Mikhail I. Kolobov

Observation of extreme temporal events in CW-pumped supercontinuum

We study experimentally and numerically the temporal features of supercontinuum generated with a continuous-wave ytterbium-doped fiber laser. We show that the temporal output of the supercontinuum is characterized by strong and brief power fluctuations, i.e. so-called optical rogue waves. We demonstrate numerically that these rare and strong events that appear and disappear from nowhere result from solitonic collisions.

Sub-shot-noise microscopy: imaging of faint phase objects with squeezed light.

We propose a scheme that uses spatially multimode squeezed light, generated by means of a traveling-wave optical parametric amplifier, with which a faint phase object can be imaged with sensitivity better than the shot-noise limit.

Squeezed states of light and noise-free optical images

Abstract The regularity of photocount statistics in space, related to the wide-band squeezing, is demonstrated. The resolving power of low-noise spatial measurements is evaluated.

Experimental realization of optical eigenmode super-resolution.

We experimentally demonstrate the feasibility of a super-resolution technique based on eigenmode decomposition. This technique has been proposed theoretically but, to the best of our knowledge, has not previously been realized experimentally for optical imaging systems with circular apertures. We use a standard diffraction-limited 4f imaging system with circular apertures for which the radial eigenmodes are the circular prolate spheroidal functions. For three original objects with different content of angular information we achieve 45%, 49%, and 89% improvement of resolution over the Rayleigh limit. The work presented can be considered as progress towards the goal of reaching the quantum limits of super-resolution.

Multimode Squeezing, Antibunching in Space and Noise-Free Optical Images

Three-dimensional antibunching of photons by observation of multimode-squeezed light is considered. The phenomenon is of practical importance for producing photon beams which are regular not only in time but also in space. The possible experiment to observe the space correlations of photocounts is discussed.

Degenerate four-wave mixing as a source for spatially-broadband squeezed light

Abstract It is shown that spatially-broadband squeezed light is generated at the output of a four-wave mixer that is configured in either the backward or the forward geometry. It follows from estimations that the bandwidth of spatial squeezing is much larger in the backward four-wave mixing configuration than in the forward one. Such spatially-broadband squeezed light can be used for imaging faint objects with sensitivity that is better than the shot-noise limit.

Quantum limits of super-resolution in reconstruction of optical objects

We investigate analytically and numerically the role of quantum fluctuations in reconstruction of optical objects from diffraction-limited images. Taking as example of an input object two closely spaced Gaussian peaks, we demonstrate that one can improve the resolution in the reconstructed object over the classical Rayleigh limit. We show that the ultimate quantum limit of resolution in such a reconstruction procedure is determined not by diffraction but by the signal-to-noise ratio in the input object. We formulate a quantitative measure of super-resolution in terms of the optical point-spread function of the system.

Impact of the third-order dispersion on the modulation instability gain of pulsed signals

We demonstrate that modulation instability gain of time-localized signals (i.e., pulsed signals) depends strongly on the third-order dispersion, contrary to the well-known case of time-extended signals (cw signals). This surprising contribution of an odd dispersion term on this four-photon-mixing process is established analytically and confirmed by numerical simulations.

Squeezed-light source for superresolving microscopy

We propose a source of multimode squeezed light that can be used for superresolving microscopy. This source is an optical parametric amplifier with a properly chosen diaphragm on its output and a Fourier lens. We demonstrate that such an arrangement produces squeezed prolate spheroidal waves that are the eigenmodes of the optical imaging scheme used in microscopy and discuss the conditions of the degree of squeezing and of the number of spatial modes in illuminating light.

Quantum limits of super-resolution of optical sparse objects via sparsity constraint

Sparsity constraint is a priori knowledge of the signal, which means that in some properly chosen basis only a small percentage of the total number of the signal components is nonzero. Sparsity constraint has been used in signal and image processing for a long time. Recent publications have shown that the Sparsity constraint can be used to achieve super-resolution of optical sparse objects beyond the diffraction limit. In this paper we present the quantum theory which establishes the quantum limits of super-resolution for the sparse objects. The key idea of our paper is to use the discrete prolate spheroidal sequences (DPSS) as the sensing basis. We demonstrate both analytically and numerically that this sensing basis gives superior performance of super-resolution over the Fourier basis conventionally used for sensing of sparse signals. The explanation of this phenomenon is in the fact that the DPSS are the eigenfunctions of the optical imaging system while the Fourier basis are not. We investigate the role of the quantum fluctuations of the light illuminating the object, in the performance of reconstruction algorithm. This analysis allows us to formulate the criteria for stable reconstruction of sparse objects with super-resolution. Our results imply that sparsity of the object is not the only parameter which describes super-resolution achievable via sparsity constraint.