The palette of laser technology has significantly been enriched by the innovations in ultrafast optical pulse generation. Our knowledge of the complex pulse dynamics, which is often highly nonlinear and stochastic in nature, is however limited by the scarcity of technologies that can measure fast variation/fluctuation of the spectral phase (or coherence) and amplitude in real-time, continuously. To achieve this goal, we demonstrate ultrafast interferometry enabled by optical time-stretch for real- time spectral coherence characterization with microsecond-resolution. Accessing the single-shot interferograms continuously, it further reveals the degree of second-order coherence, defined by the cross-spectral density function, at high speed-a capability absent in any existing spectroscopic measurement tools. As the technique can simultaneously measure both the high-speed variations of spectrally resolved coherence and intensity, time-stretch interferometry could create a new arena for ultrafast pulse characterization, especially favorable for probing and understanding the non-repetitive or stochastic dynamics in real-time.

We investigate the fundamental limitation of the full-field retrieval of optical pulses based on a time-equivalent Gerchberg-Saxton (GS)-like algorithm, in which the Fourier transformation of the temporal signal is performed by the group velocity dispersion (GVD) of optical fibers. The insufficient knowledge of the input pulse intensity fundamentally limited by the bandwidth of the photodetector influences the accuracy of the retrieved phase using the algorithm. To this end, we propose a modified GS algorithm, which involves multi-step intensity-only measurements, to mitigate this limitation. By studying the influence of spectral phase and amplitude modulations on the retrieval error, we show that the modified GS algorithm demonstrates a significant improvement in phase retrieval accuracy. More importantly, we anticipate the present study will provide valuable insight in understanding how the spectral variation generally influences the recovery accuracy in time-stretch-based GS algorithm, and thus identify its potential applications, particularly for those requiring ultrafast measurements.

Real-time experimental measurements of the spectrally-resolved noise properties of supercontinuum (SC) have been challenging because of the lack of ultrafast optical spectrometer technologies. Understanding the SC noise is increasingly important because it not only can gain new insight of the complex spectral dynamics of SC generation, but also provides clues to search for stable SC source. Driven by the intense interest in the active seeding mechanism for SC generation, we experimentally demonstrate real-time spectrally-resolved, broadband, statistical characterization of minute continuous-wave (CW) seeded SC, enabled by an ultrahigh-speed spectral acquisition technique called optical time-stretch (OTS). The shot-to-shot statistical analysis shows that the seeded SC exhibits a general compromise between SC bandwidth and spectral stability. OTS also allows us to experimentally identify the seeding condition for SC suppression, in which the spectral broadening is mainly contributed by the cascaded parametric process that delays Akhmediev Breather breakup process and subsequent soliton self-frequency shift. Additionally, the characteristic spectral signature of the Raman solitons, which are becalmed by the minute CW seed, can be clearly captured in real-time by OTS operated at a spectral acquisition rate as high as 20 MHz. We anticipate the OTS technique could provide further new insights for understanding more complex mechanisms of seeded-SC generation which can be examined experimentally.

Nonlinearly generated broadband ultrafast laser have been increasingly utilized in many applications. However, traditional techniques of characterizing these sources lack the ability to observe the instantaneous features and transitory behaviours of both amplitude and phase. With the advent of the optical time stretch techniques, the instantaneous shotto-shot spectral intensity can be directly measured continuously at an unprecedentedly high speed. Meanwhile, the information of the real-time phase variation, which is carried by the frequency-time mapped spectral signal has yet been fully explored. We present a technique of experimentally measuring the spectral coherence dynamics of broadband pulsed sources. Our method relies on a delayed Young's type interferometer combined with optical time-stretch. We perform the proof-of-principle demonstrations of spectral coherence dynamics measurement on two sources: a supercontinuum source and a fiber ring buffered cavity source, both with a repetition rate of MHz. By employing the optical time stretch with a dispersive fiber, we directly map the spectral interference fringes of the delayed neighbouring pulses and obtain a sufficiently large ensemble of spectral interferograms with a real-time oscilloscope (80Gb/s sampling rate). This enables us to directly quantify the spectral coherence dynamics of the ultrafast sources with a temporal resolution down to microseconds. Having the ensemble of single-shot interferograms, we also further calculate the cross spectral coherence correlation matrices of these ultrafast sources. We anticipate that our technique provides a general approach for experimentally evaluating the spectral coherence dynamics of ultrafast laser generated by the nonlinear processes e.g. modulation instability, supercontinuum generation, and Kerr resonator.

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