Far-field Intensity Distribution Research Articles

The degenerating diffraction far-field propagation properties of the conical double half-Gaussian hollow beams

The far-field propagation properties of conical double half-Gaussian hollow beams in the condition of Collins formula are studied. Because of the cone angle of this kind of hollow beams, the diffraction is compensated and the inner diameter is turning bigger by the rule of geometric optics as the propagation distance is increasing, whereas the degenerating diffraction phenomenon is turned out. The far-field intensity distribution of the conical double half-Gaussian hollow beams in the condition of in-Collins formula is researched, and the results show that the far-field propagation properties can be depicted by this model. In the experiment, this kind of hollow beams are obtained by means of the dual-reflecting splitting optical system, and the inner diameter of the hollow beams is tested. The results show good agreement with the propagation theory in the condition of in-Collins formula.

Consistency of the directionality of partially coherent beams in turbulence expressed in terms of the angular spread and the far-field average intensity

Under the quadratic approximation of the Rytov's phase structure function, this paper derives the general closed-form expressions for the mean-squared width and the angular spread of partially coherent beams in turbulence. It finds that under a certain condition different types of partially coherent beams may have the same directionality as a fully coherent Gaussian beam in free space and also in atmospheric turbulence if the angular spread is chosen as the characteristic parameter of beam directionality. On the other hand, it shows that generally, the directionality of partially coherent beams expressed in terms of the angular spread is not consistent with that in terms of the normalized far-field average intensity distribution in free space, but the consistency can be achieved due to turbulence.

Optical field distribution in ZnO/MgZnO quantum dot nanostructure at 375-nm wavelength

Computer analysis of near and far-field intensities in zinc oxide based quantum dot nanostructure has been carried out for the optimization of smaller active region volume of quantum dot to achieve desired modal gain. Near and far-field intensity distribution along junction plane has been studied as a function of mole fractions of Mg and for varying quantum dot thickness. Solutions to the wave equations have been obtained for the transverse electric mode. Effective index method has been used to deduce the propagation constants in various regions of optical wave-guide. Excellent confinement of near field intensity for greater values of Mg composition has been attributed to the increased values of refractive index step between dot and barrier regions. For the thicker dots, greater fraction of the optical field has been confined to the dot region. Near field intensity spread has been deduced and articulated in terms of full width of half maximum (FWHM) as a function of Mg mole fraction and a dot thickness. It clearly shows nonlinear decrease with increase of both the Mg mole fraction and a dot thickness. The surface image clearly reveals a bright spot in the center corresponding to far-field emitted from the dot region at 375-nm wavelength. Far-field intensity reveals divergence of 16°.

Far-field characteristics of coherently combined beams emitted from arrays on multiple polygons

By using Fourier Optics, the general analytical expression of intensity distribution for the coherently combined beams positioned on the X– Y plane, which is applicable to both Gaussian and non-Gaussian beams, can be derived. Considering the fact that in many cases the array configuration can be regarded as composed of several regular polygons with a common center, an explicit analytical expression of the far-field intensity distribution for these cases has been derived. As an example, the above expression has been applied to study a 19 emitter array. Studies have also been done on the dark fringes of the far-field pattern for the specific emitters, whose numbers are 2 and 4, respectively.

Beam Quality and Power Scalability of Various Multicore Fiber Lasers

Beam quality and power scalability analyses for various multicore fiber lasers (MFL) are presented. In-phase complex amplitude and corresponding far-field intensity distribution of each type of MFL is calculated using the finite-difference time-domain method. It is revealed that the hexagonal ring-type MFL has the best performance in power handling and maintaining beam quality. Further calculation indicates that power encircled in the diffraction-bucket of L-core MFL scales with no more than 0.4L, which challenges the practical worthiness of fielding MFL with a large number of cores.

Coherent combining of fiber lasers using a ring coupled cavity and single-mode fiber filtering

Coherent combining of two fiber lasers has been experimentally demonstrated by using a ring coupled cavity and single-mode fiber filtering technique. Their phases are primarily synchronized due to mutual injection coupling introduced by a common ring coupled cavity, and efficient phase locking is realized by utilizing a single-mode feedback fiber to filter the far-field pattern. The detailed experimental investigations indicate that the stability of phase locking can be improved significantly by this spatial filtering technique, and the far-field intensity distribution can be manipulated by controlling the position of the filtering fiber.

Gerchberg—Saxton algorithm: experimental realisation and modification for the problem of formation of multimode laser beams

An original method is proposed to calculate the formation of specified far-field intensity distributions by a bimorph mirror in the case of initial transverse-multimode beams. The method is based on the Gerchberg—Saxton algorithm with replacement of the phase function in the plane of the control element by a function that takes into account both the intensity and phase distributions of each mode. The numerical results on the formation of a beam with the third-order super-Gaussian intensity distribution from beams composed of two or four lowest transverse modes are discussed. The experimental results on using the conventional Gerchberg—Saxton algorithm to form a desired intensity distribution from single-mode laser beams using a liquid-crystal modulator are presented.

Adaptive aberration correction based on ant colony algorithm for solid-state lasers: numerical simulations

We describe an adaptive aberration correction technique based on an ant colony algorithm for solid-state lasers and a general class of other adaptive optics systems. We show that it is possible to compensate phase aberrations without wavefront sensing in this approach, which iteratively adjusts the control voltages of a deformable mirror to maximize certain system performance metrics of the far-field intensity distribution of the laser beam. The effectiveness of this approach is analyzed numerically by use of a 37-element piezoelectric deformable mirror and a variation of the Strehl ratio as the metric. Results demonstrate that this approach can effectively compensate the phase distortions of laser beams and significantly improve beam quality. A comparison indicates that this approach is much faster than a genetic algorithm while achieving almost the same beam quality.

Real structure effects in X-ray waveguide optics: The influence of interfacial roughness and refractive index profile on the near-field and far-field distribution

We generalize the optical treatment of X-ray waveguides to index profiles of arbitrary shape. The modes of the waveguides are computed numerically by Numerov’s method. The method is first validated by considering profiles for which analytical solutions exist. Next, the effects of different shape functions and of interfacial roughness on the near and far-field intensity distributions are studied. The results are helpful to judge the real structure effects, e.g. resulting from fabrication imperfections, on the optical performance, as well as to optimize optical properties by designing generalized index profiles.

Binary gratings with random heights

We analyze the far-field intensity distribution of binary phase gratings whose strips present certain randomness in their height. A statistical analysis based on the mutual coherence function is done in the plane just after the grating. Then, the mutual coherence function is propagated to the far field and the intensity distribution is obtained. Generally, the intensity of the diffraction orders decreases in comparison to that of the ideal perfect grating. Several important limit cases, such as low- and high-randomness perturbed gratings, are analyzed. In the high-randomness limit, the phase grating is equivalent to an amplitude grating plus a "halo." Although these structures are not purely periodic, they behave approximately as a diffraction grating.

Optimal Truncation of Element Beam in a Coherent Fiber Laser Array

The beam quality of a coherent fiber laser array often suffers from the low fill factor of the Gaussian laser array. One simple and effective approach to improve the fill factor is to truncate the array element properly. An analytical expression for far-field intensity distribution of a truncated coherent fiber laser array is derived. Optimal truncation of the element beam in different coherent fiber laser arrays is obtained by using energy encircled in the far-field central-lobe as the beam quality criterion. By optimal truncation, energy encircled in the central-lobe can be 97% compared with the ideal case. The shift in optimal truncation parameter in the case of phase noise is also analyzed.

Observation of coherent terahertz edge radiation from compressed electron beams

Coherent radiation emitted from a compressed electron bunch as it traverses the sharp edge regions of a magnetic chicane has been investigated at the Brookhaven National Laboratory Accelerator Test Facility. Electron beam measurements using coherent transition radiation interferometry indicate a 100 fs rms bunch accompanied by distinct distortions in energy spectrum due to strong self-fields. These self-fields are manifested in emitted high power THz radiation, which displays signatures of the phenomenon known as coherent edge radiation. Radiation characterization studies undertaken include spectral analysis, far-field intensity distribution, polarization, and dependence on the electron bunch length. The observed aspects of the beam and radiation allow detailed comparisons with start-to-end simulations.

Directionality of Gaussian array beams propagating in atmospheric turbulence

The angular spread is chosen as the characteristic parameter of beam directionality, and the directionality of Gaussian array beams propagating in atmospheric turbulence is studied. The consistency of the directionality of Gaussian array beams expressed in terms of the angular spread and the normalized far-field average intensity distribution is also examined. Closed-form expressions for the mean-squared beam width and angular spread of Gaussian array beams propagating in atmospheric turbulence are derived. It is found that for the case of coherent combination, under a certain condition array beams exist that may have the same directionality (i.e., the same angular spread) as a fully coherent Gaussian laser beam in free space and also in turbulence. However, the directionality of Gaussian array beams in terms of the angular spread is not consistent with that in terms of the normalized far-field average intensity distribution in free space, whereas they may be consistent as a result of turbulence.

The far-field divergence angle and the far-field radiant intensity distribution of Gaussian Schell-model array beams

The analytical expressions for the mean-squared beam width, the far-field divergence angle and the far-field radiant intensity of Gaussian Schell-model （GSM） array beams are derived, and the condition under which GSM array beams have the same far-field divergence angle as a single Gaussian beam. It is shown that GSM array beams and a Gaussian beam which have the same far-field divergence angle may have different far-field radiant intensity distribution, which is quite different from the behavior of GSM beams.

The relation between UV conversion efficiency and focused green Gaussian beam waist in BBO crystal

Here we present a theory which predicts the process of ultraviolet generation by frequency doubling of focused green Gaussian beam in BBO crystal. In this theory, phase matching acceptance angle, walk-off angle and the divergence of fundamental beam have been considered. Numerically computed results show that the variations of the waist of Gaussian beam can lead to changes in conversion efficiency and in the ultraviolet transverse intensity distribution of far-field. Comparison between the numerical simulation and experimental results supported our theoretical analysis.

Four-core fiber-based bending sensor

A novel four-core fiber-based bending sensor has been proposed. The four-core fiber is used as the sensing element, the four cores of the fiber act as a four-beam interferometer, and the far-field interferogram grids with periodical distributions are formed on the fiber output end. Since the phase difference is a function of the radius of curvature, the change of the radius of curvature shifts the far-field interferometric grid pattern. A low-coherence laser diode with wavelength of 650 nm is adopted to illuminate the fiber, and the interferogram pattern in the far-field is recorded by a CCD camera. The relationship between the far-field grid pattern intensity distribution and the radius of curvature is established theoretically and confirmed experimentally.

Current- and Temperature-Induced Beam Steering in 7.8-${\mu}$m Emitting Quantum-Cascade Lasers

We report large current- and temperature-induced beam-steering effects, observed in the far-field distribution of InP-based quantum-cascade lasers emitting around 7.8-mum wavelength operated in pulsed mode. Changing the temperature within a narrow range of ~10degC around room-temperature leads to a change in the direction of the output beam, as given by the central lobe in the far-field intensity distribution, from +11deg to -13deg as measured relative to the resonator axis. This beam steering effect is linked to changes in the lateral mode distribution, as revealed by time-resolved spectroscopy of the lasing spectrum.

Analysis of directional emission via surface modes on photonic crystals

Directional emission of light exiting a photonic crystal waveguide by a coherent action of radiative surface modes was recently demonstrated [E. Moreno et al., Phys. Rev. B 69 (2004) 121402], and subsequently the substantial enhancement of the directional emission was achieved by engineering the surface and adjusting relevant parameters [S.K. Morrison et al., Appl. Phys. Lett. 86 (2005) 081110]. Here we present the analysis of surface modes causing directional emission by the plane wave expansion method and the finite-difference time-domain method. Then we numerically investigate the effects of surface termination on directional emission. We find another surface termination condition with a positive surface displacement. Our surface termination is more effective than the original structure, and nearly as effective as the termination for the enhancement. Besides, our termination is simpler than that for the enhancement. We confirm its effectiveness in the far-field beam profile and radiation intensity distribution of directional emission from our termination.

Analysis of near- and far-field intensities in ZnO based heterostructure waveguides

Analysis of near- and far-field intensities in a simple double heterostructure of ZnO/Mg x Zn1 − x O and hybrid double heterostructure of Al x Ga1 − x N/ZnO have been carried out at 375 nm wavelength. Near- and far-field intensity distribution along the junction plane has been studied as a function of mole fractions of Mg and Al for varying active layer thickness. The spread of the near- and far-field intensities has been estimated and articulated as full width at half maximum (FWHM). For near-field, FWHM was found to be decreasing nonlinearly with increase of Mg mole fraction in the simple heterostructure and increasing in a nonlinear manner with the increase of Al mole fraction in the hybrid heterostructure. FWHM deduced from our analysis was 0.355 µm for 7% and 0.156 µm for 27% Mg mole fraction. For the hybrid heterostructure, the FWHM values estimated were 0.1275 and 0.1397 µm, respectively. Confinement factor as a function of mole fractions and active layer thickness has been explored and it was found to be increasing with active layer thickness. The FWHM of far-field intensity shows a vertical divergence of 26○ and showed a minor variation with the active layer thickness. Finally, it is inferred from our analysis that confinement of the near-field was strongly influenced by the mole fraction and the active layer thickness while the far-field was weakly influenced.

The directionality of partially coherent beams expressed in terms of the far-field divergence angle and of the far-field radiant intensity distribution

Taking the partially coherent cosh-Gaussian beam (ChG) as an illustrative example, the far-field divergence angle and directionality of partially coherent beams are studied. There are three competing physical mechanisms, i.e., the spatial coherence, diffraction and decentration, which affect the far-field divergence angle of partially coherent ChG beams. Two partially coherent ChG beams may generate the same far-field divergence angle, and partially coherent ChG beams may also have the same far-field divergence angle as a fully coherent ChG beam or as a fully coherent Gaussian laser beam if the three physical mechanisms are appropriately balanced. The consistency of the directionality of partially coherent beams expressed in terms of the far-field divergence angle and in terms of the far-field radiant intensity distribution is examined. Generally, two partially coherent beams with the same far-field divergence angle have not certainly the same far-field radiant intensity distribution. However, under certain conditions, it is possible to achieve the consistency of the directionality expressed in terms of the far-field divergence angle and of the normalized far-field radiant intensity distribution.