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CHAPTER 3 28 DIFFRACTIVE LENS THEORY The advantages of using diffractive lenses and the intended application for them have been discussed in the preceding chapters. In this chapter, the discussion will focus on the basic operating principles and fabrication methods of diffractive lenses. It is necessary to point out there is a hierarchy of components that can be thought of as diffractive lenses. The operating effect of these components can be based on diffraction by a Fresnel zone plate (FZP). The operating principal of the FZP is thus considered first. This theory is then extended to discuss binary diffractive lenses, kinoforms, and multilevel approximations to the kinoform. The diffraction efficiency and method of fabrication of diffractive lenses are also discussed. 3.1 Basic Principles For a general case, a diffractive lens illuminated by a plane monochromatic wave (Figure 3-1) splits the incoming wave into many spherical waves or diffraction orders. The foci of the lens occur where these diffracted orders cross the optical axis. The diffraction angle of each order is controlled by the period of the lens and may be calculated using the grating equation. The amount of light directed into each of these orders is in turn determined by the shape of the lens which modulates the phase of the incoming wave. The principle of operation of a diffractive lens may be better understood by first examining the zone construction of Fresnel. 31,32 A monochromatic
29 spherical wave emitted from a point source at S and traveling to a point P maybe divided into circular zones. If the the radius of each zone is given as r-], T2> rg,... r m, then the distance from the edge of each zone to point P is given as f + A/2, f + 2A/2, f+ 3A/2,... f + mAV2 as shown in Figure 3-2. These zones are defined as Fresnei half period zones and there is a 7J2 optical path difference between successive zones. From Huygen's principle, each point on a spherical wave front maybe considered a source for a secondary wavelet of the same phase traveling to a point P on axis. The phase of the wavelets arriving at point P from points within successive zones will differ in phase by n due to the A/2 optical path difference introduced between successive zones. This means the amplitude of light reaching point P from successive zones will alternate in sign. The total light amplitude at point P is the sum of the amplitudes of light coming from each zone, A=Al -A2 + A3-.. .+(-l) mA A m 31 where A is the total light amplitude at P and A m is the amplitude of light from the m th zone. If a circular aperture of radius ^ + r 2 , for example, is placed in front of the wave front at a point Q, only the first two Fresnei half zones will be transmitted by the aperture. The resultant amplitude at point P will now be A= A\ - A2 3 2 which is approximately equal to zero. If instead an aperture consisting of alternating transparent and opaque zones matching the radii of the Fresnei half
Page 1: INFORMATION TO USERS This manuscrip
Page 5 and 6: DIFFRACTIVE MICROLENSES FOR FIBER O
Page 7 and 8: ACKNOWLEDGEMENTS 3 I would like to
Page 9 and 10: 5 Page 4.3 Photoresist Deposition 4
Page 11 and 12: 7 Page 4-2 Exposure test results fr
Page 13 and 14: ABSTRACT 9 The design, fabrication,
Page 15 and 16: 11 architectures. 3,4 5 8 In all of
Page 17 and 18: 13 microlenses have been presented
Page 19 and 20: 15 element acts as an interface bet
Page 21 and 22: CHAPTER 2 17 LENS PARAMETERS FOR FI
Page 23 and 24: 19 power coupling efficiency, T, be
Page 25 and 26: lens is, 21 NAflber = ^=m^. R R . 2
Page 27 and 28: 2.3 Chromatic Aberration 23 Despite
Page 29 and 30: 25 JL 0.985 0.99 0.995 .005 .015 >r
Page 31: 27 Propagation Distance (mm) Figure
Page 35 and 36: 31 zones is used, the light from ev
Page 37 and 38: 33 OPD=Jrl+f 2 3 3 The incident pla
Page 39 and 40: 3.3 Multi-level Diffractive Lenses
Page 41 and 42: 37 four level approximation. As the
Page 43 and 44: 39 a) T/N b) t(x) T/N ej2ro|> - I-*
Page 45 and 46: 41 A m = e-^sinci^j^t ij = 0 3.17 a
Page 47 and 48: 43 defining the structure of the le
Page 49 and 50: 45 where n is the index of the subs
Page 51 and 52: 47 B Q B mosiac aligned misaligned
Page 53 and 54: 49 4.3 Photoresist Deposition Shipl
Page 55 and 56: 51 Kfl A) 0 . . t .. .'i'S'l'lTtj
Page 57 and 58: 53 A. Substrate Preparation: 1. Soa
Page 59 and 60: 55 modulation is calculated using E
Page 61 and 62: Figure 4-5 Photographs from a scann
Page 63 and 64: 59 was taken as the distance the kn
Page 65 and 66: 61 SAMPLE 1 t IMAX=40.37% SAMPLE 2
Page 67 and 68: 63 670 nm Laser diode Microlens Arr
Page 69 and 70: 65 1 Experimental data n Ideal Gaus
Page 71 and 72: 67 /OwQ\ xCX /TK X~X Fiber Figure 5
Page 73 and 74: 5.4 Conclusions 69 The design, fabr
Page 75 and 76: Appendix A: MATLAB PROGRAM
Page 77 and 78: theta=4*lammm/pi/dmm; z=0:100; dg=d
Page 79 and 80: 75 4" MASK 1" SQUARE CENTER I NOTES
Page 81 and 82: TWP67 V=2mm H=5mm, 77 TWD671 BL1 AM
Page 83 and 84:
15 J.Jahns and A. Huang, "Planar in
Page 85:
"J.L. Vossen and W. Kem, Thin Film
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