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

Ec

nE

02

2

xm

k

dt

xd

02 22

2

2

2

2

2

2

Ekc

n

y

E

x

E

z

Eik

z

E

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

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wreII

2

20

0 1

w

zww

2

0wzR

0w

zw

00

637.02

ww

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 / ( d2FWHM)

• Overestimates peak: I0 = Iavg/1.4

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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