Propagation of super-Lorentzian beams through a paraxial ABCD optical system

Based on the Collins integral, analytical propagation formulae of super-Lorentzian (SL) SL₀₁, SL₁₀, and SL₁₁ beams passing through a paraxial ABCD optical system are derived by means of the convolution theorem of the Fourier transform. The propagation properties of the SL₀₁ and SL₁₁ beams in free space are graphically illustrated with numerical examples. The power in the bucket of the SL₀₁ and SL₁₁ beams has been also examined in the far-field plane. This research is useful to the applications of super-Lorentzian beams.     

Propagation of a four-petal Gaussian vortex beam through a paraxial ABCD optical system

Based on the Collins diffraction integral formula, an analytical expression of a general four-petal Gaussian vortex beam passing through a paraxial ABCD optical system is derived by means of the mathematical technique. As a numerical example, the normalized intensity distribution of a four-petal Gaussian vortex beam propagating in free space is graphically demonstrated. The influences of beam order and topological charge on the normalized intensity distribution are discussed in detail. This research is useful to the optical trapping, optical communications, and beam splitting techniques, etc.     

厄米-高斯光束通过多个硬边光阑复杂光学系统变换的计算模拟

 用Wen的方法研究了厄米－高斯光束通过含有多个硬边光阑复杂光学系统的传输,推导出了具有快速计算优点的传输公式,使计算时间大为减少。高斯光束传输可作为理论模型的特例得出。数值计算例表明使用该解析公式所得结果和直接对Collins公式作数值积分的结果符合较好。对所用方法和所得结果的进一步推广作了讨论。     

Spectral shift of partially coherent flattened multi-Gaussian beams with a hole passing through ABCD optical systems

Based on flattened multi-Gaussian beam model and partially coherent theory, the expression for cross-spectral density of partially coherent flattened multi-Gaussian beam with a hole was given. The analytical expression for on-axis spectrum of partially coherent flattened multi-Gaussian beam with a hole passing through a paraxial ABCD optical system was derived. The spectral shifts of the partially coherent flattened multi-Gaussian beam with a hole propagating in free space and passing through the lens have been analyzed. The effects of the beam profile, spatial coherence parameter and the system parameters on the relative spectral shift have been discussed. Our results show that the inner radius of flattened multi-Gaussian beam with a hole determines its relative spectral shift in near field and its outer radius determines that in far field. For the flattened multi-Gaussian beam with a hole passing through a lens, the on-axis relative spectral shift changes sharply near the focal plane with the increase in Fresnel number and the spatial coherence parameter.     

Approximate analytical representation of Wigner distribution function for Gaussian beams passing through ABCD optical systems with hard aperture

Based on the treatment that a rectangular function can be expanded as an approximate sum of complex Gaussian functions with finite numbers, the analytical expression of the Wigner distribution function for a Gaussian beam passing through a paraxial ABCD optical system with hard-edged aperture is obtained. By numerical simulation, it is shown that the effect of the aperture on the Wigner distribution function is prominent. By comparing the analytical results with the numerical integral results, it is shown that this method of expanding hard-edged aperture into Gaussian functions with finite numbers is proper and ascendant. This method could be extended to study the Wigner distribution functions of other light beams passing through a paraxial ABCD optical system with hard-edged aperture.     

Propagation properties of partially polarized Gaussian Schell-model beams through an axis-unsymmetric paraxial ABCD system

By using the beam coherence-polarization (BCP) matrix approach, analytical propagation equations of partially polarized Gaussian Schell-model (PGSM) beams through an axis-unsymmetric paraxial optical ABCD system are derived, which enable us to study the propagation-induced polarization changes and irradiance distributions at any propagation distance of PGSM beams through axis-unsymmetric systems within the framework of the paraxial approximation. Detailed numerical results for a PGSM beam passing through a bifocal lens are presented to illustrate the propagation properties of PGSM beams. A comparison with the previous work is also made.     

Multiplication rule of similarity transformations in the coherent state representation and its mapping onto quantum optical generalized ABCD law

We find that classical similarity transformations in the coherent state representation projects onto the similarity transformation operators (STO), these operators constitute a loyal representation of symplectic group. Remarkably, the multiplication rule of the STOs naturally leads to the quantum optical generalized ABCD law, which is the quantum mechanical correspondence of the classical optical ABCD law. Throughout the whole derivation, the technique of integration within an ordered product (IWOP) of operators is employed.     

Propagation properties of the beam generated by Gaussian mirror resonator passing through a paraxial ABCD optical system

By expanding a hard aperture function into a finite sum of complex Gaussian functions, approximate propagation formula is derived in the situation that the beam generated by Gaussian mirror resonator passes through a paraxial ABCD optical system with an annular aperture. The corresponding forms for a circular aperture and a circular black screen are also given. Some numerical simulations are shown to illustrate propagation properties and focusing properties of the beam passing through a paraxial ABCD optical system with the three different kinds of aperture.     

Propagation characteristics of linearly polarized Bessel-Gaussian beams through an annular apertured paraxial ABCD optical system

By means of Collins diffraction integral formula in the paraxial approximation and based on the fact that a hard aperture function can be expanded into a finite sum of complex Gaussian functions, an approximate analytical expression for linearly polarized Bessel-Gaussian beams passing through a paraxial ABCD optical system with an annular aperture has been derived. The results provide more convenient for studying their propagation and transformation than the usual way by using diffraction integral directly. By using the analytical expression and the diffraction integral formula some numerical simulations are done to illustrate for the propagation characteristics of a linearly polarized Bessel-Gaussian beam through an optical system with an annular aperture.     

Approximate analytical expressions of Laguerre-Gaussian beams passing through a paraxial optical system with an annular aperture

On the basis of the expansion of the hard aperture function into a finite sum of complex Gaussian functions, the approximate analytical expression of Laguerre-Gaussian beams passing through an annular apertured paraxial ABCD optical system is derived. Meanwhile, the corresponding closed-forms for the unapertured or circular apertured or circular black screen cases have also been given. Numerical examples are given to illustrate the propagation characteristics of Laguerre-Gaussian beams.     

The approximate ABCD matrix for a parabolic lens of revolution and its application in calculating the coupling efficiency

Using ray optics, we present an explicit formulation of the ABCD matrix for reflection and refraction of light beams at a parabolic interface separating media of different refractive indices under paraxial approximation. Based on the formulated ABCD matrix for refraction by a parabolic lens tip, we present a simple theoretical investigation of the coupling efficiency between a laser diode and a single-mode fiber with a parabolic lens formed on the fiber tip. The results show that this technique is effective and will be of benefit to designing suitable microlenses applying the laser-coupling technique.     

通过有光阑近轴ABCD光学系统激光束的近似解析传输公式

 用傅立叶级数展开法研究光束通过有光阑限制的近轴ABCD光学系统的传输特性,导出了光阑透射率函数不同时的传输公式。硬边光阑的情况可作为其它光阑的特例得到,其它光阑也可视作硬边光阑来处理。数值计算表明了该方法快速的优点,并得到与用Collins公式直接积分一致结果。     

通过有光阑近轴ABCD光学系统激光束的近似解析传输公式

用傅立叶级数展开法研究光束通过有光阑限制的近轴ABCD光学系统的传输特性,导出了光阑透射率函数不同时的传输公式。硬边光阑的情况可作为其它光阑的特例得到,其它光阑也可视作硬边光阑来处理。数值计算表明了该方法快速的优点,并得到与用Collins公式直接积分一致结果。     

A detailed study of Mathieu-Gauss beams propagation through an apertured ABCD optical system

Using Collins formula and the expansion of Mathieu beams in terms of Bessel beams we derive the exact propagation equations of Mathieu-Gauss beams through an apertured paraxial ABCD optical system. A comparison between the exact propagation equations and the approximated ones, which are derived by expanding the circ function into a finite sum of Gaussian functions, is presented. The propagation characteristics of zeroth-order Mathieu-Gauss beams in (y-z) and (x-z) planes are analyzed with detailed numerical calculations. It is found that the profile of the propagated Mathieu-Gauss beam is similar to that of Bessel-Gauss beam. Furthermore, the focalization of the Mathieu-Gauss beams through a thin lens is illustrated and analyzed with numerical results.     

P-n codoping induced enhancement of ferromagnetism in Mn-doped In2O3: A first-principles study

We have performed first-principles density functional theory calculation in order to investigate the feasibility of “p-n codoping method” in improving magnetic property of In₂O₃ based diluted magnetic semiconductors. We find that the ferromagnetic state is favored in Mn-doped In₂O₃, and Sn doping can increase magnetic moment in Mn-doped In₂O₃. These findings are in line with our earlier experimental observation. Along with previous works, we now have enough evidences to support that p-n codoping is a valid method to improve magnetism of oxides based diluted magnetic semiconductors.     

Simulation of NEXAFS spectra of a photo-reactive copolymer with considerably large monomer units: An ab initio molecular orbital study

We performed the simulation of near edge X-ray absorption fine structure (NEXAFS) spectra of a photo-reactive copolymer with considerably large monomer units by ab initio molecular orbital calculation, in order to explain the spectral change induced by irradiation of the linearly polarized near ultra-violet (LPNUV) light. The “building block approach” is applied for the theoretical calculation to calculate the core-excited states of the polymer with such large monomer units; the monomer unit is divided into subunits, whose core-excited states are calculated individually, and the results are summed up to simulate the spectra of the polymer. With the result of the simulation, the peaks in the observed spectra were assigned. The spectral change after the LPNUV-irradiation is attributed to the change in the electronic structure caused by the breakdown of the π-conjugation system of chalconyl group after photo-dimerization.     

A comparative study of continuous laser operation on the F3/2-I9/2 transitions of Nd:GdVO4 and Nd:YVO4 crystals

A comparative study of Nd:GdVO₄ and Nd:YVO₄ crystal lasers pumped by a fiber-coupled diode array has been conducted at the ⁴F_3/2-⁴I_9/2 transitions wavelengths of 912 nm and 914 nm, as well as when intracavity frequency-doubled to 456 nm and 457 nm, respectively. At the fundamental wavelength of 912 nm and second harmonic wavelength of 456 nm, maximum output powers from the Nd:GdVO₄ crystal laser were 7.85 W and 4.6 W at a pump power of 29 W. All the results obtained from Nd:GdVO₄ were superior to those of Nd:YVO₄, indicating that Nd:GdVO₄ is a more efficient laser crystal than Nd:YVO₄ for laser operation on the ⁴F_3/2-⁴I_9/2 transitions.     

Surface chemistry of NO and NO2 on the Pt(1 1 0)-(1 × 2) surface: A comparative study

The surface chemistry of NO and NO₂ on clean and oxygen-precovered Pt(1 1 0)-(1 × 2) surfaces were investigated by means of high resolution electron energy loss spectroscopy (HREELS), X-ray photoelectron spectroscopy (XPS) and thermal desorption spectroscopy (TDS). At room temperature, NO molecularly adsorbs on Pt(1 1 0), forming linear NO(a) and bridged NO(a). Coverage-dependent repulsive interactions within NO(a) drive the reversible transformation between linear and bridged NO(a). Some NO(a) decomposes upon heating, producing both N₂ and N₂O. For NO adsorption on the oxygen-precovered surface, repulsive interactions exist between precovered oxygen adatoms and NO(a), resulting in more NO(a) desorbing from the surface in the form of linear NO(a). Bridged NO(a) experiences stronger repulsive interactions with precovered oxygen than linear NO(a). The desorption activation energy of bridged NO(a) from oxygen-precovered Pt(1 1 0) is lower than that from clean Pt(1 1 0), but the desorption activation energy of linear NO(a) is not affected by the precovered oxygen. NO₂ decomposes on Pt(1 1 0)-(1 × 2) surface at room temperature. The resulted NO(a) (both linear NO(a) and bridged NO(a)) and O(a) repulsively interact each other. Comparing with NO/Pt(1 1 0), more NO(a) desorbs from NO₂/Pt(1 1 0) as linear NO(a), and both linear NO(a) and bridged NO(a) exhibit lower desorption activation energies. The reaction pathways of NO(a) on Pt(1 1 0), desorption or decomposition, are affected by their repulsive interactions with coexisting oxygen adatoms.