopy or microscopy applications.
In this paper, we proposed and experimentally demonstrated a new type of ultrafast discrete swept source based on two chirped optical frequency combs (OFCs) with different repetition rates. The frequency sweeping is implemented by the Vernier effect between the two OFCs rather than any inertial filtering component. Different swept rates from 10 kHz to 129 kHz, 329 kHz, 857 kHz and 1.03 MHz are demonstrated by simply changing the repetition rate difference between the two OFCs. The wavelength step is proportional to the swept rate, and calculated to be about 3.8 pm at 10-kHz. Simultaneously, the instantaneous linewidth is estimated to be about 0.03 nm using the roll-off performance of the point spread functions (PSFs). High linearity (R2 = 0.999998) frequency sweeping is verified by extracting the phase of the interference signal. We demonstrated this new type of swept source for high-speed wavelength-encoded microscopic imaging. High spatial resolution of 4.4 μm is achieved at 329-kHz frame rate, which is currently limited by NA of the objective lens. Although only 0.31-ns/nm dispersion is used in the swept source system, the wavelength-to-time mapping factor is as large as 87 ns/nm at 329-kHz swept rate, corresponding to about 4300 km single mode fiber (SMF). Therefore, low bandwidth (below 90 MHz) signal acquisition system can be used to capture the time mapped information. Furthermore, since the swept source is discrete both in the time domain and frequency domain, the exposure time of a specific position of the object plane can be much longer as compare to the traditional time-stretch microscopy, which may provide better sensitivity.
2. Principle of operation
Figure 1(a) explained the principle for generating a discrete swept source though four-wave mixing (FWM) process between two chirped OFCs. The two combs with repetition rates of f and f + Δf are time stretched before serving as the signal and pump, respectively. Throughout the text, two pulses with the same index from the two combs will be called the nearest neighbors. Time delay between the m-th nearest neighbors is Δtm = m∙Δf /f 2, which discretely increases in step of δt = Δf / f 2. As shown in Fig. 1(b), when the chirping rate of the signal pulses is twice that of the pump pulses, a quasi-continuous and frequency sweeping idler pulse train will be generated. The time delay between the nearest neighbors is proportionally converted to the frequency shift of the corresponding idler pulse, which is similar to the time-and-delay concept that widely used for narrowband terahertz generation [52]. A detailed theoretical derivation is given as follows. Assuming that the two combs are stretched by two dispersive elements with different group delay dispersions (GDDs) of Φs and Φp, respectively. The nearest neighbors with relative time delay Δt can be respectively expressed as Es(t) = as(t) ∙ exp(–jωst)exp(–jt2/2Φs) and Ep(t) = ap(t + Δt) ∙ exp[–jωp(t + Δt)]exp[–j(t + Δt)2/2Φp], where as(∙) and ap(∙) are their amplitude envelopes, ωs and ωp are their carrier frequencies. The field of the generated idler can be expressed as:
where ωi = 2ωp – ωs, the phase of ai(t) is a constant when Δt is specified. If satisfied the chirping rate matching condition that Φp = 2Φs = 2Φ0, Eq. (1) can be simplified as:The idler is a quasi-monochromatic light considering the envelope of ai(∙). Its carrier frequency is linearly dependent on the time delay Δt, namely ω = ωi + Δt/Φ0. Scanning the time delay with fixed step size, we can get a linear and discrete frequency swept source. Fortunately, this scanning process can be naturally realized by utilizing the Vernier effect between two OFCs with different repetition rates. Therefore, the generated idler is a discrete frequency swept pulse source with swept rate of Δf, the pulse repetition rate is f and the frequency interval between two adjacent pulses is:The equivalent dispersion (frequency-to-time mapping factor of the swept source) is Φeq = Φ0 ∙ f /Δf, so that the required acquisition bandwidth can be compressed by M = f /Δf times while keeping the same spectral resolution, as compare to the traditional time stretch based swept source. It can be seen from Eq. (3) that there exist a trade-off between the swept rate Δf and the wavelength step. Figure 1(c) gives the frequency-to-time mapping relation of the generated swept source.
Fig. 1 (a) The principle of the proposed ultrafast swept source. (b) The frequency-to-time mapping relation of the FWM process. (c) Frequency versus time of the output swept source.
3. Experimental setup and performance characterization
Figure 2(a) gives the detailed experimental setup to demonstrate the proposed swept source. The two combs used for signal and pump are generated from mode-locked fiber lasers (MLFLs) based on nonlinear polarization rotation. Their repetition rates are locked to the RF references from the signal generator (SG) by the active phase locking loops (black dashed line). The repetition rate of the signal comb is fixed at 91.86 MHz, while that of the pump comb can be tuned in a range of tens of kilohertz around 91.86 MHz by changing the frequency of its RF reference. A high-pass filter is used to select part of the signal comb (1570~1610nm) and an optical band-pass filters centered at 1559.5 nm (7.0-nm bandwidth) is used to filter the pump comb. The dispersion module (DM) contains 3-km dispersion-compensating fiber (DCF) and 22.5-km large effective-area fiber (LEAF), with total dispersion of about 0.31 ns/nm. The fiber lengths of the DCF and LEAF is carefully designed that a linear dispersion is achieved, with the third-order dispersion compensated [53]. To satisfy the dispersion (chirping rate) matching condition, the pump pass through the DM twice by utilizing two circulators C1 and C2, while the signal pass through the DM once. The pump is boost to 16.8 dBm before coupling into the 100-m highly nonlinear fiber (HNLF) (zero dispersion wavelength λ0 = 1561.5 nm, nonlinear parameter γ = 10 w−1 km−1). An optical spectrum analyzer (OSA, 0.02-nm resolution) and a 4-GHz oscilloscope are used to measure the spectrum and the temporal waveform of the generated swept source, respectively. The repetition rate difference between the two combs, namely the swept rate, is firstly tune to 10 kHz, and Fig. 2(b) gives the FWM spectrum. Figure 2(c) is the idler amplified to about 7.9 dBm, which indicates a wavelength swept range of about 20 nm (1530~1550nm). The swept range is decided by the spectral widths of the pump and signal, but finally limited by the FWM conversion bandwidth. A wideband FWM process [54] is benefit for producing wideband swept source that can be used for high-resolution OCT application. The poor flatness of the spectrum can be mainly attributed to three factors. Firstly, the spectral shapes of the pump and signal have important impact on the idler spectrum. Secondly, different time delays (corresponds to different idler wavelengths) between the pump and signal cause different conversion efficiency. In addition, the wavelength dependent conversion efficiency of the FWM process also affect the idler spectrum. Finally, the amplifier that used to amplify the generated idler may also reshape its spectrum. The waveform of the swept source is given in Fig. 3(a), and the zoom-in observations to the center and edge of the envelope are depicted in Fig. 3(b). The pulsewidth is about 2.2 ns at the center, and reduced to 1.2 ns at the edge where the pump is seriously misaligned with the signal. According to the time-bandwidth product, the linewidth will be broadened at the two ends of the sweeping. According to Eq. (3), the wavelength step, namely wavelength difference between two adjacent pulses in Fig. 3(b), can be as fine as 3.8 pm. Due to the limited tuning ability through stretching the fiber by the PZT, higher swept rates at 129 kHz, 329 kHz, 857 kHz and 1.03 MHz are achieved by artificially cutting the pump laser cavity length shorter. The corresponding waveforms is given in Figs. 3(c)-3(f).
Fig. 2 (a) Detailed experimental setup to demonstrate the proposed swept source. EDF: Erbium doped fiber, PC: polarization controller, PZT: piezoelectric ceramic transducer; PID: proportional-integral-differential controller; SG: signal generator. (b) Optical spectrum of the FWM process. (c) Optical spectrum of the swept source.
Fig. 3 (a) Temporal waveform of the swept source at 10 kHz and (b) its zoom-in observations. (c-f) Temporal waveforms of the swept source at different swept rates.
The static linewidth of the swept source is measured by the OSA when set Δf = 0. An optical delay line is used to adjust the time delay between the pump and the signal, so that quasi-monochromatic idler at different wavelengths are generated. As the green line in Fig. 4(a) shown, the linewidth at the center of the swept range is about 0.015 nm, which may be limited by the resolution of the OSA. While at the two ends of the swept range the linewidths are broadened because the pulse become narrower. The measurement results in Fig. 4(a) given that the linewidth is 0.041 nm at 1530.6 nm (blue line) and 0.035 nm at 1549.6 nm (red line). The instantaneous linewidth of the swept source at 10 kHz swept rate is also measured. The PSFs in Fig. 4(d) are measured by a simplified interferometer, the sampling arm of which is moved by a stepper motor. The slope of the roll-off curve is about 2.87 mm/dB, and 6 dB roll-off position is ~17.2 mm, corresponding to ~0.03 nm linewidth [55].
Fig. 4 (a) Static linewidth at different wavelength measured by OSA. (b) The PSFs measured by an interferometer.
The linearity of the swept source is also investigated. The blue line in Fig. 5(a) is the interference signal in a single period when the optical path length difference (OPLD) between the two arms are set to be 12 mm, with the zoom-in observations at different time positions shown in Fig. 5(b). Hilbert transformation was implemented here to retrieve the phase of the fringe [41], and the unwrapped phase is depicted with the red line in Fig. 5(a). The high linearity (R2 = 0.999998) of the curve indicate that linear frequency sweeping is realized, and no recalibration or resampling is required. The spectra of the fringes in Fig. 5(b) is depicted in Fig. 5(c), and the results revealed that there is no obvious frequency chirping in the interference signal. The high linearity of the swept source is further verified.
Fig. 5 (a) Interference signal (blue line) and its unwrapped phase (red line) at 12- mm OPLD. (b) Fringes at different child windows and (c) their normalized spectra.
4. High-speed microscopic imaging
Figure 6 is the schematic diagram of the microscopic imaging using the proposed swept source. The swept source is first launched by a fiber collimator, and the 3-mm beam size is expanded to 15 mm through the followed beam expander. The 600-lines/mm diffraction grating has β = 4.58° incident angle and θ = 61.95° diffraction angle, and resulted in 0.18-nm spectral resolution. The diffracted beam is converged by a lens with 10-mm focal length, and the final imaging process is implemented by a × 10 objective lens with NA of 0.25. It should be noted that the objective lens is ignored in Fig. 6 for simple. Therefore, the 'sample' in Fig. 6 is actually the image of the target. The space-to-wavelength conversion factor Cx can be calculated to be 12.76 μm/nm, just like that in [51], therefore the spatial resolution decided by the grating is ~2.3 μm. According to the Rayleigh criterion, the resolution limit brings by the objective lens is given by 0.61λ0/NA ≈3.8 μm. That is to say the spatial resolution of the system is limited by the objective lens rather than the grating. Thanks to the discrete wavelength swept feature, a single wavelength or pulse is converged to a specific position of the sample. The exposure time for one wavelength is much longer than that of the traditional continuous wavelength swept source, which has benefit for better sensitivity. Furthermore, the equivalent dispersion is amplified by M = f /Δf times as compare to the time stretch based swept source, thereby low bandwidth acquisition system including a 400-MHz PD and a 4-GHz oscilloscope can be used to detect the temporal signal. Actually, acquisition bandwidth as low as 90 MHz is enough even at 1.03-MHz swept rate, if a low pass filter is used before the PD rather than computer-aided filtering in the post processing. We will give a comparison between the proposed swept source and the time-stretch method in terms of the required acquisition bandwidth, as below. According to the analysis in [42], the acquisition bandwidth fdet and the spectral resolution δλ of the time-stretch microscopy have the relation as:
where D = 2πcΦ0/λ2 0. Considering the 3.8-μm resolution decided by the objective lens, δλ should smaller than 0.3 nm to avoid bringing limitation to the imaging resolution. Therefore, acquisition bandwidth as high as ~3.8 GHz is required in the traditional case.Fig. 6 The schematic diagram of the microscopy system utilizing the proposed swept source. A personal computer (PC) is used to implement low-pass filtering in the post-processing and reconstruct the image.
A standard resolution test target (USAF 1951), whose group 7 covers the linewidth from 2.2 μm to 3.9 μm, is tested by the system. Figure 7(a) is the result imaged by an amplified spontaneous emission (ASE) source and an OSA, and serves as a reference. Figures 7(b)-7(f) is the results imaged by the proposed swept source at different swept rates. The imaging quality is evaluated by the peak signal-to-noise ratio (PSNR) [56]. It can be seen that good imaging quality can be achieved when the swept rate is below 329 kHz. The line-scans of the smallest element in group 7 is depicted in Figs. 7(g) and 7(h). It's clear that the smallest element is resolved when the swept rate is slower than 329 kHz. Since the linewidth of element 6 in group 7 is 2.2 μm, the spatial resolution of the imaging system is 4.4 μm at 329 kHz frame rate, approaching the limit of the objective lens. The imaging process of this system is equivalent to discrete sampling of the target. According to the Nyquist sampling theorem, the spatial sampling interval should be smaller than 2.2 μm to achieve 4.4-μm resolution. This interval corresponds to 0.17-nm wavelength step. Therefore, according to Eq. (3), when the swept rate is slower than 447 kHz, the wavelength step is fine enough to avoid bringing limit to the resolution. The wavelength swept step is too large at higher swept rate, so that the discrete sampling to the sample is too sparse thereby some information is lost, just like the results in Figs. 7(e) and 7(f).
Fig. 7 (a) Reference image captured by OSA. (b-f) Images created by the proposed swept source at different swept rates, with PSNR to evaluate the image quality. (g-h) The line scans of the element 6 in group 7.
5. Conclusion
In conclusion, we experimentally demonstrated an ultrafast discrete swept source in this paper. The time delay variation between two chirped pulses is converted to wavelength change through FWM process. Thanks to the discrete time delay sweeping provided by the Vernier effect between two chirped OFCs with different repetition rates, an inertial-free ultrafast discrete wavelength sweeping source is achieved. Wavelength step as fine as 38 pm at 100 kHz can be realized, which is suitable for high-resolution spectroscopy or microscopy. The experiment result demonstrated 10 kHz, 129 kHz, 329 kHz, 857 kHz, and 1.03 MHz swept rates while keeping instantaneous linewidth as narrow as 0.03 nm. The swept rate tuning is realized by changing the repetition difference between the two OFCs. The frequency sweeping is highly linear and stable so that no recalibration or resampling is required. This swept source is also demonstrated for high-speed microscopic imaging. Thanks to the large wavelength-to-time mapping factor of the swept source, acquisition bandwidth below 90 MHz can be used to capture the wavelength encoded information while achieving good spectral resolution thereby good spatial resolution. The standard resolution test target imaging results verified 4.4-μm spatial resolution at 329 kHz frame rate. As a comparison, ~3.8 GHz acquisition bandwidth is required to achieve such a resolution when using traditional time stretch based swept source. Moreover, the discrete wavelength sweeping provides much longer exposure time for a single wavelength so that better sensitivity can be realized.
Funding
National Natural Science Foundation of China (Grants No. 61125501, 61320106016, 61505060, 61631166003, 61675081, and 61735006); Wuhan National Laboratory for Optoelectronics (WNLO).
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