Baida Lü

Spectral shifts and spectral switches in diffraction of ultrashort pulsed beams passing through a circular aperture

Summary Based on the Fourier transform method, a simple closed-form expression for the on-axis power spectrum of ultrashort Gaussian pulsed beams in diffraction at a circular aperture is derived, which permits us to study spectral changes both analytically and numerically. It is shown that for diffracted pulsed beams there exist spectral red and blue shifts, spectral narrowing, and spectral switches in the near field. The aperture diffraction plays an important role in spectral switching, but both the truncation parameter and bandwidth (or equally, Fourier transform limited pulse duration) affect the behavior of spectral switches.

Propagation of the kurtosis parameter of elegant Hermite-Gaussian and Laguerre-Gaussian beams passing through ABCD systems

Summary By using the propagation formulae of elegant Hermite-Gaussian beams (EHGBs) and Laguerre-Gaussian beams (ELGBs), the closed-form propagation expressions for the kurtosis parameter K of EHGBs and ELGBs in passage through paraxial ABCD optical systems are derived, which enable us to calculate the K parameter of EHGBs and ELGBs at any propagation plane. Detailed numerical examples are given to illustrate our analytical results

Recurrence propagation equation of Hermite-Gaussian beams through a paraxial optical ABCD system with hard-edge aperture

Summary Based on the generalized Huygens-Fresnel diffraction integral, a recurrence propagation equation of Hermite-Gaussian (H-G) beams through a paraxial optical ABCD system with hard-edge aperture is derived, which permits us to obtain the analytical propagation expression for H-G beams of any order. The advantages of our analytical results are analyzed, and the application is illustrated with numerical examples.

Approximate analytical propagation equations of Gaussian beams through hard-aperture optics

Summary By using the method of expanding the aperture function into a finite sum of complex Gaussian functions, approximate closed-form propagation equations of Gaussian beams through a paraxial multi-apertured ABCD optical system are derived and illustrated with numerical examples. The numerical results find an agreement with those by straightforward integral of the Collins formula, but the computing time is strongly reduced.

Propagation of a flattened Gaussian beam through multi-apertured optical ABCD systems

Summary By expanding the hard-aperture function into a finite sum of complex Gaussian functions, the recurrence propagation formula of a flattened Gaussian beam through multi-apertured optical ABCD systems is derived, and the propagation of a Gaussian beam is regarded as a special case in our theoretical model. The extension to the three-dimensional case is described. Numerical examples of the beam propagation through a multiple aperture-lens system and an aperture-spatial filter are given and compared with those by the straightforward numerical integration of the Collins formula. It is shown that our analytical results give a good trade-off between the computational time and accuracy, and provide a useful tool for simulating the beam propagation through complicated optical systems including multiple apertures and spatial filters. Finally, a comparison with the previous work is made and the main results obtained in this paper are summarized.

Propagation of the kurtosis parameter of Hermite-cosh-Gaussian beams

Summary Starting from the propagation equation of Hermite-cosh-Gaussian (HChG) beams and the intensity moments definition, an analytical expression for the propagation of the kurtosis parameter of unapertured HChG beams passing through paraxial optical ABCD systems is derived and illustrated numerically. Special interesting cases are discussed, in particular, the kurtosis parameter of HChG beams at the waist plane is obtained readily from our general propagation expression.

A comparison of the vectorial nonparaxial approach with Fresnel and Fraunhofer approximations

Summary Based on the vectorial Rayleigh diffraction integrals, a nonparaxial propagation equation of vectorial plane waves diffracted at a circular aperture is derived. The nonparaxial far-field expression, Fresnel and Fraunhofer diffraction formulae are given and treated as special cases of our general expression. The theoretical formulation permits us to study and compare the transversal and axial intensity distributions of diffracted plane waves both analytically and numerically. Illustrative numerical examples are given. It is shown that the vectorial nonparaxial approach has to be used if the aperture size is comparable with or less than the wavelength, and the knowledge of both transversal and axial intensity distributions is required to provide a comprehensive comparison of the paraxial and nonparaxial results.

Beam propagation factor of apertured super-Gaussian beams

Summary Starting from the generalized truncated second-order moments definition, an explicit expression for the beam propagation factor ( M 2 -factor) of apertured super-Gaussian beams is derived and illustrated with numerical examples. Some special cases of our analytical result are discussed.

Spectral behavior of diffracted chirped Gaussian pulses in the far field

Summary Based on the Fourier transform method, the analytical expression for the power spectrum of diffracted chirped Gaussian pulses in the far field is derived. Detailed numerical calculations are performed to illustrate the far-field spectral behavior and temporal intensity distributions of diffracted chirped Gaussian pulses. It is shown that the spectrum may be redshifted, blueshifted, and split into two or more than two parts, and the shifting of maximum and splitting of temporal intensity profiles occur. The far-field spectral behavior and temporal intensity distributions of ultrashort chirped Gaussian pulses diffracted at an aperture depend on the truncation parameter δ, pulse duration T, chirp parameter C and diffraction angle α. Specifically, for ultrashort chirped pulses there exists also the spectral switch.

The polarization property and irradiance distribution of incoherent and coherent Gaussian beam combinations

Summary Based on the beam coherence-polarization (BCP) matrix, the polarization property of coherent and incoherent Gaussian beam combinations is studied in detail. The general expressions for the degree of polarization P of the resulting beam in case of incoherent and coherent combinations are derived. It is shown that P is dependent on the incoherent or coherent combination, propagation distance, separation, azimuth of the polarization plane and numbers of beamlets in general. The irradiance distribution of the resulting beam for the coherent cases depends on the azimuth of the polarization plane of beamlets. However, for the incoherent case it does not.