Performance of real-time adaptive optics compensation in a turbulent channel with high-dimensional spatial-mode encoding.

The orbital angular momentum (OAM) of photons is a promising degree of freedom for high-dimensional quantum key distribution (QKD). However, effectively mitigating the adverse effects of atmospheric turbulence is a persistent challenge in OAM QKD systems operating over free-space communication channels. In contrast to previous works focusing on correcting static simulated turbulence, we investigate the performance of OAM QKD in real atmospheric turbulence with real-time adaptive optics (AO) correction. We show that even though our AO system provides a limited correction, it is possible to mitigate the errors induced by weak turbulence and establish a secure channel. The crosstalk induced by turbulence and the performance of AO systems is investigated in two configurations: a lab-scale link with controllable turbulence, and a 340 m long cross-campus link with dynamic atmospheric turbulence. Our experimental results suggest that an advanced AO system with fine beam tracking, reliable beam stabilization, precise wavefront sensing, and accurate wavefront correction is necessary to adequately correct turbulence-induced error. We also propose and demonstrate different solutions to improve the performance of OAM QKD with turbulence, which could enable the possibility of OAM encoding in strong turbulence.

Temporal coherence effects on target-based phasing of laser arrays.

This paper studies how temporal coherence (in particular, linewidth broadening introduced to suppress stimulated Brillouin scattering) affects target-based phasing of fiber laser arrays. A radio-frequency modulated array whose elements are fed by a broadband laser source phasing on a remote step target is theoretically analyzed. An expression for the detector plane irradiance, ultimately used to phase the array on the target, is derived and discussed in detail. Simulation results of a seven-element hexagonal array phasing on a distant step target with scattering surfaces separated by many coherence lengths are presented to validate the theoretical findings.

Spatial-temporal-covariance-based modeling, analysis, and simulation of aero-optics wavefront aberrations.

We introduce a framework for modeling, analysis, and simulation of aero-optics wavefront aberrations that is based on spatial-temporal covariance matrices extracted from wavefront sensor measurements. Within this framework, we present a quasi-homogeneous structure function to analyze nonhomogeneous, mildly anisotropic spatial random processes, and we use this structure function to show that phase aberrations arising in aero-optics are, for an important range of operating parameters, locally Kolmogorov. This strongly suggests that the d5/3 power law for adaptive optics (AO) deformable mirror fitting error, where d denotes actuator separation, holds for certain important aero-optics scenarios. This framework also allows us to compute bounds on AO servo lag error and predictive control error. In addition, it provides us with the means to accurately simulate AO systems for the mitigation of aero-effects, and it may provide insight into underlying physical processes associated with turbulent flow. The techniques introduced here are demonstrated using data obtained from the Airborne Aero-Optics Laboratory.

Rigorous investigation of the array-tilt aberration for hexagonal, optical phased arrays.

An investigation of the array-tilt aberration for hexagonal, optical phased arrays is presented. The investigation begins with theoretical derivations of the far-zone radiated field, the array factor, and the far-field radiated power for the seven-element hexagonal array with array tilt present. Physical insights gained from this analysis are discussed. An analytical treatment of correlation-based array-tilt estimators is also undertaken. Two novel array-tilt estimation techniques are developed from the analysis. The new techniques are shown to be significantly more efficient computationally than the traditional estimation approach. Simulation and experimental results are presented to validate the new array-tilt estimation methods.

Accommodation of speckle in object-based phasing.

This work addresses the physical basis of the measurement process for object-based phasing of an array of telescopes. In this regard an enhanced least-squares estimator that is capable of differentiating among three families of array aberrations in an object-based phasing system is developed. In a system of this nature the system to be phased illuminates the object of interest and the return radiation is detected. Telescope aberrations, atmospheric aberrations, and speckle-induced aberrations are all reported by the estimator to facilitate correction of telescope and atmospheric aberrations. This is accomplished by proper handling of the unobservable modes and recognizing that the five global aberrations-telescope array piston, atmospheric array piston and tilt, and speckle array piston and tilt-cannot be measured accurately so they need to be projected out of the estimated piston commands. Except for these relatively benign array aberrations, the disturbances for all three families of array aberrations are estimated exactly. An interesting feature of the speckle array aberrations is that a synthetic aperture is developed that is almost twice as large as the array of telescopes under consideration.

Spatial bandwidth considerations for optical communication through a free space propagation link.

This Letter concentrates on the transverse limitations imposed by a finite aperture optical propagation link that supports free space optical communication. Here it is assumed that a series of states, which are the spatial component of the message, are sent through the communication channel. The spatial bandwidth of the propagation link expressed as bits per transmitted photon is computed as the product of the average link efficiency times the entropy of the link. To facilitate the evaluation, it is assumed that the transmitted states are minimum energy loss orbital angular momentum states expressed in the form of f(nm)(r)exp(imθ), where the radial function is controlled to ensure that, for each quantum number denoted by the values of n and m, the minimum energy loss is obtained. The results illustrate that the bandwidth in units of bits per transmitted photon is very nearly equal to log(2)(N(2)(f)here log(2)(·) denotes the logarithm in base 2 and the Fresnel number, N(f)=(π/4)D(1)D(2)/(λz), where D(1) is the diameter of the transmitting aperture, D(2) is the diameter of the receiving aperture, λ is the wavelength of the light used, and z is the propagation distance.

Influence of atmospheric turbulence on the propagation of quantum states of light carrying orbital angular momentum.

We analyze the influence of atmospheric turbulence on the propagation of an optical vortex beam having the form V(r,theta)=A(0)e(imtheta). The probability that a detected photon after propagating through the atmosphere has the same value of the orbital angular momentum as the launched photon is found to be given by s(0)=[1+(1.845D/r(0))(2)](-1/2), where D is the aperture diameter and r(0) is the Fried coherence diameter. These vortex beams behave very similarly to Laguerre-Gauss beams under the influence of atmospheric turbulence. These results have important implications for atmospheric laser communication systems that employ quantum encryption.

Assessment of the statistics of the Strehl ratio: predictions of central limit theorem analysis.

For a beam propagating through turbulence, the statistics of the Strehl ratio are determined by recognizing that the real and imaginary parts of the on-axis far-field pattern can be represented as the sum of many contributions from the aperture. With this in mind, the central limit theorem (CLT) can be used to develop the statistics of the real and imaginary parts of the optical field, which through the appropriate mathematical manipulations as described here can then be used to develop the probability distribution of the far-field irradiance. The results obtained in this way (which we call the CLT theory or analysis) provide an analytic expression that agrees with the results of detailed wave-optics simulations. This provides an approach by which the statistics of the Strehl ratio can be rapidly determined. A key feature of this work is that the analytic results depend on the values of a few relevant turbulence parameters that include r0,fG, and sigma2(l). Therefore, a measurement of these parameters at various sites of interest allows us to rapidly assess the detailed nature of the statistical fluctuations of the far-field irradiance that will be experienced at these locations.

Adaptive optics compensation for propagation through deep turbulence: initial investigation of gradient descent tomography.

To implement adaptive optics compensation for propagation through deep turbulence, the concept of gradient descent tomography has been developed. Here two or more deformable mirrors are controlled by an efficient iterative algorithm that optimizes the integral I(2) image-sharpening metric. In this work a difficult case involving imaging over a 2 km path with a C(n)(2) of 2 x 10(-13)m(-2/3) is considered. For a wavelength of 1.06 microm and a 10-cm-diameter aperture, lambda/D is seven times the isoplanatic angle (theta(0)=1.54 microrad), and the Rytov number is 5.5. For three points placed along a line spanning approximately 70 isoplanatic patch sizes all three points are compensated somewhat, illustrating that anisoplanatism is addressed. The fact that the corresponding performance improvement ratios are 1.20, 1.34, and 3.26 in the presence of such strong scintillation and anisoplanatism is quite significant.