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We demonstrate a radio frequency (RF) phase-stable transmission over fiber based on microwave photonic phase shifter. In the proposed system, both assistant RF signals are applied to drive two arms of a dual-drive Mach-Zehnder modulator (DMZM), respectively. An optical bandpass filter is followed to filter out the first-order sideband of optical modulated signal. Due to the phase independence between two optical sidebands, the phase perturbation caused by fiber-length variations can be compensated automatically via controlling the direct-current bias voltage of the DMZM. We have performed RF transfer in a 155 km single-mode fiber with a frequency instability of 3.05 × 10−17 at 10,000 s averaging time.

Single-shot supercontinuum spectral interferometry is a powerful technique for measuring transient refractive index changes. In principle, its time resolution is limited only by the available probe bandwidth. However, this assumes that the phase extraction has sufficient spectral resolution and that the probe spectral phase is exactly known. Using an analytical model for the spectral phase and amplitude modulation of a chirped probe pulse by a weak transient phase perturbation, we show how the probe chirp and spectral resolution determine the achievable time resolution. A simple, practical technique for precise in situ measurement of the probe spectral phase is described in detail, and the sensitivity of the extracted temporal phase profile to uncertainty in the probe spectral phase is demonstrated in numerical simulations.

Two modified Gerchberg-Saxton (GS) iterative phase retrieval algorithms are proposed. The first we refer to as the spatial phase perturbation GS algorithm (SPP GSA). The second is a combined GS hybrid input-output algorithm (GS/HIOA). In this paper (Part I), it is demonstrated that the SPP GS and GS/HIO algorithms are both much better at avoiding stagnation during phase retrieval, allowing them to successfully locate superior solutions compared with either the GS or the HIO algorithms. The performances of the SPP GS and GS/HIO algorithms are also compared. Then, the error reduction (ER) algorithm is combined with the HIO algorithm (ER/HIOA) to retrieve the input object image and the phase, given only some knowledge of its extent and the amplitude in the Fourier domain. In Part II, the algorithms developed here are applied to carry out known plaintext and ciphertext attacks on amplitude encoding and phase encoding double random phase encryption systems. Significantly, ER/HIOA is then used to carry out a ciphertext-only attack on AE DRPE systems.

The Laboratory for Laser Energetics plans to install KDP wedges on each beam line of the OMEGA laser system in order to improve the on-target laser uniformity by decreasing the instantaneous speckle through spatial averaging of the two resultant orthogonally polarized beams. The proposed wedge-production method, diamond turning, produces small residual scratch marks, causing each beam to acquire a pseudorandom phase perturbation. In addition, the orthogonally polarized beams interfere such that their combined polarization state continuously cycles through all elliptical states along any transverse plane. Since the nonlinear refractive index depends on the polarization state, intense beams accumulate a periodic phase perturbation that is greater for linear polarization. Propagation of both types of phase perturbation yields an intensity modulation that tends to be larger in the neighborhood of linear polarization, through a combination of diffraction and self- and cross-phase modulation. However, one- and two-dimensional calculations using a symmetrized split-step Fourier method demonstrate that diamond-turned KDP wedges are not a significant source of intensity modulation under OMEGA laser conditions. Installation of diamond-turned rather than polished wedges will reduce costs without adversely affecting the system performance.

It is shown that when branch points are present in the phase of a turbulence-distorted optical field, the ability of an adaptive optics system that utilizes a least mean square error type of wave-front reconstructor to sense all of the turbulence-induced phase perturbations is limited. There is a portion of the turbulence-induced phase perturbation, which portion we refer to as the hidden phase, that such a least mean square error type of wave-front reconstructor will, in effect, ignore. It is shown that the presence of branch points indicates that the measured phase-difference vector field cannot be considered to be simply the gradient of some scalar potential—the phase function—but is in part also the curl of a vector potential function. A solution is developed for this vector potential, and from this a simple closed-form solution for the hidden phase is developed. Sample numerical results are presented showing the nature of the hidden phase. Suggestions are provided for a branch-point-tolerant wave-front reconstructor based on use of the closed-form solution for the hidden phase.

The reflectivity of p- and s-polarized light incident upon a one-dimensional, randomly rough, dielectric surface is calculated for several angles of incidence, when the plane of incidence is normal to the generators of the surface, by a second-order small-amplitude perturbation theory, by a second-order self-energy perturbation theory, and by a second-order phase perturbation theory. The wavelength of the incident light is λ = 0.6328 μm, and the dielectric constant of the scattering medium is ∊ = 2.25. The surface roughness is characterized by a rms height δ and a transverse correlation length a. From a comparison of the results of these approximate calculations with those obtained by a numerical simulation approach for each polarization of the incident light, and for several angles of incidence, curves of δ/λ as a function of a/λ are constructed, below which each perturbative method is valid with an error that is smaller than 2.5%. It is found that, for a given value of a/λ, the reflectivity of s- and p-polarized light is given most accurately by the phase perturbation theory and least accurately by small-amplitude perturbation theory.

We have utilized the extended Huygens-Fresnel principle to make an analysis of the first- and second-order statistics of the received intensity for speckle propagation through the turbulent atmosphere. The treatment includes the effects of the turbulent atmosphere on the laser beam as it propagates to the target and on the speckle as it propagates back to the receiver. Formulations have been developed for both the focused and collimated cases. It is assumed in the analysis that phase perturbation of the waves is the dominant effect due to the atmosphere. Utilizing this assumption it can be shown that the fields at the receiver are marginally Gaussian and that the space-averaged, spatial power spectral density at the receiver is “white.” Because of these results, we have assumed that the field statistics at the receiver are jointly Gaussian. This appears to be a reasonable assumption and allows a closed form solution for the variance and covariance to be derived. For a point detector it is found that the normalized variance is unity and independent of the turbulence strength, and that the transverse correlation length becomes proportional to ρ0 as the turbulence strength increases.

The phase-perturbation method for the computation of fields scattered by rough surfaces is reviewed and then a method for calculating moments of the field scattered from randomly rough surfaces is investigated. In previous work, the authors have shown that the phase-perturbation method can provide an accurate approximation to the fields scattered from deterministic rough surfaces, even in cases when the rms surface-height variation is significant compared to the radiation wavelength. The present work employs cumulants to develop a systematic averaging procedure that retains this advantage, in the case of scalar-wave scattering from surfaces on which Dirichlet boundary conditions hold. The resulting expressions for the moments of the scattered field are shown to reduce to classical small roughness and physical-optics expressions in the appropriate limits. Numerical results for the magnitude of the coherent reflection coefficient in two test cases are also presented.

The resonant frequencies and diffraction losses of two-mirror open resonators which depart somewhat from an ideal configuration are evaluated by a perturbative technique. Detailed results are derived and discussed for flat mirrors of rectangular or circular aperture with a parabolic phase perturbation as well as flat-roof and conical systems with large apex angle.