1MIT 2.71/2.71009/12/05 wk2-a-1Prisms, fibers, and reflective lenses• Total internal reflection•Prisms• Dispersion• Optical fibers and other waveguides• Reflection from paraboloidal mirrorsMIT 2.71/2.71009/12/05 wk2-a-2Total Internal Reflection (TIR)θθnn′reflectedincident...? 1sin ifwhat sinsin sinsin>′′=′⇒′′=θθθθθnnnnnnE.g. interfacefrom glass to airn=1.5, n’=1o8.41sinif 1sin1crit=′=>>′−nnnnθθθ2MIT 2.71/2.71009/12/05 wk2-a-3Total Internal Reflection (TIR)θθnn′reflectedincidentreflected isenergy all ,disappears beam reflected when imaginary becomes crit⇒>′θθθno light enters the opticallyless dense space(in actuality the light fieldin the optically dense spaceis evanescentevanescent, i.e.exponentially decaying)MIT 2.71/2.71009/12/05 wk2-a-4Prismsglassair airTIRTIRglassair airairair45°45°3MIT 2.71/2.71009/12/05 wk2-a-5Frustrated Total Internal Reflection (FTIR)nn′≈nAngle of incidenceexceeds critical angleReflected rays are missingwhere index-matched surfacestouch ⇒ shadow is formedair gapglassother materialTIRTIRno TIRno TIRMIT 2.71/2.71009/12/05 wk2-a-6Fingerprint sensorslaserilluminationfingerright-angleprismdigitalcamera4MIT 2.71/2.71009/12/05 wk2-a-7Optical waveguidesTIRTIRTIRTIRno TIRno TIR“planar” waveguide: high-index dielectric materialsandwiched between lower-index dielectricsMIT 2.71/2.71009/12/05 wk2-a-8Optical waveguides: numerical aperture (NA)TIRTIRTIRTIRno TIRno TIRhigh index contrast (n1/n2) ⇔ high NANA=sin(largest anglethat is waveguided)2n1nair(n=1)0θ1θ22210sinNA nn −≤=θ2n5MIT 2.71/2.71009/12/05 wk2-a-9Optical fiberscladding(lower index)core(higher index)Core diameter = 8-10µm (commercial grade)Cladding diameter = 250µm (commercial grade)Index contrast ∆n = 0.007 (very low NA)attenuation = 0.25dB/kmMIT 2.71/2.71009/12/05 wk2-a-10Optical fibers: gradient indexcladding(lower index)core ofgraduallydecreasingindexoptical rays “swirl” around the axis of the core!6MIT 2.71/2.71009/12/05 wk2-a-11Gradient index waveguides in nature:insect eyes (composite eyes)MIT 2.71/2.71009/12/05 wk2-a-12DispersionRefractive index n is function of the wavelengthwhite light(all visiblewavelengths)Newton’s prismredgreenblueglassair7MIT 2.71/2.71009/12/05 wk2-a-13Dispersion measuresReference color linesC (H- λ=656.3nm, red), D (Na- λ=589.2nm, yellow), F (H- λ=486.1nm, blue)Crown glass has52933.1F=n52300.1D=n52042.1C=n1DCF−−=nnnVCFD11nnnVv−−==Dispersive powerDispersive indexMIT 2.71/2.71009/12/05 wk2-a-14Curved reflecting surfaces(e.g. satellite dish)radiation from satellitereflectivedishdetector8MIT 2.71/2.71009/12/05 wk2-a-15Paraboloid mirror: perfect focusings(x)xz(e.g. satellite dish)What should the shape function s(x) be in order for the incoming parallel ray bundle to come to perfect focus?MIT 2.71/2.71009/12/05 wk2-a-16Paraboloid mirror: perfect focusings(x)xz(e.g. satellite dish)()fxxs42=ff: focal
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