Class 1. Introduction to Nonlinear Optics

Transcription

1 Class 1 Introduction to Nonlinear Optics Prof. Cleber R. Mendonca

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3 Outline Linear optics Introduction to nonlinear optics Second order nonlinearities Third order nonlinearities Two-photon absorption Conclusions

4 Linear optics vs Nonlinear optics Optics is a branch of physics that describes the behavior and properties of light and the interaction of light with matter. Explains optical phenomena. Nonlinear Optics The branch of optics that t describes optical phenomena that t occur when very intense light is used

5 Linear optics Maxwell equations ρ: charge density J: current density P: electric polarization M: magnetization

6 Linear optics P e M: response of the media to the applied field Electric Polarization p

7 Linear optics Maxwell equations can be combined, leading to a equation describing the electromagnetism Constitutive relationships r r P = χe r r M = χ H m r r J = σe response of the media to the applied field

8 Linear optics wave equation ( ρ = 0 ; J r = 0 ) left right Light propagation in vacuum Matter-light interaction

9 Linear optics E rad. << E inter. harmonic oscillator electron on a spring oscillation frequency k m e ω 0 = k me

10 electron on a spring Linear optics equation of motion

11 Linear optics harmonic oscillator Steady state: electron oscillates at driving frequency

12 Linear optics Oscillating dipole Polarization oscillator P( t) Ne 2 / ω = ( 2 ω ) m E iωγ P = χe linear response

13 Linear optics by comparison ~ χ Ne 2 / m = ( 2 ω ω 2 ) iωγ 0 0 which is a complex number then where and are the real and imaginary parts of the complex index of refraction refraction absorption

14 Linear optics

15 Linear optical process absorption refraction α 0 does not depend on light intensity n 0 does not depend on light intensity absorption of 10 % index of refraction 1.3

16 Nonlinear optics high light intensity E rad.~ E inter. How high should be the light intensity?

17 Nonlinear optics Inter-atomic electric field cw laser 2P πw P = 20 W I = w o = 20 μm 2 0 I = W/m 2 e = C r ~ 4 Å E ~ V/m E o = V/m

18 Nonlinear optics Inter-atomic electric field pulsed laser I = 10 GW/cm 2 = W/m 2 E ~ V/m E o = V/m

19 Nonlinear optics high light intensity E rad.~ E inter. anharmonic oscillator anharmonic term

20 Nonlinear optics anharmonic oscillator potential energy charge displacement P nonlinear polarization response P = χ ( 1 ) E + χ ( 2 ) E 2 + χ ( 3 ) E E

21 Nonlinear optics high light intensity E rad.~ E inter. anharmonic oscillator nonlinear polarization response P = χ ( 1 ) E + χ ( 2 ) E 2 + χ ( 3 ) E

22 wave equation ( ρ = 0 ; J r = 0 ) Nonlinear optics left right Light propagation in vacuum Matter-light interaction

23 Nonlinear optics nonlinear expansion of the polarization r P r r r ( 1) ( 2 ) ( 3 ) = χ.e + χ : EE + χ M r r r EEE +... linear SHG THG processes Kerr effect

24 Nonlinear optics nonlinear expansion of the polarization

25 χ (2) Second order processes Nonlinear Optics ω 1 ω χ (2) ω 1 +ω ω 1 ω 2 If ω 1 = ω 2 second harmonic generation: 2 ω optical retificatio: 0

26 Nonlinear Optics Second order processes ( 2 ) χ Second Harmonic Generation ω 2ω λ = 1064nm λ = 532nm

27 Second Harmonic Generation ( 2 ) χ 1- higher energy light 2- transparent material

28 Second Harmonic Generation ( 2 ) χ Phase Matching ( ω ) ( 2ω ) v = v

29 Nonlinear Optics in medium with inversion symmetry y and consequently

30 Nonlinear Optics Third order processes (3) χ ω 1 ω 1 +ω 2 +ω 3 ω 2 χ (3) ω 1 ω 2 ω 3 ω 3 ω 1 ω 2 +ω 3 If ω 1 = ω 2 = ω 3 Third harmonic generation: 3 ω Self phase modulation: ω

31 Third Harmonic Generation χ (3) ω 3ω ω Nonlinear media

32 Nonlinear Optics χ ( 2 ) = 0 (3) χ Third order processes Nonlinear polarization Third order polarization

33 Nonlinear Optics consequently and Kerr media n = n + 0 n2i

34 Nonlinear Optics Third order processes ( 3 ) χ n 2 χ 2 ( 3 ) Kerr media: n = n n I Index of refraction depends on the light intensity

35 Kerr media: n Self phase modulation centre symmetric: = ( ) 3 n n I P NL = χ 3 E χ () 2 = 0 n 2 >0 2 Material behaves as a convergent lens xd f y z Sample

36 Optical switching response time: s response time GHz 1 THz 1 million times faster

37 Nonlinear optics 2ω ω Nonlinear material ω? 3ω Intense light induced nonlinear response in the material Material change the light in a nonlinear way Self action effect

38 χ (3) is a complex quantity Nonlinear Optics

39 Third order processes: χ (3) Refractive process: Absorptive process: = n n I α α + β I n + = β self-phase modulation lens-like effect nonlinear absorption two-photon absorption

40 Two-photon absorption (2PA) process Phenomenon does not described for the Classical Physics and does not observed until the development of the Laser. 1-photon absorption (Linear) 2-photon absorption (Nonlinear) Theoretical model: Maria Göppert-Mayer, 1931 Two photons from an intense laser light beam are simultaneously absorbed p g y in the same quantum act, leading the molecule to some excited state with energy equivalent to the absorbed two photons.

41 two-photon absorption 2ω ω Abs α α + βi = 0 ω λ Applications: optical limiting fluorescence microscopy microfabrication

42 two-photon fluorescence α = α 0 + βi ω ω light emission fluorescence

43 localization of the excitation with 2PA dilute solution of fluorescent dye 2PA 1PA spatial confinement of excitation

44 excitation profile along z Radius, area and intensity it of focused beam A( z ω( z ) ω0 1 + z z ) I( z ) = = 0 + = 2 2 πω = πω0 1 z 0 E At 1 = A 1 z 2 z πω z 0 Normalized excitation rates (ignoring beam attenuation) ation) 2 2 one photon I( z ) z = 1 + I( 0 ) z 0 2 two photon I( z ) z 1 0 = + I( ) z0 4

45 Class 2 Studying optical nonlinearities iti Prof. Cleber R. Mendonca

46 Investigating nonlinear optical materials Very intense light: femtosecond pulses Ti:Sapphire lasers 100 fs 50 fs 20 fs 1fs= s 1 fs 1s Laser intensities ~ 100 GW/cm 2 1 x W/cm 2 Laser pointer: 1 mw/cm 2 (1 x10-3 W/ cm 2 )

47 Organic materials Flexibility to tune the nonlinear optical response by manipulating the molecular structure π-conjugated structures σ C C Conjugation: alternation of single and doubles bonds π between carbon atoms

48 Conjugation π-conjugation σ bond: forms a strong chemical bond; localized π bond: weaker bond; out of the C atoms axis Free electrons that are easier to move under an applied electric filed π bond in conjugated system: delocalized electrons high optical nonlinearities χ (3)

49 Research Understanding the physical principles behind two-photon absorption Understanding the relationship between molecular structure and two-photon absorption Developing molecules with high optical nonlinearities that can be p g g p used for application

50 Z-scan closed aperture Z-scan = n n I z<0 n z>0 norma alized transmitta ance Normalized Transmittace Z ΔT n2i

51 Nonlinear refraction normalized Transm mitância transmittance Z (mm) Aminoacids COO H - C CH 2 C CH C 2 L-Proline 2 π Δ T pv = ΔΦ 0 = n 2 I 0 L λ 150 fs 100 GW/cm 2 n χ ( 3 ) nm

52 Nonlinear refraction L-Proline COO - C H C C CH 2 CH 2

53 Z-scan (nonlinear absorption) open aperture Z-scan z<0 α ( I ) = α0 + βi rmalized transm mittance alized Trans mittace nor Norm z> Z T ( z) = ΔTT βi [ q0 ( z,0) ] 3 / 2 ( m 1) = + m q m 2 2 ( z / ) 0( z,t ) = βi0l / 1 z0

54 two-photon absorption cross-section A pair of photon incident on a molecule For two-photon absorption to occur, a pair of photons must be incident within a cross sectional area and within the lifetime of the virtual sate, τ s

55 Nonlinear spectrum nonlinear absorption intense laser (ultra short pulses) α = α + β 0 I discrete λ s δ(λ) n 2 2( (λ) nonlinear refraction n = n + 0 n2i nonlinear spectrum???

56 Nonlinear absorption spectrum Optical parametric amplifier nm 120 fs μj

57 Two-photon absorption 1.00 DR13 Normaliz zed Transmit ttance nm 750 nm 860 nm 930 nm 1010 nm O 2 N Cl N N N CH 2 CH 3 CH 2 CH 2 OH 0.85 [ ( )] q0 z,0 T ( z) = 3 / 2 Z / cm m= 0 ( m + 1 ) m α α + βiβ I = 0 β: two-photon absorption coefficient

58 Azoaromatic samples N N AZO H 2 N N N NH 2 DIAMINO H 2 N N N p-amino H 2 N N N NO 2 DO3 Cl HO H 2 C HO H 2 C H 2 C H 2 C N N N NO 2 DR19Cl HO H 2 C HO H 2 C H 2 C H 2 C N N N NO 2 Cl DR19 HO H 2 C H 2 C H 3 C H 2 C N N N NO 2 DR13 HO H 2 C H 2 C H 3 CH 2 C N N N NO 2 DR1

59 0.9 Psuedostilbenos DO3 600 Aminoazobenzenos PAMINO DR1 DR Absorb bance DIAMINO δ (GM M) DR λ (nm) 0 Absorbance DR19-Cl δ (GM) δ 2 ν A ( ) + 1 A2 ν ( ) ( ) ( ) ν i0 ν + Γi0 ν f 0 2ν + Γ f 0 ν f 0 2ν + Γ f λ (nm)

60 Planarity of the π-bridge Thermally induced torsion in the molecular structure

61 Molecular design strategy Increasing the molecular conjugation Adding charged groups to the molecule Keep molecular planarity

62 Increasing the conjugation π-bridge π-bridge Increase in the optical nonlinearity π-bridge Increasing the π-conjugation π-bridge

63 Donor and acceptor groups electron donor electron acceptor e - e - π-bridge bid R + R - Incorporating electron donor and acceptor groups in a predictable way leads to an enhancement of the optical nonlinearity

64 Planarity of the π-bridge Perylene compounds are very planar molecules, which explains its high optical nonlinearities

65 Class 3 Applications of nonlinear optics Prof. Cleber R. Mendonca

66 Sculpturing with light: micro/nanofabrication using ultrashort t pulses

67 laser microfabrication focus laser beam on material s surface

68 laser microfabrication

69 laser microfabrication

70 laser microfabrication surface microstructuring

71 laser microfabrication examples of fabricated surfaces 20 μm 40 μm

72 fs-laser microfabrication photon energy < bandgap nonlinear interaction

73 fs-laser microfabrication nonlinear interaction E gap E f = hν

74 fs-laser microfabrication nonlinear interaction E gap E f = hν multiphoton absorption

75 fs-laser microfabrication focus laser beam inside material

76 fs-laser microfabrication curved waveguides inside glass

77 fs-laser microfabrication 3D waveguides in PMMA cross-section view Applied Surface Science, 254, (2007) Optics Express, 16, (2008)

78 fs-laser microfabrication Novel concept: build a microstructure using fs-laser and nonlinear optical processes

79 photonic crystal J. W. Perry two-photon polymerization 20 µm

80 two-photon polymerization applications micromechanics i waveguides microfluidics biology optical devices

81 Outline two-photon polymerization microfabrication microstructures containing MEH-PPV waveguiding the MEH-PPV emission other studies summary

82 Two-photon absorption Third order processes ( 3 ) χ 2ω ω ω ance absorba α α + βi = 0 wavelength 0 wavelength

83 Two-photon absorption Nonlinear interaction provides spatial confinement of the excitation fs-microfabrication α = α 0 α = α 0 + βi

84 Two-photon absorption spatial confinement of excitation

85 Two-photon polymerization Monomer + Photoinitiator Polymer light Photoinitiator is excited by two-photon absorption R2 PA I The polymerization is confined to the focal volume. 2 High spatial resolution

86 Two-photon polymerization setup Beam Expansion y x Laser Scanning Mirror Ti:sapphire laser oscillator 130 fs 800 nm 76 MHz 20 mw CCD camera Objective glass (150 micron) spacer resin glass (150 micron) Objective z Illumination 40 x 0.65 NA

87 Resin preparation Monomers Monomer A Monomer B reduces the shrinkage upon polymerization gives hardness to the polymeric structure Photoinitiator iti t Lucirin TPO-L Appl. Phys. A, 90, (2008)

88 Two-photon polymerization After the fabrication, the sample is immersed in ethanol to wash away any unsolidified resin and then dried

89 Two-photon polymerization Microstructures fabricated by two-photon polymerization 50 μm 20 µm 20 μm 20 µm

90 Microstructures containing active compounds monomer monomer Optical active dye Active Polymer

91 Microstructures containing MEH-PPV MEH-PPV Fluorescence Electro Luminescent Conductive

92 Microstructures containing MEH-PPV MEH-PPV: up to 1% by weight laser power 40 mw a-scanning electron microscopy b,c - Fluorescence microscopy of the microstructure with the excitation OFF (b) and ON (c)

93 Microstructures containing MEH-PPV d - Emission of the microstructure (black line) and of a film with the same composition (red line)

94 Microstructures containing MEH-PPV Fluorescent confocal microscopy images in planes separated by 16 μm in the pyramidal microstructure. Appl. Phys. Lett 95, (2009)

95 Microstructures containing MEH-PPV waveguiding of the microstructure fabricated on porous silica substrate (n= 1.185) 185) Applications: micro-laser; fluorescent microstructures; conductive microstructures

96 Other studies 3D cell migration studies in micro-scaffolds SEM of the scaffolds 110 µm pore size 52 µm pore size Top view 110, 52, 25, 12 µm pore size Side view 25, 52 µm pore size

97 Other studies 3D cell migration studies in micro-scaffolds Advanced Materials, 20, (2008)

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