azu_td_1349475_sip1_... - Arizona Campus Repository

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Setting w (x) equal to zero and solving first for the case of a lens with no 20 aberrations, the integral in Equation 2.6 may be converted into polar coordinates, | «muz 2 I exp[-{\+o 2 ) r 2 ] 2itrdr Jo 2.8 Rmax is the maximum radius of the exit pupil as determined by h, the aperture stop radius, r = -hmax ®S. 2.9 To maximize coupling between the source and receiving fibers, the mode profile of the source must match the mode profile of the receiver. Setting a equal to one to satisfy this condition, and solving Equation 2.8 gives the coupling efficiency between the two fibers, T = [l-exp{-2r% iax)] 2 m 2.10 Equation 2.10 may be rewritten in terms of the NA of the source fiber and lens NA. With the aperture stop at the lens, the lens NA is defined by NA lens = - h 7 R 2.11 where R' is the distance from the exit pupil plane to the image plane. For a Gaussian mode, the NA of the source fiber defined on the receiver side of the
lens is, 21 NAflber = ^=m^. R R . 2.12 Assuming a one to one imaging condition, the magnification (m) is equal to one. Substituting Equations 2.11 and 2.12 into Equation 2.9 and solving for r max yields 2.13 The coupling efficiency may now be written in terms of the lens NA, 2.14 The NA of the lens will effect how efficiently light from the source fiber is coupled into the receiving fiber. If the lens does not collect all the light from the source, the coupling efficiency between the source and receiving fibers will decrease. From section 2.1, it was shown that the mode diameter at the fiber end was 1.28 times larger than the fiber core. Hence the NA of the lens needs to be larger than the NA of the source fiber to capture all of the signal for efficient coupling. Figure 2-1 is a plot of Equation 2.14 showing this effect. At a lens NA to fiber NA ratio of 1.6, transmission loss is less than 0.06 dB and coupling efficiency is approximately 99%.
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: 19 power coupling efficiency, T, be
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 and 32: 27 Propagation Distance (mm) Figure
Page 33 and 34: 29 spherical wave emitted from a po
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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