Introduction to Lasers `\ \ \ \ \ \ `Sept. 6, 2017

• Laser -- optical oscillator, i.e. amplifier + feedback
Animination of laser oscillation

• Threshold for oscillations: round trip gain * loss `>= 1`

• Laser = Light Amplification by Stimulated Emission of Radiation.

History of laser: A team afford, maser `->` lasers covering a wide spectrum from far infra-red to X-ray.
(Theory: Townes, Schawlow and Prokhorov. Practice: Maiman.)

• Laser market: Diode laser (semi-conductor) versus nondiode laser; material processing, medicine, communication, R&D, optical memory & entertainment.

• Radiation: material transition from excited state to ground state; candidates -- atomic transition levels, molecular vibration levels and energy bands.

• Radiative processes: Stimulated emission `->` optical amplification with uniformity of freq., direction, polarization and phase (time delay) `=>` `bb{coherent}`.
Spontaneous emission `->` noise
Absorption `->` inverse of stimulated emission

• Photon energy: `E= E_2 - E_1 = h nu` where `h -` planck constant, `nu -` optical frequency and `h nu` is photon energy; `E(eV) = E / q` or in wavelength `lambda ( mu m ) = 1.24 / {E (eV)}`.

Population inversion (`N_2 > N_1`): require 3-level and 4-level atomic systems for lasing.

• Pumping sources: electrical, chemical, optical, thermal, nuclear.

• CW & pulse: average power (W), peak power (W), fluence (energy density) `(J/{m^2})`, intensity (average power density) `(W/{m^2})`; pulse width -- Full Width Half Max (FWHM) or `e^{-2}` full width.

• Linewidth and coherency: conversion between freq width (bandwidth) `Delta nu` and wavelength width (linewidth) `Delta lambda` (again FWHM): `{Delta lambda}/ lambda = {Delta nu}/ nu`
temporal coherence `-\ delta tau = 1 /{Delta nu}` or `l_c = c_o delta tau`;
spatial coherence `-\ l_t = {r lambda} / s`;
coherence measured by interferometer.

• Transverse and longitudinal modes: transverse mode -- interference pattern labeled by `TEM_{n,m}` for laser;
longitudinal mode -- mode spacing (free spectral range) `Delta nu_{FSR} = 1/ {round\ trip\ time}`.

• Gain profile: spectral width of gain provided by a medium `Delta nu_{g} > Delta nu_{FSR} >` bandwidth of cavity `Delta nu`.

• Uncertainty relationship & pulse spreading:
Nyquist theorem `Delta omega Delta t >= 1/2`; `Delta k Delta x >= 1/2`.

Laser Engineering Chapter 1

Energy level and quantum mechanics

Last Modified: Sept. 5, 2017
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