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, 가을학기

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 nm 1961, A. Javan : He-Ne 1.15  m, nm …

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

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.

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)

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

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

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 

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

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, =>

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

Nonlinear Optics Lab. Hanyang Univ. =>

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

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

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

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

Nonlinear Optics Lab. Hanyang Univ.

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

Nonlinear Optics Lab. Hanyang Univ. example) Focusing a Gaussian beam 11 ? ?

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.

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

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)

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

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)

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

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