Graph-based model for adaptive simulation of beam propagation in turbulent media.

A graph-based approach uses a triangular adaptive mesh for simulating the propagation of light beams through the atmosphere. In this approach, the atmospheric turbulence and the beam wavefront are signals in a graph, with vertices representing an irregular distribution of signal points and edges between vertices showing their relationships. The adaptive mesh provides a better representation of the spatial variations in the beam wavefront, resulting in increased accuracy and resolution compared to regular meshing schemes. The adaptability of this approach to the propagated beam characteristics makes it a versatile tool for simulating beam propagation in various turbulence conditions.

Proof of concept for adaptive sequential optimization of free-space communication receivers.

In a downlink scenario, the performance of laser satellite communications is limited due to atmospheric turbulence, which causes fluctuations in the intensity and the phase of the received signal, leading to an increase in bit error probability. In principle, a single-aperture phase-compensated receiver, based on adaptive optics, can overcome atmospheric limitations by adaptive tracking and correction of atmospherically induced aberrations. However, under strong turbulence situations, the effectiveness of traditional adaptive optics systems is severely compromised. We have developed an alternative intensity-based technique that corrects the wavefront by iteratively updating the phases of individual focal-plane speckles, which maximizes the power coupled into a single-mode fiber. Here, we present the proof of concept for this method. We show how this technique offers around 4 dB power gain with fewer than 60 power measurements under strong turbulence conditions. It delivers a good performance in different turbulent regimes, and it shows robustness against severe deterioration of the signal-to-noise ratio.

Intensity-based adaptive optics with sequential optimization for laser communications.

Wavefront distortions of optical waves propagating through the turbulent atmosphere are responsible for phase and amplitude fluctuations, causing random fading in the signal coupled into single-mode optical fibers. Wavefront aberrations can be confronted, in principle, with adaptive optics technology that compensates the incoming optical signal by the phase conjugation principle and mitigates the likeliness of fading. However, real-time adaptive optics requires phase wavefront measurements, which are generally difficult under typical propagation conditions for communication scenarios. As an alternative to the conventional adaptive optics approach, here, we discuss a novel phase-retrieval technique that indirectly determines the unknown phase wavefront from focal-plane intensity measurements. The adaptation approach is based on sequential optimization of the speckle pattern in the focal plane and works by iteratively updating the phases of individual speckles to maximize the received power. We found in our analysis that this technique can compensate the distorted phasefront and increase the signal coupled with a significant reduction in the required number of iterations, resulting in a loop bandwidth utilization well within the capacity of commercially available deformable mirrors.

Effect of atmospheric anisoplanatism on earth-to-satellite time transfer over laser communication links.

The need for an accurate time reference on orbiting platforms motivates study of time transfer via free-space optical communication links. The impact of atmospheric turbulence on earth-to-satellite optical time transfer has not been fully characterized, however. We analyze limits to two-way laser time transfer accuracy posed by anisoplanatic non-reciprocity between uplink and downlink. We show that despite limited reciprocity, two-way time transfer can still achieve sub-picosecond accuracy in realistic propagation scenarios over a single satellite visibility period.

Digital equalization of time-delay array receivers on coherent laser communications.

Field conjugation arrays use adaptive combining techniques on multi-aperture receivers to improve the performance of coherent laser communication links by mitigating the consequences of atmospheric turbulence on the down-converted coherent power. However, this motivates the use of complex receivers as optical signals collected by different apertures need to be adaptively processed, co-phased, and scaled before they are combined. Here, we show that multiple apertures, coupled with optical delay lines, combine retarded versions of a signal at a single coherent receiver, which uses digital equalization to obtain diversity gain against atmospheric fading. We found in our analysis that, instead of field conjugation arrays, digital equalization of time-delay multi-aperture receivers is a simpler and more versatile approach to accomplish reduction of atmospheric fading.

Generation of atmospheric wavefronts using binary micromirror arrays.

To simulate in the laboratory the influence that a turbulent atmosphere has on light beams, we introduce a practical method for generating atmospheric wavefront distortions that considers digital holographic reconstruction using a programmable binary micromirror array. We analyze the efficiency of the approach for different configurations of the micromirror array and experimentally demonstrate the benchtop technique. Though the mirrors on the digital array can only be positioned in one of two states, we show that the holographic technique can be used to devise a wide variety of atmospheric wavefront aberrations in a controllable and predictable way for a fraction of the cost of phase-only spatial light modulators.

Limits to the information gain from lidar measurements.

Measurements over the return signal are an integral part of lidar remote sensing by which we gather information about the characteristics of specific targets. But how much information is gained by performing a given lidar measurement? By defining Shannon's mutual information of a lidar observation, here we consider the bits of information content on the measurement and describe mathematically the capacity of lidar estimates to represent a corresponding property in the target. For heterodyne Doppler lidars in particular, we have found simple analytical formulas that consider the information gain in mean-frequency estimates.

Measuring the translational and rotational velocities of particles in helical motion using structured light.

We measure the rotational and translational velocity components of particles moving in helical motion under a Laguerre-Gaussian mode illumination. The moving particle reflects light that acquires an additional frequency shift proportional to the velocity of rotation in the transverse plane, on top of the usual frequency shift due to the longitudinal motion. We determined both the translational and rotational velocities of the particles by switching between two modes: by illuminating with a Gaussian beam, we can isolate the longitudinal frequency shift; and by using a Laguerre-Gaussian mode, the frequency shift due to the rotation can be determined. Our technique can be used to characterize the motility of microorganisms with a full three-dimensional movement.

Direction-sensitive transverse velocity measurement by phase-modulated structured light beams.

The use of structured light beams to detect the velocity of targets moving perpendicularly to the beam's propagation axis opens new avenues for remote sensing of moving objects. However, determining the direction of motion is still a challenge because detection is usually done by means of an interferometric setup, which only provides an absolute value of the frequency shift. In this Letter, we present a novel method that addresses this issue. It uses dynamic control of the phase in the transverse plane of the structured light beam so that the direction of the particles' movement can be deduced. This is done by noting the change in the magnitude of the frequency shift as the transverse phase of the structured light is moved appropriately. We demonstrate our method with rotating microparticles that are illuminated by a Laguerre-Gaussian beam with a rotating phase about its propagation axis. Our method, which only requires a dynamically configurable optical beam generator, can easily be used with other types of motion by appropriate engineering and dynamic modulation of the phase of the light beam.

Limits to the representation capacity of imaging in random media.

The information capacity of an image in the atmosphere, ocean, or biological media does not grow indefinitely with increasing light power but has well defined limits. Here, the exact effects of the propagation of light in random inhomogeneous media are elucidated and upper bounds to the capacity of image pixels to represent a corresponding point in the object are described.

Experimental detection of transverse particle movement with structured light.

One procedure widely used to detect the velocity of a moving object is by using the Doppler effect. This is the perceived change in frequency of a wave caused by the relative motion between the emitter and the detector, or between the detector and a reflecting target. The relative movement, in turn, generates a time-varying phase which translates into the detected frequency shift. The classical longitudinal Doppler effect is sensitive only to the velocity of the target along the line-of-sight between the emitter and the detector (longitudinal velocity), since any transverse velocity generates no frequency shift. This makes the transverse velocity undetectable in the classical scheme. Although there exists a relativistic transverse Doppler effect, it gives values that are too small for the typical velocities involved in most laser remote sensing applications. Here we experimentally demonstrate a novel way to detect transverse velocities. The key concept is the use of structured light beams. These beams are unique in the sense that their phases can be engineered such that each point in its transverse plane has an associated phase value. When a particle moves across the beam, the reflected light will carry information about the particle's movement through the variation of the phase of the light that reaches the detector, producing a frequency shift associated with the movement of the particle in the transverse plane.

Digital coherent receiver for orbital angular momentum demultiplexing.

We put forward a type of receiver for coherent detection of the photon orbital angular momentum (OAM). A coherent array receiver, consisting of multiple subapertures, with each subaperture coupled to a single-mode fiber, maps the complex optical field in the image plane. Using digital samplers connected to each array element, the local electrical signals resulting from the detection process can be measured coherently, moving the complexity of the full OAM measurement from the optical domain to the digital domain. By computer processing the coherent electrical patterns obtained, one can retrieve full information (amplitude and phase) of the different OAM components that constitute any incoming beam.

Self-homodyne detection of the light orbital angular momentum.

A simple optical system for the self-homodyne detection of the orbital angular momentum (OAM) carried by optical beams is introduced. We propose two different schemes based on the use of optical hybrids, which could detect the OAM mode number, even when the input beam might be slightly distorted. A balanced receiver is used to perform a self-homodyne measure of the optical signal from two different locations at the beam wavefront.

Optical Doppler shift with structured light.

When a light beam with a transverse spatially varying phase is considered for optical remote sensing, in addition to the usual longitudinal Doppler frequency shift of the returned signal induced by the motion of the scatter along the beam axis, a new transversal Doppler shift appears associated to the motion of the scatterer in the plane perpendicular to the beam axis. We discuss here how this new effect can be used to enhance the current capabilities of optical measurement systems, adding the capacity to detect more complex movements of scatters.

Statistical model for fading return signals in coherent lidars.

A statistical model for the return signal in a coherent lidar is derived from the fundamental principles of atmospheric scattering and turbulent propagation. The model results in a three-parameter probability distribution for the coherent signal-to-noise ratio in the presence of atmospheric turbulence and affected by target speckle. We consider the effects of amplitude and phase fluctuations, in addition to local oscillator shot noise, for both passive receivers and those employing active modal compensation of wavefront phase distortion. We obtain exact expressions for statistical moments for lidar fading and evaluate the impact of various parameters, including the ratio of receiver aperture diameter to the wavefront coherence diameter, the speckle effective area, and the number of modes compensated.

Efficiency of complex modulation methods in coherent free-space optical links.

We study the performance of various binary and nonbinary modulation methods applied to coherent laser communication through the turbulent atmosphere. We compare the spectral efficiencies and SNR efficiencies of complex modulations, and consider options for atmospheric compensation, including phase correction and diversity combining techniques. Our analysis shows that high communication rates require receivers with good sensitivity along with some technique to mitigate the effect of atmospheric fading.

Capacity of coherent free-space optical links using diversity-combining techniques.

We study the performance of diversity combining techniques applied to synchronous laser communication through the turbulent atmosphere. We assume that a single information-bearing signal is transmitted over two or more statistically independent fading channels, and that the multiple replicas are combined at the receiver to improve detection efficiency. We consider the effects of log-normal amplitude fluctuations and Gaussian phase fluctuations, in addition to local oscillator shot noise. We study the effect of various parameters, including the ratio of receiver aperture diameter to wavefront coherence diameter, the scintillation index, and the number of independent diversity branches combined at the receiver. We consider both maximal-ratio combining (MRC) and selective combining (SC) diversity schemes. We derive expressions for the outage Shannon capacity, thus placing upper bounds on the spectral efficiency achievable using these techniques.

Capacity of coherent free-space optical links using atmospheric compensation techniques.

We analyze the ergodic capacity and epsilon-outage capacity of coherent optical links through the turbulent atmosphere. We consider the effects of log-normal amplitude fluctuations and Gaussian phase fluctuations, in addition to local oscillator shot noise, for both passive receivers and those employing active modal compensation of wavefront phase distortion. We study the effect of various parameters, including the ratio of receiver aperture diameter to wavefront coherence diameter, the strength of the scintillation index, and the number of modes compensated.

Performance of synchronous optical receivers using atmospheric compensation techniques.

We model the impact of atmospheric turbulence-induced phase and amplitude fluctuations on free-space optical links using synchronous detection. We derive exact expressions for the probability density function of the signal-to-noise ratio in the presence of turbulence. We consider the effects of log-normal amplitude fluctuations and Gaussian phase fluctuations, in addition to local oscillator shot noise, for both passive receivers and those employing active modal compensation of wave-front phase distortion. We compute error probabilities for M-ary phase-shift keying, and evaluate the impact of various parameters, including the ratio of receiver aperture diameter to the wave-front coherence diameter, and the number of modes compensated.

Influence of atmospheric phase compensation on optical heterodyne power measurements.

The simulation of beam propagation is used to examine the uncertainty inherent to the process of optical power measurement with a practical heterodyne receiver because of the presence of refractive turbulence. Phase-compensated heterodyne receivers offer the potential for overcoming the limitations imposed by the atmosphere by the partial correction of turbulence-induced wave-front phase aberrations. However, wave-front amplitude fluctuations can limit the compensation process and diminish the achievable heterodyne performance.