Microsoft PowerPoint - Chapter 7.ppt

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1 E ˆ ˆ 0 = xexo ye yo (a) (b) (c) Polarization Linearly polarized Plane polarized Unpolarized Polarizer E = E cos( ω t kz) x xo E = E cos( ωt kz + ) y yo Add electric field components (1) () E = xe ˆ + ye ˆ = xe ˆ cos( ωt kz) ye ˆ cos( ωt kz) x y xo yo E = E cos( ω t kz) E ˆ ˆ 0 = xe ye o xo yo

2 E = Acos( ωt kz) x E = Asin( ωt kz) y E + E = A x y (5a) (5b) (6) (a) (b) (c) π π π π (a) (b) (c) (d) π π

3 I( ) = I(0)cos Liquid Crystal Liquid Crystal LCD There are many modes operation TN 90 deg twist STN 70 deg twist IPS in plane switching Patterned vertical alignment MVA multi-domain vertical alignment

$Principal refractive indices n 1, n and n 3 Principal axes x, y and z Biaxial crystals -Two optic axes Uniaxialcrystals -One optic axis (n 1 =n ) Positive, n 3 >n 1 Negative, n 3 <n 1 Crystals are$

4 Principal refractive indices n 1, n and n 3 Principal axes x, y and z Biaxial crystals -Two optic axes Uniaxialcrystals -One optic axis (n 1 =n ) Positive, n 3 >n 1 Negative, n 3 <n 1 Crystals are generally anisotropic Many properties depend on the crystal direction Electronic polarization depends on the crystal direction The refractive index, or dielectric constant, of a crystal depends on the direction of the electric field in the propagation beam. Noncrystalline materials and cubic crystals are For all classes of crystals, excluding cubic structures, the refractive index depends on the and the. Birefringence Doubly refracted Flurite Quartz Rutile Calcite Tourmaline

$direction => not necessary Optic axis Direction: two waves with the same velocity Opticalindicatrix-- Fresnel s refractive index ellipsoid Two orthogonally polarized EM waves Minor AOA n 1 =n =n o$

5 Two orthogonal linearly polarized waves Ordinary (o) wave Same velocity in all directions extraordinary (e) wave Velocity depends on the polarization direction Electric field phase propagation direction => not necessary Optic axis Direction: two waves with the same velocity Opticalindicatrix-- Fresnel s refractive index ellipsoid Two orthogonally polarized EM waves Minor AOA n 1 =n =n o Major BOB 1 cos sin = + n ( ) n n n 1 =n e o e n 1 =n =n o 1 cos sin = + n ( ) n n e o e (a) (b)

6 (a) (b) (a) (b) Cleaved form: rhombohedron: calcite rhomb Principal selection: contains optical axis and is normal toa pair of opposite crystal surfaces Optical absorption in a substance depends on the and of the light beam Dichroic crsytals E.g. tourmaline (aluminum borosilicate) o-wave is much more heavilyabsorped

7 α 0 < α α (a) (b) Positiveuniaxial: α π = ( ne no ) L

8 Optical Compensator: control the retardation S.-B. Compensator: control and analyze the polarization state Quartz Rutile Calcite Tourmaline 1 π = ( nd e + nd o ) π = ( nd o + nd e ) Phase difference = 1 π = ( ne no )( D d )

9 Quartz: right-handed or left handed (atomic Arrangement) Many biological substances, liquid solution (e.g. corn syrup) Specific rotatorypower (/L) Wavelength dependent E.g. quartz: 400nm, 650nm Diff. speeds for left and right circularly polarized waves, i.e., diff. n A linearly polarized wave Sum of left- and right-handed circularly polarized waves (fig. 7.18) π = ( nr nl) L Circular birefringence If the direction of the light wave is reversed, the ray simply itself. Optical activity the rotation of the plane of polarization by a substance spiraling or helical motion of electrons magnets Clockwise (dextrorotatory) or counterclockwise (levorotatory) retardation Observer receiving the wave α = β α β clockwise α β α β

10 Asymmetry in the structure (- n,-e) and (+ n, +E) Not in noncrystallinematerials Centrosymmetric materials, e.g. NaCl Only in noncentrosymmetric crystals, e.g. GaAs Depends on the directions of applied field, propagation and polarization. E.g. GaAs isotropic => uniaxial Uniaxial=> biaxial: e.g. KDP and LiNbO3 Propagation in z-direction (same in x, y directions) KDP Ea in z (Fig. 7.19(b)) LiNbO3 Ea in y (Fig. 7.19(c)) Induce birefringence Changes in refractive index of a material induced by application of an, which modulates the optical properties. External field Changes in electron motions or in crystal structure Changes in optical properties EO effects n = n+ ae+ ae + ' 1 ' 1 3 n1 n1+ nre 1 o ' 1 3 n n nre o r : Pockels coeffcient Pockels effect (linear effect) (a) (b) (c) n= ae 1 Kerr effect (second effect) n= ae = ( ke )

11 ' 1 3 ' 1 3 n1 n1+ nr 1 Eo and n n nr E πn πl 1 V ( ) d ' = L = n + 0 nr 0 o π 3 L = 1 = nr 0 V d = π <=> V = V / half-wave voltage Polarization modulator 45 Total e-field at the analyzer r Eo Eo E = x? cos( ωt) + y cos( ωt + ) Detected I = Io sin 1 Field pass through A 1 1 E = Eosin sin ωt+ I π V = Io sin V / Applied field distorts the electron motions n o => n e n=ke a I (a) (b) 45 /

12 π 3 L = x y =Γ nr 0 V LV d Spatial overlap efficiency: Γ=0.5~0.7 P P out out ( ) = cos (0) Integrated optics:

13 (a) (b) Photoelasticeffect Induced strain => refractive index change 1 = ps n Depends on the directions (Cf. Elements of Photonics) Piezoelectric effect Generation of strain by applying an external field (Fig. 7.8) Surface acoustic wave (SAW) by modulating voltage at RF Periodic n due to periodic S due to photoelasticeffect β. (π β PB( Lo) P (0) A = f( β)

14 Λ sin = /n : Bragg angle A A' B Λ P Λsin v O O' Q Λsin ω' = ω±ω due to Doppler effect Ω : acoustic wave freq. B' Faraday effect Optically inactive material, e.g. glass, is placed in a strong magnetic field (e.g. solenoid) Light polarization propagating in the direction of magnetic field is rotated = ϑbl ϑ : Verdet constant E.g. glass L=0 mm in B ~ 0.1T, =1º Comparison Optical activity Faraday effect = ϑbl ϑ : Verdet constant

15 P = εχ E+ εχ E and E = E sin( ωt) P o 1 o P = εχ E sin( ωt) εχ E cos( ωt) + εχe o 1 o 0 o ο o P + P - P + P ω ω P - (a) (b) (c) ± ω ω Linear P=εχE χ: electric susceptibility o Constructive interference => same velocity => n( ω) = n( ω) 3 Nonlinear P = εχ o 1E+ εχ o E + εχ o 3E χ 1 : linear susceptibility χ : second order susceptibility, non-centrosymmetric e.g. quartz (also piezoelectric) χ 3 : third order susceptibility

16 5. 眼睛在不同的亮度下, 其對不同波長的 sensitivity 也不同, 在正常亮度下, 對黃 - 綠光最敏感 (0.55 um) 在昏暗下, 對綠光 (0.51 um ) 較敏感 Index matching n ( ω) = n ( ω) e o at phase matching angle ω ω The relative sensitivity of the eye to different wavelengths for normal levels of illumination (photopic vision )and under conditions of dark adaption (scotopic vision) CFLIN Fundamental photon, k 1 Conservation of momentum v Conservation of energy ω ω ω = = = = v k k1 k1 Second harmonic photon, k hk + hk = hk 1 1 hω1+ hω1 = hω SHG is only effective over a coherence length π lc = k = k k1 k The relative sensitivity of rods and cones as a function of wavelength. hω 1 Photonic interpretation of second hω harmonic generation (SHG) 1 hω Fundamental photon, k 1 Dipole moment-photon interaction region CFLIN

17 Photopic and Scotopic Spectral Luminous Efficiency Functions V() Wavelength Photopic Scotopic Wavelength Photopic Scotopic Photopic and Scotopic Spectral Luminous Efficiency Functions V() Wavelength Photopic Scopotic Wavelength Photopic Scopotic

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投影片 1 Coherence ( ) Temporal Coherence Michelson Interferometer Spatial Coherence Young s Interference Spatiotemporal Coherence 參料 [1] Eugene Hecht, Optics, Addison Wesley Co., New York 2001 [2] W. Lauterborn,