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ENE 451

ENE 451. Fundamental of Optical Engineering Lecture 8. Example of polarizations. A linearly polarized plane wave with Ē vector described by

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ENE 451

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  1. ENE 451 Fundamental of Optical Engineering Lecture 8

  2. Example of polarizations • A linearly polarized plane wave with Ē vector described by is incident on an optical element under test. Describe the state of polarization of the output wave (linear, elliptrical, or circular) if the optical element is:

  3. Example of polarizations • (a) A linear polarizer oriented to transmit light polarized in the ex direction.

  4. Example of polarizations • (b) A half-wave plate with birefringence axes oriented to coincide with ex and ey.

  5. Example of polarizations • (c) A half-wave plate with birefringence axes oriented at 45º relative to ex and ey .

  6. Example of polarizations • (d) A quarter-wave plate with birefringence axes oriented to coincide with ex and ey .

  7. Example of polarizations • (e) A quarter-wave plate with birefringence axes oriented at 45º relative to ex and ey .

  8. Example of polarizations • (f) A half-wave plate with birefringence axes oriented at 25º relative to ex and ey .

  9. Example of polarizations • (g) A quarter-wave plate with birefringence axes oriented at 25º relative to ex and ey .

  10. Example of polarizations • A linearly polarized light propagating in the z-direction with polarization vector in the x-direction is incident on a birefringent crystal. What is the state of polarization of the light after passing through the crystal if: (a) the crystal is a quarter-wave plate with optic axis in the xy plane oriented at 30º relative to the y-axis?

  11. Example of polarizations • (b) the crystal is a half-wave plate with optic axis in the y-direction?

  12. Example of polarizations • (c) the crystal is a half-wave plate with optic axis in the xy plane oriented at 11º relative to the x-axis?

  13. Example of polarizations • (d) the crystal is a quarter-wave plate with optic axis in the xy plane oriented at 45º relative to the y-axis?

  14. Example of polarizations • (e) the crystal is a quarter-wave plate with optic axis in the z-direction?

  15. Example of birefringence • For a birefringent median with n0 = 1.654 and nE = 1.485 as shown in the figure. Find the length L that makes it be (a) a full wave plate (b) a half wave plate (c) a ¼ -wave plate if the wavelength is 656 nm.

  16. Example of birefringence

  17. Electrooptic modulator • This makes use of electrooptic effect (applied electric fields used to change the optical properties). • There are 2 kinds of electrooptic effect: linear and quadratic.

  18. Pockels effect • The linear electrooptic effect is called “Pockels effect”. • This refers to the change in the indices of the ordinary and extranordinary rays proportional to applied electric field. • This effect exists only in crystals without an inversion symmetry such as LiNbO3.

  19. Kerr effect • For a crystal with an inversion symmetry, the linear electrooptic effect can not exist, while the quadratic electrooptic effect known as “Kerr effect” is observed. • This is where the induced index change is proportional to the square of applied electric field.

  20. Optical modulator

  21. Optical modulator • V (pi-voltage) or half-wave voltage is the applied voltage that makes the relative phase shift be  in a cube of material. • In general, = refractive index changes produced by applied voltage.

  22. Optical modulator • It is preferable to design L >> h to have a low applied voltage V. • After applying a voltage, indices are changed as

  23. Example • V for the material is 2,700 V, L = 2 cm, and h = 0.5 mm. Find applied voltage V to have Δ =  (complete extinction).

  24. Example • An electrooptic crystal has dimensions of 2x2x3 along the x,y, and z axes with nE = 1.487 and nO = 1.536. An input wave propagating in the z-direction at λ = 0.63 μm is linearly polarized at a 45º angle relative to the x- and y- axes. A voltage V applied across the crystal in the x-direction. The voltage is increased from V = 0 until, when V = 245 V, the output polarization from the crystal is the same as that observed for V = 0. Assume that optic axis is along the y-axis. • (a) What is the total phase retardation, in rad, for V = 0? • (b) What is pi-voltage for the material? • (c) What is the refractive index change Δnx produced by the applied voltage of 245 V, assuming Δny =0?

  25. Interference in thin films • Recall: interference eq.

  26. Interference in thin films • Assume that

  27. Interference in thin films • Reflectance • We can consider R into 3 cases: • n1 = n3. • n1 < n2, n2>n3 , n1≠ n3. • n1 < n2 < n3.

  28. Interference in thin films • Case 1: n1 = n3 • From a definition: Aij = Aji

  29. Interference in thin films • Max in R for • Min in R for

  30. Example • n1 = 1.5, n2 = 1.6, and λ = 0.63 μm. Find t2 for Rmax and Rmin.

  31. Interference in thin films • Case 2: n1 < n2, n2>n3 , n1≠ n3.

  32. Interference in thin films • Max in R for • Min in R for

  33. Example • n1 = 1.5, n2 = 1.6, n3 = 1.4, λ = 0.63 μm. Find t2 for Rmax and Rmin.

  34. Interference in thin films • Case 3: n1 < n2 < n3

  35. Interference in thin films • Max in R for • Min in R for

  36. Example • n1 = 1.5, n2 = 1.6, n3 = 1.7, λ = 0.63 μm. Find t2 for Rmax and Rmin.

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