Time-to-space mapping of femtosecond pulses

Single-shot ultrafast optical imaging

Single-shot ultrafast optical imaging can capture two-dimensional transient scenes in the optical spectral range at ≥100 million frames per second. This rapidly evolving field surpasses conventional pump-probe methods by possessing the real-time imaging capability, which is indispensable for recording non-repeatable and difficult-to-reproduce events and for understanding physical, chemical, and biological mechanisms. In this mini-review, we survey comprehensively the state-of-the-art single-shot ultrafast optical imaging. Based on the illumination requirement, we categorized the field into active-detection and passive-detection domains. Depending on the specific image acquisition and reconstruction strategies, these two categories are further divided into a total of six sub-categories. Under each sub-category, we describe operating principles, present representative cutting-edge techniques with a particular emphasis on their methodology and applications, and discuss their advantages and challenges. Finally, we envision prospects of technical advancement in this field.

Single-shot optical recorder with sub-picosecond resolution and scalable record length on a semiconductor wafer

We demonstrate a novel, single-shot recording technology for transient optical signals. A resolution of 0.4 ps over a record length of 54 ps was demonstrated. Here, a pump pulse crossing through a signal samples a diagonal "slice" of space-time, enabling a camera to record spatially the time content of the signal. Unlike related χ⁽²⁾-based cross-correlation techniques, here the signal is sampled through optically pumped carriers that modify the refractive index of a silicon wafer. Surrounding the wafer with birefringent retarders enables two time-staggered, orthogonally polarized signal copies to probe the wafer. Recombining the copies at a final crossed polarizer destructively interferes with them, except during the brief stagger window, where a differential phase shift is incurred. This enables the integrating response of the rapidly excited but persistent carriers to be optically differentiated. This sampling mechanism has several advantages that enable scaling to long record lengths, including making use of large, inexpensive semiconductor wafers, eliminating the need for phase matching, broad insensitivity to the spectral and angular properties of the pump, and overall hardware simplicity.

Realization of temporal linear transformations by the use of a spatial-diffraction-based optical system

Signal processing in general, and optical signal processing in particular, make extensive use of linear transformations. The temporal nature of many optical signals (e.g., in optical communication systems) makes the realization of temporal transformations a desired extension. We present a system making possible the realization of arbitrary temporal linear transformation. The system supports real-time changes of the realized transformation. The mathematical analysis is derived, and computer simulations are presented.

Spatial phase information transmission through an optical fiber by coherence function synthesis

Transmission of one-dimensional spatial phase information by low-coherence light through a single-mode optical fiber is experimentally demonstrated by use of space-time conversion at a 4-f Fourier coherence function shaper and time-space conversion with spectral holography. The dispersion during the fiber propagation can be automatically compensated for with spectral holography. However, space-time coupling caused by the transmitter limits the capacity of information transmittable with one coherence function shaping. A significant advantage in the space-time-space conversion with low-coherence light is that an infinite number of signal channels can be multiplexed with a newly invented delay-time division scheme, which can extend this analog transmission to two-dimensional spatial phase patterns.

Two-Dimensional Image Transmission Based on the Ultrafast Optical Data Format Conversion between a Temporal Signal and a Two-Dimensional Spatial Signal

We have experimentally demonstrated a two-dimensional (2-D) image transmission based on the ultrafast optical data format conversion between a temporal signal and a spatial signal with an ultrashort optical pulse. In the proposed system we adopt a spectral holography technique to transmit a one-dimensional (1-D) spatial signal and use a spatial-domain time-frequency transform to realize a transform between 1-D and 2-D spatial signals. By use of these techniques, a low-optical-loss transmission system can be constructed. To demonstrate a 2-D image transmission with this technique, we achieved experimentally transmission of the alphabet letter T as a 3 x 3 pixel 2-D spatial image.

Fundamental functions for ultrafast optical routing by temporal frequency-to-space conversion

We demonstrate fundamental functions for ultrafast optical routing by using an elemental part of an ultrafast optical technique for conversion of time to two-dimensional space. A preliminary experimental result shows that recognition of header signals can be achieved at a rate of more than 600 Gbytes/s.

Joint transform correlator for optical temporal signals

Correlation is considered to be a fundamental operation in the field of signal processing. The fact that this operation can be implemented optically in a relatively simple manner is an important advantage of utilizing optical systems for signal processing. The VanderLugt 4-f system and the joint transform correlator (JTC) are the two most popular configurations for performing a spatial correlation operation optically. So far the JTC architecture has been used for performing correlation between two images, which are illuminated by a quasi-monochromatic light source. We propose a generalization of the JTC that performs a correlation between two temporal optical signals.

Wigner-related phase spaces for signal processing and their optical implementation

Phase spaces are different ways to represent signals. Owing to their properties, they are often used for signal compression and recognition with high discrimination abilities. We present several recently introduced Wigner-related sets of representations that have improved signal processing performance, and we introduce an optical implementation. This study deals with the generalized Wigner spaces, the fractional Fourier transform, and the x-p and the r-p representations. The optical implementations are demonstrated and discussed.

Secure ultrafast communication with spatial-temporal converters

An encrypted database interfaced with an ultrafast secure data communication system using spatial-temporal converters is proposed. The original spatial signal is optically encrypted, and the encrypted signal is holographically stored in a storage medium such as photorefractive materials. The spatially encrypted signal is sampled to avoid the overlap of each datum at the receiver. The sampled data are converted into a temporal signal to transmit the information through an optical fiber. At the receiver the temporal signal is converted back into the spatially encrypted signal. Retrieval of the original data can be achieved when the correct phase key is used in the decryption system. We developed an expression for encrypted output and decrypted data. We numerically evaluate the effect of sampling the spatially encrypted signal on the quality of the decrypted data.

Single-shot measurement of temporal phase shifts by frequency-domain holography

Frequency-domain holography is used to measure ultrafast phase shifts induced either by the nonlinear susceptibility ?(3) of fused silica or by ionization fronts in air over a temporal region of 1 ps with 70-fs resolution in a single shot. The use of an imaging spectrometer adds one-dimensional spatial resolution to the single-shot temporal measurements.

Femtosecond single-shot correlation system: a time-domain approach

We introduce, analyze, and experimentally demonstrate what to the best of our knowledge is a new pulse correlation technique that is capable of real-time conversion of a femtosecond pulse sequence into its spatial image. Our technique uses a grating at the entrance of the system, thus introducing a transverse time delay (TTD) into the transform-limited reference pulse. The shaped signal pulses and the TTD reference pulse are mixed in a nonlinear optical crystal (LiB(3)O(5)), thus producing a second-harmonic field that carries the spatial image of the temporal shaped signal pulse. We show that the time scaling of the system is set by the magnification of the anamorphic imaging system as well as by the grating frequency and that the time window of the system is set by the size of the grating aperture. Our experimental results show a time window of approximately 20 ps. We also show that the chirp information of the shaped pulse can be recovered by measurement of the spectrum of the resulting second-harmonic field.

Analysis of spatial-temporal converters for all-optical communication links

We analyze parallel-to-serial transmitters and serial-to-parallel receivers that use ultrashort optical pulses to increase the bandwidth of a fiber-optic communication link. This method relies on real-time holographic material for conversion of information between spatial and temporal frequencies. The analysis reveals that the temporal output of the pulses will consist of chirped pulses, which has been verified experimentally. When the signal pulses are transmitted along with a reference pulse, the distortions of the received signal, caused by dispersion and other factors in the fiber, are canceled because of the phase-conjugation property of the receiver. This self-referencing scheme simplifies the receiver structure and ensures perfect timing for the serial-to-parallel conversion.

Real-time edge enhancement of femtosecond time-domain images by use of photorefractive quantum wells

Dynamic holograms written in a photorefractive multiple quantum well placed inside a Fourier femtosecond pulse shaper convert a space-domain image into the time domain. We demonstrate that edge-enhancement processing of the time-domain image can be performed by controlling hologram-writing intensities.

Femtosecond pulse shaping by dynamic holograms in photorefractive multiple quantum wells

Femtosecond pulses can be shaped in the time domain by diffraction from dynamic holograms in a photorefractive multiple quantum well placed inside a Fourier pulse shaper. We present several examples of shaped pulses obtained by controlling the amplitude or the phase of the hologram writing beams, which modifies the complex spectrum of the femtosecond output.

Multidimensional shaping of ultrafast optical waveforms

Simultaneous temporal and spatial shaping of ultrashort optical pulses is demonstrated. A two-dimensional mask pattern is used to filter spatially separated frequency components along one coordinate and to impart a shaped spatial (or wave-vector) profile along the perpendicular coordinate, yielding a spatially and temporally coherent output waveform. As an example, a single input pulse is transformed into 11 spatially separated output beams, each with an independently specified temporal profile.

Time-domain images

We demonstrate that, using a hologram, we can convert a spatial x-y image into an x-t image, where one spatial dimension is now transformed into the time domain. In particular, we generate the temporal equivalent of our corporate logo, where every pixel of the image is now represented by a short optical pulse.