06 laser-basics

Laser basics

Optics, Eugene Hecht, Chpt. 13;Optical resonator tutorial:

http://www.dewtronics.com/tutorials/lasers/leot/

Laser oscillationLaser is oscillator• Like servo with positive feedback • Greater than unity gain

Ruby laser example

Laser turn-on and gain saturation

Laser gain and losses

Gain decreases as output power increases• Saturation

Fabry-Perot cavity for feedback• High reflectivity mirrors• Low loss per round trip• Must remember resonance conditions

– round trip path is multiple of

• High reflectivity Fabry-Perot cavity• Boundary conditions

– field is zero on mirrors• Multiple wavelengths possible

– agrees with resonance conditions

Laser longitudinal modesClassical mechanics analog

Multi-mode laser

Fabry-Perot boundary conditions

Multiple resonant frequencies

Single longitudinal mode lasers• Insert etalon into cavity• Use low reflectivity etalon

– low loss

Laser transverse modes• Wave equation looks like harmonic oscillator

• Ex: E = E e -it

• Separate out z dependence

• Solutions for x and y are Hermite polynomials

Frequencies of transverse modes

Transverse laser modes

02

2

EcnE

02

2

xmk

dtxd

02 22

2

2

2

2

2

2

Ek

cn

yE

xE

zEik

zE

Single transverse mode lasers• Put aperture in laser• Create loss for higher order modes

Multi-longitudinal Multi-transverse&long. Single mode

Gaussian beams• Zero order mode is Gaussian• Intensity profile:• beam waist: w0

• confocal parameter: z

• far from waist

• divergence angle

22 /20

wreII

2

20

0 1

wzww

2

0wzR

0wzw

00

637.02ww

Gaussian propagation

Power distribution in Gaussian• Intensity distribution:• Experimentally to measure full width at half maximum (FWHM) diameter• Relation is dFWHM = w 2 ln2 ~ 1.4 w• Define average intensity• Iavg = 4 P / ( d2

FWHM)

• Overestimates peak: I0 = Iavg/1.4

22 /20

wreII

Resonator options• Best known -- planar, concentric, confocal• Confocal unique

– mirror alignment not critical– position is critical– transverse mode frequencies identical

Types of resonators

Special cases