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Nonlinear Optics Lab. Hanyang Univ. Laser Optics ( 레이저 광학 ) 담당 교수 : 오 차 환 교 재 : P.W. Miloni, J.H. Eberly, LASERS, John Wiley & Sons, 1991 부교재 : W. Demtroder, Laser Spectroscopy, Springer-Verlag, 1998 F. L. Pedrotti, S.J., L.S. Pedrotti, Introduction to Optics, Prentice-Hall, 1993 2006 가을학기

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Nonlinear Optics Lab. Hanyang Univ. Chapter 1. Introduction to Laser Operation 1.1 Introduction LASER : Light Amplification by the Stimulated Emission of Radiation 1916, A. Einstein : predicted stimulated emission 1954, C. H. Townes et al. : developed a MASER 1958, A. Schawlow, C.H. Townes : adapted the principle of MASER to light 1960, T.H. Maiman : Ruby laser @ 694.3 nm 1961, A. Javan : He-Ne laser @ 1.15 m, 632.8 nm …

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Nonlinear Optics Lab. Hanyang Univ. Einstein’s quantum theory of radiation [light-matter interaction] * N 1, N 2 : No. of atoms at E 1, E 2 * : photon density * A 21 =1/ 21 : spontaneous emission rate * B 12, B 21 : stimulated absorption/emission coefficients [radiative processes] (stimulated) absorption stimulated emission spontaneous emission B 12 N 1 B 21 N 2 A 21 N 2 E2E2 E1E1

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Nonlinear Optics Lab. Hanyang Univ. Spontaneous & Stimulated emissions Spontaneous emission Stimulated emission Phase and propagation direction of created photon is random. Created photon has the same phase, frequency, polarization, and propagation direction as the input photon.

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Nonlinear Optics Lab. Hanyang Univ. Einstein’s A, B coefficients Rate equation : (thermal equilibrium) (Boltzman distribution of atoms) (Planck’s blackbody radiation law) (population inversion) Light amplification ! (Lasing)

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Nonlinear Optics Lab. Hanyang Univ. Four key elements of a LASER - Gain medium (Active medium) - Pumping source - Cavity (Resonator) - Output coupler pumping laser relaxation Laser light pumping source gain medium cavity (resonator) output coupler total reflector

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Nonlinear Optics Lab. Hanyang Univ. 1) Pumping source - Optical : Nd-YAG, Ruby, Dye, Ti:sapphire, … - Electrical : He-Ne, Ar +, CO 2, N 2, LD, … - Chemical : HF, I 2, … 2) Active medium - Gas : He-Ne, Ar+, CO 2, N 2, … - Liquid : Dye - Solid : Nd-YAG, Ruby, Ti:sapphire, LD, … 3) Cavity or Resonator - Resonator with total reflector : Maximizing the light amplification - Output coupler : Extracting a laser light - Resonance condition : m /2=L (m:integer) Four key elements of a LASER

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Nonlinear Optics Lab. Hanyang Univ. 1.2 Lasers and Laser Light (Characteristics of laser light) Monochromaticity ( 단색성 ) - Linewidth(FWHM) : 7.5 kHz (He-Ne laser) << 940 MHz (low pressure Cd lamp) Coherence ( 결맞음 ) - Definite phase correlation in the radiation field at different locations(spatial) and different times(temporal) Directionality ( 지향성 ) - Divergence angle : D < D (diffraction limit angle) Brightness ( 높은 휘도 ) - Radiance : 10 6 W/cm 2 -sr (4mW, He-Ne laser) << 250 W/cm 2 -sr (super-high-pressure Hg lamp) Focusability ( 집속도 ) - Focusing diameter : d ~ f

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Nonlinear Optics Lab. Hanyang Univ. 1.5 Einstein theory of light-matter interaction (Laser action) - Number of photons, stimulated emission loss - In steady state : : threshold number of atoms : Minimum(threshold) pumping condition - Number of atoms in level 2, spontaneous emission pumping

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Nonlinear Optics Lab. Hanyang Univ. Spatial distribution of laser beam (Gaussian beam) Maxwell’s curl equations : Scalar wave equation Put, (monochromatic wave) => Helmholtz equation : => Assume, => Put, =>

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Nonlinear Optics Lab. Hanyang Univ. => is must be a complex ! => Assume, is pure imaginary. => put,( : real) At z = z 0, Beam radius at z=0, : Beam Waist at arbitrary z, => : Complex beam radius

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Nonlinear Optics Lab. Hanyang Univ. =>

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Nonlinear Optics Lab. Hanyang Univ. Wave field where, : Beam radius : Radius of curvature of the wave front : Confocal parameter(2z 0 ) or Rayleigh range

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Nonlinear Optics Lab. Hanyang Univ. Gaussian beam I Gaussian profile spread angle : Near field (~ plane wave) Far field (~ spherical wave)

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Nonlinear Optics Lab. Hanyang Univ. Propagation of Gaussian beam - ABCD law Matrix method (Ray optics) yiyi yoyo ii oo optical elements : ray-transfer matrix

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Nonlinear Optics Lab. Hanyang Univ. 1) Free space r1r1 r2r2 z1z1 z2z2 r 2 = r 1 + d constant (paraxial ray approximation) d n 1 /s + n 2 /s’ = (n 2 -n 1 )/R r constant n 1 /n 2 – (1- n 1 /n 2 ) (r 1 /R) 2) Refracting surface ss’ r n1n1 n2n2 R … Ray-transfer matrices

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Nonlinear Optics Lab. Hanyang Univ.

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ABCD law for Gaussian beam optical system ABCD law for Gaussian beam :

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Nonlinear Optics Lab. Hanyang Univ. example) Focusing a Gaussian beam 11 ? ?

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Nonlinear Optics Lab. Hanyang Univ. - If a strong positive lens is used ;=> - If=> : f-number ; The smaller the f# fo the lens, the smaller the beam waist at the focused spot. Note) To satisfy this condition, the beam is expanded before being focused.

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Nonlinear Optics Lab. Hanyang Univ. Chapter 2. Classical Dispersion Theory 2.1 Introduction Maxwell’s equations : (for nonmagnetic media) Wave equations : (2.1.13)

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Nonlinear Optics Lab. Hanyang Univ. 2.2 The Electron Oscillator Model Equation of motion for the electron : Electric-dipole approximation : where, : relative coordinate of the e-n pair : center-of-mass coordinate of the e-n pair : reduced mass Electron oscillator model (Lorentz model)

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Nonlinear Optics Lab. Hanyang Univ. 2.3 Refractive Index and Polarizability Consider a monochromatic plane wave, Dipole moment : where, polarizability : Polarization :

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Nonlinear Optics Lab. Hanyang Univ. From (2.1.13), : dispersion relation in a medium For a medium with the z electrons in an atom : : refractive index of medium (2.3.22a)

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Nonlinear Optics Lab. Hanyang Univ. Electric susceptibility (macroscopic parameter), :

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Nonlinear Optics Lab. Hanyang Univ. 2.4 The Cauchy Formula From (2.3.22), If <<, If we suppose further that(as in like a gas medium) where, : Cauchy formula

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