Spectral line-by-line pulse shaping

Multicascade-linked synthetic-wavelength digital holography using a line-by-line spectral-shaped optical frequency comb

Phase imaging without a phase wrapping ambiguity is required for wide-axial-range 3D imaging in the fields of surface topography measurement and biomedical imaging. Although multicascade-linked synthetic-wavelength digital holography (MCL-SW-DH) using an optical frequency synthesizer (OFS) is a promising method to meet this requirement, the slow switching of multiple optical wavelengths in the OFS prevents rapid imaging. In the work described in this article, a line-by-line spectral-shaped electro-optics-modulator-based optical frequency comb (EOM-OFC) is used as a light source in MCL-SW-DH to achieve rapid image acquisition. While MCL-SW-DH enables surface topography measurement with millimeter-order axial range and micrometer-order axial resolution, the line-by-line spectral-shaped EOM-OFC extracts a single narrow-linewidth OFC mode from the 10 GHz-spacing EOM-OFC at a center wavelength of 1545 nm within a spectral range of 30 nm at an interval of 500 ms. The effectiveness of the proposed MCL-SW-DH was highlighted by performing surface topography measurement with four step differences of sub-millimeter to millimeter size with an axial uncertainty of 2.08 µm in the image acquisition time of several seconds. The proposed MCL-SW-DH will be a powerful tool for 3D imaging with a wide axial range and high axial resolution.

A Programmable Mode-Locked Fiber Laser Using Phase-Only Pulse Shaping and the Genetic Algorithm

A novel, programmable, mode-locked fiber laser design is presented and numerically demonstrated. The laser programmability is enabled by an intracavity optical phase-only pulse shaper, which utilizes the same linearly chirped fiber Bragg grating (LC-FBG) from its two opposite ends to perform real-time optical Fourier transformation. A binary bit-pattern generator (BPG) operating at 20-Gb/s and producing a periodic sequence of 32 bits every 1.6 ns, is subsequently used to drive an optical phase modulator inside the laser cavity. Simulation results indicate stable programmable intensity profiles for each optimized user defined 32 code words. The laser operated in the self-similar mode-locking regime, enabling wave-breaking free operation. The programmable 32 bit code word targeting a specific intensity profile was determined using 100 generations of the genetic algorithm. The control of ultrashort pulse intensity profiles on the picosecond and femtosecond time scales is difficult. The process of stretching and compressing the pulse in the time domain allows for a slower BPG to impose a predefined phase modulation prior to pulse compression. This results in control over the fine features of the intensity profile of the compressed pulse on a picosecond or femtosecond time scale inside the laser cavity. The stability of the proposed scheme depends on the consistency and accuracy of the BPG rise and fall times in practice.

Multicascade-linked synthetic wavelength digital holography using an optical-comb-referenced frequency synthesizer

Digital holography (DH) is a promising method for non-contact surface topography because the reconstructed phase image can visualize the nanometer unevenness in a sample. However, the axial range of this method is limited to the range of the optical wavelength due to the phase wrapping ambiguity. Although the use of two different wavelengths of light and the resulting synthetic wavelength, i.e., synthetic wavelength DH, can expand the axial range up to several hundreds of millimeters, its axial precision does not reach sub-micrometer. In this article, we constructed a tunable external cavity laser diode phase-locked to an optical frequency comb, namely, an optical-comb-referenced frequency synthesizer, enabling us to generate multiple synthetic wavelengths within the range of 32 µm to 1.20 m. A multiple cascade link of the phase images among an optical wavelength ( = 1.520 µm) and 5 different synthetic wavelengths ( = 32.39 µm, 99.98 µm, 400.0 µm, 1003 µm, and 4021 µm) enables the shape measurement of a reflective millimeter-sized stepped surface with the axial resolution of 34 nm. The axial dynamic range, defined as the ratio of the axial range ( = 2.0 mm) to the axial resolution ( = 34 nm), achieves 5.9 × 10⁵, which is larger than that of previous synthetic wavelength DH. Such a wide axial dynamic range capability will further expand the application field of DH for large objects with meter dimensions.

Integrated line-by-line optical pulse shaper for high-fidelity and rapidly reconfigurable RF-filtering

We present a 32 channel indium phosphide integrated pulse shaper with 25 GHz channel spacing, where each channel is equipped with a semiconductor optical amplifier allowing for programmable line-by-line gain control with submicrosecond reconfigurability. We critically test the integrated pulse shaper by using it in comb-based RF-photonic filtering experiments where the precise gain control is leveraged to synthesize high-fidelity RF filters which we reconfigure on a microsecond time scale. Our on-chip pulse shaping demonstration is unmatched in its combination of speed, fidelity, and flexibility, and will likely open new avenues in the field of advanced broadband signal generation and processing.

Compression of ultra-long microwave pulses using programmable microwave photonic phase filtering with > 100 complex-coefficient taps

Microwave photonic filters with arbitrary phase response can be achieved by merging high-repetition-rate electro-optic frequency comb technology with line-by-line pulse shaping. When arranged in an interferometric configuration, the filter features a number of programmable complex-coefficient taps equal to the number of available comb lines. In this work, we use an ultrabroadband comb generator resulting in a microwave photonic phase filter with >100 complex-coefficient taps. We demonstrate the potential of this filter by performing programmable chirp control of ultrawideband waveforms that extend over long (>10 ns) temporal apertures. This work opens new possibilities for compensating realistic linear distortion impairments on ultrabroadband wireless signals spanning over dozens of nanosecond temporal apertures.

Pair-by-pair pulse shaping for optical arbitrary waveform generation by dual-comb heterodyne

We present a novel optical arbitrary waveform generation approach based on pair-by-pair pulse shaping. Based on the heterodyne between a pair of optical frequency combs with different repetition rates, the repetition rate of the generated signals can be flexibly tuned from MHz to GHz without changing the setup. The restriction of the spectral resolution of the optical spectrum processor is overcome by the pair-by-pair approach while the spectral resolution of the system can be improved to MHz by dual-comb heterodyne. Hyperfine control of a higher resolution spectrum at MHz is achieved, which benefits the generation of the ultrawideband signals.

Exploring constrained quantum control landscapes

The broad success of optimally controlling quantum systems with external fields has been attributed to the favorable topology of the underlying control landscape, where the landscape is the physical observable as a function of the controls. The control landscape can be shown to contain no suboptimal trapping extrema upon satisfaction of reasonable physical assumptions, but this topological analysis does not hold when significant constraints are placed on the control resources. This work employs simulations to explore the topology and features of the control landscape for pure-state population transfer with a constrained class of control fields. The fields are parameterized in terms of a set of uniformly spaced spectral frequencies, with the associated phases acting as the controls. This restricted family of fields provides a simple illustration for assessing the impact of constraints upon seeking optimal control. Optimization results reveal that the minimum number of phase controls necessary to assure a high yield in the target state has a special dependence on the number of accessible energy levels in the quantum system, revealed from an analysis of the first- and second-order variation of the yield with respect to the controls. When an insufficient number of controls and/or a weak control fluence are employed, trapping extrema and saddle points are observed on the landscape. When the control resources are sufficiently flexible, solutions producing the globally maximal yield are found to form connected "level sets" of continuously variable control fields that preserve the yield. These optimal yield level sets are found to shrink to isolated points on the top of the landscape as the control field fluence is decreased, and further reduction of the fluence turns these points into suboptimal trapping extrema on the landscape. Although constrained control fields can come in many forms beyond the cases explored here, the behavior found in this paper is illustrative of the impacts that constraints can introduce.

Optical sinc-shaped Nyquist pulses of exceptional quality

Sinc-shaped Nyquist pulses possess a rectangular spectrum, enabling data to be encoded in a minimum spectral bandwidth and satisfying by essence the Nyquist criterion of zero inter-symbol interference (ISI). This property makes them very attractive for communication systems since data transmission rates can be maximized while the bandwidth usage is minimized. However, most of the pulse-shaping methods reported so far have remained rather complex and none has led to ideal sinc pulses. Here a method to produce sinc-shaped Nyquist pulses of very high quality is proposed based on the direct synthesis of a rectangular-shaped and phase-locked frequency comb. The method is highly flexible and can be easily integrated in communication systems, potentially offering a substantial increase in data transmission rates. Further, the high quality and wide tunability of the reported sinc-shaped pulses can also bring benefits to many other fields, such as microwave photonics, light storage and all-optical sampling.

Line-by-line pulse shaping with spectral resolution below 890 MHz

Line-by-line pulse shaping is demonstrated on a 890 MHz repetition rate mode-locked titanium sapphire laser. The high resolution pulse shaper is based on a virtual imaged phased array (VIPA) with a free spectral range of 25 GHz. For our implementation, the mask repeats every VIPA free spectral range, which corresponds to every 28 comb lines. Individual frequency modes from the laser are also resolved using the same VIPA paired with a diffraction grating to achieve a resolution of 357 MHz. Several output waveforms are compared with simulation to understand differences with the ideal case.

Silicon-based monolithic optical frequency comb source

We demonstrate the generation of broad-bandwidth optical frequency combs from a CMOS-compatible integrated microresonator. We characterize the comb quality using a novel self-referencing method and verify that the comb line frequencies are equidistant over a bandwidth of 115 nm (14.5 THz), which is nearly an order of magnitude larger than previous measurements.

Generation and delivery of 1-ps optical pulses with ultrahigh repetition-rates over 25-km single mode fiber by a spectral line-by-line pulse shaper

A spectral line-by-line pulse shaper is used to experimentally generate and deliver ~1 ps optical pulses of 31~124 GHz repetition-rates over 25.33 km single-mode fiber without dispersion-compensating fiber. The correlation of such delivery capability to temporal Talbot effect is experimentally demonstrated. Incorporating shaper periodic phase control, the repetition-rates of these~1 ps optical pulses are further multiplied up to 496 GHz and delivered over 25.33 km single-mode fiber.

Grism-based pulse shaper for line-by-line control of more than 600 optical frequency comb lines

We construct a line-by-line pulse shaper using a grism (grating plus prism) dispersive element, which provides constant angular dispersion over 13.4 THz centered at ~311 THz (965 nm). When combined with a dual-mask liquid crystal modulator, this grism-based shaper is capable of line-by-line amplitude and phase control of over 600 modes of a 21 GHz stabilized optical frequency comb.

Optical arbitrary waveform characterization using linear spectrograms

We demonstrate the first application of linear spectrogram methods based on electro-optic phase modulation to characterize optical arbitrary waveforms generated under spectral line-by-line control. This approach offers both superior sensitivity and self-referencing capability for retrieval of periodic high repetition rate optical arbitrary waveforms.

Analysis of time-multiplexed optical line-by-line pulse shaping: application for radio-frequency and microwave photonics

Time-multiplexed optical line-by-line pulse shaping with specific application to rapid update radio-frequency (RF) waveform generation is modeled. The effects of fundamental pulse shaping parameters on generated RF waveforms are numerically analyzed. Experimental and theoretical results are compared and are in excellent agreement.

Line-by-line control of 10-THz-frequency-spacing Raman sidebands

We report line-by-line control of a coherent discrete spectrum (Raman sidebands) with a frequency spacing of 10.6 THz that is produced by an adiabatic Raman process. We show that the spectral phase of the Raman sidebands is finely controlled to the target (flat relative-spectral-phase). This is achieved by employing a combination of a spatial phase controller and a spectral interferometer, which are specifically designed for a high-power discrete spectrum. We also show that such spectral-phase control produces a train of Fourier transform limited pulses with an ultrahigh repetition rate of 10.6 THz in the time domain.

Dual-comb electric-field cross-correlation technique for optical arbitrary waveform characterization

We present an electric-field cross-correlation technique that uses a pair of frequency combs to sweep phase and group delays independently without a mechanical stage. We demonstrate this technique for characterization of optical arbitrary waveforms composed of ~30 spectral lines from a 10 GHz frequency comb. Rapid data acquisition (tens of microseconds) enables interferometric spectral phase measurement of pulses subject to propagation over 20 km of optical fiber.

Single shot amplitude and phase characterization of optical arbitrary waveforms

Using a time-gated dual quadrature spectral interferometry technique, for the first time we demonstrate single-shot characterization of both spectral amplitude and phase of approximately 1THz bandwidth optical arbitrary waveforms generated from a 10 GHz frequency comb. Our measurements provide a temporal resolution of 1ps over a record length of 100ps. Singleshot characterization becomes particularly relevant when waveform synthesis operations are updated at the repetition rate of the comb allowing creation of potentially infinite record length waveforms. We first demonstrate unambiguous single shot retrieval using rapidly updating waveforms. We then perform additional single-shot measurements of static user-defined waveforms generated via line-by-line pulse shaping.

Dynamic spectral line-by-line pulse shaping by frequency comb shifting

Traditionally, reconfigurable optical pulse shaping is performed by using programmable spatial light modulators or tunable optical attenuators and phase shifters. We propose a technique to achieve tunability in the line-by-line pulse-shaping regime by controlling the offset frequency of an optical frequency comb. The method requires a high-spectral-resolution line-by-line shaper with channel spacing equal to a submultiple of the comb spacing. As a particular example, we numerically analyze tunable pulse-repetition-rate multiplication by grating-based line-by-line pulse shaping using a fixed phase-only mask.

Optical arbitrary waveform characterization via dual-quadrature spectral shearing interferometry

We demonstrate a new dual-quadrature spectral shearing interferometry technique appropriate for spectral phase characterization of arbitrary optical waveforms generated by line-by-line shaping of high-repetition- rate (approximately 10 GHz) optical frequency combs. Spectral shearing interferograms are generated through sum-frequency mixing of the frequency comb field with a pair of reference tones generated via intensity modulation of a continuous-wave laser. Although related to the well known SPIDER method, our approach relaxes spectral resolution requirements and operates in a collinear interaction geometry compatible with the use of high sensitivity, aperiodically poled lithium niobate nonlinear waveguide devices.

Optical arbitrary waveform characterization via dual-quadrature spectral interferometry

We introduce the use of dual-quadrature spectral interferometry for amplitude and phase characterization of 100% duty factor optical arbitrary waveforms generated via spectral line-by-line pulse shaping. We demonstrate this technique for measurement of optical arbitrary waveforms composed of approximately 30 spectral lines from a 10 GHz frequency comb with 1.4 micros data acquisition time at an average power level of 10 microwatts. We then demonstrate coherent spectral phase measurements of pulses strongly dispersed by propagation over 50 km of optical fiber.

Femtosecond pulse shaping in two dimensions: towards higher complexity optical waveforms

We demonstrate a new Fourier pulse shaping apparatus capable of achieving simultaneous high resolution and broad bandwidth operation by dispersing frequency components in a two dimensional geometry through simultaneous use of a high resolution and a broad bandwidth spectral disperser. We show experimental results which demonstrate significant improvements in achievable waveform complexity (number of controllable temporal/spectral features). We also demonstrate experiments of line-by-line pulse shaping with optical frequency combs. In this regime our configuration would allow significant enhancement of the number of controllable spectral lines which may further enhance recently demonstrated massively parallel approaches to spectroscopic sensing using frequency combs.

Bright and dark 40 GHz parabolic pulse generation using a picosecond optical pulse train and an arrayed waveguide grating

We demonstrate parabolic optical pulse generation by manipulating the intensity and phase of individual longitudinal modes of a 40 GHz picosecond optical pulse train in the spectral domain. Bright and dark parabolic pulses were generated from a 40 GHz mode-locked fiber laser using a 64-channel arrayed waveguide grating pulse shaper. The obtained parabolic pulse, which can easily generate a linear chirping, is useful for a number of applications to optical signal processing applications, including pulse compression and time-domain optical Fourier transformation.

Molecular fingerprinting with the resolved modes of a femtosecond laser frequency comb

The control of the broadband frequency comb emitted from a mode-locked femtosecond laser has permitted a wide range of scientific and technological advances--ranging from the counting of optical cycles for next-generation atomic clocks to measurements of phase-sensitive high-field processes. A unique advantage of the stabilized frequency comb is that it provides, in a single laser beam, about a million optical modes with very narrow linewidths and absolute frequency positions known to better than one part in 10(15) (ref. 5). One important application of this vast array of highly coherent optical fields is precision spectroscopy, in which a large number of modes can be used to map internal atomic energy structure and dynamics. However, an efficient means of simultaneously identifying, addressing and measuring the amplitude or relative phase of individual modes has not existed. Here we use a high-resolution disperser to separate the individual modes of a stabilized frequency comb into a two-dimensional array in the image plane of the spectrometer. We illustrate the power of this technique for high-resolution spectral fingerprinting of molecular iodine vapour, acquiring in a few milliseconds absorption images covering over 6 THz of bandwidth with high frequency resolution. Our technique for direct and parallel accessing of stabilized frequency comb modes could find application in high-bandwidth spread-spectrum communications with increased security, high-resolution coherent quantum control, and arbitrary optical waveform synthesis with control at the optical radian level.

The impact of optical comb stability on waveforms generated via spectral line-by-line pulse shaping

Optical arbitrary waveform generation using the line-by-line pulse shaping technique has been shown to be sensitive to variations in the offset frequency of the input frequency comb due to time-domain waveform interference. Here we present a frequency-domain model that is able to predict waveform changes arising from offset frequency variations. In experiments we controllably shift the frequency of a comb derived from a phase-modulated CW laser, which allows us to quantitatively investigate waveforms generated by pulse shaping as a function of offset frequency. Experimental data are in excellent agreement with the predictions of our frequency-domain model. In addition, we propose and analyze new waveforms designed for monitoring of offset frequency variations by pulse shaping.