Closed-form expression for mutual intensity evolution of Hermite -Laguerre -Gaussian Schell-model beams

We derive a comprehensive closed-form expression for the evolution of themutual intensity (MI) ofHermite -Laguerre Gaussian Schell-model beams (HLG-SMBs) during propagation through rotationally symmetric optical systems. We demonstrate that the MI of the beam associated with a given HLG mode at any transverse plane can be presented as a linear superposition of the MIs of the SMBs associated with the equal and lower index modes of the same type, but of complex argument. The obtained expression allows easy analysis of the evolution of the intensity distribution and the CCF of such beams and, in particular, an understanding of the coherence singularity formation and modification during the beam propagation. (C) 2017 Optical Society of Americ

Coherence singularities: birth, evolution, possible applications

Coherent singular beams, in particular optical vortices, are attractive for different applications: free-space optical communication, imaging, particle manipulation, etc. However, their deformation during propagation through random media and speckle noise forced to look to their partially coherent analogues. The singularities of partially coherent beams associated with zero points of the cross-correlation function have been theoretically predicted and experimentally demonstrated for some particular cases of Laguerre-Gaussian (LG) and Hermite-Gaussian (HG) Schell-model beams (SMBs). Here we establish a theoretical background for explanation of these singularities evolution during propagation of the SMBs associated with structurally stable Hermite-Laguerre-Gaussian modes, which include as a particular case the LG and HG ones. The derived a closed-form expression for the evolution of the mutual intensity of such beams allows easily calculating the intensity distribution and cross-correlation function at every plane of paraxial optical system. The birth and evolution of the cross- correlation singularities is analyzed. Their structure in far field serves as a fingerprint of the associated mode while the intensity distribution may not resemble the mode shape. The robustness of these singularities can be exploited for information encoding and random medium monitoring

INVESTIGATION OF INVERSE PROBLEMS AND AUTOMODEL SOLUTIONS OF SHREDINGER EQUATION

The analytical connection between modulus and argument function of the complex-valued solution of the Shredinger equation and also the properties in the solution invariance of the Shredinger equation at the Fourie type integral transformations are considered, the search of the new automodel solutions for Shredinger equation is performed. The new solutions of the Shredinger equation and new integral correlations between known solutions of the Shredinger equation which can find application in the theory of special functions, theory of equations in the partial derivatives and in laser optics have been foundAvailable from VNTIC / VNTIC - Scientific & Technical Information Centre of RussiaSIGLERURussian Federatio

Rotating beams in isotropic optical system

Based on the ray transformation matrix formalism, we propose a simple method for generation of paraxial beams performing anisotropic rotation in the phase space during their propagation through isotropic optical systems. The widely discussed spiral beams are the particular case of these beams. The propagation of these beams through the symmetric fractional Fourier transformer is demonstrated by numerical simulations

Astigmatic-Invariant Structured Singular Beams

We investigate the transformation of structured Laguerre–Gaussian (sLG) beams after passing through a cylindrical lens. The resulting beam, ab astigmatic structured Laguerre–Gaussian (asLG) beam, depends on quantum numbers (n,ℓ) and three parameters. Two of them are control parameters of the initial sLG beam, the amplitude ϵ and phase θ. The third one is the ratio of the Rayleigh length z0 and the focal length f of the cylindrical lens. It was theoretically revealed and experimentally confirmed that the asLG beam keeps the intensity shape of the initial sLG beam when the parameters satisfy simple conditions: ϵ is unity and the tangent of the phase parameter θ/2 is equal to the above ratio. We also found sharp bursts and dips of the orbital angular momentum (OAM) in the asLG beams in the vicinity of the point where the OAM turns to zero. The heights and depths of these bursts and dips significantly exceed the OAM maximum and minimum values of the initial sLG beam and are controlled by the radial number n

Astigmatic-Invariant Structured Singular Beams

We investigate the transformation of structured Laguerre–Gaussian (sLG) beams after passing through a cylindrical lens. The resulting beam, ab astigmatic structured Laguerre–Gaussian (asLG) beam, depends on quantum numbers (n,ℓ) and three parameters. Two of them are control parameters of the initial sLG beam, the amplitude ϵ and phase θ. The third one is the ratio of the Rayleigh length z0 and the focal length f of the cylindrical lens. It was theoretically revealed and experimentally confirmed that the asLG beam keeps the intensity shape of the initial sLG beam when the parameters satisfy simple conditions: ϵ is unity and the tangent of the phase parameter θ/2 is equal to the above ratio. We also found sharp bursts and dips of the orbital angular momentum (OAM) in the asLG beams in the vicinity of the point where the OAM turns to zero. The heights and depths of these bursts and dips significantly exceed the OAM maximum and minimum values of the initial sLG beam and are controlled by the radial number n

Shaping of light beams along curves in three dimensions

We present a method for efficient and versatile generation of beams whose intensity and phase are prescribed along arbitrary 3D curves. It comprises a non-iterative beam shaping technique that does not require solving inversion problems of light propagation. The generated beams have diffraction-limited focusing with high intensity and controlled phase gradients useful for applications such as laser micro-machining and optical trapping. Its performance and feasibility are experimentally demonstrated on several examples including multiple trapping of micron-sized particles