Ultrafast single-shot measurement techniques with high throughput are needed for capturing rare events that occur over short time scales. Such instruments unveil non-repetitive dynamics in complex systems and enable new types of spectrometers, cameras, light scattering, and lidar systems. Photonic time stretch stands out as the most effective method for such applications. However, practical uses have been challenged by the reliance of current time stretch instruments on costly supercontinuum lasers and their fixed spectrum. The challenge is further exacerbated by such a laser’s rigid self-pulsating characteristic, which offers no ability to control the pulse timing. The latter hinders the synchronization of the optical source with the incoming signal—a crucial requirement for the detection of single-shot events. Here, we report the first demonstration of time stretch using electro-optically modulated continuous wave lasers. We do this using diode lasers and modulators commonly used in wavelength-division-multiplexing optical communication systems. This approach offers more cost-effective and compact time stretch instruments and sensors and enables the synchronization of the laser source with the incoming signal. Limitations of this new approach are also discussed, and applications in time stretch microscopy and light scattering are explored.

The detection and acquisition of ultrafast, rare events in an optical system are of vital importance, with applications in imaging, sensing, and communication. This is normally done by converting the optical signal into the electrical domain and digitizing it with an analog-to-digital converter (ADC). However, such a system is highly limited by the ADC’s real-time speed and dynamic range, as well as by the speed of the photodetection circuit.

Photonic time stretch has been the most successful approach to single-shot realtime data acquisition.1 It utilizes wideband optical components and signal processing to achieve the sampling and readout of ultrafast optical events.2 A typical time stretch system is shown in Fig. 1(a). It starts with a pulsed broadband optical carrier. The femtosecond optical pulse first travels through the dispersive element, which “stretches” the carrier by inducing an initial chirp. The amount of dispersion is small so that the chirped pulse remains short. The carrier is then spectrally modulated with the ultrafast input information, i.e., the signal to be captured. The input depends on the application and encompasses ultrafast temporal signals (time stretch digitizer), spatial information (time stretch microscopy), and angular scattered light (time stretch light scattering) that need to be captured by time stretch. The information is then read out by sending the modulated pulse into an optical element with a large dispersion so that the information can be “stretched” (slowed down) so it can be captured in realtime. This process slows down the fast signal so that it can be captured using lower bandwidth photodetectors (PDs) and digitizers. The above explanation describes a unified time stretch architecture that is not tied to a specific domain of the input information (temporal, spatial, or angular).2 

FIG. 1.

(a) The universal time stretch system with four steps:2 carrier stretch, information modulation, information stretch, and analog-to-digital conversion. In the carrier stretch, a broadband femtosecond optical pulse (carrier) with electric field E1 is temporally chirped by the dispersive element D1. Here, the color-coded spectrum of E1 spreads out vertically, indicating a transform-limited laser pulse with all the wavelengths synchronized and, therefore, temporally overlapping (chirp-free). This chirp is not necessary for applications such as time stretch imaging or time stretch spectroscopy but usually exists due to the residual temporal dispersions induced by diffraction gratings when creating the wavelength-encoded spatial illumination. The electric field of the chirped pulse is denoted as E2. The horizontal spread of the spectrum implies that wavelengths are separated in time as the result of dispersion (chirped pulse). In the information modulation step, the information S (the ultrafast signal that is to be captured) is modulated (encoded) onto the chirped carrier. This creates a one-to-one mapping between the data samples and optical wavelengths on the modulated carrier E3. Time dilation by the dispersive element D2 expands the temporal scale, slowing down the signal over time. The stretched electric field, E4, is then detected by the photodetector (PD). The slowed-down signal is digitized by an analog-to-digital converter (ADC) for storage and classification. (b) The continuous wave (CW) implementation utilizing electro-optically pulsed wavelength-division-multiplexing (WDM) lasers.

FIG. 1.

(a) The universal time stretch system with four steps:2 carrier stretch, information modulation, information stretch, and analog-to-digital conversion. In the carrier stretch, a broadband femtosecond optical pulse (carrier) with electric field E1 is temporally chirped by the dispersive element D1. Here, the color-coded spectrum of E1 spreads out vertically, indicating a transform-limited laser pulse with all the wavelengths synchronized and, therefore, temporally overlapping (chirp-free). This chirp is not necessary for applications such as time stretch imaging or time stretch spectroscopy but usually exists due to the residual temporal dispersions induced by diffraction gratings when creating the wavelength-encoded spatial illumination. The electric field of the chirped pulse is denoted as E2. The horizontal spread of the spectrum implies that wavelengths are separated in time as the result of dispersion (chirped pulse). In the information modulation step, the information S (the ultrafast signal that is to be captured) is modulated (encoded) onto the chirped carrier. This creates a one-to-one mapping between the data samples and optical wavelengths on the modulated carrier E3. Time dilation by the dispersive element D2 expands the temporal scale, slowing down the signal over time. The stretched electric field, E4, is then detected by the photodetector (PD). The slowed-down signal is digitized by an analog-to-digital converter (ADC) for storage and classification. (b) The continuous wave (CW) implementation utilizing electro-optically pulsed wavelength-division-multiplexing (WDM) lasers.

Close modal

Photonic time stretch has led to qualitatively new instruments for the detection of rare events. It has been widely adopted for characterizing ultrafast phenomena and pushing the resolution limits of high-speed ADCs.3,4 Furthermore, it has facilitated the development of diverse real-time instruments for scientific, medical, and engineering applications.1,5 The time stretch based system has demonstrated remarkable success in discovering “rare events” such as optical rogue waves,6 exploring the internal dynamics of soliton molecules,7,8 investigating shock waves,9 observing the birth of laser mode-locking,10 conducting single-shot spectroscopy of chemical bonds,11,12 monitoring chemical transients in combustion,13 and directly observing the microstructures of relativistic electron bunches in a storage ring accelerator with sub-picosecond resolution.14–16 In addition, it has been instrumental in various applications, such as ultra-wideband single-shot instantaneous frequency measurements,17 gyroscopes,18 ultrafast biological microscopy, cancer cell classification,19–22 and others.23–28 A time-stretch accelerated processor (TiSAP) was employed for the first time on a commercial optical networking platform to conduct real-time, in-service signal integrity analysis of high bandwidth streaming video packets.29 

One of the most promising new directions in the field of time stretch instruments is upconversion time-stretch infrared spectroscopy for molecular science.30 This high-speed vibrational spectroscopy technique obtains the vibrational spectra of molecules using a femtosecond mid-IR optical parametric oscillator as the light source. It then upconverts the spectrum to the 1550 nm telecommunication band for time stretching using low loss and high dispersive fibers that are readily available in this band, which enables the measurement of ultrafast dynamics of irreversible phenomena in realtime and at high frame rates. This new modality in mid-infrared (MIR) spectroscopy is a powerful, non-invasive tool for identifying molecular species and sensing changes in molecular structures caused by the molecule’s environment. Specific applications include environmental gas monitoring, combustion analysis, photoreactive protein analysis, and liquid biopsy.30 

A key component of all time stretch systems is a femtosecond laser pulse, usually a supercontinuum mode-locked laser. The use of such lasers leads to several limitations. First, a typical mode-locked laser is expensive and bulky, preventing the use of time-stretch techniques in cost-sensitive applications that also require reliable and robust hardware. Second, such lasers have limited spectral coverage. In contrast, many important sensing applications are in the visible and UV bands. Crucially, the mode-locked laser has a fixed repetition rate. Synchronizing the laser pulses with the ultrafast event (information) that is to be measured is exceedingly difficult.

To overcome the aforementioned challenges, we propose and demonstrate a new approach to time stretch using continuous-wave (CW) wavelength-division-multiplexing (WDM) lasers and frequency combs as the light source. Instead of a femtosecond mode-locked laser, we use a bank of CW lasers that are time-gated (pulsed) via electro-optic (EO) modulation, as shown in Fig. 1(b). Unlike supercontinuum lasers, in the proposed architecture, the spectrum of the broadband optical pulse is no longer continuous. Instead, it consists of discrete wavelength channels. Therefore, during carrier stretch (Fig. 1), the chromatic dispersion assigns different delays to each discrete channel so that they are separated in time, becoming a pulse train. The pulse train is modulated with the incoming ultrafast signal during the information modulation stage, with each WDM channel capturing a discrete sample of the signal. The sampled signal is then slowed down during the information stretch and read out through the ADC.

This approach to time stretch takes advantage of the significant advancements in semiconductor WDM lasers, optical comb sources, and electro-optic modulation fueled by explosive growth in optical data communication and networking.31 

To demonstrate the validity of this concept, a series of studies were first conducted at the University of California, Los Angeles (UCLA), utilizing a tunable laser (EXFO T100S-HP) to demonstrate and characterize the fundamental phenomenon of time-wavelength mapping using a CW laser for the first time. For system-level experiments, the work was continued at a larger and better-equipped facility at the National Institute of Information and Communications Technology (NICT) in Japan. These experiments employed a sophisticated WDM laser array (Anritsu MU950012A) and a time stretch data acquisition backend. Detailed information can be found in Fig. 9 as well as in the Methods section. All experiments are supported by simulations using the industry standard design tool from Virtual Photonics, Inc. The simulations provide design guidelines, such as the effect of modulation pulse width and dispersion on the sampling resolution. We also describe applications aimed at time stretch imaging and time stretch angular light scattering, where the discrete spectrum of the WDM comb is mapped into space or angles using diffraction gratings.

We further show that by utilizing a nonuniform WDM wavelength spacing, it is possible to correct for the intrinsic wavelength-to-space nonlinearity of a diffraction grating and achieve linear wavelength-to-space and wavelength-to-angle mapping. This creates the uniform spatial and angular sampling desired in time stretch microscopy and time stretch light scattering instruments. These experiments highlight another advantage of the proposed approach as it relates to being able to adapt the optical spectrum to the requirements of the instrument—a feat that is much more challenging in conventional time stretch systems because they rely on passively mode-locked lasers with a fixed spectrum.

The experimental work was a collaboration between research groups from UCLA in the United States and NICT in Japan. The focus of the UCLA team was to showcase the fundamental phenomenon of wavelength-to-time mapping with CW lasers, while the experiments at NICT were focused on system-level demonstrations.

As depicted in Fig. 1, a crucial effect in a time stretch system is the mapping of the optical spectrum of the laser source to its temporal waveform. It is essential to verify that wavelength-to-time mapping can be achieved using a CW WDM source. In this section, we analyze the performance and limits of this phenomenon through simulation, employing the system illustrated in Fig. 2(a).

FIG. 2.

(a) Block diagram of a simplified continuous wave (CW) time stretch system. We note that this is not a complete system but a simplified version for studying the time-wavelength mapping phenomenon. It comprises a wavelength-division-multiplexing (WDM) laser source, an electro-optic (EO) modulator, a dispersive optical element, a photodetector (PD), and an analog-to-digital converter (ADC). The CW WDM laser undergoes time gating in an EO modulator, where a programmable pulse from a digital pattern generator is modulated onto the laser. The optical pulse is subsequently directed to a dispersive optical element for time stretch and finally detected by a PD, followed by an ADC. (b) The optical spectrum of the WDM laser source. It encompasses eight CW lasers, each with a distinct wavelength, on a DWDM grid with a channel spacing of Δλ = 0.4 nm. (c) The temporal waveform of the WDM laser source exhibiting a continuous waveform with an interference pattern. (d) The optical spectrum of the pulsed laser. (e) The temporal waveform of the pulsed laser. It displays a near Gaussian envelope while preserving the interference pattern. The temporal ambiguity (full width half maximum, FWHM) of this pulse is denoted as δTa. (f) The temporal waveform of after time stretch. ΔTWDM represents the temporal spacing between WDM channels after the time stretch. For (b) and (d), the horizontal axis represents the wavelength, and the vertical axis represents the power. For (c), (e), and (f), the horizontal axis represents the time, and the vertical axis represents the power. All the waveforms presented here were obtained through simulation. Further details can be found in the Methods section.

FIG. 2.

(a) Block diagram of a simplified continuous wave (CW) time stretch system. We note that this is not a complete system but a simplified version for studying the time-wavelength mapping phenomenon. It comprises a wavelength-division-multiplexing (WDM) laser source, an electro-optic (EO) modulator, a dispersive optical element, a photodetector (PD), and an analog-to-digital converter (ADC). The CW WDM laser undergoes time gating in an EO modulator, where a programmable pulse from a digital pattern generator is modulated onto the laser. The optical pulse is subsequently directed to a dispersive optical element for time stretch and finally detected by a PD, followed by an ADC. (b) The optical spectrum of the WDM laser source. It encompasses eight CW lasers, each with a distinct wavelength, on a DWDM grid with a channel spacing of Δλ = 0.4 nm. (c) The temporal waveform of the WDM laser source exhibiting a continuous waveform with an interference pattern. (d) The optical spectrum of the pulsed laser. (e) The temporal waveform of the pulsed laser. It displays a near Gaussian envelope while preserving the interference pattern. The temporal ambiguity (full width half maximum, FWHM) of this pulse is denoted as δTa. (f) The temporal waveform of after time stretch. ΔTWDM represents the temporal spacing between WDM channels after the time stretch. For (b) and (d), the horizontal axis represents the wavelength, and the vertical axis represents the power. For (c), (e), and (f), the horizontal axis represents the time, and the vertical axis represents the power. All the waveforms presented here were obtained through simulation. Further details can be found in the Methods section.

Close modal

The simulation setup includes a WDM laser source, an EO modulator, a dispersive optical element, a photodetector (PD), and an analog-to-digital converter (ADC). The WDM laser source consists of multiple channels (eight channels in this simulation), where each channel represents a narrow linewidth CW laser with a distinct wavelength [Fig. 2(b)]. The spacing between neighboring channels is denoted as Δλ. A value of 0.4 nm was used to be consistent with the DWDM standard.

In the time domain, the overlapping CW channels generate a continuous waveform exhibiting a fast-oscillating interference pattern [Fig. 2(c)]. To facilitate time stretch, the continuous laser is time-gated (pulsed) via EO modulation. During the time-gating, all CW channels are simultaneously pulsed, resulting in a polychromatic optical pulse that represents the overlap of all eight monochromatic optical pulses. For this simulation, a Gaussian pulse with a full width half maximum (FWHM) of Tp is used as the electric pulse for EO modulation. The generated optical pulse possesses temporal pulse width δTa (δTa = Tp), as shown in Fig. 2(e), which is also referred to as optical ambiguity. In addition, the EO modulation generates a Gaussian spectrum at the center wavelength of each channel [Fig. 2(d)]. The high-frequency modulation pattern on the temporal waveform of the multiplexed CW lasers [Figs. 2(c) and 2(e)] is caused by interference between the CW lines and is normally not observable because it is filtered out by the limited bandwidth of the detector.

To achieve time stretch, the pulsed laser is directed into a dispersive optical element (in this study, a dispersive fiber), where the chromatic dispersion maps the laser’s spectrum [Fig. 1(d)] into time [Fig. 2(f)]. This mapping process involves separating the overlapped channels in time with a temporal spacing of ΔTWDM and subsequently directing them to a PD followed by an ADC. This simulation successfully demonstrates the mapping from the optical spectrum (wavelength) to the temporal waveform (time). This indicates that the wavelength-to-time mapping effect can be achieved using a WDM CW source, thereby highlighting its potential in the realm of time stretch. Further details can be found in the Methods section.

The concept of wavelength-to-time mapping relies on achieving a distinct temporal separation among the individual channels, enabling each channel to function as a spectral sampler of the information, as illustrated in Fig. 1(b). To prevent channel overlapping, it is crucial for the temporal channel spacing, ΔTWDM, to exceed the optical pulse’s ambiguity, δTa. There are two possible approaches to satisfy this condition: either reducing the optical ambiguity, δTa, or increasing the temporal spacing, ΔTWDM. In the subsequent sections, we explore both approaches to investigate their feasibility and effectiveness.

As illustrated in Fig. 2(a), the optical pulse width is directly related to the full width half maximum (FWHM) of the modulation pulse (Tp). By manipulating Tp using the electric pulse generator, we have the ability to control the optical pulse width during simulations. This allows us to investigate scenarios with consistent dispersion (−750 ps/nm) and varying values of δTa while maintaining the same temporal channel spacing (ΔTWDM).

In the case of the baseline scenario [Fig. 3(b), δTa = 100 ps], all the channels exhibit clear separation. However, when the pulse width is increased [Fig. 3(a), δTa = 1 ns], only a single pulse is observed. This outcome arises from the fact that the temporal spacing between the channels becomes smaller than the pulse width, causing overlap in neighboring channels. Therefore, for successful and resolvable wavelength-time mapping, it is crucial to ensure that the optical pulse duration is sufficiently short.

FIG. 3.

Effect of pulse width on the sampling pattern. Results show wavelength-time mapping in continuous wave (CW) time stretch for different EO modulated pulse widths. The width is denoted as temporal ambiguity (δTa). (a) δTa = 1 ns, (b) δTa = 100 ps, (c) δTa = 20 ps, and (d) δTa = 10 ps. In each case, the horizontal axis represents time, and the vertical axis represents the detected voltage. The primary distinction among the four cases lies in the optical pulse width, while the total dispersion of the dispersive fiber remains constant at −750 ps/nm. For this value of dispersion, the optimum pulse width is 100 ps (b).

FIG. 3.

Effect of pulse width on the sampling pattern. Results show wavelength-time mapping in continuous wave (CW) time stretch for different EO modulated pulse widths. The width is denoted as temporal ambiguity (δTa). (a) δTa = 1 ns, (b) δTa = 100 ps, (c) δTa = 20 ps, and (d) δTa = 10 ps. In each case, the horizontal axis represents time, and the vertical axis represents the detected voltage. The primary distinction among the four cases lies in the optical pulse width, while the total dispersion of the dispersive fiber remains constant at −750 ps/nm. For this value of dispersion, the optimum pulse width is 100 ps (b).

Close modal

However, the reduction of the optical pulse width is subject to certain limitations. In addition to constraints imposed by the electric bandwidth, a fundamental limitation arises from the spectral channel spacing of the WDM laser source. As illustrated in Fig. 2(d), the pulsation process broadens the spectrum of each wavelength channel, where the bandwidth δλ is inversely proportional to the optical pulse width (δTa), according to the Fourier transform. Consequently, a shorter pulse duration (lower δTa) results in a broader bandwidth (higher δλ). Naturally, there exists a critical point where the pulse duration becomes so short that the bandwidth of each individual channel (δλ) approaches the channel spacing (Δλ), resulting in the undesirable spectral overlap of neighboring channels. This overlap subsequently prevents temporal separation between the channels. Figures 3(c) and 3(d) illustrate this scenario, where wavelength-to-time mapping fails despite δTa being significantly smaller than ΔTWDM. While for Fig. 3(c), the peak of each individual channel can still be observed despite an apparent merging at the bottom, the wavelength-to-time mapping fails completely for Fig. 3(d).

To circumvent the point where the optical pulse duration becomes the limit, we shift our focus toward increasing the temporal channel spacing ΔTWDM. This spacing can be calculated using the following equation:
(1)
where D is the dispersion parameter and L is the fiber length. This equation illustrates that the temporal channel spacing can be adjusted by varying the group velocity dispersion (GVD = D · L). Consequently, with an adequate amount of GVD, it becomes feasible to achieve temporal resolution for each channel without the need to modify the optical pulse width. In order to investigate this phenomenon, simulations are performed while maintaining the optical pulse width at a constant value of 100 ps and considering different GVD values. The simulation results, presented in Fig. 4, encompass two dispersion scenarios: low dispersion (GVD = 250 ps/nm) and high dispersion (GVD = 750 ps/nm). The outcomes illustrate that insufficient dispersion (250 ps/nm) leads to the group delay (100 ps) coinciding with the ambiguity of the optical pulse (δTa = 100 ps), resulting in an indistinguishable waveform [Fig. 4(a)]. Conversely, high dispersion (750 ps/nm) effectively separates the individual wavelength channels (ΔTWDM = 300 ps), thereby generating a discernible pulse train [Fig. 4(b)]. The desirability of achieving higher dispersion is evident from the results. However, it should be noted that adjusting the dispersion parameter (D) poses inherent challenges. As a result, the GVD is commonly controlled through the manipulation of the fiber length. It is important to acknowledge that the selection of fiber length also impacts the total system loss, which is directly proportional to the length of the fiber. Consequently, the total dispersion is subject to inherent limitations, necessitating careful consideration in the choice of fiber length to ensure optimal performance of the system.
FIG. 4.

Wavelength-time mapping in continuous wave (CW) time stretch under different fiber dispersions. (a) Group velocity dispersion (GVD) of 250 ps/nm results in a temporal channel spacing of 100 ps. This is the same as the pulse width (100 ps) and, therefore, fails to separate wavelength channels in time (b). GVD 750 ps/nm results in a temporal channel spacing of 300 ps. This is three times the pulse width and leads to successful channel separation. For both figures, the horizontal axes are time, and the vertical axes are voltage.

FIG. 4.

Wavelength-time mapping in continuous wave (CW) time stretch under different fiber dispersions. (a) Group velocity dispersion (GVD) of 250 ps/nm results in a temporal channel spacing of 100 ps. This is the same as the pulse width (100 ps) and, therefore, fails to separate wavelength channels in time (b). GVD 750 ps/nm results in a temporal channel spacing of 300 ps. This is three times the pulse width and leads to successful channel separation. For both figures, the horizontal axes are time, and the vertical axes are voltage.

Close modal

Following the simulation study, we proceeded with experimental validation to corroborate our findings. The experimental setup closely resembles the system depicted in Fig. 2(a), with the sole distinction lying in the laser source employed. Instead of utilizing a WDM laser comb, we employ a tunable CW laser to examine each channel individually. Given the singular channel configuration in our experimental system, each capture corresponds to a solitary pulse. By varying the wavelength of the laser source, we observe the relative time delay of the detected pulse. In particular, the main focus of this section is to analyze the relative delay observed between the channels under varying values of GVD. As delineated in Fig. 5(a), the observed relative delay between all the channels and the reference channel (channel 1 at 1545 nm) exhibits a direct proportionality to the wavelength difference. Furthermore, the slope of the observed trend (line fit) agrees well with the labeled GVD [Fig. 5(b), with certain discrepancies partly coming from other dispersive elements such as fiber patch cords in the system], thereby conforming to the relationship described by Eq. (1). These experimental findings unequivocally demonstrate the feasibility of achieving temporal separation between individual spectral channels. A comprehensive account of the experimental details can be found in the Methods section.

FIG. 5.

Experimental demonstration of wavelength-to-time mapping with electro-optic modulated CW lasers. Here, we employ a wavelength-tunable continuous wave (CW) laser. The laser, time-gated into an optical pulse, is sent through a dispersive fiber and converted into an electric pulse by a photodetector. The propagation time delay in the optical fiber is recorded. (a) Measured time delay between channels (relative to the first channel at 1545 nm) is observed for different group velocity dispersion (GVD) values. The dots are the experiment data, and the dashed lines are the linear fit. (b) The comparison between the manufacturer’s GVD fiber specification and the slopes of the fitted lines. Discrepancies may be due to other dispersive elements, such as fiber patch cords in the system. (c) Overlayed individual channels under a low dispersion fiber (GVD = −250 ps/nm). Insufficient dispersion causes pulses from adjacent channels to overlap (and merge when using WDM sources). (d) Overlayed individual channels under a high dispersion fiber (GVD = −740 ps/nm). The WDM channels are clearly separated in time. In (c) and (d), the horizontal axes are the time, and the vertical axes are the voltage measured by the oscilloscope. The difference in the pulse shape is due to sampling and comes from the relative jitter between the pulse generator and the digitizer’s sampling clock.

FIG. 5.

Experimental demonstration of wavelength-to-time mapping with electro-optic modulated CW lasers. Here, we employ a wavelength-tunable continuous wave (CW) laser. The laser, time-gated into an optical pulse, is sent through a dispersive fiber and converted into an electric pulse by a photodetector. The propagation time delay in the optical fiber is recorded. (a) Measured time delay between channels (relative to the first channel at 1545 nm) is observed for different group velocity dispersion (GVD) values. The dots are the experiment data, and the dashed lines are the linear fit. (b) The comparison between the manufacturer’s GVD fiber specification and the slopes of the fitted lines. Discrepancies may be due to other dispersive elements, such as fiber patch cords in the system. (c) Overlayed individual channels under a low dispersion fiber (GVD = −250 ps/nm). Insufficient dispersion causes pulses from adjacent channels to overlap (and merge when using WDM sources). (d) Overlayed individual channels under a high dispersion fiber (GVD = −740 ps/nm). The WDM channels are clearly separated in time. In (c) and (d), the horizontal axes are the time, and the vertical axes are the voltage measured by the oscilloscope. The difference in the pulse shape is due to sampling and comes from the relative jitter between the pulse generator and the digitizer’s sampling clock.

Close modal

To further demonstrate the wavelength-to-time mapping, we plot the eight channels (with 0.4 nm/50 GHz channel spacing) that are captured individually on the same figure. The central wavelength of the band is set at 1550 nm. The results of these measurements are presented in Fig. 5. Two experiments with different dispersion values are conducted as follows: −250 ps/nm [Fig. 5(c)] and −740 ps/nm [Fig. 5(d)]. The plots clearly illustrate that higher dispersion results in increased temporal separation between the channels, leading to a more distinguishable temporal waveform. The major components of this experiment are listed in Fig. 9, and a detailed description can be found in the Methods section. Additional experimental studies on wavelength-to-time mapping conducted by NICT are included in the supplementary material.

Having established the feasibility of CW time stretch, we propose the following two applications: CW time stretch microscope [Fig. 10(a)] and CW time stretch light scattering [Fig. 10(b)]. In these applications, the optical spectrum is first mapped into the spatial domain using free-space optical components such as lenses and diffractive gratings. This wavelength-to-space mapped light then illuminates the samples. For microscopic imaging applications, light from different wavelength channels illuminates different spatial coordinates along one line of a two-dimensional image plane. Thus, each wavelength channel is mapped to a specific spatial coordinate. In light scattering applications, light from different wavelength channels illuminates an object at different angles of incidence along one sector of the two-dimensional illumination. Thus, each wavelength channel is mapped to a specific incidence angle. By illuminating the samples with wavelength-to-space mapped light, the sample’s distribution of spatial features (microscopy) or angular features (light scattering) is encoded onto the optical spectrum and subsequently read out using a time stretch data acquisition back-end. These applications leveraging wavelength-to-space mapping have been widely reported in prior publications, such as,21,32 and their detailed implementations are reserved for the Methods section in the present paper.

To investigate the limitations and applications of the proposed techniques, we have developed a simulation system based on the structure depicted in Fig. 6(a), which follows that in Fig. 1(b). In this system, a WDM CW laser source is time-gated by an EO modulator. The information is then encoded onto the spectrum of the optical pulse through a spectral modulator, specifically a reconfigurable spectral amplitude filter. By using previously captured experimental and simulation data as input, we can demonstrate microscopy and light scattering applications. For the time stretch microscope application, the input information is a spatial line-scan of a human colon cancer cell (SW-480), while for the light scattering application, it is a simulated angular scattering profile of the sample particle. The encoded information is subsequently read out through a dispersive element, followed by a photodiode (PD) and analog-to-digital converter (ADC). This simulation employs a 64-channel laser with a channel spacing of 50 GHz. The central wavelength of the entire band is set at 1550 nm. More comprehensive details regarding the simulation system can be found in the Methods section.

FIG. 6.

(a) Block diagram of the simulation system for CW time stretch microscopy and light scattering. A wavelength-division-multiplexed (WDM) laser source is time-gated by an electro-optic (EO) modulator. The input information is encoded onto the spectrum of the optical pulse through a spectral modulator (a reconfigurable optical filter). The information is then read out by a dispersive element, followed by a photodetector (PD) and analog-to-digital converter (ADC). Two different applications are demonstrated by using different data as input: (b) Time stretch microscope and (c) time stretch light scattering. For (b), the input information is the spatial feature of a human colon cancer cell (SW-480). For (c), it is the simulated Mie angular scattering profile of a collection of 20 nm diameter particles with a refractive index of 1.57. The blue curve represents the temporal pulse train (in log scale) after time stretch, and the red curve represents the input information encoded onto the optical spectrum. For the blue curves in both figures, the horizontal axes represent time, and the vertical axes represent power. The red curve in (b) represents the spatial feature distribution of the cancer cell along a 1-D scan line, and the one in (c) represents the power of the scattered light across different angles.

FIG. 6.

(a) Block diagram of the simulation system for CW time stretch microscopy and light scattering. A wavelength-division-multiplexed (WDM) laser source is time-gated by an electro-optic (EO) modulator. The input information is encoded onto the spectrum of the optical pulse through a spectral modulator (a reconfigurable optical filter). The information is then read out by a dispersive element, followed by a photodetector (PD) and analog-to-digital converter (ADC). Two different applications are demonstrated by using different data as input: (b) Time stretch microscope and (c) time stretch light scattering. For (b), the input information is the spatial feature of a human colon cancer cell (SW-480). For (c), it is the simulated Mie angular scattering profile of a collection of 20 nm diameter particles with a refractive index of 1.57. The blue curve represents the temporal pulse train (in log scale) after time stretch, and the red curve represents the input information encoded onto the optical spectrum. For the blue curves in both figures, the horizontal axes represent time, and the vertical axes represent power. The red curve in (b) represents the spatial feature distribution of the cancer cell along a 1-D scan line, and the one in (c) represents the power of the scattered light across different angles.

Close modal

By comparing the input data with the captured waveform, as shown in Figs. 6(b) and 6(c), we observe a high degree of agreement for both applications. The minor discrepancies could be caused by timing synchronization or timing jitter. In particular, in the CW time stretch, information is carried by the peak of each pulse, so accurate sampling of the peaks is expected. However, if the ADC samples the pulse train at a rate that is not an integer multiple of the modulator’s pulse repetition rate, it results in different sampling points for each pulse, leading to a misrepresentation of the signal and causing discrepancies. In addition, jitter noise in the ADC can create ambiguity in sampling time, further contributing to these discrepancies.

As demonstrated in the preceding section, time stretch technology finds crucial application in the field of ultrafast microscopy. This is achieved through a two-step process: initially, the broadband CW WDM laser source that is time-gated by an electro-optic modulator is time-stretched into a pulse train. Subsequently, the pulse train is mapped into free space for sampling the spatial features of the target in time, acting as a scanner. Here, the time stretch is accomplished before coupling the light to free space. This is a common practice33,34 because the best dispersive element is single-mode fiber. Coupling the light back into the single-mode fiber after sampling the target in free space is extremely lossy. Building upon the successful wavelength-to-time mapping in the previous section, we now shift our focus to the second step of the process, which involves mapping the spatial features of the target onto the optical spectrum of a pre-stretched WDM laser comb through wavelength-to-space mapping. To accomplish this, we employ the system illustrated in Fig. 7. In this setup, the time-gated multi-channel WDM laser comb [shown in the inset of Fig. 7(a), detailed information is included in the supplementary material] is first coupled into space using a fiber collimator and a polarizer. The collimated beam is then expanded using diffractive gratings, resulting in an ensemble of beams, with each beam corresponding to an individual channel. The ensemble is subsequently compressed by a lens pair before being directed to an objective lens. The objective lens focuses the beam onto an infrared (IR) camera placed at the image plane, producing a series of light spots, each corresponding to a single channel. Through this configuration, each wavelength channel is mapped into a distinct spatial location, effectively serving as a “flashlight” to probe the spatial features at that particular location. In this study, we focus on the probing part of the wavelength-to-space mapping, leaving the readout part for future investigation. While the free-space optical elements in the system, such as the grating and lenses, do add a small residual temporal dispersion, the amount is negligible compared to the dispersion introduced by the primary dispersive element used for time stretch. This role of residual temporal dispersion introduced by spatial diffraction in time stretch imaging has been quantified and explained fully in our previous publication on the unified time stretch.2 

FIG. 7.

(a) The block diagram illustrates the experimental system designed to achieve wavelength-to-space mapping. The system comprises a pulse-modulated (upper right) wavelength-division multiplexing (WDM) comb source, a fiber collimator, a rotatory polarizer, a pair of diffractive gratings, a pair of lenses, and an objective lens. An infrared (IR) camera is used to image the position of WDM lines in space. The WDM comb source consists of 15 wavelength channels, each generated by a distributed-feedback (DFB) laser diode (LD), as shown in the inset in the upper right. These lasers are multiplexed using an optical coupler, followed by time-gating via a lithium niobate (LN) modulator, and are subsequently amplified. Time stretch and wavelength-to-time mapping are performed in a dispersive fiber. To equalize the power of each wavelength channel, a Waveshaper is positioned after the dispersive fiber. The single arrow points in the direction of light propagation. Additional detail about the source is provided in the supplementary material. The pair of gratings separates the channels in space and collimates the group. Then a pair of lenses reduces the beam waist, allowing it to enter the objective lens. Finally, the objective lens focuses the beam in front of the IR camera. Here, y is the spatial coordinate of each beam along the axis that is perpendicular to the optical axis, and X is the distance between the gratings along the incident beam direction. α is the incident beam angle, β is the diffracted beam angle, θ is the light divergence angle after the objective lens, and h is the distance between the objective lens focal point and the imaging plane. (b) A photograph of the free-space imaging system for this study.

FIG. 7.

(a) The block diagram illustrates the experimental system designed to achieve wavelength-to-space mapping. The system comprises a pulse-modulated (upper right) wavelength-division multiplexing (WDM) comb source, a fiber collimator, a rotatory polarizer, a pair of diffractive gratings, a pair of lenses, and an objective lens. An infrared (IR) camera is used to image the position of WDM lines in space. The WDM comb source consists of 15 wavelength channels, each generated by a distributed-feedback (DFB) laser diode (LD), as shown in the inset in the upper right. These lasers are multiplexed using an optical coupler, followed by time-gating via a lithium niobate (LN) modulator, and are subsequently amplified. Time stretch and wavelength-to-time mapping are performed in a dispersive fiber. To equalize the power of each wavelength channel, a Waveshaper is positioned after the dispersive fiber. The single arrow points in the direction of light propagation. Additional detail about the source is provided in the supplementary material. The pair of gratings separates the channels in space and collimates the group. Then a pair of lenses reduces the beam waist, allowing it to enter the objective lens. Finally, the objective lens focuses the beam in front of the IR camera. Here, y is the spatial coordinate of each beam along the axis that is perpendicular to the optical axis, and X is the distance between the gratings along the incident beam direction. α is the incident beam angle, β is the diffracted beam angle, θ is the light divergence angle after the objective lens, and h is the distance between the objective lens focal point and the imaging plane. (b) A photograph of the free-space imaging system for this study.

Close modal

Figures 8(a)8(c) present the experimental results obtained from the setup in Fig. 7, showing how the WDM channels are projected into space for applications in time stretch microscopy and time stretch light scattering. In this setup, the source is a time-stretched 15-channel CW WDM laser comb with uniform 200 GHz channel spacing. The spectrum of the WDM comb is depicted in Fig. 8(a), while the captured images by the infrared (IR) camera are shown in Fig. 8(b) (odd channels) and Fig. 8(c) (even channels). The separation of even and odd channels into distinct plots allows for enhanced visibility of the channel spacing. The results demonstrate clear separation between wavelengths for both even and odd channels, providing unequivocal evidence that complete separation can be achieved when all 15 channels are included in an appropriate configuration. This experiment effectively validates the successful implementation of wavelength-to-space mapping using a CW laser comb. The major components used in this experiment are listed in Fig. 9, and a detailed description can be found in the Methods section.

FIG. 8.

Experimental results, obtained from the setup in Fig. 7, show how the WDM channels are projected into space for applications in time stretch microscopy and time stretch light scattering. These results show how the non-linear mapping between wavelength and space, intrinsic to a diffraction grating and problematic in microscopy and light scattering applications, can be corrected by properly designing the WDM spectrum. The source is a time-stretched 15-channel CW WDM laser comb. The figure shows the spatial locations and spot sizes of the channels when their wavelength spacings are chosen to be uniform vs nonuniform. To clearly see the spatial behavior of the channels in the image, only odd or even channels are enabled each time. (a) Spectrum of WDM channels with 200 GHz uniform spacing. (b) The image captured by the IR camera with only odd channels enabled. (c) The image captured by the IR camera with only even channels enabled. (d) Spectrum of WDM channels with nonuniform spacing—inversely designed using Eq. (6). (e) The image captured by the IR camera with only odd channels enabled. Nonuniform wavelength spacing leads to uniformly spaced spatial sampling pulses, as desired in microscopy and light scattering applications. The residual nonuniform spot sizes arise due to the non-linear mapping between wavelength and space intrinsic to a diffraction grating. Means to mitigate this effect are discussed in the text.

FIG. 8.

Experimental results, obtained from the setup in Fig. 7, show how the WDM channels are projected into space for applications in time stretch microscopy and time stretch light scattering. These results show how the non-linear mapping between wavelength and space, intrinsic to a diffraction grating and problematic in microscopy and light scattering applications, can be corrected by properly designing the WDM spectrum. The source is a time-stretched 15-channel CW WDM laser comb. The figure shows the spatial locations and spot sizes of the channels when their wavelength spacings are chosen to be uniform vs nonuniform. To clearly see the spatial behavior of the channels in the image, only odd or even channels are enabled each time. (a) Spectrum of WDM channels with 200 GHz uniform spacing. (b) The image captured by the IR camera with only odd channels enabled. (c) The image captured by the IR camera with only even channels enabled. (d) Spectrum of WDM channels with nonuniform spacing—inversely designed using Eq. (6). (e) The image captured by the IR camera with only odd channels enabled. Nonuniform wavelength spacing leads to uniformly spaced spatial sampling pulses, as desired in microscopy and light scattering applications. The residual nonuniform spot sizes arise due to the non-linear mapping between wavelength and space intrinsic to a diffraction grating. Means to mitigate this effect are discussed in the text.

Close modal
FIG. 9.

Major components in experiments at UCLA and NICT. Details can be found in the Methods section.

FIG. 9.

Major components in experiments at UCLA and NICT. Details can be found in the Methods section.

Close modal

Although Figs. 8(b) and 8(c) have demonstrated the successful implementation of wavelength-to-space mapping using a CW WDM comb source, an important observation can be made regarding the nonuniform displacement of each channel in this particular setup. This nonuniform displacement arises due to the non-linear mapping between channel wavelengths and the spatial displacement of the imaging beam within the system, which is intrinsic to the diffraction grating. It is crucial to note that in time stretch microscopy and light scattering applications, each channel serves as a “probe” responsible for sampling the spatial features of the target. Hence, a nonuniform displacement is considered problematic as it would result in nonuniform sampling, potentially introducing distortions in the imaging process.

To address the nonuniform spatial displacement caused by the non-linear mapping between channel wavelengths and the spatial displacement that originates from the intrinsic behavior of gratings, we establish a mathematical model to investigate the root cause of this effect. In the system depicted in Fig. 7(a), the WDM comb source is initially coupled into free space using a collimator. Following the collimator, a polarizer is employed to optimize the polarization of the laser beam for enhanced efficiency at the gratings. A pair of gratings is utilized to spatially separate each wavelength channel, resulting in the transformation of a single polychromatic laser beam into a collection of collimated monochromatic beams. Finally, a lens pair is employed to compress the beams. Such a system originates from Ref. 32, which also provided the spatial coordinates of the beams after the lens pair
(2)
Here, y is the spatial coordinate of each beam along the axis that is perpendicular to the optical axis. M is the magnification factor of the telescope setup. X is the distance between the gratings along the incident beam direction. λ is the wavelength. α is the incident beam angle, and β is the diffracted beam angle, which can be derived via
(3)
where m is the diffraction order (usually 1), and d represents the grating groove spacing. The compressed beam is then fed into an objective lens, which focuses the beam. Since the wavelength channels are separated along the vertical axis of the lens, each channel has a unique diverging angle,
(4)
where P is the objective lens entrance pupil diameter, NA is the objective lens numerical aperture, and dcorr is a correction term representing potential beam center misalignment with respect to the objective lens entrance pupil diameter P. θ(λ) is the exiting angle of each beam corresponding to a wavelength channel. Therefore, the position of the spot on the image plane can be derived as
(5)
where S(λ) is the spatial coordinate of the beam spot captured by the IR camera along the vertical axis of the image plane. h is the distance between the objective lens focal point and the image plane. Using Eqs. (2)(5), the relationship between the wavelength and the spatial coordinate of the spot can be approximated,
(6)
Using Eq. (6), we implement a predistortion scheme. This scheme aims to design the channel spacing of a WDM laser comb to achieve a uniform spatial displacement. To demonstrate the effectiveness of this approach, we conducted experiments using the same system described in Fig. 7, but with the WDM source having an adjusted channel spacing. Figures 8(d)8(f) showcase the results of this predistortion technique. Figure 8(d) presents the pre-corrected WDM spectrum with a nonuniform channel spacing that has been inversely designed according to Eq. (6). With the implementation of this new WDM source, the spatial displacement becomes nearly uniform, as illustrated in Figs. 8(e) and 8(f).

An important observation that merits discussion is the nonuniformity of spot sizes despite achieving a uniform spatial displacement between channels. This phenomenon is evident in both Figs. 8(e) and 8(f), where longer wavelengths correspond to larger spot sizes. The reason for this variation is attributed to the fact that although the channel spacing design has been successfully implemented in the current system, the spectral bandwidth of each individual channel remains uniform. Consequently, the non-linear mapping between wavelength and space intrinsic to a diffraction grating results in variations in spot sizes across the channels. This observation highlights the need to consider the sampling effect induced by spot size variation in probing the spatial features of the target.

To address the issue of nonuniform spot size, one can make the individual channel linewidths nonuniform. The linewidths will then be guided by Eq. (6). This works when the linewidth for each channel is determined by that of the CW laser. In general, the channel bandwidth is determined by two factors: the laser linewidth and the modulation bandwidth of the time-gating pulse. When the bandwidth is dominated by the laser linewidth, uniform sampling (i.e., uniform spot size) can be achieved by adjusting the linewidth of each individual channel laser. On the other hand, when the bandwidth is dominated by the modulation process, it becomes more challenging to adjust the individual channel bandwidths. This is because the pulsation of all channels occurs simultaneously, leaving no control over individual channel bandwidths.

In this paper, we introduce a novel implementation of continuous wave (CW) photonic time stretch that effectively maps wavelengths to time, enabling wavelength-time mapping. Through simulation, we demonstrate two potential applications of this technique. In particular, we focus on the feasibility of free-space applications. The new time stretch technology employing continuous-wave lasers can characterize and measure two-dimensional (2D) spatial images of transient events and two-dimensional (2D) patterns of the scattering of light by an object. A practical method to capture 2D images or 2D scattering patterns of transient phenomena would be a great advance in the field of instrumentation and measurements. It can enable the discovery of new scientific phenomena in the same manner that the original time stretch led to the discovery of optical rogue waves, soliton molecule dynamics, and relativistic electron bunch behavior.1 However, it is important to note that there are certain limitations that need to be further investigated.

In a typical time stretch system (Fig. 1), the information is initially encoded onto the spectrum of the laser source. The spectral resolution of the system plays a fundamental role in determining the minimum resolvable wavelength and, consequently, affects the sampling of the information. In an imaging system,21 the maximum spatial resolution is limited by the spectral resolution of the time stretch system and the angular diffraction of the diffractive grating. For a time stretch ADC,3 the maximum temporal input bandwidth is limited by the spectral resolution and the dispersion of the chirp fiber.

The spectral resolution in traditional time stretch systems is impacted by various factors, including the stationary phase approximation (SPA), the ADC sampling rate, and the analog bandwidth of the detection system.33 In the case of the CW time stretch technique proposed in this paper, the discrete nature of the optical spectrum introduces further constraints, particularly related to the spectral channel spacing. To comprehensively explore these limitations, mathematical models are developed to analyze the combined effects of the newly introduced constraints and the existing limitations in conventional systems.

From Ref. 33, we have learned that the spectral resolution brought by SPA can be written in the following form:
(7)
where λc is the center wavelength of the laser band, D is the dispersion parameter of the dispersive fiber, L is the fiber length, and c is the speed of light. As for the spectral resolution based on the ADC sampling rate and analog bandwidth of the detection system, we have
(8)
(9)
where Fs is the digital sampling rate of the ADC and B is the analog bandwidth of the detection system.
In the case of the proposed CW time stretch technology, an additional limitation arises due to the discrete nature of the optical spectrum. During the time gating process, an electric pulse with a pulse width of Tp is temporally modulated onto the WDM laser source, which creates an optical pulse with a temporal pulse width of δTa (δTa = Tp). This temporal modulation induces a spectral sideband at the center wavelength of each channel. The bandwidth of this sideband is inversely proportional to the optical pulse width,
(10)
where λ is the center wavelength of each channel. To avoid inter-channel-interference, the sideband between the neighboring channels should not overlap. Therefore, it needs to satisfy
(11)
After pulsation, the input data are encoded onto the spectrum of the pulsed WDM laser, where each channel represents a sampling point. Consequently, the channel spacing Δλ is equivalent to the spectral resolution. During the time stretch process, the spectral channel spacing is mapped to the temporal separation of the channels, as described by Eq. (1). In order to ensure distinguishable pulse trains and prevent temporal overlap between the channels, the temporal separation should be greater than the width of the pulsed CW laser, δTa,
(12)
With the above equation, we can derive the following:
(13)
This can also be written in the form of
(14)
where ΔΩ is the spectral channel spacing in Hz.
Therefore, the resolution of a CW time stretch system can be given as
(15)
The resolution induced by CW channel spacing, δλCH, is a new phenomenon that is negligible in a conventional time stretch system that relies on femtosecond supercontinuum lasers. The channel spacing can be chosen such that its influence on the resolution is negligible compared to other factors, such as the SPA, ADC sampling rate, and analog bandwidth of the detection systems mentioned above. In this way, the resolution of a CW time stretch system could be similar to that of a conventional time stretch system based on a supercontinuum femtosecond laser.

The equations derived above can be used to study various metrics, such as temporal resolution. It is well-known that temporal resolution is of vital importance for time domain signal acquisition. As shown in Fig. 1(b), in CW time stretch, since each pulse corresponds to one sampling point, the temporal resolution is determined by the pulse duration in time, δTa, which is proportional to the inverse of the channel linewidth. According to Eq. (10), high temporal resolution requires a large channel bandwidth, necessitating wider spectral channel spacing. This increases the requirement for the total spectral span, especially when a large number of samples are needed to capture the signal. Fortunately, the operating wavelength range of the Mach–Zehnder modulator is wide (around 100 to a few hundred nanometers34) and can be easily extended by using multiple modulators working in different bands.

When the overall wavelength span is limited, this creates certain constraints. For applications aiming to capture time domain signals, a limited spectral span results in a trade-off between temporal resolution and the number of sampling points (the number of WDM channels), as previously discussed. For a fixed spectral span, a greater number of samples (channels) leads to smaller spectral channel spacing (Δλ). According to Eq. (13), to maintain the overall spectral resolution, the total dispersion (D · L) needs to increase. This is usually achieved by extending the length of the dispersive fiber (L), which could also increase the transmission loss and subsequently impact the Signal-to-Noise Ratio (SNR).

For applications such as microscopic imaging, spatial resolution is also important. This has been thoroughly discussed for the conventional time stretch in our previous publication,35 and can be easily reformulated for the CW time stretch.

Another limitation arises from the acquisition system. The time stretch technique produces a pulse train with the information encoded into its envelope. Each pulse within the train represents an individual sample of the input information. To accurately measure each sample, it is necessary to obtain the peak value of each pulse. However, due to the requirement for short pulses (in this paper, 100 ps), high detection bandwidth, high sampling rate, low jitter noise, and advanced interpolation and peak finding algorithms are needed. This poses a trade-off between the optical source and the detection system. While the source becomes more cost-effective and simpler compared to conventional approaches, the detection system becomes more complex. Nevertheless, recent advancements have made it more convenient to integrate high-performance detection systems compared to mode-locked lasers.

Apart from time stretch, the time lens technique also offers a different and related approach to ultrafast measurements.36 In the future, the realization of a time lens with CW lasers would be an interesting research direction.

In this section, we provide detailed information on the following: (1) simulation system, (2) experiment setup for investigating wavelength-to-time mapping, (3) experiment setup for investigating wavelength-to-space mapping, and (4) details on the time stretch applications mentioned in the main text.

A mathematical simulation system is developed to investigate the wavelength-time mapping in a CW time stretch system. The simulation setup, as depicted in Fig. 2(a), comprises a multi-channel WDM laser source, an EO modulator, a dispersive fiber, a photodetector, and an ADC. The WDM laser source consists of CW lasers with a linewidth of 10 MHz and an optical power of 5 mW. The channels are evenly distributed around the center wavelength of 1550 nm, with a channel spacing of 0.4 nm. Depending on the specific application, the number of channels varies. For the investigation of wavelength-time mapping, an eight-channel WDM laser is employed, while for demonstrating the application of CW time stretch [Fig. 6(a)], 64 channels are utilized. The laser output is modulated by an EO modulator using a Gaussian electric pulse, where the full width at half maximum (FWHM) of the electric pulse (Tp) determines the width of the resulting optical pulse (Ta). The pulse width is set to 100 ps. The pulsed laser is then transmitted through a dispersive fiber, characterized by a dispersion coefficient of 100 ps/nm/km and a loss of 0.4 dB/km. The length of the fiber, typically set to 7.5 km, is chosen to achieve the desired total GVD. In addition, a simulation with a fiber length of 2.5 km is performed to investigate the effect of low dispersion. Finally, a photodetector captures the optical pulse train. The detected signal is sampled and digitized using an ADC with a sampling rate of 50 GS/s and an 8-bits quantization resolution.

The simulation model is implemented in VPI photonics running on a server equipped with 64 GB of RAM and an Nvidia RTX TITAN GPU with 24 GB of memory.

In this experimental study focusing on wavelength-time mapping, a wavelength-tunable single-channel laser (EXFO T100S-HP) with an average optical power output of 20 mW is employed as the laser source. The laser pulsation is achieved using a Mach–Zehnder modulator (FTM7939EZ) from FUJITSU. The modulated electric signal is a Gaussian pulse with a FWHM of 100 ps and a repetition rate of 37.7 MHz, generated using a mode-locked laser29 followed by a 10 GHz bandwidth photodetector (Discovery DSC-30S). It is worth noting that a simpler and more cost-effective circuit can be used as an alternative pulse generator. To compensate for the loss in the dispersive fiber, an Erbium Doped Fiber Amplifier (EDFA) (IPG Photonics, EAD-2-CL) is placed after the modulator. Several spools of fibers from Amonics with different dispersions are used as the dispersive media, including −740, −300, −250, −100, 100, and 300 ps/nm. The pulse trains are detected using a photodetector (Discovery DSC-50S) with a 10 GHz analog bandwidth. The analog-to-digital conversion is performed using a Tektronix DPO71604B oscilloscope with a 16 GHz analog bandwidth and a sampling resolution of 50 GS/s. This experiment was designed and conducted at the UCLA Photonic Laboratory in the United States.

The wavelength-space mapping system, illustrated in Fig. 7, comprises several components: a CW WDM comb source, a fiber collimator, a rotatory polarizer, a pair of diffractive gratings, a pair of lenses, an objective lens, and an IR camera. In the system, the laser beam is initially collimated into free space using the collimator. The polarizer is employed to optimize the polarization of the laser for enhanced efficiency during grating operation. The grating pair serves to expand the laser beam, resulting in the spatial displacement of each wavelength. The distance between the short and long wavelength sides of the spatially displaced laser beam was ∼16.98 mm, and it was subsequently compressed using the telescope configuration formed by the lens pair, enabling it to fit within the objective lens. Finally, the objective lens focuses the beam onto the IR camera, facilitating image capture and analysis.

In this experiment, the comb source utilized is an Anritsu MU950012A module housed inside an MT9812B multi-channel box. This source allows for the generation of multiple channels, each offering a maximum power output of 8 dBm with a linewidth of 10 MHz. The nominal channel spacing is set at 50 GHz, with a tuning range of ±25 GHz. The CW lasers are initially coupled together via a PLC splitter (PLCS-24-1550-D1-1/0.5-SC/UPC-B) from Accelink. Subsequently, they are time-gated (pulsed) via an EO modulator (Fujitsu LN-MOD FTM H74M-5208) and time-stretched into a pulse train through a dispersive fiber (−300 ps/nm dispersion). The details can be found in Fig. S2 (supplementary material). The two gratings employed are both first-order blazed gratings with a line density of 1100 lines/mm, sourced from Shimadzu Corp. The first grating has an effective breadth of 25 mm (Shimadzu Corp. S813-1073), while the second grating has an effective breadth of 60 mm (Shimadzu Corp. G-NIR-110-6030-S). For the telescope setup, two plano–convex lenses from Thorlabs are used. The first lens, AC254-100-C-ML, possesses a focal length of 100 mm, while the second lens has a focal length of 10 mm. The objective lens employed in the experiment is a Mitutoyo WE30035219 lens, featuring a magnification of 50×, a numerical aperture of 0.42, and an effective focal length of 4 mm. Finally, the IR camera employed is a GaAs camera provided by Hamamatsu (C10633).

In the experiment depicted in Figs. 8(a)8(c), a WDM source is employed to generate 15 wavelength channels with a channel spacing of 200 GHz, ranging from 1575.2 to 1595.4 nm. On the other hand, in the experiment illustrated in Figs. 8(d)8(f), the spacing between the 15 wavelength channels is adjusted based on Eq. (6) to achieve uniform spatial separation of each channel. The experiment described in this section was designed and conducted at the NICT laboratories in Japan.

This section presents background information on the proposed applications of the CW time stretch discussed earlier. Two specific scenarios are examined: time stretch microscopic imaging and spectrally encoded angular light scattering.

Time stretch microscope: The time stretch microscope, initially proposed in Ref. 21 and depicted in Fig. 10(a), operates as follows: A broadband laser pulse is dispersed in space using a pair of diffractive gratings, resulting in the mapping of the optical spectrum to spatial coordinates. The dispersed pulse is then focused onto biological samples [corresponding to the imaging plane shown in Fig. 7(a)], allowing the spatial features of the samples to be encoded onto the optical spectrum of the laser pulse. The returning pulse is directed into a dispersive fiber for time stretch and, subsequently, read out using a real-time ADC. This approach enables the mapping of the spatial information of biological samples into the temporal domain, facilitating real-time data collection. For the simulation study in this paper, we employ intensity-only data obtained from previous studies,22 serving as input to the spectral modulator module in VPI photonics.

FIG. 10.

Introduction to time stretch microscopy and time stretch light scattering. (a) In the time stretch quantitative phase imaging (TS-QPI) system,21,22 broadband pulses are diffracted spatially into rainbow flashes that illuminate the target. The spatial characteristics of the target are then encoded into the spectrum of the broadband optical pulses, with each pulse representing a one-dimensional line-scan. By utilizing a Michelson interferometer, the phase shift and amplitude morphology of the sample are encoded into the spectral interference patterns. Subsequently, these encoded spectrograms are temporally stretched using the time stretch and captured by a photodetector (PD) and an analog-to-digital converter (ADC). The image is reconstructed by DSP utilizing the Hilbert transform. (b) The spectrally encoded angular light scattering system32 encodes the angular scattering profile of a sample onto the spectrum of a broadband laser. The system employs broadband pulses as the optical source. An optical equalization filter is introduced after the laser to modify the optical spectrum of the laser pulse, concentrating more power within the desired angular band. The equalized optical pulse is then transformed into a collimated, one-dimensional rainbow using a pair of diffraction gratings. The resulting beam is compressed using a telescope setup and, subsequently, focused onto the sample under test by an objective lens. This optical technique maps the wavelength to the angle of illumination. This arrangement allows the sample to be illuminated with light at different incident angles, enabling the measurement of the angular scattering characteristic of the sample using a single detector at a fixed angle. The scattered light is fed into a time stretch spectrometer for high-speed measurements. Alternatively, a conventional optical spectrum analyzer can be used for lower-speed measurements.

FIG. 10.

Introduction to time stretch microscopy and time stretch light scattering. (a) In the time stretch quantitative phase imaging (TS-QPI) system,21,22 broadband pulses are diffracted spatially into rainbow flashes that illuminate the target. The spatial characteristics of the target are then encoded into the spectrum of the broadband optical pulses, with each pulse representing a one-dimensional line-scan. By utilizing a Michelson interferometer, the phase shift and amplitude morphology of the sample are encoded into the spectral interference patterns. Subsequently, these encoded spectrograms are temporally stretched using the time stretch and captured by a photodetector (PD) and an analog-to-digital converter (ADC). The image is reconstructed by DSP utilizing the Hilbert transform. (b) The spectrally encoded angular light scattering system32 encodes the angular scattering profile of a sample onto the spectrum of a broadband laser. The system employs broadband pulses as the optical source. An optical equalization filter is introduced after the laser to modify the optical spectrum of the laser pulse, concentrating more power within the desired angular band. The equalized optical pulse is then transformed into a collimated, one-dimensional rainbow using a pair of diffraction gratings. The resulting beam is compressed using a telescope setup and, subsequently, focused onto the sample under test by an objective lens. This optical technique maps the wavelength to the angle of illumination. This arrangement allows the sample to be illuminated with light at different incident angles, enabling the measurement of the angular scattering characteristic of the sample using a single detector at a fixed angle. The scattered light is fed into a time stretch spectrometer for high-speed measurements. Alternatively, a conventional optical spectrum analyzer can be used for lower-speed measurements.

Close modal

Spectrally encoded angular light scattering: The spectrally encoded angular light scattering technique, initially proposed in Ref. 32 and illustrated in Fig. 10(b), is employed for quantitative analysis of various characteristics of microparticles. The system operates by dispersing a broadband laser pulse into space using a pair of diffractive gratings, compressing it with a telescope setup, and directing it to an objective lens. The objective lens then focuses the beam onto the particle samples. Due to the spatial dispersion of the laser, each wavelength corresponds to a specific axial position upon entering the objective lens, leading to different incident angles on the sample. As a result, wavelength-encoded angular scattering light is generated. This mapping of wavelength to incident and scattering angles allows for the measurement of the light scattering coefficient at various angles for the target particle samples. During the simulation study in this paper, data generated by a MATLAB model in Fig. 10(b) is employed as input to the spectral modulator module in VPI photonics.

The supplementary material presents extended studies on wavelength-to-time mapping conducted at the National Institute of Information and Communications Technology (NICT). The first section introduces an experiment demonstrating successful wavelength-to-time mapping using a Wavelength-Division-Multiplexing (WDM) comb source with 44 continuous wave (CW) channels. The second section provides a detailed description of the time-stretched, spectral-shaped WDM laser source utilized for showcasing wavelength-to-space mapping, as depicted in the inset of Fig. 7(a).

We gratefully acknowledge the collaboration between the UCLA Photonics Laboratory and NICT for this research. The original idea was proposed by B.J. At UCLA, T.Z. conducted the simulation and the experimental study. T.Z. performed data analysis for both the simulation and the experiment. At NICT, H.F. and N.W. provided supervision for the study, while Y.G. and T.M. performed the experiments and data analysis. The manuscript was prepared by T.Z., C.M., A.M.M., and B.J.

The authors have no conflicts to disclose.

Tingyi Zhou: Conceptualization (supporting); Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (lead); Validation (equal); Visualization (equal); Writing – original draft (equal). Yuta Goto: Data curation (equal); Investigation (equal); Methodology (equal); Validation (equal); Visualization (equal); Writing – review & editing (equal). Takeshi Makino: Data curation (supporting); Formal analysis (supporting); Writing – review & editing (supporting). Callen MacPhee: Data curation (supporting); Visualization (supporting). Yiming Zhou: Methodology (supporting); Writing – review & editing (supporting). Asad M. Madni: Writing – review & editing (equal). Hideaki Furukawa: Project administration (equal); Supervision (equal); Writing – review & editing (supporting). Naoya Wada: Funding acquisition (equal); Project administration (equal); Supervision (supporting). Bahram Jalali: Conceptualization (lead); Formal analysis (lead); Funding acquisition (lead); Investigation (equal); Project administration (lead); Resources (lead); Supervision (lead); Writing – original draft (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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