1 / 20

OPTICAL SYSTEM FOR VARIABLE RESIZING OF ROUND FLAT-TOP DISTRIBUTIONS

This paper presents an optical system for resizing round flat-top distributions by imaging and resizing flat-top beams. The system is experimentally validated, showing promising results for obtaining flat-top spots at a target plane.

annedavis
Download Presentation

OPTICAL SYSTEM FOR VARIABLE RESIZING OF ROUND FLAT-TOP DISTRIBUTIONS

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. OPTICAL SYSTEM FOR VARIABLE RESIZING OF ROUND FLAT-TOP DISTRIBUTIONS George Nemeş, Astigmat, Santa Clara, CA, USA gnemes@astigmat-us.com John A. Hoffnagle, IBM Almaden Research Center, San Jose, CA, USA hoffnagl@almaden.ibm.com

  2. OUTLINE 1. INTRODUCTION 2. OPTICAL SYSTEMS AND BEAMS – MATRIX TREATMENT 3. VARIABLE SPOT RESIZING OPTICAL SYSTEM (VARISPOT) 4. EXPERIMENTS 5. RESULTS AND DISCUSSION 6. CONCLUSION

  3. 1. INTRODUCTION • Importance of flat-top beams and spots • Obtaining flat-top beams • - Directly in some lasers, at least in one transverse direction • (transverse multimode lasers; excimer) • - From other beams with near-gaussian profiles – beam shapers • (transverse single-mode lasers) • Obtaining flat-top spots at a certain target plane • - Superimposing beamlets on that target plane (homogenizing) • - From flat-top beams by imaging and resizing  this work

  4. 2. OPTICAL SYSTEMS AND BEAMS: MATRIX TREATMENT Basic concepts: rays, optical systems, beams Ray: R RT = (x(z) y(z) u v)

  5. Optical system: S A11 A12 B11 B12 A B A21 A22 B21 B22 S == C D C11 C12 D11 D12 C21 C22 D21 D22 • Properties: • 0 I 1 0 0 0 • S J ST = J ; J = ; J2 = - I; I = ; 0 = • - I 0 0 1 0 0 • ADT – BCT = I • ABT = BATdet S = 1; S - max. 10 independent elements • CDT = DCT • A, D elements: numbers • B elements: lengths (m) • C elements: reciprocal lengths (m-1) • Ray transfer property of S:Rout= S Rin

  6. Beam: P Beams in second - order moments: P = beam matrix <x2> <xy> <xu> <xv> <xy> <y2> <yu> <yv> W M W elements: lengths2 (m2) P = <RRT> = =;M elements: lengths (m) <xu> <yu> <u2> <uv> MT U U elements: angles2 (rad2) <xv> <yv> <uv> <v2> Properties: P > 0; PT= P  WT= W; UT= U; MT M  P - max. 10 independent elements Beam transfer property (beam "propagation" property) of S: Pout = S Pin ST W = W I Example of a beam (rotationally symmetric, stigmatic) and its "propagation" M = M I U = U I W= W0W2 = AATW0 + BBTU0 In waist: M = 0 ; Output M2 = ACT W0 + BDTU0 U = U0 plane: U2 = CCT W0 + DDTU0 Beam spatial parameters: D = 4W1/2; q = 4U1/2; M2= (p/4)D0q/l; zR = D0/q

  7. 3. VARIABLE SPOT RESIZING OPTICAL SYSTEM (VariSpot) Block diagram 3 - lens system: + cyl. lens, cyl. axis vertical ( f, 0) - cyl. lens, cyl. axis rotatable about z (-f, a) + sph. lens (f0) + free-space of length d = f0 (back-focal plane) + Cyl. (f, 0) – Cyl. (–f, α) Sph. f0 Quasi – Image Plane y x Round spot D(α) z Incoming beam D0 f0

  8. VariSpot input-output relations W2 = W2I; W2 = A2 W0 + B2 U0 W2(a) = [(f02/f2) sin2(a)] W0 + (f02) U0 = W0 [(f02/f2) sin2(a) + f02/z2R] D(a) = D0 [(f02/f2) sin2(a) + f02/z2R]1/2 = Dm[1 + sin2(a)/sin2(aR)]1/2 Compare to free-space propagation: D(z) = Dm[1 + z2/z2R]1/2 Dm = D2(a = 0) = D0 f0 / zR = q0 f0 DM = D2(a = p/2) = D0 [(f02/f2) + f02/z2R]1/2D0 f0/ f (for f/zR <<1) sin(aR) = f/zR;aR = “angular Rayleigh range” Perfect imager  B = 0  W2 = A2 W0 beam-independent “Image-mode” of optical system + incoming beam (beam-dependent - Rayleigh range zR): A2 W0 >> B2 U0 A2 >> B2/z2R f/zR = sin(aR) << sin(a)  1 VariSpot“image-mode”  D(a)  D0 (f0/f) sin(a)

  9. 4. EXPERIMENTS Experimental setup

  10. Data on experiment Incoming beam data (l = 514 nm) CCD camera data (type Dalsa D7) - Gaussian beam Pixel size: 12 mm D0 = 4.480 mm Detector size: 1024 x 1024 pixels q = 0.154 mrad Dynamic range: 12 bits (4096 levels) zR = 29.1 m Noise level: 2 levels M2 = 1.05 Attenuator: Al film; OD  3 - Flat-top (Fermi-Dirac) beam D0 = 6.822 mm q = 0.149 mrad zR = 45.8 m M2 = 1.55 VariSpot data fCyl = +/- 500 mm f0 = 1000 mm a = - 900 - 00 - 900 (manually rotatable mount, +/- 0.250 resolution)

  11. Fermi-Dirac (F-D) beam profile I(r) = I0 / {1 + exp [b (r/R0 - 1)]} R0 = 3.25 mm b = 16.25 I0 = 0.0298 mm2 M2(ideal F-D) = 1.50 M2(experimental F-D) = 1.55

  12. 5. RESULTS AND DISCUSSION Exact  D(a) = D0 [(f02/f2) sin2(a) + f02/z2R]1/2 = = Dm[1 + sin2(a)/sin2(aR)]1/2 Image-mode D(a) D0(f0/f)sin(a) = DMsin(a) Gaussian beam D(a) vs. a D(a) vs. sin(a) E = dmin/dmax vs. a

  13. Exact  D(a) = D0 [(f02/f2) sin2(a) + f02/z2R]1/2 = = Dm[1 + sin2(a)/sin2(aR)]1/2 Image-mode D(a)  D0(f0/f)sin(a) = DMsin(a) Flat-top (Fermi-Dirac) beam D(a) vs. a D(a) vs. sin(a) E = dmin/dmax vs. a

  14. Estimating the zoom range in image-mode (“angular far-field”) D(a) vs. a (small angles) Kurtosis vs. a Blue lines  Image-modea 40 D(a) D0(f0/f)sin(a) = DMsin(a) a 30 - 40 Zoom range in image-mode (FD  FD) 13 x - 15 x

  15. Examples of spots - Gaussian beam Incoming gaussian beam; D0 = 4.480 mm Gaussian beam in back-focal plane of f0 = 1 m spherical lens Df = 0.154 mm

  16. Examples of spots - flat-top (Fermi-Dirac) beam Incoming Fermi-Dirac beam; D0 = 6.822 mm Fermi-Dirac beam in back-focal plane of f0 = 1 m spherical lens Df = 0.149 mm

  17. Examples: VariSpot at working distance Gaussian beam a = 500 a = 100a = 40 Fermi-Dirac beam a = 500

  18. Discussion - Zoom (image-mode) range (DM/Dmin) scales with zR/f - Variable spot size scales with f0 - Cheap off the shelf lenses used, no AR coating - This arrangement already shows (13 - 15) : 1 zoom range for flat-top profiles. Dmin 1.0 mm; DM 13.6 mm - Estimated (20 - 50) x zoom range for flat-top profiles - Estimated 50 mm minimum spot size with flat-top profile - Analysis  smaller spots in “focus-mode”, (“Fourier-transformer-mode”, “angular near-field”) regime (not discussed here)

  19. Prototype Zoom = 7 : 1 Dmin 1 mm; DM 7 mm

  20. 6. CONCLUSION • New zoom principle demonstrated to resize a flat-top beam at a fixed working distance • Zoom factor (dynamic range of flat-top spot sizes): (13 - 15) : 1 • Dmin1.0 mm; DM 13.6 mm • Reasonable good round spots with flat-top profiles • Estimated results using this approach (with good incoming flat-top beams and good optics): Dmin 50 mm Zoom factor: (20 - 50) : 1

More Related