Transcription of Fabry-Perot interferometers
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Fabry-Perot interferometers
1 MIT Optics10/24/05 wk8-a-1 Today s summary Multiple beam interferometers : Fabry-Perot resonators Stokes relationships Transmission and reflection coefficients for a dielectric slab Optical resonance Principles of lasers Coherence: spatial / temporalMIT Optics10/24/05 wk8-a-2 Fabry-Perot interferometers2 MIT Optics10/24/05 wk8-a-3 Relation between r, r and t, t aaratair glassa a r a t 12= + = ttrrrProof: algebraic from the Fresnel coefficientsor using the property of preservation of thepreservation of thefield properties upon time reversalfield properties upon time reversalglass airStokes relationshipsMIT Optics10/24/05 wk8-a-4 Proof using time reversalaaratair glassatt aratair glassatr artar2()()10 22= + = + = = +ttrattrarrtrra 3 MIT Optics10/24/05 wk8-a-5 Fabry-Perot InterferometerLincidentreflectedtransmit tedResonancecondition: reflected wave = 0 all reflected waves interfere destructivelynmL2 =wavelength in free spacerefractive indexMIT Optics10/24/05 wk8-a-6 Calculation of the reflected waveincoming areflected artransmitted atei reflected atei2 r transmitted atei t reflected atei3 (r )2transmitted atei2 r t reflected atei4 (r )3transmitted atei3 (r t )2reflected atei5 (r )4transmitted atei4 (r )3t air, n=1glass, nair, n=1 nL2=4 MIT Optics10/24/05 wk8-a-7 Calculation of the reflected wave()
2 MIT 2.71/2.710 Optics 10/24/05 wk8-a-3 Relation between r, r’ and t, t’ a ar at air glass a’ a’r’ a’t’ 2 + ′=1 ′=− r tt r r Proof: algebraic from the Fresnel coefficients or using the property of preservation of the field properties upon time reversal
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