José Azaña

REAL-TIME FOURIER TRANSFORMER BASED ON FIBER GRATINGS

We use the well-known duality between paraxial diffraction in space and dispersion in time to propose a time-domain analog to spatial Fraunhofer diffraction. This analog permits the design of real-time optical Fourier-transformer systems. These systems are shown to be realizable by use of linearly chirped fiber gratings as dispersive media.

Temporal self-imaging effects: theory and application for multiplying pulse repetition rates

A time-domain equivalent of the spatial Talbot or self-imaging phenomenon appears when a periodic temporal signal propagates through a dispersive medium under first-order dispersion conditions. The effect is of great interest because it can be applied for multiplying the repetition rate of an arbitrary periodic pulse train without distorting the individual pulse features and essentially without loss of energy. In this way, pulse sequences in the terahertz regime can be generated from typical mode-locked pulse streams (with a few gigahertz repetition rates). The Talbot-based repetition-rate-multiplication technique can be implemented by using a linearly chirped fiber grating (LCFG) as the dispersive medium. As compared with other alternatives, an LCFG can be designed to provide the required bandwidth and dispersion characteristics in significantly more compact forms. Here, by using a signal-theory-based approach, we carry out a general theoretical analysis of the temporal self-imaging phenomenon and derive analytical expressions for all cases of interest (integer and fractional self-imaging effects). We also show how to design a LCFG for implementing the repetition-rate-multiplication technique and discuss the impact of nonidealities in the gratings response on the multiplication process. Results of our study are relevant from both a physical and a practical perspective.

Real-time optical spectrum analysis based on the time-space duality in chirped fiber gratings

Based on time-space duality, we deduce a time-domain equivalent to the Fraunhofer (far-field) approximation in the problem of spatial diffraction. We can use this equivalence to carry out a real-time optical spectrum analysis, which is shown to be realizable by using, as the dispersive media, filtering devices based on chirped distributed resonant coupling. In particular, we present the design of linearly chirped fiber gratings (reflection configurations) and linearly chirped intermodal couplers (transmission configurations) to work as real-time spectrum analyzers. The proposed systems are shown to work properly by means of simulation tools. Furthermore, we use joint time-frequency signal representations to get a better understanding of the physical processes that determine the behavior of these systems. In this way, we demonstrate that the propagation of a given signal through a chirped fiber grating (or a chirped intermodal coupler), under the temporal Fraunhofer conditions, translates into a temporal separation of the spectral components of the signal. The results of our study indicate potential important applications based on this effect.

Ultrafast all-optical differentiators

We report the experimental realization of an ultrafast all-optical temporal differentiator. Differentiation is obtained via all-fiber filtering based on a simple diffraction grating-assisted mode coupler (uniform long-period fiber grating) that performs full energy conversion at the optical carrier frequency. Due to its high bandwidth, this device allows processing of arbitrary optical signals with sub-picosecond temporal features (down to 180-fs with the specific realizations reported here). Functionality of this device was tested by differentiating a 700-fs Gaussian optical pulse generated from a fiber laser (@ 1535nm). The derivative of this pulse is an odd-symmetry Hermite-Gaussian waveform, consisting of two linked 500-fs-long, pi-phase-shifted temporal lobes. This waveform is noteworthy for its application in advanced ultrahigh-speed optical communication systems.

Technique for multiplying the repetition rates of periodic trains of pulses by means of a temporal self-imaging effect in chirped fiber gratings

We show that a temporal effect that is equivalent to the spatial self-imaging (Talbot) effect applies to the reflection of periodic signals from linearly chirped fiber gratings. The effect can be used for multiplying the repetition frequency of a given periodic pulse train without distorting the individual pulse characteristics. The practical limit on the frequency-multiplication factor depends only on the temporal width of the individual pulse. Thus we demonstrate that a suitable combination of well-known techniques for short-pulse generation, such as pulse mode locking, and the technique proposed here allows us to obtain short-pulse trains with ultrahigh repetition rates (in the terahertz regime). Results from simulations show good agreement with those predicted by theory.

On-chip CMOS-compatible all-optical integrator

One reason for using photonic devices is their speed—much faster than electronic circuits—but there are many challenges in integrating the two technologies. Ferrera et al. construct a CMOS-compatible monolithic optical waveform integrator, a key building block for photonic circuits.

Temporal differentiation of optical signals using a phase-shifted fiber Bragg grating

We propose and experimentally demonstrate an all-optical (all-fiber) temporal differentiator based on a simple pi-phase-shifted fiber Bragg grating operated in reflection. The proposed device can calculate the first time derivative of the complex field of an arbitrary narrowband optical waveform with a very high accuracy and efficiency. Specifically, the experimental fiber grating differentiator reported here offers an operation bandwidth of approximately 12 GHz. We demonstrate the high performance of this device by processing gigahertz-bandwidth phase and intensity optical temporal variations.

Long-period fiber gratings as ultrafast optical differentiators.

It is demonstrated that a single, uniform long-period fiber grating (LPFG) working in the linear regime inherently behaves as an ultrafast optical temporal differentiator. Specifically, we show that the output temporal waveform in the core mode of a LPFG providing full energy coupling into the cladding mode is proportional to the first derivative of the optical temporal signal (e.g., optical pulse) launched at the input of the LPFG. Moreover, a LPFG providing full energy recoupling back from the cladding mode into the core mode inherently implements second-order temporal differentiation. Our numerical results have confirmed the feasibility of this simple, all-fiber approach to processing optical signals with temporal features in the picosecond and subpicosecond ranges.

Nonreciprocal waveguide Bragg gratings.

The use of a complex short-period (Bragg) grating which combines matched periodic modulations of refractive index and loss/gain allows asymmetrical mode coupling within a contra-directional waveguide coupler. Such a complex Bragg grating exhibits a different behavior (e.g. in terms of the reflection and transmission spectra) when probed from opposite ends. More specifically, the grating has a single reflection peak when used from one end, but it is transparent (zero reflection) when used from the opposite end. In this paper, we conduct a systematic analytical and numerical analysis of this new class of Bragg gratings. The spectral performance of these, so-called nonreciprocal gratings, is first investigated in detail and the influence of device parameters on the transmission spectra of these devices is also analyzed. Our studies reveal that in addition to the nonreciprocal behavior, a nonreciprocal Bragg grating exhibits a strong amplification at the resonance wavelength (even with zero net-gain level in the waveguide) while simultaneously providing higher wavelength selectivity than the equivalent index Bragg grating. However, it is also shown that in order to achieve non-reciprocity in the device, a very careful adjustment of the parameters corresponding to the index and gain/loss gratings is required.

Ultrafast all-optical first- and higher-order differentiators based on interferometers

We demonstrate that a conventional two-arm interferometer can implement first-order temporal differentiation of ultrafast arbitrary optical waveforms. Straightforward extension of this technique to nth-order optical differentiation is also suggested. This approach is experimentally demonstrated by an efficient and accurate first- and second-order temporal differentiation of (sub-)picosecond Gaussian optical pulses.