[Paper Review] Turbulence Mitigation in Phase-Conjugated Two-Photon Imaging

David S. Simon, Alexander V. Sergienko|arXiv (Cornell University)|May 1, 2011

Random lasers and scattering media56 references3 citations

TL;DR

This paper proposes a phase-conjugated two-photon imaging scheme that mitigates atmospheric turbulence by exploiting quantum correlations between photon pairs. By conjugating the phase of one photon in a correlated pair, turbulence-induced phase distortions cancel pairwise, enabling undistorted ghost imaging through turbulent media, even under strong phase fluctuations.

ABSTRACT

It is shown that the use of phase conjugation in one arm of a correlated two-photon imaging apparatus allows undistorted ghost imaging through a region with randomly-varying phase shifts. The images are formed from correlated pairs of photons in such a way that turbulence-induced phase shifts gained by the photons during passage through the medium cancel pairwise.

Motivation & Objective

• To address the degradation of image quality in two-photon ghost imaging caused by atmospheric turbulence.
• To develop a method that preserves image fidelity in the presence of randomly varying phase shifts during photon propagation.
• To demonstrate that phase conjugation in one arm of a two-photon system can cancel turbulence-induced phase distortions.
• To validate the theoretical framework through analytical modeling of correlated photon pairs under turbulent conditions.
• To extend the applicability of quantum ghost imaging to real-world environments with strong atmospheric turbulence.

Proposed method

• Utilizes correlated two-photon states generated via spontaneous parametric down-conversion (SPDC) to enable ghost imaging.
• Applies phase conjugation in one arm of the imaging setup using a four-wave mixing process to reverse phase distortions.
• Models the system using complex amplitude functions and transfer functions to describe beam propagation through turbulent media.
• Derives analytical expressions for the effective beam parameters (e.g., beam width, curvature) under turbulence with and without phase conjugation.
• Introduces a phase-conjugate mirror (PCM) model that modifies the beam propagation equations to include cancellation of phase aberrations.
• Solves the resulting coupled equations to show that phase distortions from turbulence cancel pairwise in the correlated photon pairs.

Experimental results

Research questions

• RQ1 Can phase conjugation in a two-photon ghost imaging system effectively cancel turbulence-induced phase distortions?
• RQ2 How do correlated photon pairs maintain image fidelity when one photon traverses a turbulent medium while the other is phase-conjugated?
• RQ3 What is the theoretical limit of turbulence mitigation achievable through phase conjugation in two-photon imaging?
• RQ4 How does the inclusion of a phase-conjugate mirror affect the beam parameters and image formation in the presence of random phase fluctuations?
• RQ5 To what extent can phase conjugation restore image quality in a system where turbulence causes significant wavefront distortion?

Key findings

• Phase conjugation in one arm of the two-photon system enables undistorted ghost imaging through a turbulent medium by canceling turbulence-induced phase shifts pairwise.
• Theoretical analysis confirms that phase distortions gained by photons during propagation through a turbulent region are canceled when the conjugated beam is used in coincidence detection.
• The system maintains image quality even under strong phase fluctuations, as shown by the recovery of beam parameters to their original values in the absence of turbulence.
• The model predicts that the effective beam width and curvature remain stable when phase conjugation is applied, indicating robustness to turbulence.
• The key mechanism is the symmetric cancellation of phase errors between the two correlated photons, which is preserved due to quantum correlation.
• The results are validated analytically by showing that the phase-conjugated system reduces to the turbulence-free solution when turbulence parameters (α₁, α₂) are set to zero.