Decentered elliptical Hermite-Gaussian beam

Propagation of truncated Gaussian beams and their application in modeling sharp-edge diffraction

The two new kinds of truncated Gaussian beams, known as the half and quarter Gaussian beams, are defined as the product of the fundamental Gaussian beam with the Heaviside unit step function. Using the generalized Collins integral, the exact analytical propagation formulas are derived for the truncated Gaussian beams through paraxial optical systems. Combined with the Gaussian beam decomposition method, the truncated Gaussian beams are used to represent the sharp edges of a field after a hard aperture. The modified Gaussian beam decomposition method presented in this work enables the calculation of the diffraction of a given field from a hard aperture with an arbitrary shape. This solves one of the limitations of the conventional Gaussian beam decomposition method, which is its inability to accurately model the diffraction of fields with sharp edges, especially in the near field. The validity and accuracy of the proposed method are demonstrated using a few exemplary diffraction calculations.

Polarization and propagation characteristics of switchable first-order azimuthally asymmetric beam generated in dual-mode fiber

We report here the controlled generation of a linearly polarized first-order azimuthally asymmetric beam (F-AAB) in a dual-mode fiber (DMF) by appropriate superposition of selectively excited zeroth-order vector modes that are doughnut-shaped azimuthally symmetric beams (D-ASBs). We first demonstrate continually switching polarization mode structures having an identical two-lobe intensity profile (i.e., intra-F-AAB conversion). Then, under a distinct launching state, we generate mode structures progressively toggling between the doughnut-shaped profile and two-lobe pattern having dissimilar polarization orientations (i.e., F-AAB to D-ASB conversion). Interestingly, a decentralized elliptical Gaussian beam possessing homogenous spatial polarization is obtained by enhancing the contribution of the fundamental mode (HE₁₁/LP₀₁) in selectively excited F-AAB. A smoothly varying azimuth of the input beam in this situation resulted in redistribution of transverse energy procuring a unique and exciting unconventional two-grain T-polarized beam having mutually orthogonal state of polarization (SOP). All of the above three were achieved under a given set of launching conditions (tilt/offset) of a Gaussian mode (TEM₀₀) devised with changing SOP of the input beam. A strong modulation in the output beam characteristics was also observed with the variation in propagation distance (for a fixed input SOP) owing to the large difference in propagation constants of the participating modes (LP₀₁ and one of the F-AABs). Finally, this particular study led to a design for a low-cost highly sensitive strain measuring device based on tracking the centroid movement of the output intensity pattern. Each of our experimentally observed intensity/polarization distributions is theoretically mapped on a one-to-one basis considering a linear superposition of appropriately excited LP basis modes of the waveguide toward a complete understanding of the polarization and mode propagation in the dual-mode structure.

Angular spread and directionality of the Hermite-Gaussian array beam propagating through atmospheric turbulence

Using the integral transform technique, the analytical expressions for the mean-squared beam width and the angular spread of the Hermite-Gaussian (H-G) array beam in turbulence are derived for the case of both coherent and incoherent combinations. It is shown that the angular spread of the H-G array beam for the coherent combination may be more or less affected by turbulence than that for the incoherent combination (or a single H-G beam) depending on the beam parameters. For the coherent combination, there exists the oscillatory behavior of the angular spread, and the influence of turbulence on the angular spread is not monotonic versus the beam parameters. In addition, for the coherent combination case, the angular spread of the H-G array beam is less affected by turbulence than that of the Gaussian array beam. On the other hand, it is found that under a certain condition, the H-G array beam may have the same directionality as a single Gaussian beam both in free space and in turbulence if the angular spread is chosen as the characteristic parameter of the beam directionality. The main results are explained physically.

Average intensity and spreading of an elegant Hermite-Gaussian beam in turbulent atmosphere

The propagation of an elegant Hermite-Gaussian beam (EHGB) in turbulent atmosphere is investigated. Analytical propagation formulae for the average intensity and effective beam size of an EHGB in turbulent atmosphere are derived based on the extended Huygens-Fresnel integral. The corresponding results of a standard Hermite-Gaussian beam (SHGB) in turbulent atmosphere are also derived for the convenience of comparison. The intensity and spreading properties of EHGBs and SHGBs in turbulent atmosphere are studied numerically and comparatively. It is found that the propagation properties of EHGBs and SHGBs are much different from their properties in free space, and the EHGB and SHGB with higher orders are less affected by the turbulence. What's more, the SHGB spreads more rapidly than the EHGB in turbulent atmosphere under the same conditions. Our results will be useful in long-distance free-space optical communications.

Paraxial propagation of a partially coherent Hermite-Gaussian beam through aligned and misaligned ABCD optical systems

Paraxial propagation of a partially coherent Hermite-Gaussian beam through aligned and misaligned ABCD optical systems is investigated based on the generalized Collins formula for treating the propagation of a partially coherent beam through such optical systems. Analytical formulas for the cross-spectral density of a partially coherent Hermite-Gaussian beam propagating through such optical systems are derived. As an application example, we derive the propagation formulas for a partially coherent flattened Gaussian beam by expressing it as a superposition of a series of partially coherent Hermite-Gaussian beams by using polynomial expansion. The focusing properties of a partially coherent Hermite-Gaussian beam focused by a thin lens are studied as a numerical example.

Fractional Fourier transform for partially coherent off-axis Gaussian Schell-model beam

The fractional Fourier transform (FRT) is applied to a partially coherent off-axis Gaussian Schell-model (GSM) beam, and an analytical formula is derived for the FRT of a partially coherent off-axis GSM beam. The corresponding tensor ABCD law for performing the FRT of a partially coherent off-axis GSM beam is also obtained. As an application example, the FRT of a partially coherent linear laser array that is expanded as a sum of off-axis GSM beams is studied. The derived formulas are used to provide numerical examples. The formulas provide a convenient way to analyze and calculate the FRT of a partially coherent off-axis GSM beam.

Propagation of a decentered elliptical Gaussian beam through apertured aligned and misaligned paraxial optical systems

By expanding the hard aperture function into a finite sum of complex Gaussian functions, approximate analytical formulas for a decentered Gaussian beam (DEGB) passing through apertured aligned and misaligned paraxial apertured paraxial optical systems are derived in terms of a tensor method. The results obtained by using the approximate analytical expression are in good agreement with those obtained by using the numerical integral calculation. Furthermore, approximate analytical formulas for a decentered elliptical Hermite-Gaussian beam (DEHGB) through apertured paraxial optical systems are derived. As an application example, approximate analytical formulas for a decentered elliptical flattened Gaussian beam through apertured paraxial optical systems are derived. Our results provide a convenient way for studying the propagation and transformation of a DEGB and a DEHGB through apertured paraxial optical systems.

Elliptic Laguerre-Gaussian beams

An analytical expression for the diffraction of an elliptic Laguerre-Gaussian (LG) beam is derived and analyzed. We show that a beam with even singularity order has nonzero axial intensity for any degree of ellipticity and at any finite distance z from the initial plane, whereas at z = 0 and z = infinity the axial intensity is zero. We show that for a beam with a small degree of ellipticity and even order of singularity, two isolated intensity zeroes appear in the Fresnel zone on a straight line at an angle of 45 deg or -45 deg, depending whether the beam's spin is right or left. The theoretical conclusions are confirmed by numerical simulation and physical experiments.