arXiv subjects

Davood Mardani

Publications and source records attributed to Davood Mardani.

5 recordsLinked to original sources

arXiv2019

What is the maximum differential group delay achievable by a space-time wave packet in free space?

The group velocity of 'space-time' wave packets $-$ propagation-invariant pulsed beams endowed with tight spatio-temporal spectral correlations $-$ can take on arbitrary values in free space. Here we investigate theoretically and experimentally the maximum achievable group delay that realistic finite-energy space-time wave packets can achieve with respect to a reference pulse traveling at the speed of light. We find that this delay is determined solely by the spectral uncertainty in the association between the spatial frequencies and wavelengths underlying the wave packet spatio-temporal spectrum $-$ and not by the beam size, bandwidth, or pulse width. We show experimentally that the propagation of space-time wave packets is delimited by a spectral-uncertainty-induced `pilot envelope' that travels at a group velocity equal to the speed of light in vacuum. Temporal walk-off between the space-time wave packet and the pilot envelope limits the maximum achievable differential group delay to the width of the pilot envelope. Within this pilot envelope, the space-time wave packet can locally travel at an arbitrary group velocity and yet not violate relativistic causality because the leading or trailing edge of superluminal and subluminal space-time wave packets, respectively, are suppressed once they reach the envelope edge. Using pulses of width $\sim$4ps and a spectral uncertainty of $\sim$ 20 pm, we measure maximum differential group delays of approximately $\pm$ 150 ps, which exceed previously reported measurements by at least three orders of magnitude.

physics.optics↗

arXiv2018

Interferometry-based modal analysis with finite aperture effects

We analyze the effects of aperture finiteness on interferograms recorded to unveil the modal content of optical beams in arbitrary basis using generalized interferometry. We develop a scheme for modal reconstruction from interferometric measurements that accounts for the ensuing clipping effects. Clipping-cognizant reconstruction is shown to yield significant performance gains over traditional schemes that overlook such effects that do arise in practice. Our work can inspire further research on reconstruction schemes and algorithms that account for practical hardware limitations in a variety of contexts.

physics.ins-det↗

arXiv2017

Signal Reconstruction from Interferometric Measurements under Sensing Constraints

This paper develops a unifying framework for signal reconstruction from interferometric measurements that is broadly applicable to various applications of interferometry. In this framework, the problem of signal reconstruction in interferometry amounts to one of basis analysis. Its applicability is shown to extend beyond conventional temporal interferometry, which leverages the relative delay between the two arms of an interferometer, to arbitrary degrees of freedom of the input signal. This allows for reconstruction of signals supported in other domains (e.g., spatial) with no modification to the underlying structure except for replacing the standard temporal delay with a generalized delay, that is, a practically realizable unitary transformation for which the basis elements are eigenfunctions. Under the proposed model, the interferometric measurements are shown to be linear in the basis coefficients, thereby enabling efficient and fast recovery of the desired information. While the corresponding linear transformation has only a limited number of degrees of freedom set by the structure of the interferometer giving rise to a highly constrained sensing structure, we show that the problem of signal recovery from such measurements can still be carried out compressively. This signifies significant reduction in sample complexity without introducing any additional randomization as is typically done in prior work leveraging compressive sensing techniques. We provide performance guarantees under constrained sensing by proving that the transformation satisfies sufficient conditions for successful reconstruction of sparse signals using concentration arguments. We showcase the effectiveness of the proposed approach using simulation results, as well as actual experimental results in the context of optical modal analysis of spatial beams.

cs.IT↗

arXiv2017

Compressive optical interferometry

Compressive sensing (CS) combines data acquisition with compression coding to reduce the number of measurements required to reconstruct a sparse signal. In optics, this usually takes the form of projecting the field onto sequences of random spatial patterns that are selected from an appropriate random ensemble. We show here that CS can be exploited in `native' optics hardware without introducing added components. Specifically, we show that random sub-Nyquist sampling of an interferogram helps reconstruct the field modal structure. The distribution of reduced sensing matrices corresponding to random measurements is provably incoherent and isotropic, which helps us carry out CS successfully.

cs.IT↗

arXiv2016

Basis-neutral Hilbert-space analyzers

Interferometry is one of the central organizing principles of optics. Key to interferometry is the concept of optical delay, which facilitates spectral analysis in terms of time-harmonics. In contrast, when analyzing a beam in a Hilbert space spanned by spatial modes -- a critical task for spatial-mode multiplexing and quantum communication -- basis-specific principles are invoked that are altogether distinct from that of `delay.' Here, we extend the traditional concept of temporal delay to the spatial domain, thereby enabling the analysis of a beam in an arbitrary spatial-mode basis -- exemplified using Hermite-Gaussian and radial Laguerre-Gaussian modes. Such generalized delays correspond to optical implementations of fractional transforms; for example, the fractional Hankel transform is the generalized delay associated with the space of Laguerre-Gaussian modes, and an interferometer incorporating such a `delay' obtains modal weights in the associated Hilbert space. By implementing an inherently stable, reconfigurable spatial-light-modulator-based polarization- interferometer, we have constructed a `Hilbert-space analyzer' capable of projecting optical beams onto any modal basis.

physics.optics↗