Based on Fourier transform,the angular spectrum equation and its discrete model of the inverse source problem of the two-dimensional Helmholtz equation are derived.By transforming the two-dimensional inverse source pr...Based on Fourier transform,the angular spectrum equation and its discrete model of the inverse source problem of the two-dimensional Helmholtz equation are derived.By transforming the two-dimensional inverse source problem in the spatial domain into the inverse source problem in the one-dimensional Fourier domain,the source intensity angular spectrum vector in the Fourier domain is calculated by the one-dimensional method of moments.Then,using the discrete Fourier inverse transform,a multi-frequency angular spectrum method of moments is proposed to reconstruct the inverse source problem of the two-dimensional Helmholtz equation.The reconstruction accuracy and stability of this method are improved by optimizing the excitation wavenumber sequence.Simulation calculations show that the multi-frequency angular spectrum method of moments has high reconstruction accuracy and anti-noise ability,and can also design the reconstruction model according to the effective frequency band of the acoustic sensor to achieve the highest resolution.In addition,since the calculation of the coefficient matrix of the proposed method is independent of the distribution of the source intensity function and does not require regularization processing,when the size and resolution of the required source intensity distribution area are determined,after the coefficient matrix is calculated and saved,the source intensity function corresponding to the region of interest can be reconstructed according to different sound pressure detection data,with high calculation accuracy and efficiency.展开更多
The vectorial structure of an optical field with hybrid states of polarization （SOP） in the near-field is studied by using the angular spectrum method of an electromagnetic beam. Physical images of the longitudinal ...The vectorial structure of an optical field with hybrid states of polarization （SOP） in the near-field is studied by using the angular spectrum method of an electromagnetic beam. Physical images of the longitudinal components of evanescent waves are illustrated and compared with those of the transverse components from the vectorial structure. Our results indicate that the relative weight integrated over the transverse plane of the evanescent wave depends strongly on the number of the polarization topological charges. The shapes of the intensity profiles of the longitudinal components are different from those of the transverse components, and it can be manipulated by changing the initial SoP of the field cross-section. The longitudinal component of evanescent wave dominates the near-field region. In addition, it also leads to three-dimensional shape variations of the optical field and the optical spin angular momentum flux density distributions.展开更多
基金supported by the National Natural Science Foundation of China(51775121,12364055).
文摘Based on Fourier transform,the angular spectrum equation and its discrete model of the inverse source problem of the two-dimensional Helmholtz equation are derived.By transforming the two-dimensional inverse source problem in the spatial domain into the inverse source problem in the one-dimensional Fourier domain,the source intensity angular spectrum vector in the Fourier domain is calculated by the one-dimensional method of moments.Then,using the discrete Fourier inverse transform,a multi-frequency angular spectrum method of moments is proposed to reconstruct the inverse source problem of the two-dimensional Helmholtz equation.The reconstruction accuracy and stability of this method are improved by optimizing the excitation wavenumber sequence.Simulation calculations show that the multi-frequency angular spectrum method of moments has high reconstruction accuracy and anti-noise ability,and can also design the reconstruction model according to the effective frequency band of the acoustic sensor to achieve the highest resolution.In addition,since the calculation of the coefficient matrix of the proposed method is independent of the distribution of the source intensity function and does not require regularization processing,when the size and resolution of the required source intensity distribution area are determined,after the coefficient matrix is calculated and saved,the source intensity function corresponding to the region of interest can be reconstructed according to different sound pressure detection data,with high calculation accuracy and efficiency.
基金supported by the Zhejiang Provincial Natural Science Foundation,China(Grant Nos.LZ17A040001 and LY16A040014)the National Natural Science Foundation of China(Grant Nos.11574271 and 11574272)+1 种基金the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministrythe Science Research Foundation of Zhejiang Sci-Tech University(ZSTU),China(Grant No.14062078-Y)
文摘The vectorial structure of an optical field with hybrid states of polarization （SOP） in the near-field is studied by using the angular spectrum method of an electromagnetic beam. Physical images of the longitudinal components of evanescent waves are illustrated and compared with those of the transverse components from the vectorial structure. Our results indicate that the relative weight integrated over the transverse plane of the evanescent wave depends strongly on the number of the polarization topological charges. The shapes of the intensity profiles of the longitudinal components are different from those of the transverse components, and it can be manipulated by changing the initial SoP of the field cross-section. The longitudinal component of evanescent wave dominates the near-field region. In addition, it also leads to three-dimensional shape variations of the optical field and the optical spin angular momentum flux density distributions.
