Real-time Fourier transformation of lightwave spectra and application in optical reflectometry.

We propose and experimentally demonstrate a fiber-optics scheme for real-time analog Fourier transform (FT) of a lightwave energy spectrum, such that the output signal maps the FT of the spectrum of interest along the time axis. This scheme avoids the need for analog-to-digital conversion and subsequent digital signal post-processing of the photo-detected spectrum, thus being capable of providing the desired FT processing directly in the optical domain at megahertz update rates. The proposed concept is particularly attractive for applications requiring FT analysis of optical spectra, such as in many optical Fourier-domain reflectrometry (OFDR), interferometry, spectroscopy and sensing systems. Examples are reported to illustrate the use of the method for real-time OFDR, where the target axial-line profile is directly observed in a single-shot oscilloscope trace, similarly to a time-of-flight measurement, but with a resolution and depth of range dictated by the underlying interferometry scheme.

Real-time ultrawide-band group delay profile monitoring through low-noise incoherent temporal interferometry.

A simple, highly accurate measurement technique for real-time monitoring of the group delay (GD) profiles of photonic dispersive devices over ultra-broad spectral bandwidths (e.g. an entire communication wavelength band) is demonstrated. The technique is based on time-domain self-interference of an incoherent light pulse after linear propagation through the device under test, providing a measurement wavelength range as wide as the source spectral bandwidth. Significant enhancement in the signal-to-noise ratio of the self-interference signal has been observed by use of a relatively low-noise incoherent light source as compared with the theoretical estimate for a white-noise light source. This fact combined with the use of balanced photo-detection has allowed us to significantly reduce the number of profiles that need to be averaged to reach a targeted GD measurement accuracy, thus achieving reconstruction of the device GD profile in real time. We report highly-accurate monitoring of (i) the group-delay ripple (GDR) profile of a 10-m long chirped fiber Bragg grating over the full C band (~42 nm), and (ii) the group velocity dispersion (GVD) and dispersion slope (DS) profiles of a ~2-km long dispersion compensating fiber module over an ~72-nm wavelength range, both captured at a 15 frames/s video rate update, with demonstrated standard deviations in the captured GD profiles as low as ~1.6 ps.

New design for photonic temporal integration with combined high processing speed and long operation time window.

We propose and experimentally prove a novel design for implementing photonic temporal integrators simultaneously offering a high processing bandwidth and a long operation time window, namely a large time-bandwidth product. The proposed scheme is based on concatenating in series a time-limited ultrafast photonic temporal integrator, e.g. implemented using a fiber Bragg grating (FBG), with a discrete-time (bandwidth limited) optical integrator, e.g. implemented using an optical resonant cavity. This design combines the advantages of these two previously demonstrated photonic integrator solutions, providing a processing speed as high as that of the time-limited ultrafast integrator and an operation time window fixed by the discrete-time integrator. Proof-of-concept experiments are reported using a uniform fiber Bragg grating (as the original time-limited integrator) connected in series with a bulk-optics coherent interferometers' system (as a passive 4-points discrete-time photonic temporal integrator). Using this setup, we demonstrate accurate temporal integration of complex-field optical signals with time-features as fast as ~6 ps, only limited by the processing bandwidth of the FBG integrator, over time durations as long as ~200 ps, which represents a 4-fold improvement over the operation time window (~50 ps) of the original FBG integrator.

All-optical 1st and 2nd order integration on a chip.

We demonstrate all-optical temporal integration of arbitrary optical waveforms with temporal features as short as ~1.9ps. By using a four-port micro-ring resonator based on CMOS compatible doped glass technology we perform the 1st- and 2nd-order cumulative time integral of optical signals over a bandwidth that exceeds 400GHz. This device has applications for a wide range of ultra-fast data processing and pulse shaping functions as well as in the field of optical computing for the real-time analysis of differential equations.

Photonic temporal integration of broadband intensity waveforms over long operation time windows.

We propose and experimentally demonstrate a novel design for temporal integration of microwave and optical intensity waveforms with combined high processing speed and a long operation time window. It is based on concatenating in series a discrete-time (low-speed) photonic integrator and a high-speed analog time-limited intensity integrator. This scheme is demonstrated here using a cascaded fiber-based interferometers' system (as a passive eight-point discrete-time integrator) and an analog time-limited intensity integrator. The latter is based on temporal intensity modulation of the input waveform with a rectangular-like incoherent energy spectrum followed by linear dispersion. Using this setup, we experimentally achieve accurate time integration of intensity signals with ~36 GHz bandwidths over an operation time window of ~4 ns, corresponding to a processing time-bandwidth product of >144.

Reconfigurable optical differential phase-shift-keying pattern recognition based on incoherent photonic processing.

We propose and experimentally demonstrate asynchronous optical differential phase-shift-keying (DPSK) pattern recognition using a fully reconfigurable technique. The proposed method uses optical phase-to-bipolar intensity conversion through all-optical differentiation in conjunction with an incoherent time-spectrum convolution system where the pattern to be recognized is implemented directly in the spectral domain through optical amplitude-only linear filtering. Full reconfigurability in terms of bit rate, pattern sequence, and pattern length is achieved using electronically programmable optical filters. We demonstrate dynamically switching recognition of different 64 bit patterns in a continuous 12 Gb/s DPSK pseudorandom optical bit stream with contrast ratio up to 3.8 dB.

Ultrahigh dispersion of broadband microwave signals by incoherent photonic processing.

We propose and demonstrate a fiber-optic incoherent signal processing scheme to achieve extraordinary dispersion amounts on arbitrary microwave signals with bandwidths over tens of GHz. Using this new scheme, we experimentally achieve microwave dispersion values approaching 24 ns/GHz (equivalent to the dispersion induced by a section of standard single-mode fiber with a length of approximately 185,000 km). The scheme is used for real-time Fourier transformation (linear frequency-to-time mapping) of nanosecond-long microwave signals, including a square-like waveform, a sinusoidal pulse and a double pulse waveform, with bandwidths over 20 GHz.

Complex-field measurement of ultrafast dynamic optical waveforms based on real-time spectral interferometry.

Several methods are now available for single-shot measurement of the complex field (amplitude and phase profiles) of optical waveforms with resolutions down to the sub-picosecond range. As a main critical limitation, all these techniques exhibit measurement update rates typically slower than a few Hz. It would be very challenging to directly upgrade the update rate of any of these available methods beyond a few kHz. By combining spectral interferometry with dispersion-induced real-time optical Fourier transformation, here we demonstrate single-shot complex-field measurements of optical waveforms with a resolution of approximately 400 fs over a record length as long as approximately 350 ps, corresponding to a large record-length-to-resolution ratio of approximately 900. This performance is achieved at a measurement update rate of approximately 17 MHz, i.e. at least one thousand times faster than with any previous single-shot complex-field THz-bandwidth optical signal characterization method.

Simultaneous single-shot real-time measurement of the instantaneous frequency and phase profiles of wavelength-division-multiplexed signals.

A self-reference, single-shot characterization technique is proposed and demonstrated for simultaneously measuring the instantaneous frequencies and phases of multi-wavelength optical signals using a single processing and detection platform. The technique enables direct real-time optical sampling of the instantaneous frequencies of amplitude and/or phase modulated signals simultaneously at different wavelengths without requiring the use of any optical reference. Simultaneous real-time instantaneous frequency and phase measurements of a chirped 1 GHz-sinusoid intensity modulation signal and a 3 Gbps-PRBS (pseudo-random binary sequence) phase-modulated signal at two different wavelength channels have been performed for the proof-of-concept demonstration.

Efficient wavelength conversion and net parametric gain via four wave mixing in a high index doped silica waveguide.

We demonstrate sub-picosecond wavelength conversion in the C-band via four wave mixing in a 45cm long high index doped silica spiral waveguide. We achieve an on/off conversion efficiency (signal to idler) of + 16.5dB as well as a parametric gain of + 15dB for a peak pump power of 38W over a wavelength range of 100nm. Furthermore, we demonstrated a minimum gain of + 5dB over a wavelength range as large as 200nm.

Optical signal processors based on a time-spectrum convolution.

We show that a fiber-optics architecture conventionally used for microwave photonic filtering can implement a time-spectrum convolution (TSC) process of general interest for a wide range of fundamental optical signal processing and analysis operations. This process is practically implemented by temporally modulating a specially filtered broadband incoherent light source followed by propagation through a suitable linear dispersive medium. The TSC concept allows the time-domain realization of fundamental analog processing operations over both temporal and spectral intensity waveforms. Three particular, relevant signal-processing operations are proposed and experimentally demonstrated here to illustrate the broad potential of application of the TSC concept, namely time-integration, spectrum-integration, and time-frequency correlation of discrete binary codes.

Linear, self-referenced technique for single-shot and real-time full characterization of (sub-)picosecond optical pulses.

We propose and experimentally demonstrate single-shot, real-time ultrashort pulse intensity and phase characterization using a self-referenced and highly sensitive (linear) technique. The proposed method is based on a direct reconstruction of the spectral phase of the pulse-under-test (PUT) from three different measured spectra, two of which are obtained by a suitable time-synchronized electro-optic intensity modulation of the PUT. The required set of spectra are temporally interleaved and mapped along the time domain by linear dispersion for single-shot acquisition using a real-time scope. A dynamic nonlinear compression experiment of a picosecond pulse is fully monitored in real time using the proposed method.

Difference of body compositional changes according to the presence of weight cycling in a community-based weight control program.

Many obese people who try to control body weight experience weight cycling (WC). The present study evaluated the importance of WC in a community-based obesity intervention program. We analyzed the data of 109 Korean participants (86% women) among 177 subjects who had completed a 12-week intervention program at two public health centers in Korea from April to December, 2007. Completion of a self-administrated questionnaire at baseline was used to obtain anthropometric measurements, and laboratory testing was done before and after the program. Differences in body composition change and obesity-related life style between the two groups were compared with respect to WC and non-weight cycling (NWC). After 12 weeks, both groups showed reductions in weight, waist circumference, and body mass index. The group differences were not significant. However, significant differences were evident for the WC group compared to the NWC group in fat percent mass (WC vs. NWC, -3.49+/-2.31% vs. -4.65+/-2.59%, P=0.01), fat free mass (WC vs. NWC, -0.95+/-1.37 kg vs. -0.38+/-1.05 kg, P=0.01), and total cholesterol (WC vs. NWC, -3.32+/-14.63 vs. -16.54+/-32.39, P=0.005). In conducting a community-based weight control program that predominantly targets women, changes of body composition and total cholesterol may be less effective in weight cyclers than in non-weight cyclers.

Real-time complex temporal response measurements of ultrahigh-speed optical modulators.

We demonstrate a technique for direct, real-time characterization of the complex (amplitude and phase) temporal response of ultrahigh-speed (GHz-bandwidth) optical modulators. The demonstrated technique is based on pulse interferometry combined with time-frequency mapping processes using fiber linear dispersion. A new mechanism is incorporated to overcome the temporal resolution (bandwidth) limitation of the detectable modulation response in our previously reported setup. This mechanism, referred to as 'common-path temporal image magnification', lowers the required detection bandwidth by a factor of more than 10, enabling real-time single-shot waveform acquisition without loss of information using a conventional temporal digitizer. The design specifications of the proposed measurement setup are derived and discussed in detail. As a proof-of-concept experiment, real-time characterization of a complex electro-op c modulation temporal response with time features as fast as approximately 35 ps (modulation bandwidth > 40-GHz) was obtained and displayed at a video rate of 30 frames/sec.

Nonlinear pulse compression of picosecond parabolic-like pulses synthesized with a long period fiber grating filter.

tract: We demonstrate high quality pulse compression at high repetition rates by use of spectral broadening of short parabolic-like pulses in a normally-dispersive highly nonlinear fiber (HNLF) followed by linear dispersion compensation with a conventional SMF-28 fiber. The key contribution of this work is on the use of a simple and efficient long-period fiber grating (LPFG) filter for synthesizing the desired parabolic-like pulses from sech(2)-like input optical pulses; this all-fiber low-loss filter enables reducing significantly the required input pulse power as compared with the use of previous all-fiber pulse re-shaping solutions (e.g. fiber Bragg gratings). A detailed numerical analysis has been performed in order to optimize the system's performance, including investigation of the optimal initial pulse shape to be launched into the HNLF fiber. We found that the pulse shape launched into the HNLF is critically important for suppressing the undesired wave breaking in the nonlinear spectral broadening process. The optimal shape is found to be independent on the parameters of normally dispersive HNLFs. In our experiments, 1.5-ps pulses emitted by a 10-GHz mode-locked laser are first reshaped into 3.2-ps parabolic-like pulses using our LPFG-based pulse reshaper. Flat spectrum broadening of the amplified initial parabolic-like pulses has been generated using propagation through a commercially-available HNLF. Pulses of 260 fs duration with satellite peak and pedestal suppression greater than 17 dB have been obtained after the linear dispersion compensation fiber. The generated pulses exhibit a 20-nm wide supercontinuum energy spectrum that has almost a square-like spectral profile with >85% of the pulse energy contained in its FWHM spectral bandwidth.

First-order loss-less differentiators using long period gratings made in Er-doped fibers.

An active-fiber-based all-optical first-order temporal differentiator with power efficiency surpassing 100% is demonstrated experimentally. It is based on a long-period fiber grating (LPFG) inscribed into a piece of highly-doped Erbium-doped fiber (EDF). The performed theoretical analysis considers effects like relative position of the LPFG with respect to the input end of the EDF and influence of the input signal power. In the design, parameters like noise characteristics and level of non-linear interaction are taken into account. The advantages of such an implementation over the setup using concatenation of a passive LPFG with an amplifier lies in reducing the unwanted nonlinearities and reducing the amplified spontaneous emission (ASE).

Terahertz-bandwidth high-order temporal differentiators based on phase-shifted long-period fiber gratings.

We report the fabrication of a pi-phase-shifted long-period fiber grating (LPFG) capable of operating as a terahertz-bandwidth second-order temporal differentiator. We demonstrate its operation experimentally by differentiating subpicosecond long optical pulses. A new scheme for achieving high-order photonic temporal differentiation based on LPFG filters is also proposed and demonstrated. In particular, we prepared a LPFG-based first-order differentiator that was frequency and bandwidth matched to the second-order device and demonstrated the cascadability of these devices leading to the implementation of a third-order differentiator. By also employing these devices in reflection, up to the fifth-order differentiation is demonstrated experimentally.

Single-shot real-time frequency chirp characterization of telecommunication optical signals based on balanced temporal optical differentiation.

A simple single-shot frequency chirp characterization technique for telecommunication optical waveforms is introduced. The proposed technique is based on what we believe to be a novel balanced all-optical ultrafast differentiation scheme, and it enables a real-time conversion of the instantaneous frequency variation of an arbitrary complex (amplitude and phase) optical signal into a temporal intensity profile while simultaneously providing an efficient cancellation of the intensity noise. Single-shot real-time frequency chirp measurements of gigahertz-bandwidth phase-only and amplitude and phase temporal modulation waveforms are performed.

All-optical temporal integration of ultrafast pulse waveforms.

An ultrafast all-optical temporal integrator is experimentally demonstrated. The demonstrated integrator is based on a very simple and practical solution only requiring the use of a widely available all-fiber passive component, namely a reflection uniform fiber Bragg grating (FBG). This design allows overcoming the severe speed (bandwidth) limitations of the previously demonstrated photonic integrator designs. We demonstrate temporal integration of a variety of ultrafast optical waveforms, including Gaussian, odd-symmetry Hermite Gaussian, and (odd-)symmetry double pulses, with temporal features as fast as ~6-ps, which is about one order of magnitude faster than in previous photonic integration demonstrations. The developed device is potentially interesting for a multitude of applications in all-optical computing and information processing, ultrahigh-speed optical communications, ultrafast pulse (de-)coding, shaping and metrology.

Photonic temporal integrator for all-optical computing.

We report the first experimental realization of an all-optical temporal integrator. The integrator is implemented using an all-fiber active (gain-assisted) filter based on superimposed fiber Bragg gratings made in an Er-Yb co-doped optical fiber that behaves like an 'optical capacitor'. Functionality of this device was tested by integrating different optical pulses, with time duration down to 60 ps, and by integration of two consecutive pulses that had different relative phases, separated by up to 1 ns. The potential of the developed device for implementing all-optical computing systems for solving ordinary differential equations was also experimentally tested.