高斯光速过透镜课件

1、Strongly focused light beams interacting with single atoms in free space,1,PPT学习交流,1 Strongly focused Gaussian beams,We 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 helic

2、ity The modes are thus characterized by the four numbers,2,PPT学习交流,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 sum

3、mation over v is a short-hand notation for,3,PPT学习交流,正交条件,4,PPT学习交流,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,5,PPT学习交流,The action of the lens is mod

4、eled 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,6,PPT学习交流,If we approximate the incoming beam by a circularly polarized (lowest-order) Gaussian beam wi

5、th Rayleigh range,7,PPT学习交流,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 .,8,PPT学习交流,The largest component of the output field is the component, which is giv

6、en by,When the paraxial approximation is valid for the outgoing beam, we may take out a factor extend the integration limit to infinity,use,defining,9,PPT学习交流,Outside the paraxial limit, the focal plane is no longer at z=z0 but moves towards the lens by several wavelengths, furthermore, unlike in th

7、e paraxial approximation, the shape of the field is not just determined by the value of but depends on as well,The plots of the transverse-mode profiles show that beyond a certain point the width of the field no longer decreases with stronger focusing. One cannot focus down a laser field to below a

8、certain limit, roughly about half a wavelength, with the idea lens factor, no matter how small becomes. Moreover, no one notes the asymmetry of the outgoing beam around the focal plane, in contrast to a paraxial beam that is symmetry under reflections in the focal plane, this fact should not be surp

9、rising.,10,PPT学习交流,FIG 1 (a) field strength,of strongly focused Gaussian beams on the z axis as a function,Note that maximum strength of the incoming field is 1. The lens is located at z=0 and characterized by, so that,The incoming Gaussian beam has increasing calues of,respectively, for the bottom

10、to top curves. This implies, for the outgoing beam, decreasing values of,(b) field strength in the focal plane as a function of the transverse coordinate,.,11,PPT学习交流,12,PPT学习交流,Fig. 2. Lommel field, which describes the focus of a lens with uniform illumination in the paraxial limit for the case NA

11、= 0.1 and f= 1000 .(a) Amplitude u( ) in the focal plane z = 0 according to relation (9). (b) Intensity distribution in the ( , z) plane according to relation (8). The intensity ( ) contours indicate intensities of , .; the intensity in the geometrical focus (0, 0) is normalized to 1.,13,PPT学习交流,In