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Based on the Collins diffraction integral formula and irradiance moment definition, the propagation characteristics of the kurtosis parameter of a Gaussian beam through fractional Fourier transformation (FRFT) systems with spherically aberrated lens are studied in detail. By using the efficient algorithm introduced in this paper, some numerical calculations are done. It is shown that the kurtosis parameter of a Gaussian beam passage through FRFT systems with spherically aberrated lens is very different from that of a Gaussian beam through ideal FRFT systems. What’s more, the effect of different kinds or values of spherical aberration coefficients on the kurtosis parameter is in great difference. The values of the kurtosis parameter of a Gaussian beam through the two types of Lohmann’s systems respectively are no longer equal even in the case of the same fractional orders and the same spherical aberration coefficients. The kurtosis parameter of a Gaussian beam passage through ideal FRFT systems keeps invariable and its value is 3 in the one-dimensional case.

Laser-induced white light emission from nano-carbon as well as other nanostructured materials in vacuum is presented in this article. It is observed only when the excitation laser intensity is higher than a threshold value (10 3 -10 6 W/cm 2 ). For the semiconductor nano-materials such as a cadmium sulphide (CdS) nano-crystal, a deep UV emission is also captured besides the white light emission. Spectra show that the nano-CdS radiate the stronger deep UV light with peak wavelengths about 210 and 215 nm. According this, a strong deep UV emission with a concomitant second harmonic generation at room temperature is also observed in a normal InGaAs laser diode (LD) operating at 980 nm. The output power of the UV radiation is estimated approaching to 0.1 mW. Since the wavelengths of the UV emission from nano-CdS are a little shorter than those of the InGaAs LD. These make it possible to develop deep UV wavelength LDs by doping different semiconductor nano-materials into the active layers besides using the III-nitride compound and ZnO semiconductor materials.

Based on the nonparaxial moment theory of light beam propagation, the propagation characteristics of nonparaxial scalar Gaussian beam, nonparaxial TEM and TE vector Gaussian beams have been investigated. The results reveal that both the transversal beam widths follow a simple hyperbolic law upon propagation. The analytical expressions of the beam propagation factor, beam waist and far field divergence angle are presented, respectively. Furthermore, the formulae can be very concise for highly nonparaxial cases. TE or TM polarization will result in different propagating features in the two transversal directions. The maximum transverse divergence angles of nonparaxial scalar and vector Gaussain beams are different, which indicates that nonparaxial scalar Gaussian beam is no longer approximate at subwavelength scales. When extending to the paraxial case, the results obtained are slightly different from the formerly paraxial ones. Moreover, in this case the beam propagation factor will always be greater than unity. This research also denotes some properties of subwavelength optics.

By introducing a method that a hard-edged aperture function can be expanded into an approximate sum of complex Gaussian functions with finite numbers, the analytical expression of Wigner distribution function for a Gaussian beam passing through a cylindrical symmetric and paraxial ABCD optical system with a hard-edged aperture is obtained. Numerical calculations show that the effect of an aperture on the Wigner distribution function is prominent. The analytical results are also compared with the integral calculation results and they show that this method of expanding a hard aperture into Gaussian functions with finite numbers is proper and ascendant. This method could also be extended to studying the Wigner distribution functions of other light beams passing through a paraxial ABCD optical system with a hard-edged aperture.

Based on the generalized Huygens-Fresnel diffraction integral and the expansion of the hard aperture function into a finite sum of complex Gaussian functions, approximate analytical expressions of standard and elegant Laguerre-Gaussian beams passing through a paraxial ABCD optical system with a hard-edged aperture are derived. On the basis of the truncated second-order moments method in the cylindrical coordinate system and the expansion of the hard aperture function into a finite sum of complex Gaussian functions, an approximate method for calculating the generalized beam propagation factor is proposed. Closed-form expressions for the generalized beam propagation factor of a truncated standard and elegant Laguerre-Gaussian beam are derived that depend on the orders of Laguerre polynomial and the beam truncation parameter. Some typical numerical examples are given and compared. It is shown that the results obtained by using the obtained analytical method accord with those by using the numerical integration method.

Some developments on fractional Fourier optics are reported in this paper. First, a thick lens can be regarded as a fractional Fourier transformer. Second, relations between the Collins formulae and the fractional Fourier transform or fractional Hankel transform are bridged, we show that the Collins formulae in spatial domain or in spatial-frequency domain can be described by the fractional Fourier transform or fractional Hankel transform. Third, connections between the multi-element resonators and the scaled fractional Fourier transforms are established, it is shown that there exists twice scaled fractional Fourier transform for beams in completing one round trip, the beam oscillation in resonator can be viewed as a process of consecutive implementing scaled fractional Fourier transform. Finally, some extensions of the fractional Fourier transforms to misaligned optical systems are simply reviewed.

There are four kinds of reflectors: 1, flat mirror; 2, common retroreflectors; 3, phase conjugate mirror (PCM) and 4, the fourth one. "Corner cube" belongs to 2. However, if the dihedral angle lines and their images of the corner cube are taken into account, it is recognized as super-conjugator. The terminal mirror of laser cavity is replaced by such an element, it has ability to compensate distortions inside the cavity and misalignments insensitive and has being rapidly used. How to perform nonlinear phenomena by a well known linear element? Here we show the essentials by way of special array concept.

The variations of group velocities for Gaussian beams under different hypotheses were studied, and the rationality of the results were discussed and analysed. Then we show that the beam waist radius should be proportional to the square root ofwavelength. Under this condition, the group velocities are all equal to c on the beam axis and smaller than c off the axis.

A novel method for laser beam smoothing by rotating random phase plate is presented in this paper. A random phase plate for CO 2 laser was made, and satisfactory results were obtained. The experimental results coincide very well with theoretical analysis.

According to the more complete diffraction theory, a series of new beams was invented both outside and inside laser cavity by using (lambda) /2 phase plate. A new beam with equivalent beam quality factor Me2 less than 1 is achieved on ten-watt CO2 laser and on hundred-Watt and thousand-Watt CO2 laser with axial express flux. It may be named as the first kind of new beam laser. From the point of view of practical applications, we designed and produced a new structure of laser cavity whose output mirror was a special mirror with step reflectivity. We have realized 1000 W new beam on CO2 laser with transverse express flux, which is close to the fundamental mode. It may be named as the second kind new laser beam. Its structure is simpler than others, but it brings excellent results.

A new suggestion that there is a phase jump of (pi) in the boundary wave is put forward in this paper. This suggestion may be a supplement of Huygens-Fresnel principle. Based on this new suggestion, a series of new beam was invented, both outside and inside laser cavity. Especially, a new CO2 laser with equivalent beam quality factor M2 < 1 is achieved. it can be considered as the result of some controllable nonlinear self-focusing, and the physical background of deformed quantum mechanics.© (1996) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Focal shift of the zone plate is completely different from the corresponding circular and annular apertures. Focal powers of the zone plate are constant under some conditions but for the latter they are always variables. Astigmatism for a zone plate is also investigated. The sagittal focal surfaces are unchanged but the tangential focal surfaces are changed as a function: cos2(Theta) , besides, it has neither spherical aberration nor coma. They are also completely different from conventional imaging devices.© (1993) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Propagation, transformation and self-consistent solution of laser beams could be treated by advanced matrix methods clearly, e.g.: misaligned laser systems are analyzed by augmented 4x4 matrix, phase conjugate mirrors are described by matrices with variable elements, nonsymmetrical laser systems are treated by tensor ABCD law, optical arrays are performed as pseudo-conjugators, a new Fresnel number for Gaussian beams is defined and finally, hard aperture is written in terms of matrix and so, all the transformation of laser beams has to be reconsidered.