Itroductio to Photoics Photo Optics ad Photo Statistics
Historical Origi Photo-electric Effect (Eistei, 905) Clea metal V stop Differet metals, same slope Light I Slope h/q ν c/λ Curret flows for λ < λ 0, for ay itesity of light pply stoppig potetial Higher voltage required for shorter λ The slopes are idepedet of light itesity, but curret is proportioal to light itesity. h ν qv + W E ph hν Eergy of light (Kietic eergy of the electro) + (Work fuctio) Eergy of quatum of light (Smallest eergy uit): Photo Lih Y. Li
Photo Eergy E hν ω h 6.63 0 h / π 34 Joule Sec : Plak s costat λ ( µ m).4 E (ev) Lih Y. Li 3
Photo Positio Heiseberg s Ucertaity Priciple ( z) ( p) 4 Photo positio caot be determied exactly. It eeds to be determied with probability. p ( r) d I( r) d Example: () Photo positio probability i a Gaussia beam. () Trasmissio of a sigle photo through a beam-splitter. () () Lih Y. Li 4
Plae wave Photo mometum Photo Mometum E( r, t) exp( jk r)exp( jπνt) eˆ p k p k h λ Radiatio Pressure p h λ Force: Pressure: p t Force rea h λ t N h λ Example: Photo-mometum recoil versus thermal velocity. Lih Y. Li 5
Optical Tweezer Forces arisig from mometum chage of the light F P t a I (a-b) q p Out (c-d) p q b p P B Q 3. µm Movig a DN-tethered bead with a optical tweezer (5 mw) (http://www.bio.bradeis.edu/~gelles/stall/) q pp Q c C Resultat gradiet force D d E.g., λ 064 m, P 00 mw, diameter of polystyree sphere 5 µm F 3.8 x 0 - N. shki, et al., Observatio of radiatio pressure trappig of particles by alteratig laser beams, Phys. Rev. Lett., V. 54, p. 45-48, 985 0 µm sphere (http://www.phys.umu.se/laser/tweezer.htm) Lih Y. Li 6
7 Lih Y. Li Photo Polarizatio Liearly Polarized Photos ( ) ( ) y x y y x x y x y x t j jkz t t j jkz t + ω + ω +, ) )exp( ˆ')exp( ˆ' ( ), ( ) )exp( ˆ)exp( ˆ ( ), ( ' ' ' ' y x r E y x r E Photo polarized alog x-directio Example: Trasmissio of a liearly-polarized photo through a polarizer
Quatum Commuicatio Secured Iformatio Trasmissio with Sigle Photos Qubit: α 0>+β > lice Bob Codig Ecryptio (Determie α ad β) Eve Without the key give by lice, obtais the wrog result with high probability, ad destroys the qubit. With the key give by lice, obtais the same result as lice s. Polarizatio codig lice: : 0> : > Bob: Measure with or basis Lih Y. Li 8
Photo Polarizatio Circularly Polarized Photos ad Photo Spi E( r, t) eˆ R ( eˆ + eˆ ) R (ˆ x + R jyˆ) L L exp( eˆ L jkz)exp( jπνt) (ˆ x Example: () liearly-polarized photo trasmittig through a circular polarizer. () right-circularly-polarized photo trasmittig through a liear polarizer. jyˆ) Photo Spi Photo has itrisic agular mometum. Photo spi: S ± For right-circularly-polarized photos, S is parallel to k. For left-circularly-polarized photos, S is ati-parallel to k. Liearly-polarized photos have a equal probability of exhibitig parallel ad ati-parallel spi. Lih Y. Li 9
Photo Iterferece ssume the mirrors ad beam-splitters are perfectly flat ad lossless. Path legth differece is d. Probability of fidig the photo at the detector? If we do t fid the photo at the detector, where is it? Lih Y. Li 0
Photo Time Heiseberg s Ucertaity Priciple also implies t E The probability of observig a photo at (r, t) withi a icremetal area of d ad durig the icremetal time iterval dt followig time t: p( r, t) ddt I( r, t) ddt U ( r, t) ddt Lih Y. Li
Mea Photo Flux Desity photos sec area Moochromatic light of frequecy ν ad itesity I(r) Photo flux desity I ( r) ϕ( r) hν Quasi-moochromatic light of cetral-frequecy Photo flux desity ϕ( r) I ( r) hν ν Lih Y. Li
Mea Photo Flux ad Mea Number of Photos photos sec Mea Photo Flux Φ P P ϕ( r) d hν I( r) d: Optical power (watts) Mea Number of Photos Time-varyig light E T 0 T 0 E Φ T hν E P T : Optical eergy (joule) Φ( t) dt P( t) dt : E hν Optical eergy (joule) Lih Y. Li 3
Radomess of Photo Flux Eve if the optical power is costat, the time of arrival of a sigle photo is govered by probabilistic laws. Lih Y. Li 4
Photo Statistics for Coheret Light Probability Mea photo umber It s possible to detect differet umber of photos at differet time itervals. Probability of detectig photos is a Poisso distributio: p( ) exp( )! Lih Y. Li 5
Photo Statistics for Coheret Light Mea, Variace, ad SNR Mea: 0 p( ) σ Variace: 0 ( ) p( ) For Poisso distributio, σ Sigal-to-oise ratio: SNR (mea) Variace σ For Poisso distributio, SNR Lih Y. Li 6
7 Lih Y. Li Photo Statistics for Icoheret Light Probability follows Boltzma distributio T k E E P B exp ) ( J/k 0.38 3 B k : Boltzma costat B B T k h T k h p ν ν exp exp ) ( exp ν T k h B p + + ) ( + σ SNR < + No matter how large the optical power is.