Diffraction Integral Theory Research Articles

A bottle beam generated by a step refractive index axicon

Step refractive index axicon for generating bottle beam is proposed for the first time, and the two kinds of models-refractive index step-increase or decrease in radial direction are discussed. The principle of the bottle beam generation is analyzed by geometrical optics. The optical field distribution and 2D light spot image at different propagation distance behind the two kinds of axicons are numerically simulated using the diffraction integral theory. Research result shows that the step-decrease refractive index axicon generates single bottle beam, and the step-increase refractive index axicon generates periodic bottle beams. Bottle beam has a wild application in atom guiding and trapping,optical capture and optical tweezers. Research results in this paper give the significant guidance for the practical applications of the bottle beam.

Effect of elliptical manufacture error of an axicon on the diffraction-free beam patterns

Based on the generalized Huygens-Fresnel diffraction integral theory and the stationary-phase method, we analyze the influence on diffraction-free beam patterns of an elliptical manufacture error in an axicon. The numerical simulation is compared with the beam patterns photographed by using a CCD camera. Theoretical simulation and experimental results indicate that the intensity of the central spot decreases with increasing elliptical manufacture defect and propagation distance. Meanwhile, the bright rings around the central spot are gradually split into four or more symmetrical bright spots. The experimental results fit the theoretical simulation very well.

衍射理论对局域空心光束及无衍射光束重建的描述

衍射理论对局域空心光束及无衍射光束重建的描述

Influence of astigmatism on the diffraction property of the axicon and its correction

The diffraction field will show aberration if an axicon has astigmatism for beams incident at an angle. In this paper, the diffractional optical field expression of an axicon with astigmatism was derived based on the diffraction integral theory. The influence of the astigmatism on the diffraction property of the axicon was analyzed through the numerical simulation of the diffraction pattern with different astigmatism and the optical intensity distribution along the propagation direction for a given astigmatism. The method of correcting the beam aberration caused by the astigmatism is proposed and realized by the experiment using a precise tunable rotator. Experimental results agree with the theoretical analysis. The result extends the field of applications of the axicon.

The description of bottle beam based on the interferential theory

For the description of the focusing properties of a Bessel beam generated by an axicon, we first deduce a type of analytic expression other than Huygens-Fresnel diffraction integral theory. Based on the interferential theory, the analytic expression can be used to calculate the focusing beam evolution behind the focal plane of the positive lens and under the circumstance of the positive lens placed beyond the maximum non-diffraction distance, and can better illustrate the formation of the optical bottle beam. These results can not be described based on the Huygens-Fresnel diffraction integral theory. In addition, we get a different result from the one (that if z0max, hollow beam will be generated) obtained by Wei adopting geometrical optics. All of our theoretical calculations are confirmed by the experimental results.

Characteristics of beam profile of Gaussian beam passing through an axicon

Bessel beam can overcome the limitation of the Rayleigh range of Gaussian beam with the same spot size propagation without any spreading due to diffraction, which is considered as an useful function in guiding particles in the next generation of optical tweezers. The mathematical description of the Bessel beam generated by an axicon is usually based on the Fresnel diffraction integral theory. In this paper, we deduce another type of analytic expression suitable for describing the beam profile generated from the axicon illuminated by the Gaussian beam based on the interferential theory. Compared with the Fresnel diffraction integral theory, this theory does not use much approximation in the process of mathematical analysis. According to the derived expression, the beam intensity profiles at any positions behind the axicon can be calculated not just restricted inside the cross region as the Fresnel diffraction integral theory gives. The experiments prove that the theoretical results fit the experimental results very well.

Cavity modelling in stacked quantum well slabs for optically pumped lasers

The paper discusses a model to estimate the diffraction loss in stacked quantum well slabs for optically pumped lasers. Two quantum well slabs, cleaved from the same strip, are stacked together with the front sides facing each other to form the laser cavity. Misalignment and different slab sizes are possible, which may result in additional diffraction loss. The model is based on the diffraction integral theory to calculate the fundamental mode in a plane mirror resonator. Model results suggest that, for a small misalignment size of a few percent of the wavelength, the diffraction loss is relatively small compared with other sources of loss in the laser system. Hence, the stacked scheme is feasible for the long wavelength far-infrared region but not suitable for shorter wavelengths in the mid- or near-infrared regions. This model is in general applicable to other optically pumped quantum well lasers.

TRANSFORMATION CHARACTERISTICS OF LASER BEAM THROUGH A RANDOM PHASE PLATE

Based on the diffraction integral theory,the near far-field characteristics of a laser-beamtrans-formed random phase plate have been studied theoretically and numerically ain a rather general case.The spot smoothing,profile controlling and speckle inhibiting by introducing the random phase plate have been analyzed in detail.Some new results obtained here are useful for practical applications of the random phase plate.

TWO GENERALISED THEORIES DESCRIBING LIGHT DIFFRACTION BY ULTRASONIC PULSES :A. GENERATING-FUNCTION METHODB. LAPLACE-TRANSFORM METHOD

As an extension from previous studies concerning the interaction of light with ultrasound of a purely sinusoidal form, two theoretical models describing light diffraction by ultrasonic pulses are derived starting from the Maxwell equations. Based on a generating function, the first model provides finite solutions for the amplitudes and intensities of the diffraction pattern and is restricted in validity to the Raman-Nath region. The second model consists of a numerical method developed by means of Laplacetransformations and covers as well the Raman-Nath as the Bragg region. Both new methods are compared with a theory based on the diffraction-integral theory, leading to the conclusion that the results of this latter method can be obtained from our models considering the extreme Raman-Nath regime ρ = 0. A general rule concerning the (a)symmetry properties of the diffraction spectrum at normal incidence has been derived from the extended Raman-Nath equations, using the generating function method.

DIFFRACTION INTEGRAL FORMULA FOR MISALIGNED OPTICAL SYSTEMS

On the basis of Collins' diffraction in tegral theory, a diffraction integral formula for misaligned optical systems has been devived employing a kernel expressed in terms of augmented 4×4 transfer matrix elements.