The Helmholtz equation is reduced to the Schrodinger-like equation and then the quantities representing the gross features for a paraxial optical beam,such as the width,divergence,radius of curvature of the wave front...The Helmholtz equation is reduced to the Schrodinger-like equation and then the quantities representing the gross features for a paraxial optical beam,such as the width,divergence,radius of curvature of the wave front,complex beam parameter,beam quality factor,and the potential function representing beam propagation stability,are studied by using the quantum mechanical methods.The results derived in other ways previously are rederived by ur formulation in a more systematical and explicit fashion analytically,and some new results are demonstrated.The general equations for the evolution of these quantities,i.e.,the first-and second-order differential equations with respect to the propagation distance,such as the universal formula for the width and curvature radius,tl~e general formula for the first derivative of the complex beam parameter with respect to the axial coordinate,the general formula for the second derivative of the width with respect to the axial coordinate,and some general criteria for the conservation of the beam quality factor and the existence of a potential well of the potential function,are derived.We also discuss the application of our formulation to nonlinear parabolic-index media.展开更多
Starting from the vector field theory,the expression of the time average energy flow densityof a paraxial scalar light beam is deduced.In terms of this expression,the x(or y)directional weighted deviation is reasonabl...Starting from the vector field theory,the expression of the time average energy flow densityof a paraxial scalar light beam is deduced.In terms of this expression,the x(or y)directional weighted deviation is reasonably defined between the real-beam wavefrontand an imaginary ellipsoidal wavefront which is used to replace the real-beam wavefront.It is proved that,when Rx and Ry are just the x and y directional effective radii of curvature,respectively,the ellipsoidal wavefront Le=x^(2)/(2Rx)+y^(2)/(2 Ry)is the best-fit one for the real-beam wavefront L.Finally,the above results are generalized for a general polychrornatic light beams.展开更多
基金Supported partly by the National Natural Science Foundation of China under Grant No.69789801the Guangdong Natural Science Foundation of China under Grant No.970842and the National Hi-Tech Inertial Confinement Commit tee.
文摘The Helmholtz equation is reduced to the Schrodinger-like equation and then the quantities representing the gross features for a paraxial optical beam,such as the width,divergence,radius of curvature of the wave front,complex beam parameter,beam quality factor,and the potential function representing beam propagation stability,are studied by using the quantum mechanical methods.The results derived in other ways previously are rederived by ur formulation in a more systematical and explicit fashion analytically,and some new results are demonstrated.The general equations for the evolution of these quantities,i.e.,the first-and second-order differential equations with respect to the propagation distance,such as the universal formula for the width and curvature radius,tl~e general formula for the first derivative of the complex beam parameter with respect to the axial coordinate,the general formula for the second derivative of the width with respect to the axial coordinate,and some general criteria for the conservation of the beam quality factor and the existence of a potential well of the potential function,are derived.We also discuss the application of our formulation to nonlinear parabolic-index media.
基金Supported by the National High Technology(863-416)Foundation of China.
文摘Starting from the vector field theory,the expression of the time average energy flow densityof a paraxial scalar light beam is deduced.In terms of this expression,the x(or y)directional weighted deviation is reasonably defined between the real-beam wavefrontand an imaginary ellipsoidal wavefront which is used to replace the real-beam wavefront.It is proved that,when Rx and Ry are just the x and y directional effective radii of curvature,respectively,the ellipsoidal wavefront Le=x^(2)/(2Rx)+y^(2)/(2 Ry)is the best-fit one for the real-beam wavefront L.Finally,the above results are generalized for a general polychrornatic light beams.
