tailieunhanh - Advances in Lasers and Electro Optics Part 12

Tham khảo tài liệu 'advances in lasers and electro optics part 12', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Beating Difraction Limit using Dark States 533 Fig. 1. a Energy diagram of a two-level system interacting with a strong drive field. b Distribution of the drive field intensity vs. a transverse spatial coordinate. c Dependence of the population excited in the atomic medium vs spatial position. _ i r rp pr 2 where r describes the relaxation processes. In particular for a two-level system the set of equation has the following form Pab VahPah I 3 Ila Yl1t I iiX tp phil . 4 where na paa nb pbb Fab Yab i Oab -v Yab 1 T2 Y 1 T1 T1 and T2 are corresponding longitudinal and transverse relaxation times . Solving Eqs. 3 4 in a steady-state regime we obtain pab f df 1 ab Then the population in the upper atomic level is given by na 2Re __ rab J 1 ab for the case of resonance v fflab it is reduced to 2 Q 271T2 - 1 4 Q 2T172 5 6 7 8 We now assume that the drive field has a spatial distribution of intensity. 534 Advances in Lasers and Electro Optics Q 2 Q 2 x . 9 where f x is the spatial distribution of the intensity of optical drive field. For example in the case of interference of two waves with wavevectors k1 and k2 the optical field is E Ele 7 l E2e - . 10 and intensity distribution is given by rf 2 i 2 2 2 2JEiE 2C0s E1-E2 r E1 - E 2 2 4 E1 2 sin22 Ei-E2 r 11 intensity at different spatial position changes between E1 - E2 2 and E1 E2 2. Introducing G 2 D0 2 T1T2 we can write Gf x l 2G x-r 12 Then for the drive field at the position being near to its zero the Rabi frequency is given by Q 2_ Qo 2 . 13 where Q0 z x0 L is the separation distance between the peaks of the drive field distribution for interference patern L E 2sin 6 2 E 2 . A typical excitation profile vs. x shown in Fig. 1 c demonstrates that the spatial width of excitation can be smaller than the intensity distribution of the optical field and even smaller than the spot size determined by diffraction limited size. Indeed the width of spatial distribution of excited atoms is given by A L L _ . .