Modelocking of a frequency-shifted feedback laser triggered by amplitude modulation.

We report an experimental technique to trigger modelocking (ML) emission in frequency-shifted feedback (FSF) lasers. These lasers feature an intracavity modulator driven by a radio frequency tone, which shifts the light spectrum every cavity round trip. The technique consists of the drive of the modulator with a second tone at the cavity free spectral range (FSR) frequency. So, in addition to the frequency shift, a weak amplitude modulation (AM) appears synchronous with the cavity round trip time. The approach is successful as FSF cavities support chirped modes evenly spaced by the FSR, whose AM coupling produces convenient seed pulses for the ML onset. This results in ML emission at arbitrary frequency shifts and initiation thresholds lower than in standard, spontaneous FSF laser ML. Simulations indicate that the role of AM is to trigger the formation of ML pulses, but the primary mechanism of pulse buildup is the Kerr effect. The technique opens a new, to the best of our knowledge, practical route to initiate ML emission in FSF lasers.

ASE recirculation effects in pulsed frequency shifted feedback lasers at large frequency shifts.

An analysis of the different emission regimes (continuous wave, Q-switched, and different forms of modelocking) of a C-band Er:fiber frequency shifted feedback laser at large frequency shifts is presented. We clarify the role of amplified spontaneous emission (ASE) recirculation in the origin of various spectral and dynamical properties of this type of laser. Specifically, we show that Q-switched pulses are supported by a noisy, quasiperiodic ASE recirculation pattern that univocally identifies the pulses within the sequence, and that these Q-switched pulses are chirped as a consequence of the frequency shift. A specific pattern of ASE recirculation, in the form of a periodic stream of pulses, is identified in resonant cavities, namely, those where the free spectral range and the shifting frequency are commensurable. The phenomenology associated with this pattern is explained through the moving comb model of ASE recirculation. Modelocked emission is induced from both integer and fractional resonant conditions. It is shown that ASE recirculation coexists with modelocked pulses, originates a secondary peak in the optical spectrum, and also drives Q-switched modelocking near resonant conditions. Harmonic modelocking with variable harmonic index is also observed in non-resonant cavities.

All-optical coherent pulse compression for dynamic laser ranging using an acousto-optic dual comb.

We demonstrate a new and simple dynamic laser ranging platform based on analog all-optical coherent pulse compression of modulated optical waveforms. The technique employs a bidirectional acousto-optic frequency shifting loop, which provides a dual-comb photonic signal with an optical bandwidth in the microwave range. This architecture simply involves a CW laser, standard telecom components and low frequency electronics, both for the dual-comb generation and for the detection. As a laser ranging system, it offers a range resolution of a few millimeters, set by a dual-comb spectral bandwidth of 24 GHz, and a precision of 20 µm for an integration time of 20 ms. The system is also shown to provide dynamic measurements at scanning rates in the acoustic range, including phase-sensitive measurements and Doppler shift velocimetry. In addition, we show that the application of perfect correlation phase sequences to the transmitted waveforms allows the ambiguity range to be extended by a factor of 10 up to ∼20 m. The system generates quasi-continuous waveforms with low peak power, which makes it possible to envision long-range telemetry or reflectometry requiring highly amplified signals.

Phase sensitive low-coherence interferometry using microwave photonics.

We report on a low-coherence interferometer based on Microwave Photonics (MWP) which allows, for the first time to the best of our knowledge, stable determination of the interferogram's phase. The interferometer is built on suppressed carrier, double-sideband modulation, dispersive propagation in a chirped fiber Bragg grating, demodulation by electro-optical frequency down-conversion, and suitable signal processing techniques to account for modulation impairments. Taking as a reference a direct normalization of the link's microwave response, the system retrieves high-resolution interferograms, both in amplitude and phase and free from distortion induced by higher-order dispersion, in an optical path difference of 16.3 mm, surpassing previously reported values based on MWP implementations. We present representative applications targeted to the characterization of C-band sources and components, such as direct analysis of interferograms with 5.5 fs temporal resolution, Fourier-transform spectroscopy with 14 GHz spectral resolution, and optical low-coherence reflectrometry of the impulse response's amplitude of fiber Bragg gratings with 0.55 µm spatial resolution.

Far-field Talbot waveforms generated by acousto-optic frequency shifting loops.

We report on the description of the optical fields generated by acousto-optic Frequency-Shifting Loops (FSL) in the temporal Fraunhofer domain when the loop is operated in the vicinity of integer or fractional Talbot conditions. Using self-heterodyne detection, we experimentally demonstrate the equivalence of the Talbot phases generated at fractional conditions with the Gauss perfect phase sequences, and identify deviations from the standard frequency-to-time mapping description of the far field. In particular, we show the existence of ripples in the pulse intensity, of unavoidable pulse-to-pulse interference in the pulse train, of small oscillations, of the order of hundreds of MHz, in the expected linear pulse chirp, and the capture of the phase at the pulse's trailing edge by the adjacent pulse. Using asymptotic analysis, we construct a field model that accounts for these features, which are due to corrections to the frequency-to-time mapped field created by the sharp spectral edge of the FSL spectrum, in analogy to diffraction. Practical design consequences for signal generation and processing systems based on FSL are discussed.

Laser ranging using coherent pulse compression with frequency shifting loops.

We report on the use of the acousto-optic frequency combs generated by frequency shifting loops as compact and versatile optical waveforms generators for pulse compression systems in the optical coherent domain. The high degree of tunability and mutual coherence of these sources permits an efficient use of the available detection bandwidth, and represent simple alternatives to broadband lasers that do not require fast electronics. The full, complex optical field is retrieved using heterodyne measurements in bandwidths as high as 20 GHz. Compression ratios up to 150 at 80-MHz repetition rate, with autocorrelation peak-to-sidelobe ratios in excess of 28 dB, are demonstrated. In a proof-of-concept ranging experiment, we obtain resolutions of 4 mm in free space at meter scales, limited by detection bandwidth. Systems based on frequency shifting loops thus enable compact implementations of the pulse compression concept in the optical coherent domain, for its use in general optical metrology systems.

Incoherent Optical Frequency-Domain Reflectometry Based on Homodyne Electro-Optic Downconversion for Fiber-Optic Sensor Interrogation.

Fiber-optics sensors using interrogation based on incoherent optical frequency-domain reflectometry (I-OFDR) offer benefits such as the high stability of interference in the radio-frequency (RF) domain and the high SNR due to narrowband RF detection. One of the main impairments of the technique, however, is the necessity of high-frequency detectors and vector network analyzers (VNA) in systems requiring high resolution. In this paper, we report on two C-band implementations of an I-OFDR architecture based on homodyne electro-optic downconversion enabling detection without VNA and using only low-bandwidth, high-sensitivity receivers, therefore alleviating the requirements of conventional I-OFDR approaches. The systems are based on a pair of modulators that are synchronized to perform modulation and homodyne downconversion at a reference frequency of 25.5 kHz. In the first system, we attain centimeter resolution with a sensitivity down to -90 dB using the modulation frequency range comprised between 3.2 and 14.2 GHz. In the second, we measured, for the first time using this approach, Rayleigh backscattering traces in standard single mode fiber with resolution of 6 m and a sensitivity of -83 dB by use of the 10.1-30.1 MHz range. These results show the feasibility of these simple, homodyne downconversion I-OFDR systems as compact interrogators for distributed or quasi-distributed optical fiber sensors.

CW-to-pulse conversion using temporal Talbot array illuminators.

We report on the linear conversion of continuous-wave (CW) laser light to optical pulses using temporal Talbot array illuminators (TAIs) with fractional orders 1/q(q≤10), implemented by use of multilevel PM and dispersive propagation in a chirped fiber Bragg grating. The generated, sub-nanosecond optical pulse trains have repetition rates in the gigahertz range and show the presence of satellite pulses originated by the finite electrical modulation bandwidth (7.5 GHz). Though this fact impacts the resulting extinction ratio, an experimental comparison with time and Fresnel lenses indicates that temporal TAIs represent compact systems with high light gathering efficiency (>87%) at moderate values of compression (q≤8), which can be tailored in repetition rate, gain, or width, through the fractional Talbot order for its use in pulse compression systems fed by CW light.

On the structure of quadratic Gauss sums in the Talbot effect.

We report on the detailed derivation of the Gauss sums leading to the weighting phase factors in the fractional Talbot effect. In contrast to previous approaches, the derivation is directly based on the two coprime integers p and q that define the fractional Talbot effect so that, using standard techniques from the number theory, the computation is reduced, up to a global phase, to the trivial completion of the exponential of the square of a sum. In addition, it is shown that the Gauss sums can be reduced to only two cases, depending on the parity of integer q. Explicit and simpler expressions for the two forms of the Talbot weighting phases are also provided. The Gauss sums are presented as a discrete Fourier transform pair between quadratic phase sequences showing perfect periodic autocorrelation and a connection with the theory of biunimodular sequences is presented. In addition, the Talbot weighting factors of orders 1/q and 2/q are reduced to a closed form, and the equivalence to existing characterizations of Talbot weighting phases is also discussed. The relationship with one-dimensional multilevel phase structures is exemplified by the study of Talbot array illuminators. These results simplify and extend the description of the role played by Gauss sums in the fractional Talbot effect, providing a compact synthesis of previous results.

Remote picometer fiber Bragg grating demodulation using a dual-wavelength source.

We report on the self-referenced, intensity-based, remote and passive interrogation of a fiber Bragg grating (FBG) for point sensing, by use of a reconfigurable dual-wavelength source composed of a tunable wavelength and subsequent suppressed-carrier, electro-optic amplitude modulation. The demodulation procedure is based on the measurement of the reflected power at two different wavelengths within the FBG spectral response. The grating was interrogated by use of conventional spectral analysis, and also after 32.9 km of single-mode fiber using a dispersive incoherent optical Fourier-domain reflectometry technique. Both procedures provide picometer resolution in the determination of Bragg wavelength shifts at a comparatively similar scan time (∼1 s) and received power (-16 dBm). The main limitations in each interrogation scheme have been identified. These results show the feasibility of interrogation systems incorporating relatively simple frequency combs at a calibrated, and eventually reconfigurable, wavelength grid with an, at least, similar performance to that of commercial FBG interrogators.

Radio-frequency low-coherence interferometry.

A method for retrieving low-coherence interferograms, based on the use of a microwave photonics filter, is proposed and demonstrated. The method is equivalent to the double-interferometer technique, with the scanning interferometer replaced by an analog fiber-optics link and the visibility recorded as the amplitude of its radio-frequency (RF) response. As a low-coherence interferometry system, it shows a decrease of resolution induced by the fiber's third-order dispersion (ß3). As a displacement sensor, it provides highly linear and slope-scalable readouts of the interferometer's optical path difference in terms of RF, even in the presence of third-order dispersion. In a proof-of-concept experiment, we demonstrate 20-µm displacement readouts using C-band EDFA sources and standard single-mode fiber.

Nonstationary elementary-field light randomly triggered by Poisson impulses.

A stochastic theory of nonstationary light describing the random emission of elementary pulses is presented. The emission is governed by a nonhomogeneous Poisson point process determined by a time-varying emission rate. The model describes, in the appropriate limits, stationary, cyclostationary, locally stationary, and pulsed radiation, and reduces to a Gaussian theory in the limit of dense emission rate. The first- and second-order coherence theories are solved after the computation of second- and fourth-order correlation functions by use of the characteristic function. The ergodicity of second-order correlations under various types of detectors is explored and a number of observables, including optical spectrum, amplitude, and intensity correlations, are analyzed.

Stochastic pulse models of a partially-coherent elementary field representation of pulse coherence.

A representation of the mutual coherence function (MCF) of a light pulse as an incoherent sum of partially-coherent elementary pulses is introduced. It is shown that this MCF can be decomposed into fully and partially-coherent constituents and three different pulse models of partially-coherent constituents are constructed: single elementary-pulse fluctuations, emission of elementary fields driven by white noise, and elementary pulses triggered by Poisson impulses. The fourth-order correlation function of this last model includes as limit cases those of the fluctuating-pulse and noise-driven-emission models. These results provide a means of extending elementary-field models to higher-order coherence theory.

Quantum model for electro-optical amplitude modulation.

We present a quantum model for electro-optic amplitude modulation, which is built upon quantum models of the main photonic components that constitute the modulator, that is, the guided-wave beamsplitter and the electro-optic phase modulator and accounts for all the different available modulator structures. General models are developed both for single and dual drive configurations and specific results are obtained for the most common configurations currently employed. Finally, the operation with two-photon input for the control of phase-modulated photons and the important topic of multicarrier modulation are also addressed.

In-fiber frequency-domain measurement of ultrashort second-order correlations of incoherent light.

The second-order correlation function of incoherent light, which is usually measured in the time domain, can be alternatively measured in the frequency domain. Here, we use an all-optical technique in a highly nonlinear fiber for measuring the full spectrum of the fluctuations of the photocurrent (rf spectrum) generated by broadband radiation with different spectral coherence properties. Our experiments reveal that the rf spectrum of a light signal depends strongly on its spectral coherence properties. From a practical perspective, this ultrafast technique constitutes an alternative for measuring the intensity correlations of spectrally incoherent radiation.

Temporal Lau effect: a multiwavelength self-imaging phenomenon.

We provide experimental evidence of the temporal analog of the spatial Lau phenomenon. This effect can be interpreted as an incoherent superposition of multiple temporal self-images. Using an array of continuous-wave lasers modulated by a single external electro-optic modulator driven by a repetitive pattern, and dispersing the light in a medium satisfying the integer Talbot self-imaging condition, each monochromatic carrier generates a temporally shifted self-image. We show experimentally that, if the wavelength separation satisfies the temporal Lau condition, the self-images appear superimposed in intensity. The requirements for this incoherent regime are analyzed. This work paves the way to achieve multiwavelength pulse trains with the ability to control the time interleaving between pulses, with potential applications for pulse shaping and high-speed sampling.

Intensity spectra after first-order dispersion of composite models of scalar cyclostationary light.

The spectrum of the intensity of dispersed waves obeying cyclostationary statistics is studied. The formalism is based on an exact formula by Marshall and Yariv [IEEE Photon. Technol. Lett.12, 302 (2000)] relating the intensity spectrum after first-order dispersion to the Fourier transform of a certain restriction of the time-averaged fourth-order correlation of the optical wave e(t) before dispersion. The formalism permits a simple computation of the spectrum of composite models defined by the independent addition or multiplication of a stationary and a cyclostationary field. The computations are simplified by introducing the auxiliary field z(tau)(t)=e(t)*e(t+tau), whose power spectral density represents the basic building block for solving the spectrum of composite models. The results are illustrated by a number of examples, including the intensity spectrum after dispersion of analog-modulated, partially coherent carriers, or the complete spectrum of intensity fluctuations of multiwavelength dispersion-based microwave photonic filters.

Hilbert and Blaschke phases in the temporal coherence function of stationary broadband light.

We show that the minimal phase of the temporal coherence function gamma (tau) of stationary light having a partially-coherent symmetric spectral peak can be computed as a relative logarithmic Hilbert transform of its amplitude with respect to its asymptotic behavior. The procedure is applied to experimental data from amplified spontaneous emission broadband sources in the 1.55 microm band with subpicosecond coherence times, providing examples of degrees of coherence with both minimal and non-minimal phase. In the latter case, the Blaschke phase is retrieved and the position of the Blaschke zeros determined.

Radio-frequency spectrum analysis of a jittery train after a second-order dispersive Talbot line.

The power spectral density of the intensity of coherent Gaussian pulse trains suffering timing jitter after a dispersive line with arbitrary first- (beta(2)) and second-order (beta(3)) dispersion is computed in the small-signal approximation. Due to timing jitter noise, the initial radio-frequency spectrum shows noise bands whose bandwidth and position depend, respectively, on the jitter's standard deviation and on the jitter's pulse-to-pulse correlation. After setting the accumulated first-order dispersion to Talbot conditions, it is shown that the influence on the noise spectrum is a multiplicative factor with a multiple-bandpass structure. This factor depends on both the dispersive characteristics of the line and the pulse parameters, but not on the timing jitter's correlation properties, and represents the filtering mechanism responsible for Talbot repetition-rate multiplication. It is shown that the integer or fractional temporal Talbot effect does not worsen the timing properties of the initial train. In addition, and depending on the type of jitter correlation, the pulse width, and the total dispersion, it is shown that the temporal Talbot effect may lead to significant jitter reduction. The theory is exemplified by use of simulations. The applicability of the model to practical situations is also analyzed.

Hybrid refractive-diffractive-gradient-index superresolving focusing device.

The focusing properties and resolving power of a device consisting of a tapered gradient-index (GRIN) lens with spherical input and output faces are investigated through the use of the ABCD formalism to achieve minimization of the Airy radius for the device. Diffractive elements, such as zone plates, can, with an appropriate choice of their parameters, increase the resolution of an imaging system compared with a conventional lens. We demonstrate that by combining both elements a hybrid refractive-diffractive-GRIN device can be designed that exhibits improved superresolution characteristics.