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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.

We propose and experimentally demonstrate an original method to analytically retrieve complete spectral phase of ultrashort pulses by measuring two modified interferometric field autocorrelation traces using thick nonlinear crystals with slightly different central phase-matching wavelengths. This new scheme requires no spectrometer, detector array, nor iterative data inversion, and is compatible with periodically poled lithium niobate (PPLN) waveguide technology offering potential for high measurement sensitivity.

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.

9.953 GHz phase-modulated continuous-wave laser combs are spectrally broadened via nonlinear propagation in normal and anomalous dispersion media and experimentally characterized using a differential phase shift keying (DPSK) decoder. DPSK bit-error rate data are in qualitative agreement with radio-frequency spectrum analyzer measurements.

Ultrafast photonic signal processing based on Fourier optics principles offers exciting possibilities to go beyond the processing speeds of electronics technologies for applications in high-speed fiber communications and ultrawideband wireless. I review our recent work on processing of ultrafast optical signals via conversion between time, space, and optical frequency (Fourier) domains. Specific topics include optical arbitrary waveform generation, application of optical pulse shaping technologies for wavelength-parallel compensation of fiber transmission impairments and for experimental studies of optical code-division multiple-access communications, and application of photonic methods for precompensation of dispersion effects in wireless transmission of radio-frequency signals over ultrawideband antenna links.

Pulse shaping theory is extended to include rapid waveform update for line-by-line pulse shaping. The fundamental tradeoff between response speed and waveform fidelity is illustrated by several examples.

For the first time, to our knowledge, radio-frequency arbitrary waveforms are time-multiplexed within 100 ps by integrating wavelength switching, optical frequency comb generation, and spectral line-by-line shaping. The novel time-multiplexed scheme demonstrated here can be extended to wide user specifications and faster waveform transition time.

We have used aperiodically poled lithium niobate waveguides to perform intensity autocorrelation and frequency-resolved optical gating (FROG) measurements for ultraweak femtosecond pulses at 1.5 microm wavelength. The required pulse energies for intensity autocorrelation and FROG are as low as 52 aJ and 124 aJ, respectively. The corresponding sensitivities are 3.2 x 10(-7) mW(2) and 2.7 x 10(-6) mW(2), about 3-5 orders of magnitude better than the previous records. The high nonlinear conversion efficiency is attributed to the long waveguide structure, and the needed broad phase-matching bandwidth is realized by chirping the poling period. We discuss the theory of intensity autocorrelation and FROG measurements in the presence of different phase-matching bandwidths, and we show, for the first time to our knowledge, that the distorted intensity autocorrelation trace due to a delta-like phase-matching spectrum is described by a modified field autocorrelation function. We also report new experimental results comparing autocorrelation traces measured with chirped and unchirped waveguide samples and demonstrating high-quality FROG measurements for cubic phase waveforms generated in a programmable pulse shaper.

We demonstrate wideband all-order polarization mode dispersion (PMD) compensation by applying high-speed spectral polarization sensing and ultrafast pulse shaping techniques to characterize and correct the frequency-dependent Jones matrix associated with PMD of optical fibers on a wavelength-by-wavelength basis. We report full compensation of approximately 800 fs pulses distorted to more than 10 ps by a PMD module with approximately 5.5 ps mean differential group delay. The sensing and compensation of Jones matrix take approximately 200 and approximately 500 ms, respectively.

We demonstrate polarization-insensitive ultralow-power second-harmonic generation frequency-resolved optical gating (FROG) measurements with a fiber-pigtailed, aperiodically poled lithium niobate waveguide. By scrambling the polarization much faster than the measurement integration time, we eliminate the impairment that frequency-independent random polarization fluctuations induce in FROG measurements. As a result we are able to retrieve intensity and phase profiles of few hundred femtosecond optical pulses with 50 MHz repetition rates at 5.2 nW coupled average power without control of the input polarization.

We demonstrate a method for all-optical, tunable pulse repetition-rate multiplication of a mode-locked laser based on spectral line-by-line control. In particular, two-to-five-times repetition-rate multiplication of a 9 GHz source is achieved with very high fidelity.

We demonstrate a Fourier pulse-shaper-based differential group delay (DGD) emulator which can be programmed to possess arbitrary user-specified frequency dependent DGD profile. The DGD produced can be up to 400ps range with <1ps accuracy. Generated frequency-dependent DGD profiles are in excellent agreement with numerical simulations.

We demonstrate full characterization of femtosecond pulse distortion induced by all-order polarization mode dispersion (PMD) at selected polarization states via second-harmonic generation (SHG) frequency-resolved optical gating (FROG) measurements at an average power of under 28 nW. By applying the inverse of the measured spectral phase via a programmable pulse shaper, we compress the distorted pulses from more than 3 ps to nearly bandwidth-limited durations of less than 500 fs. Our results show that SHG FROG measurements performed by using fiber-pigtailed aperiodically poled lithium niobate waveguides can serve as a robust and sensitive tool for characterization of PMD-induced spectral phase.

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.

Second- and third-order frequency correlations of speckle intensity patterns are used to characterize scattering media for multiple polarization states. The polarized temporal responses thus obtained are sensitive to the degree of scatter, with results being predictable by a diffusion model with sufficiently strong scatter. Experimental data are used to reconstruct various transfer functions.

Fourier synthesis pulse shaping methods allowing generation of programmable, user defined femtosecond optical waveforms have been widely applied in ultrafast optical science and technology. In the electrical domain, arbitrary waveform generation is well established at frequencies below approximately 1 GHz, but is difficult at higher frequencies due to limitations in digital-to-analog converter technology. In this paper we demonstrate a method for electrical waveform synthesis at substantially higher frequencies (approximately 20 GHz electrical bandwidth) by combining Fourier optical pulse shaping (extended to hyperfine frequency resolution) and heterodyne optical to electrical conversion. Our scheme relies on coherent manipulation of fields and phases at all stages, both for processing in the optical domain and for conversion from the optical to the electrical domain. We illustrate this technique through a number of examples, including programmable retardation or advancement of short electrical pulses in time over a range exceeding ten pulse durations. Such optically implemented, coherent Fourier transform electrical pulse shaping should open new prospects in ultrawideband electromagnetics.

An interferometric technique is utilized to measure both the time- and frequency-domain optical fields scattered by a random medium. The method uses a tunable continuous-wave laser source to make frequency-resolved measurements within a fixed-path-length interferometer. Measured frequency-domain field statistics, with a linearly polarized input, are shown to be zero-mean, circular complex Gaussian for both co- and cross-polarization states. With decreasing scatter, the extracted average impulse responses for co- and cross-polarized states show distinct differences, thereby providing insight into the scattering domain.

We retrieve intensity and phase profiles of 280 fs, 50 MHz optical pulses with 124 aJ coupled pulse energy (960 photons) by second-harmonic generation (SHG) frequency-resolved optical gating, using aperiodically poled LiNbO3 waveguides. The strong nonlinear interaction that is due to confinement within the micrometer-sized waveguide structure and the linearly chirped poling period contribute, respectively, to high SHG efficiency and broad phase-matching bandwidth. The achieved sensitivity is 2.7 x 10(-6) mW2, improving on the previous record for self-referenced complete pulse characterization by 5 orders of magnitude.

We demonstrate ultrasensitive intensity autocorrelation measurements of subpicosecond optical pulses in the telecommunication band by using aperiodically poled lithium niobate (A-PPLN) waveguides. The tightly confined optical beam in the waveguides and the chirped poling period facilitate simultaneous high second-harmonic generation (SHG) efficiency and broad phase-matching (PM) bandwidth. The resulting measurement sensitivity is 3.2 x 10(-7) mW2, approximately 500 times better than the previous record for intensity autocorrelations. We also show that chirped A-PPLN waveguides retain nearly the same SHG efficiency as the unchirped guide as long as the PM bandwidth is not significantly broader than the input spectrum.

We reconstruct the temporal response of a random medium by using speckle intensity frequency correlations. When the scattered field from a random medium is described by circular complex Gaussian statistics, we show that third-order correlations permit retrieval of the Fourier phase of the temporal response with bispectral techniques. Our experimental results for random media samples in the diffusion regime are in excellent agreement with the intensity temporal response measured directly with an ultrafast pulse laser and a streak camera. Our speckle correlation measurements also demonstrate sensitivity to inhomogeneous samples, highlighting the potential application for imaging within a scattering medium.

The virtually-imaged phased array (VIPA) is a side-entrance etalon with potential application as a high-resolution spectral disperser for wavelength division multiplexing. Here we present an approximate analytical spectral dispersion law for the VIPA, which we confirm experimentally.