Chapter 1 Introduction1.1 Classification ofoptical processesReflectionrefractionrefractiveindexPropagationn(v) = c / vTransmission(v)Snell'slawpropagationthroughtransmitted lightincident lightthe mediumabsorptionandabsorptionluminescence~resonanceOpticalmediumluminescencereflected light~spontaneousemissionscatteringelastic andInelasticscatteringnonlinear-opticsOptical mediumPropagation
Chapter 1 Introduction 1.1 Classification of optical processes • Reflection • Propagation • Transmission Optical medium Optical medium refractive index n() = c / v () Snell’s law absorption ~ resonance luminescence ~ spontaneous emission elastic and Inelastic scattering nonlinear-optics Propagation
1.2 Optical coefficientsLuminescenceexcited stateCoefficientof reflectionor reflectivity..relaxation3(R):R=reflectedpower/incidentpowerTransmissionortransmissivity(T)absorptionemissionT=transmitted power/incidentpowerR+T=1Refractive index (n):ground stateAbsorptioncoefficient(α)Theatom jumpstoanexcited statebyabsorptionofadI=-αdz*I();Photon,then relaxesto an intermediate state, beforere-emitting a photonby spontaneous emission as it fallsBeer's law.To theground state.Thephotonemitted has a smallerenergythantheabsorbed photon.Thereduction intheI(z) = IoePhotonenergy is called the Stokes shiftαis strongfunction offrequencyScatteringVariationofnofthemediumonalengthscalesmaller than the ^of the lightpropagation throughincident lightsmitted lightTthe mediunI(z)= I。 exp(-Nα,z)N: the number of scattering centres / V;os: scattering cross-section,reflected lightα=Nos1T=(1-R)eαl(1-R)=(1-R)’e-αl0.(Rayleigh scattering :2
1.2 Optical coefficients • Coefficient of reflection or reflectivity (R): R = reflected power / incident power • Transmission or transmissivity (T): T = transmitted power / incident power R + T = 1 • Refractive index (n): • Absorption coefficient () d I = - d z* I (z); Beer’s law: is strong function of frequency z I z I e − = 0 ( ) l l T R e R R e − − = − − = − 2 1 2 (1 ) (1 ) (1 ) • Luminescence The atom jumps to an excited state by absorption of a Photon, then relaxes to an intermediate state, before reemitting a photon by spontaneous emission as it falls To the ground state. The photon emitted has a smaller energy than the absorbed photon. The reduction in the Photon energy is called the Stokes shift. • Scattering Variation of n of the medium on a length scale smaller than the of the light N: the number of scattering centres / V; S: scattering cross-section; = N S Rayleigh scattering : ( ) exp( ) 0 I z I N z = − s 4 1 ( ) ~ s
1.3 The complex refractive index and dielectric constantComplexrefractiveindexTherelationshipbetweenthereal and imaginaryn=n+ikparts of two coefficients:k:extinctioncoefficient81 = n2-k2, 82 = 2nkE(z,t) = Eei(k---1)andWhere12n_n@→k=n=(n+ix)~方(8, +(e +8))nk:a/nCCC1i(on--/c-ot)E(z,t)= EpeE(-8, +( +))KV2= Eoe-x-w=/cei(o-n:=/c-01)n and , are not independent var iable s:IαEE*Forweaklyabsorbingmedium,kisverysmall2.K·04元·KK=22:α:n=Jer,元c2nComplexdielectricconstantThereflectivity(normal incidence):(n-1)2+k2n-1/2n=/e,R=(n+1)?+k2n+1l, =81 +i82In the transparent region of material :n?=E,αisverysmall,xand &,arenegligible,onemayconsideronlytherealpartsofnandIntheabsorptionregion,oneneed toknowboth the real and imaginary parts of n and
1.3 The complex refractive index and dielectric constant • Complex refractive index : extinction coefficient Where • Complex dielectric constant n = n+i ~ ( ) 0 ( , ) i k z t E z t E e − = c n i c k n c n n k ( ) ~ / 2 = = = = + = = = = − − − 2 4 ( , ) * / ( / ) 0 / ) ~ ( 0 c I EE E e e E z t E e wz c i n z c t i n z c t r r r n i n = = + = ~ ~ ~ 2 1 2 The relationship between the real and imaginary parts of two coefficients: n and are not independent iable s n and n n r var ~ ~ ( ( ) ) . 2 1 ( ( ) ) 2 1 , 2 2 1 2 1 2 2 2 1 1 2 1 2 1 2 2 2 1 1 2 2 2 1 = − + + = + + = − = For weakly absorbing medium, is very small, n n 2 , 2 1 = = The reflectivity (normal incidence) : . ( 1) ( 1) 1 ~ 1 ~ 2 2 2 2 2 + + − + = + − = n n n n R In the transparent region of material : is very small, and 2 are negligible, one may consider only the real parts of n and ; In the absorption region, one need to know both the real and imaginary parts of n and
1.4 Optical materials1.4.1 Crystallineinsulators and semiconductorsTransparency range, the indexCrystalTransparencynmaybetakentobereal withnorange (μm)imaginary component0.2-6Al2031.771 (o)UVinfrared(approximatelyconstantn=1.77)visible1.763 (c)(sapphire)LO0.2-121.476BaF2R=0.077.hence T =(1-R)2=0.85(a)2.424Diamond0.25->80sapphire0.81.564KBr0.3301.493KCI0.21-250.61.673KI0.3-400.40.12-81.379 (0)MgF21.390 (c)oePhonon absorption or lattice0.2NaCI0.21201.55absorption1.326NaF0.19-150.00.2-31.546 (0)SiO2CdSe1.555 (e)08(b)(quartz)Table1.2Approximatetransparencyrange,0.45-52.652 ()TiO20.62.958 (e)bandgapwavelengthAg,andrefractiveindex(rutile)nofanumberofcommonsemiconductors.n0.4Due to absorption by boundismeasuredat10μm.After[1],[2] and[3]0.2electronsCrystalTransparency入gnFundamental absorptionedge0.0(μum)range (μm)0.1110is determined by the band gap.Wavelength (microns)1.84.00Ge1.8-23Si1.2-151.13.42The optical properties of semiconductors are similar to0.87GaAs1.0-203.16CdTe0.9-140.832.67thoseof insulators,expect thattheelectronic and phonic0.712.50CdSe0.75-24transitions occur at longer wavelengths.Its transparency0.442.41ZnSe0.45-200.332.20range lies outside the visible spectrum, so it has a darkZns0.4-14Metallicappearance
1.4 Optical materials 1.4.1 Crystalline insulators and semiconductors Transparency range, the index may be taken to be real with no imaginary component (approximately constant n=1.77) R = 0.077, hence T =(1-R) 2=0.85 Phonon absorption or lattice absorption Due to absorption by bound electrons Fundamental absorption edge, is determined by the band gap. The optical properties of semiconductors are similar to those of insulators, expect that the electronic and phonic transitions occur at longer wavelengths. Its transparency range lies outside the visible spectrum, so it has a dark Metallic appearance
1.4 Optical materials1.4.2 GlassMost types ofglasses are made of silica (SiO2)with other chemicals. Insulator, all thecharacteristicfeaturescrystallineinsulators,thetransrangefromaround2oonmtobeyond2000nm,Small absorptionandscattering losses;n changesbyTable1.3Refractiveindexofsyntheticfusedsilicaversuswavelength,After[2]lessthan1%overthewholevisiblespectralregion;ChemicalsarecommonlyaddedtosilicaduringthefusionWavelength (nm)Refractiveindexprocesstoaltertherefractiveindex andtransmissionrange;213.91.53430Stained glass and colour glass filterare made by adding239.91.51336275.31.49591semiconductorswithgapsinvisiblespectralregion334.21.47977404.71.46962467.81.46429508.61.46186Table1.4Composition,refractive index and ultraviolettransmissionofcommonglasses.Theletters afterthenamesgivetheabbreviationsusedto546.11.46008identifytheglasstypeThecompositionfigures arethepercentagebymass.Therefractiveindexismeasuredat546.Inmandthetransmissions632.81.45702fora I cm plate at 310 nm.After [1].[4]706.51.45515TnK20CaoBaoPboP2OsNameSi02B203Al203Na20780.01.4536710601.449681.4600.91100Fused silica13951.4458396111.5130.474Crown (K)15301.4442730.35108811.51970Borosilicate crown (BK)19701.43853125701.5270.46310Phosphatecrown (PK)53423251.432935381.5850.008Light flint (LF)2744471.607Flint (F)562331.746Dense flint (SF)
1.4 Optical materials 1.4.2 Glass • Most types of glasses are made of silica (SiO2 ) with other chemicals. Insulator, all the characteristic features crystalline insulators, the trans range from around 200 nm to beyond 2000 nm; • Small absorption and scattering losses; n changes by less than 1% over the whole visible spectral region; • Chemicals are commonly added to silica during the fusion process to alter the refractive index and transmission range; • Stained glass and colour glass filter are made by adding semiconductors with gaps in visible spectral region