CREATING UNCONVENTIONALLY

Transcription

1 CREATING UNCONVENTIONALLY POLARIZED BEAMS BY STRESS INDUCED BIREFRINGENCE Jacob Chamoun Cornell University Advisors: Dr. John Noe Dr. Marty Cohen October 25, 2010

2 OUTLINE Theory i. Birefringence ii. Cylindrical vector beams Experiment i. Discrete space variant wave plates ii. Stress-engineered optical element (SOE) Results i. SOE between linear polarizers ii. Stokes polarimetry

3 BIREFRINGENCE Birefringence is a property of some materials in which incoming LP light is decomposed into two orthogonal components which travel at different speeds in the material Results from anisotropy in medium, which can come from: i. Natural crystal anisotropy ii. Stress/bending iii. Electric field (Pockels effect) or magnetic field (Faraday rotation) Can be used to change the polarization of light (wave plates)

4 FIBER POLARIZATION CONTROLLER Stress in the fiber core can change the polarization of light in single mode fiber Can be corrected using a fiber polarization controller, a device that takes advantage of stress birefringence source: thorlabs.com Output polarization responds to both winding and twist For winding, can easily derive an analytical result for retardance/length

5 CYLINDRICAL VECTOR BEAMS The wave equation for E-M waves in free space is a vector equation, so we can choose any set of basis vectors that spans the space Can reduce to a scalar equation by picking basis vectors, i.e. x-y-z, which lead to spatially constant linear or circular polarizations, but what if we used ρ-φ-z? Radially, azimuthally polarized beams

6 WHY CYLINDRICAL VECTOR BEAMS? Interesting topology in the polarization structure, full Poincare beams Radial polarization has useful focusing characteristics the longitudinal component can be focused better than a comparable LP beam; high focusing can be used for: i. High precision imaging/lithography ii. Second harmonic generation iii. Laser cutting/ablation Can associate angular momentum with beams

7 1 WHY CVB S 1 D. Biss and T. Brown, "Polarization-vortex-driven second-harmonic generation," Opt. Lett. 28, (2003).

8 MOTIVATION: SPATIALLY-VARYING WAVE PLATES 1 Approximations to these polarizations can be achieved using discrete wave plates 1 Alexis K. Spilman and Thomas G. Brown, "Stress birefringent, spacevariant wave plates for vortex illumination," Appl. Opt. 46, (2007)

9 SPATIALLY-VARYING WAVE PLATES Fun geometry problem

10 STRESS-INDUCED BIREFRINGENCE Directional stress breaks symmetries in a material, resulting in birefringence Retardance depends on wavelength, so color separation occurs Can be used to determine stress contours in a mechanical model Stress-optical coefficients p ij relate stress to change in index

11 CONTINUOUS VARIATION USING STRESS By applying a radially symmetric (m>2) force, continuously varying stress will develop Opto-elastic effects produce a spatially varying fast axis that lines up with directions of principle stress

12 APPLYING STRESS Using plexiglass as the optical material because it is more stress-optically active, more durable, and cheaper than glass

13 RESULTS Movie shows output as analyzer is rotated CCW: lobes rotate CW, indicating a counterrotating polarization pattern

14 ANALYSIS Polarimetry (using the Stokes parameters) gives a more accurate picture of the polarization structure of the beam Can extract polarization ellipse parameters (A,B,θ,h) from four measured irradiances (I,Q,U,V) Stokes vectors/mueller matrices are an alternative to Jones vectors/matrices for describing polarization

15 RESULTS ~1/8 in = 3mm

16 RESULTS

17 RESULTS Higher stress gradient results in 2 or 3 rings of half-wave retardance Circularly polarized illumination reveals contours of equal retardance

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19 CONCLUSIONS Unconventionally polarized beams can be created using stress birefringence Plexiglass advantages: i. less stress required ii. pattern could be frozen in Disadvantages: i. more deformation ii. tough to polish Conoscopic interference

20 REFERENCES Alexis K. Spilman and Thomas G. Brown, "Stress birefringent, space-variant wave plates for vortex illumination," Appl. Opt. 46, (2007) Dennis G. Hall, "Vector-beam solutions of Maxwell s wave equation," Opt. Lett. 21, 9-11 (1996) R. Ulrich, S. C. Rashleigh, and W. Eickhoff, "Bending-induced birefringence in single-mode fibers," Opt. Lett. 5, (1980) Single-mode fibre fractional wave devices and polarisation controllers H.C. Lefevre, Electron. Lett. 16, 778 (1980), DOI: /el: D. Biss and T. Brown, "Polarization-vortex-driven second-harmonic generation," Opt. Lett. 28, (2003). THANKS My thanks to Dr. Noe, Dr. Cohen, Prof. Metcalf, the other REU students, Stony Brook University, and the NSF for making this work possible. Special thanks to Jeff, Walter, and JT at the Stony Brook machine shop, and Giovanni Milione from CCNY