高斯光速过透镜.pptxVIP

会计学1高斯光速过透镜 1 Strongly focused Gaussian beamsWe use a set of eigenmodes of four commuting operators corresponding to the following four physical quantites:energy angular momentum in z direction momentum in the z direction helicity The modes are thus characterized by the four numbers 第1页/共17页 The complete orthogonal set of modes is defined such that the free electric field (the solution of the source-free Maxwell equations) can be expanded in this set as is arbitrary complex amplitudes.The function is transverse, the summation over v is a short-hand notation for第2页/共17页 正交条件第3页/共17页 For the remainder of this section ,we will only consider monochromatic beams propagating in the positive z direction. we take as a mode number instead of , and we reduce set of mode numbers by 第4页/共17页 The action of the lens is modeled here by assuming that the field distribution of the incoming field is multiplied by a local phase factor A ideal parabolic lens would be represented by a phase factor In the plane of the lens 第5页/共17页 If we approximate the incoming beam by a circularly polarized (lowest-order) Gaussian beam with Rayleigh range 第6页/共17页 第7页/共17页 When the paraxial limit is valid for the outgoing beam, i.e., when, and correspond. But also outside the paraxial limit, the focused light beam is characterized by the two parameters and . 第8页/共17页 第9页/共17页 The largest component of the output field is the component, which is given by When the paraxial approximation is valid for the outgoing beam, we may take out a factor extend the integration limit to infinityuse defining 第10页/共17页 第11页/共17页 Outside the paraxial limit, the focal plane is no longer at z=z0 but moves towards the lens by several wavelengths, furthermore, unlike in the paraxial approximation, the shape of the field is not just determined by the value of