Today s summary. MIT 2.71/2.710 Optics 10/24/05 wk8-a-1

Size: px

Start display at page:

Download "Today s summary. MIT 2.71/2.710 Optics 10/24/05 wk8-a-1"

Andra Rich
6 years ago
Views:

1 Tody s summry Multiple bem interferometers: Fbry-Perot resontors Stokes reltionships Trnsmission nd reflection coefficients for dielectric slb Opticl resonnce Principles of lsers Coherence: sptil / temporl 10/4/05 wk8--1

2 10/4/05 wk8-- Fbry-Perot interferometers

3 Reltion between r, r nd t, t r t r t ir glss glss ir r = r r + tt = 1 Stokes reltionships Proof: lgebric from the Fresnel coefficients or using the property of preservtion of the field properties upon time reversl 10/4/05 wk8--3

4 Proof using time reversl r r t t tr ir glss tt r ir glss rt ( r + r ) t = 0 r = r ( ) r + tt = r + tt = 1 10/4/05 wk8--4

5 Fbry-Perot Interferometer reflected trnsmitted incident Resonnce condition: reflected wve = 0 ll reflected wves interfere destructively L L = mλ n wvelength in free spce refrctive index 10/4/05 wk8--5

6 Clcultion of the reflected wve incoming reflected r trnsmitted te iδ r t trnsmitted te iδ reflected te iδ r trnsmitted te iδ t reflected te i3δ (r ) reflected te i4δ (r ) 3 trnsmitted tei3δ (r t ) trnsmitted te i4δ (r ) 3 t reflected te i5δ (r ) 4 nl δ = π ir, n=1 glss, n ir, n=1 λ 10/4/05 wk8--6

7 10/4/05 wk8--7 Clcultion of the reflected wve ( ) { } + = = δ δ δ δ δ 4 4 reflected e 1 1 e e e 1 e i i i i i r r tt r r r r tt r L Use Stokes reltionships 1 = + = tt r r r ( ) δ δ reflected e 1 e 1 i i r r =

8 Trnsmission & reflection coefficients reflected ( iδ 1 e ) = iδ trnsmitted iδ 1 r e r tt = 1 r e R r reflection = coefficient trnsmission = coefficient reflected trnsmitted = 4R sin δ ( 1 R) + 4Rsin δ ( 1 R) = ( 1 R) + 4R sin δ 10/4/05 wk8--8

9 Trnsmission & reflection vs pth R=0.95 R=0.5 10/4/05 wk8--9

10 Fbry-Perot terminology free spectrl rnge bnd width resonnce frequencies 10/4/05 wk8--10 mc nl ( m + 1) c ( m ) + c frequency ν nl nl

11 Fbry-Perot terminology ν FWHM ν F ν FSR bndwidth = FSR ν FWHM = ( ) FWHM Bndwidth is inversely proportionl to the finesse F (or qulity fctor) of the cvity F π 1 ν FWHM = R R c nlf ( free spectrl rnge) ( finesse) 10/4/05 wk8--11

12 Spectroscopy using Fbry-Perot cvity Gol: to mesure the specimen s bsorption s function of frequency ω Experimentl mesurement principle: light bem of known spectrum spectrum of light bem is modified by substnce scnning stge (controls cvity length L) trnsprent windows continer with specimen to be mesured prtilly reflecting mirrors (FP cvity) power meter 10/4/05 wk8--1

13 Spectroscopy using Fbry-Perot cvity Gol: to mesure the specimen s bsorption s function of frequency ω Experimentl mesurement principle: light bem of known spectrum spectrum of light bem is modified by substnce electro-optic (controls refr. (EO) modultor index n) trnsprent windows continer with specimen to be mesured prtilly reflecting mirrors (FP cvity) power meter 10/4/05 wk8--13

14 Spectroscopy using Fbry-Perot cvity I(ω) Fbry Perot trnsmissivity unknown spectrum 10/4/05 wk8--14 ω 1 smple mesured: I(ω 1 ) ω

15 Spectroscopy using Fbry-Perot cvity I(ω) Fbry Perot trnsmissivity unknown spectrum 10/4/05 wk8--15 ω smple mesured: I(ω ) ω

16 Spectroscopy using Fbry-Perot cvity I(ω) Fbry Perot trnsmissivity unknown spectrum 10/4/05 wk8--16 ω 3 smple mesured: I(ω 3 ) ω

17 Spectroscopy using Fbry-Perot cvity I(ω) unknown spectrum width should not exceed the FSR Fbry Perot trnsmissivity unknown spectrum 10/4/05 wk8--17 ω 3 smple mesured: I(ω 3 ) ω

18 Spectroscopy using Fbry-Perot cvity I(ω) spectrl resolution spectrl resolution is determined by the cvity bndwidth Fbry Perot trnsmissivity unknown spectrum 10/4/05 wk8--18 ω 3 smple mesured: I(ω 3 ) ω

19 10/4/05 wk8--19 Lsers

20 Absorption spectr Atmospheric trnsmission 10/4/05 wk8--0 humn vision λ (µm)

21 Semi-clssicl view of tom excittions Energy e - Ze + Atom in ground stte Energy Atom in excited stte 10/4/05 wk8--1

22 Light genertion Energy excited stte equilibrium: most toms in ground stte ground stte 10/4/05 wk8--

23 Light genertion Energy excited stte A pump mechnism (e.g. therml excittion or gs dischrge) ejects some toms to the excited stte ground stte 10/4/05 wk8--3

24 Light genertion Energy excited stte hν hν The excited toms rditively decy, emitting one photon ech ground stte 10/4/05 wk8--4

25 Light mplifiction: 3-level system Energy super-excited stte excited stte equilibrium: most toms in ground stte; note the existence of third, super-excited stte ground stte 10/4/05 wk8--5

26 Light mplifiction: 3-level system Energy super-excited stte excited stte Utilizing the super-excited stte s short-lived pivot point, the pump cretes popultion inversion ground stte 10/4/05 wk8--6

27 Light mplifiction: 3-level system Energy super-excited stte excited stte hν When photon enters,... ground stte 10/4/05 wk8--7

28 Light mplifiction: 3-level system Energy super-excited stte excited stte hν hν hν 10/4/05 wk8--8 When photon enters, it knocks n electron from the inverted popultion down to the ground stte, thus creting new photon. This mplifiction process is clled stimulted emission ground stte

29 Light mplifier P in Gin medium (e.g. 3-level system w popultion inversion) P out =gp in 10/4/05 wk8--9

30 Light mplifier w positive feedbck P in Gin medium (e.g. 3-level system w popultion inversion) P out =gp in When the gin exceeds the roundtrip losses, the system goes into oscilltion + Σ + g 10/4/05 wk8--30

31 Lser initil photon Gin medium (e.g. 3-level system w popultion inversion) Light Amplifiction through Stimulted Emission of Rdition Prtilly reflecting mirror 10/4/05 wk8--31

32 Lser mplified once initil photon Gin medium (e.g. 3-level system w popultion inversion) Light Amplifiction through Stimulted Emission of Rdition Prtilly reflecting mirror 10/4/05 wk8--3

33 Lser mplified once initil photon reflected Gin medium (e.g. 3-level system w popultion inversion) Light Amplifiction through Stimulted Emission of Rdition Prtilly reflecting mirror 10/4/05 wk8--33

34 Lser mplified once initil photon reflected Gin medium (e.g. 3-level system w popultion inversion) mplified twice Light Amplifiction through Stimulted Emission of Rdition Prtilly reflecting mirror 10/4/05 wk8--34

35 Lser mplified once initil photon reflected Gin medium (e.g. 3-level system w popultion inversion) mplified twice output reflected Light Amplifiction through Stimulted Emission of Rdition Prtilly reflecting mirror 10/4/05 wk8--35

36 Lser mplified once initil photon reflected Gin medium (e.g. 3-level system w popultion inversion) mplified twice output mplified gin etc. Light Amplifiction through Stimulted Emission of Rdition reflected Prtilly reflecting mirror 10/4/05 wk8--36

37 Confocl lser cvities tnθ = λ πnw 0 diffrction ngle wist w 0 Bem profile: D Gussin function TE 00 mode 10/4/05 wk8--37

38 Other trnsverse modes TE10 TE11 (usully undesirble) 10/4/05 wk8--38

39 Types of lsers Continuous wve (cw) Pulsed Q-switched mode-locked Gs (Ar-ion, HeNe, CO ) Solid stte (Ruby, Nd:YAG, Ti:S) Diode (semiconductor) Verticl cvity surfce-emitting lsers VCSEL (lso sc) Excimer (usully ultr-violet) 10/4/05 wk8--39

40 CW (continuous wve lsers) Lser oscilltion well pproximted by sinusoid 1/ν t Typicl sources: Argon-ion: 488nm (blue) or 514nm (green); power ~1-0W Helium-Neon (HeNe): 633nm (red), lso in green nd yellow; ~1-100mW doubled Nd:YG: 53nm (green); ~1-10W Qulity of sinusoid mintined over time durtion known s coherence time t c Typicl coherence times ~0nsec (HeNe), ~10µsec (doubled Nd:YAG) 10/4/05 wk8--40

41 Two types of incoherence temporl incoherence sptil incoherence r 1 r 1 point source d 1 d r mtched pths Michelson interferometer poly-chromtic light (=multi-color, brodbnd) Young interferometer mono-chromtic light (= single color, nrrowbnd) 10/4/05 wk8--41

42 Two types of incoherence temporl incoherence sptil incoherence r 1 r 1 point source d 1 d r mtched pths 10/4/05 wk8--4 wves from unequl pths do not interfere wves with equl pths but from different points on the wvefront do not interfere

43 Coherent vs incoherent bems = 1 1 e iφ 1 Mutully coherent: superposition field mplitude is described by sum of complex mplitudes = 1 + = 1 e iφ + 1 e iφ = e iφ I = = 1 + I 1 Mutully incoherent: superposition field intensity is described by sum of intensities I = I 1 + I 10/4/05 wk8--43 I (the phses of the individul bems vry rndomly with respect to ech other; hence, we would need sttisticl formultion to describe them properly sttisticl optics)

44 Coherence time nd coherence length l l 1 -l much shorter thn coherence length ct c shrp interference fringes Intensity I 0 l 1 incoming lser bem Michelson interferometer 0 l 1 -l much longer thn coherence length ct c no interference Intensity l 1 I 0 10/4/05 wk8--44 l 1

45 Coherent vs incoherent bems = 1 1 e iφ 1 Coherent: superposition field mplitude is described by sum of complex mplitudes = 1 + = 1 e iφ 1 + e iφ = e iφ I = = 1 + I 1 Incoherent: superposition field intensity is described by sum of intensities I = I 1 + I 10/4/05 wk8--45 I (the phses of the individul bems vry rndomly with respect to ech other; hence, we would need sttisticl formultion to describe them properly sttisticl optics)

46 Mode-locked lsers Typicl sources: Ti:S lsers (mjor vendors: Coherent, Spectr Phys.) Typicl men wvelengths: 700nm 1.4µm (ner IR) cn be doubled to visible wvelengths or split to visible + mid IR wvelengths using OPOs or OPAs (OPO=opticl prmetric oscilltor; OPA=opticl prmetric mplifier) Typicl pulse durtions: ~psec to few fsec (just few opticl cycles) Typicl pulse repetition rtes ( rep rtes ): MHz Typicl verge power: 1-W; pek power ~MW-GW 10/4/05 wk8--46

47 10/4/05 wk8--47 Overview of light sources Lser non-lser Therml: polychromtic, sptilly incoherent (e.g. light bulb) Gs dischrge: monochromtic, sptilly incoherent (e.g. N lmp) Light emitting diodes (LEDs): monochromtic, sptilly incoherent Continuous wve (or cw): strictly monochromtic, sptilly coherent (e.g. HeNe, Ar +, lser diodes) Pulsed: qusi-monochromtic, sptilly coherent (e.g. Q-switched, mode-locked) ~nsec pulse durtion mono/poly-chromtic = single/multi color ~psec to few fsec

Light and Optics Propagation of light Electromagnetic waves (light) in vacuum and matter Reflection and refraction of light Huygens principle

$Light and Optics Propagation of light Electromagnetic waves (light) in vacuum and matter Reflection and refraction of light Huygens principle$ Light nd Optics Propgtion of light Electromgnetic wves (light) in vcuum nd mtter Reflection nd refrction of light Huygens principle Polristion of light Geometric optics Plne nd curved mirrors Thin lenses