Lecture 2: Propagation of light waves and pulses

Size: px

Start display at page:

Download "Lecture 2: Propagation of light waves and pulses"

Emily Lamb
7 years ago
Views:

1 Lu : Popaao of lh was a pulss P Kužl Popaao of pla was la homoous soop LI ma:! fa x! sy! absopo Popaao of lh pulss:! oup loy! oup spso hp! suplumal ffs?

2 Wa quao o εµ εµ N N D B wll-ow y ε ε ε ε ε ε l osa µ ε N ε εµ fa x ε ε ε κ ε ε ε κ ε κ ε,,, κ N

3 Popaao h auum wh Ba o Maxwll s quaos: µ µ B s η s B Ω ε µ η 377 s

4 Supposos of pla was I h -spa: 3-msoal,, I h -spa: -msoal popaao alo : x y,, Puls: al fquy ; al wa o /.,,

5 Popaao h ma N N N wh Ba o Maxwll s quaos: µ µ B s η N s B N ε µ η η N s

6 Popaao o o ' /, '' κ / ' a '' a ha ff ff os:! ' os: osa phas plas! '' os: osa amplu plas '' : bouay oos of a absob sampl α α N κ '' β' ' x y

7 Popaao o o S y flow Poy o S S µ µ S R R Popaao alo // { } R { } R{ } µ { } µ "#! S η κ α µ α κ 4πκ λ

8 Opal pulss: spso Dspso lao o-absob mum: Opal puls as a la ombao of mos:, Ma fquy a wa o :, : β ψ 3 β ψ oup loy spso GVD

9 Goup loy fs o ffs Popaao of a puls $"$! #$"$! #, B A A: fl osllao wh h al fquy wa fo loy: B: popaao of lop whou fomao oup loy

10 Opal pulss: y flow Poy o / κ η S y osao law κ ε κ ε ε ε ε / U $ $! $ #$ " U η η κ η κ κ / / S, ε µ η µ ε

11 Goup loy spso GVD so o ffs Ma ff: puls boa m Ths am s ssay fo! Ulasho puls sub-5 fs popaao! Ulasho puls ps o sub-ps ao lass mulpl passs houh sps ma! Sho puls sub-s popaao fbs xmly lo sas β ψ

12 Iu am Spal ompos om fom wo s of h spum popaa wh ff los GVD s f as ψ Spa u o a hss L of h sps maal: L τ L 4l L ψ ψ L τ fo a aussa puls shap

13 xa am τ ψ τ l 4 L u am Supposo of h spal ompos β 3, O s fo a aussa puls fo a ysal lh L af all h aos:, δ δ α δ A 4l wh τ ψ αψ δ L L Spa u o a hss L of h sps maal: 4l τ ψ τ δ τ τ L L

14 3 A B C Ma fquy as m: Chp oup lay spso:, GDD Φ Φ ψl 4α α ψl ψl

15 Puls spa: xampl Dspso of a BK7 pla Puls lh af h pla fs Thss: mm 6 mm 3 mm Bawh-lm puls lh fs

16 Suplumal ffs Wha a b suplumal?! Phas loy?! Goup loy?! Vloy of a fomao? Dfo of h sp of a fomao asf

17 Ifomao sp Amplfao poss Th os a oly slow ow h fomao asf

18 Phas loy, osθ, /osθ θ,

19 Goup loy Goup loy a x h auum sp of h lh:! o of aomalous spso " l soa " a mum

20 Dl soa oup loy fa x Fquy ab. u absopo x.5 3 oup loy a b suplumal pao ph fao of λ oup loy omal o Fquy ab. u. pao ph omal o λ

21 Ga-asss suplumal lh popaao L. J. Wa, A. Kumh & A. Doau NC Rsah Isu, 4 Ip Way, Po, Nw Jsy 854, USA Ga-asss aomalous spso: Masu puls aam ospos o a a oup loy Coluso: puls maxmum a la / al of h puls a aa h s almos!! o ha h puls shap h y fs o-o sal a!! b aa

The effect on the Asian option price times between the averaging. Mark Ioffe

The effect on the Asian option price times between the averaging. Mark Ioffe 866 U Naos Plaza u 566 Nw Yok NY 7 Pho: 3 355 Fa: 4 668 fo@gach.co www.gach.co h ffc o h sa opo pc s bw h avagg Mak Ioff bsac h acl s o h calculao of h pc of sa opo. I pacula w aalz h ffc o h opo pc s