Spatial multiplexing for robust optical vortex transmission with optical nonlinearity.

Optical vortex beams, with phase singularity characterized by a topological charge (TC), introduces a new dimension for optical communication, quantum information, and optical light manipulation. However, the evaluation of TCs after beam propagation remains a substantial challenge, impeding practical applications. Here, we introduce vortices in lateral arrays (VOILA), a novel spatial multiplexing approach that enables simultaneous transmission of a lateral array of multiple vortices. Leveraging advanced learning techniques, VOILA effectively decodes TCs, even in the presence of strong optical nonlinearities simulated experimentally. Notably, our approach achieves substantial improvements in single-shot bandwidth, surpassing single-vortex scheme by several orders of magnitude. Furthermore, our system exhibits precise fractional TC recognition in both linear and nonlinear regimes, providing possibilities for high-bandwidth communication. The capabilities of VOILA promise transformative contributions to optical information processing and structured light research, with significant potential for advancements in diverse fields.

Temporal coherence of the acoustic field forward propagated through a continental shelf with random internal waves.

An analytical model derived from normal mode theory for the accumulated effects of range-dependent multiple forward scattering is applied to estimate the temporal coherence of the acoustic field forward propagated through a continental-shelf waveguide containing random three-dimensional internal waves. The modeled coherence time scale of narrow band low-frequency acoustic field fluctuations after propagating through a continental-shelf waveguide is shown to decay with a power-law of range to the -1/2 beyond roughly 1 km, decrease with increasing internal wave energy, to be consistent with measured acoustic coherence time scales. The model should provide a useful prediction of the acoustic coherence time scale as a function of internal wave energy in continental-shelf environments. The acoustic coherence time scale is an important parameter in remote sensing applications because it determines (i) the time window within which standard coherent processing such as matched filtering may be conducted, and (ii) the number of statistically independent fluctuations in a given measurement period that determines the variance reduction possible by stationary averaging.

General second-order covariance of Gaussian maximum likelihood estimates applied to passive source localization in fluctuating waveguides.

A method is provided for determining necessary conditions on sample size or signal to noise ratio (SNR) to obtain accurate parameter estimates from remote sensing measurements in fluctuating environments. These conditions are derived by expanding the bias and covariance of maximum likelihood estimates (MLEs) in inverse orders of sample size or SNR, where the first-order covariance term is the Cramer-Rao lower bound (CRLB). Necessary sample sizes or SNRs are determined by requiring that (i) the first-order bias and the second-order covariance are much smaller than the true parameter value and the CRLB, respectively, and (ii) the CRLB falls within desired error thresholds. An analytical expression is provided for the second-order covariance of MLEs obtained from general complex Gaussian data vectors, which can be used in many practical problems since (i) data distributions can often be assumed to be Gaussian by virtue of the central limit theorem, and (ii) it allows for both the mean and variance of the measurement to be functions of the estimation parameters. Here, conditions are derived to obtain accurate source localization estimates in a fluctuating ocean waveguide containing random internal waves, and the consequences of the loss of coherence on their accuracy are quantified.

Empirical dependence of acoustic transmission scintillation statistics on bandwidth, frequency, and range in New Jersey continental shelf.

The scintillation statistics of broadband acoustic transmissions are determined as a function of signal bandwidth B, center frequency f(c), and range with experimental data in the New Jersey continental shelf. The received signal intensity is shown to follow the Gamma distribution implying that the central limit theorem has led to a fully saturated field from independent multimodal propagation contributions. The Gamma distribution depends on the mean intensity and the number of independent statistical fluctuations or coherent cells micro of the received signal. The latter is calculated for the matched filter, the Parseval sum, and the bandpassed center frequency, all of which are standard ocean acoustic receivers. The number of fluctuations mu of the received signal is found to be an order of magnitude smaller than the time-bandwidth product TB of the transmitted signal, and to increase monotonically with relative bandwidth Bfc. A computationally efficient numerical approach is developed to predict the mean intensity and the corresponding broadband transmission loss of a fluctuating, range-dependent ocean waveguide by range and depth averaging the output of a time-harmonic stochastic propagation model. This model enables efficient and accurate estimation of transmission loss over wide areas, which has become essential in wide-area sonar imaging applications.

Temporal coherence after multiple forward scattering through random three-dimensional inhomogeneities in an ocean waveguide.

An analytical expression is derived for the temporal coherence of an acoustic field after multiple forward scattering through random three-dimensional (3D) inhomogeneities in an ocean waveguide. This expression makes it possible to predict the coherence time scale of field fluctuations in ocean-acoustic measurements from knowledge of the oceanography. It is used to explain the time scale of acoustic field fluctuations observed at megameter ranges in various deep ocean-acoustic transmission experiments. It is shown that this time scale is nonlinearly related to the much longer coherence time scale of deep ocean internal waves through a multiple forward scattering process. It is also shown that 3D scattering effects become pronounced when the acoustic Fresnel width exceeds the cross-range coherence length of the deep ocean internal waves, which lead to frequency and range-dependent power losses in the forward field that may help to explain historic long range measurements.