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ENE 451

ENE 451. Fundamental of Optical Engineering Lecture 9. Antireflection Coating. The amount of light reflected when a beam moves from one media to another can be reduced by placing a thin coating layer between them. Antireflection Coating. A 12 A 23 > 0 and we want R min .  cos  = -1.

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ENE 451

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  1. ENE 451 Fundamental of Optical Engineering Lecture 9

  2. Antireflection Coating • The amount of light reflected when a beam moves from one media to another can be reduced by placing a thin coating layer between them.

  3. Antireflection Coating • A12A23 > 0 and we want Rmin.  cos = -1.

  4. Example • n1 = 1.5, n3 = 1.7. What should be n2 for antireflection film?

  5. Example • Find the thinnest film to be coated to prevent the reflected light give n1 = 1 and n3 = 3.6 if λ=0.83μm.

  6. Non-normal Incidence

  7. Non-normal Incidence • Consider the case of non normal incidence as shown in the previous figure. • The emerging beam travels with an optical-path difference between them as

  8. Non-normal Incidence • By Snell’s law, and , this yields • Then we have

  9. Non-normal Incidence • So that, an optical-path difference is • As EB = tcost , finally,we have

  10. Non-normal Incidence • Therefore, a round trip phase shift in this case equals to • Therefore,

  11. Example • Consider a film of thickness t and refractive index 1.6 sandwiched between two media of refractive index 1.5. • (a) determine all values of t for which the reflectance will be a maximum at normal incidence for λ = 1 μm and calculate the reflectance.

  12. Example • (b) For an angle of incidence of 20 relative to the normal, calculate the wavelength at which the reflectance will maximum. Use the smallest value of t determined in (a).

  13. Example • (c) Calculate the reflectance for both s- and p-polarization for the case considered in (b).

  14. Interferometers • These are instruments which utilize coherent summation of wave amplitudes. • Two beam interferometer:

  15. Mach-Zehnder Interferometer

  16. Mach-Zehnder Interferometer • In general, BSx =  + BSz • Assume they are lossless beam splitters. • For 50:50 beam splitter.

  17. Mach-Zehnder Interferometer

  18. Example • Suppose in a MZ interferometer for λ = 0.6328 μm, PAx = 0 and PAz = Pin. Then, a microscope slide 2 mm thick with a reflective index of 1.55 is placed in one arm of the interferometer. What are the new values of Pax and Paz.

  19. Michelson Interferometer

  20. Michelson Interferometer

  21. Example • For a Michelson interferometer in air with λ = 1.06μm, Pout = 0.5 Pin. One of the mirrors is displaced by increasing L1 continuously and Pout increases continuously to a final value of 0.65 Pin. How large is the displacement?

  22. Fabry-Perot Interferometer

  23. Fabry-Perot Interferometer • After one round trip • After 2 round trips

  24. Fabry-Perot Interferometer • After n round trips • Steady state (N )

  25. Fabry-Perot Interferometer • Therefore,

  26. Fabry-Perot Interferometer • If  = 0 (lossless resonator), e- = 1

  27. Fabry-Perot Interferometer

  28. Example Light from a laser of wavelength λis transmitted through a lossless Fabry-Perot interferometer in air. The mirror reflectances are equal to R. As the mirror separation is increased from an initial value, the transmitted power increases to a maximum of 21 mW for a mirror separation D. As the mirror separation is further increased D+0.25 μm, the transmitted power decreases to a minimum of 0.3 mW. (a) What is λin μm? (b) What is R? (c) What is the transmitted power when the mirror separation is D + 0.99 μm?

  29. Example • Soln

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