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186   5 Near Field
                             (a)                                (b)
                                                                   PLC grating
                                        +
                                       Ar laser
                                                                                   Gold
                                                                      Water        particle   150
                                                  Sample chamber
                                                                                            mm
                                        CCD
                                                      Optical box  Coverslip  Lasers  {  l=1060nm
                                             PMT
                                                                                    l=488nm
                                                   YAG laser              Sample chamber
                            Fig. 5.22. Photograph of experimental setup of SNOM (a), and enlarged view of
                            sample chamber (b)


                            laser beam has a higher trapping efficiency than the downward one [5.25].
                            Figure 5.22a shows a photograph of the setup. The gold particle at the focal
                            point of the objective lens is in the medium of a coverslip-shield chamber and
                            is pushed onto the sample surface and scanned as shown in Fig. 5.22b.
                               An Ar +  laser (λ = 488 nm) is focused through the same objective to
                            illuminate the particle. The scattered light from the gold particle is collected
                            through the objective and imaged on the pinhole (5 µm in diameter) in front
                            of a PMT. The scattered light variation due to the interaction between the
                            gold particle and the sample surface is recorded on a personal computer (PC).
                            A CCD camera observes the operation of the gold particle in the medium. All
                            the optical elements, except the mirrors to guide the Nd:YAG laser and Ar +
                            laser, are installed inside the optical box for easy operation.

                            Trapping Principle

                            A metallic Rayleigh particle (much smaller than the wavelength) can be op-
                            tically trapped at the focal point by the gradient force. The particle in such
                            a tightly focused beam is polarized by the electric field and drawn into the
                            beam focus by the large intensity gradients created in both the axial and
                            transverse directions. The gradient force F grad for the Rayleigh particle is
                            given by [5.4,5.8]
                                                         1            2
                                                  F grad =  n 1 α grad |E|  ,             (5.20)
                                                         4
                            where n 1 is the refractive index of the medium, α is the polarizability of the
                            gold particle and E is the electric field. The polarizabiliy is given as
                                                               2
                                                              m − 1  3
                                                     α =4πεε r      r ,                   (5.21)
                                                              m +2
                                                               2
                            where m is the relative refractive index of the particle to the medium, r is the
                            radius and ε is the electric permitivity of the particle, and ε r is the free-space
                            permitivity.
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