Fractional Self-imaging Research Articles

Temporal Talbot effect of optical dark pulse trains.

The temporal Talbot effect describes the periodic self-imaging of an optical pulse train along dispersive propagation. This is well studied in the context of bright pulse trains, where identical or multiplied pulse trains with uniform bright waveforms can be created. However, the temporal self-imaging has remained unexplored in the dark pulse regime. Here, we disclose such a phenomenon for optical dark pulse trains, and discuss the comparison with their bright pulse counterparts. It is found that the dark pulse train also revives itself at the Talbot length. For higher-order fractional self-imaging, a mixed pattern of bright and dark pulses is observed, as a result of the interference between the Talbot pulses and the background. Such unconventional behaviors are theoretically predicted and experimentally demonstrated by using programmable spectral shaping as well as by optical fiber propagation.

On the generality of the Talbot condition for inducing self-imaging effects on periodic objects.

Integer and fractional self-imaging effects can be induced on periodic waveforms across the time, frequency, space, or angular frequency domains by imposing a quadratic phase profile along the corresponding Fourier dual domain. This phase must satisfy the well-known "Talbot condition." The resulting period-divided fractional self-images exhibit deterministic pulse-to-pulse phase variations that arise from the solution of a Gauss sum. In turn, these self-images can be regarded as inducing a Talbot effect in the Fourier dual domain. This suggests the possibility of observing self-imaging effects by imposing phase profiles that are not defined by the Talbot condition. In this Letter, we show otherwise that the phase profiles retrieved from a Gauss sum also satisfy the Talbot condition, which implies that this condition may encompass all possible quadratic phase patterns for inducing self-imaging effects. We establish here the precise relationships between the solutions of Gauss sums and the corresponding Talbot phases, and derive additional properties of Talbot phase patterns of fundamental and practical interest.

Angular Talbot effect

We predict the possibility of observing integer and fractional self-imaging (Talbot) phenomena on the discrete angular spectrum of periodic diffraction gratings illuminated by a suitable spherical wave front. Our predictions are experimentally validated, reporting what we believe to be the first observation of self-imaging effects in the far-field diffraction regime.

Talbot effect with matter waves

Talbot effect in the space-time evolution of matter waves is analyzed and shown that the matter waves at relativistic and non-relativistic velocities exhibit coherence beyond the grating and display Talbot self-imaging. The grating is realized by considering equidistant narrowly peaked coherent probability distributions at the onset. Theoretical frame work is based on a quantum particle at relativistic and non-relativistic velocities in a one dimensional box. The matter waves, in their evolution, display Talbot self-imaging and fractional self-imaging as restructuring, respectively, at Talbot length and fractional Talbot lengths.

Laser beam addition of planar waveguides with fractional self-imaging

Propagation characteristics of laser beams are examined in fractional self-imaging planar waveguides. A potential approach to laser beam combining is proposed by application of planar waveguides with fractional self-imaging. The influences of phase mismatch between laser beams on laser beam addition are discussed. The numerical simulation for two lasers with average power of 300 W shows that the beam addition in fractional self-imaging planar waveguide can improve the parameter M2 of combined beam effectively. The sensitivity of beam addition to the phase mismatch between laser beams has been reduced obviously.

Periodic pulse train conformation based on the temporal Radon–Wigner transform

By using the Radon–Wigner transform (RWT), we analyze the temporal selfimaging or Talbot effect for producing well-conformed pulse trains with variable repetition rates and duty-cycles. The relationships linking the selfimaging conditions with the fractional orders of the RWT are first obtained for unchirped pulse trains. Then, we extend the analysis to chirped pulse sequences by deriving the conditions to be fulfilled by an equivalent unchirped pulse train producing the same selfimage irradiances. This result becomes relevant for observing well-defined high order fractional selfimaging, which are of interest due to their repetition rate multiplication. Besides, the effect of the finite extension of the pulse train on the selfimage quality is analyzed and a condition is found for relating the required minimum pulse number with the chirp parameter of the pulses.

Spectral Talbot phenomena in sampled arbitrarily chirped Bragg gratings

We derive the general conditions for which spectral Talbot phenomena, both integer and fractional self-imaging, can be observed in sampled arbitrarily chirped fiber Bragg gratings. These results are a generalization of those previously reported in [C. Wang, J. Azaña, L.R. Chen, Opt. Lett. 29(14) (2004) 1590] in which spectral Talbot phenomena were observed in sampled linearly chirped fiber Bragg gratings. We confirm our theoretical derivations with numerical simulations.

Temporal self-imaging effects for periodic optical pulse sequences of finite duration

Integer and fractional temporal self-imaging phenomena occur when an ideal (infinite-duration) periodic optical pulse sequence propagates through a suitable dispersive medium under the first-order dispersion approximation. I analytically and numerically investigate the impact of nonidealities in the input periodic pulse sequence, especially finite duration of the sequences as well as intensity and phase fluctuations between pulses, on the temporal self-imaging phenomena. I derive conditions for which effects associated with these nonidealities can be neglected. Under these conditions, the intensity of the input nonideal finite sequence can also be self-imaged—integer and fractional self-imaging are also possible—by propagation through a suitable dispersive medium. The resulting self-images of the input signal not only maintain the temporal features of the original individual pulses (temporal shape and duration) but also the total temporal duration of the finite input sequence and the original intensity fluctuations between pulses. The analytical results are confirmed by means of numerical simulations.