Main Requirements of the Laser Optical Resonator Cavity ...gchapman/e894/e894l2j.pdfTransverse Modes...

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Main Requirements of the Laser Optical Resonator Cavity Laser Gain Medium of 2, 3 or 4 level types in the Cavity Sufficient means of Excitation (called pumping) eg. light, current, chemical reaction Population Inversion in the Gain Medium due to pumping Laser Types Two main types depending on time operation Continuous Wave (CW) Pulsed operation Pulsed is easier, CW more useful

Transcript of Main Requirements of the Laser Optical Resonator Cavity ...gchapman/e894/e894l2j.pdfTransverse Modes...

Page 1: Main Requirements of the Laser Optical Resonator Cavity ...gchapman/e894/e894l2j.pdfTransverse Modes • Comes from microwave cavities • Some waves travel off axis, but within cavity

Main Requirements of the Laser • Optical Resonator Cavity • Laser Gain Medium of 2, 3 or 4 level types in the Cavity • Sufficient means of Excitation (called pumping) eg. light, current, chemical reaction • Population Inversion in the Gain Medium due to pumping

Laser Types • Two main types depending on time operation • Continuous Wave (CW) • Pulsed operation • Pulsed is easier, CW more useful

Page 2: Main Requirements of the Laser Optical Resonator Cavity ...gchapman/e894/e894l2j.pdfTransverse Modes • Comes from microwave cavities • Some waves travel off axis, but within cavity

Optical Resonator Cavity • In laser want to confine light: have it bounce back and forth • Then it will gain most energy from gain medium • Need several passes to obtain maximum energy from gain medium • Confine light between two mirrors (Resonator Cavity) Also called Fabry Perot Etalon • Have mirror (M1) at back end highly reflective • Front end (M2) not fully transparent • Place pumped medium between two mirrors: in a resonator • Needs very careful alignment of the mirrors (arc seconds) • Only small error and cavity will not resonate • Curved mirror will focus beam approximately at radius • However is the resonator stable? • Stability given by g parameters: g1 back mirror, g2 front mirror:

ii r

L1g −=

• For two mirrors resonator stable if

1gg0 21 << • Unstable if

1gg0gg 2121 ><

• At the boundary (g1g2 = 0 or 1) marginally stable

Page 3: Main Requirements of the Laser Optical Resonator Cavity ...gchapman/e894/e894l2j.pdfTransverse Modes • Comes from microwave cavities • Some waves travel off axis, but within cavity

Stability of Different Resonators • If plot g1 vs g2 and 1gg0 21 << then get a stability plot • Now convert the g’s also into the mirror shapes

Page 4: Main Requirements of the Laser Optical Resonator Cavity ...gchapman/e894/e894l2j.pdfTransverse Modes • Comes from microwave cavities • Some waves travel off axis, but within cavity

Polarization of Light • Polarization is where the E and B fields aligned in one direction • All the light has E field in same direction • Black Body light is not polarized • But if pass though a material with parallel structure may polarize • Causes mostly light with same alignment to pass through • Caller polarizing filters • Changes unpolarized light into polarized light • Polarization also often occurs on reflection or on scattering • Polarizing filters have direction • If have two filters at 90o then almost no light passes through

Page 5: Main Requirements of the Laser Optical Resonator Cavity ...gchapman/e894/e894l2j.pdfTransverse Modes • Comes from microwave cavities • Some waves travel off axis, but within cavity

Polarization and Lasers • Lasers often need output windows on gain medium in cavity • Output windows often produce polarized light • Normal windows lose light to reflection • Least loss for windows if light hits glass at Brewster Angle • Perpendicular polarization reflected • Parallel polarization transmitted with no loss (laser more efficient) • Called a Brewster Window & the Brewster Angle is

⎟⎟⎠

⎞⎜⎜⎝

⎛= −

1

21b n

ntanθ

n1 = index of refraction of air n2 = index of refraction of glass • Example: What is Brewster for Glass of n2 = 1.5

o1

1

21b 6.56

15.1tan

nntan =⎟

⎠⎞

⎜⎝⎛=⎟⎟

⎞⎜⎜⎝

⎛= −−θ

Page 6: Main Requirements of the Laser Optical Resonator Cavity ...gchapman/e894/e894l2j.pdfTransverse Modes • Comes from microwave cavities • Some waves travel off axis, but within cavity

Laser Threshold • With good Gain Medium in optical cavity can get lasing but only if gain medium is excited enough • Low pumping levels: mostly spontaneous emission • At some pumping get population inversion in gain medium • Beyond inversion get Threshold pumping for lasing set by the losses in cavity • Very sensitive to laser cavity condition eg slight misalignment of mirrors threshold rises significantly • At threshold gain in one pass = losses in cavity

Page 7: Main Requirements of the Laser Optical Resonator Cavity ...gchapman/e894/e894l2j.pdfTransverse Modes • Comes from microwave cavities • Some waves travel off axis, but within cavity

Round Trip Power Gain • Within medium light intensity I gained in one pass

( )[ ]LgexpI)L(I 0 α−=

where g = small signal gain coefficient α = the absorption coefficient L = length of cavity • Thus calculate Round Trip Power Gain Gr • Each mirror has a reflectivity Ri R=1 for perfect reflection off a mirror

( )[ ]L2gexpRR)0(I)L2(IG 21r α−==

• At threshold Gr = 1 • Thus threshold gain required for lasing is

⎟⎟⎠

⎞⎜⎜⎝

⎛+=

21th RR

1lnL21g α

• Some of the loss = laser emission

Page 8: Main Requirements of the Laser Optical Resonator Cavity ...gchapman/e894/e894l2j.pdfTransverse Modes • Comes from microwave cavities • Some waves travel off axis, but within cavity

Transition Line Shape • Distribution of energy levels creates width of emission • Usually Gaussian shape • Width broadened by many mechanisms • Most more important in gases • Doppler Broadening (movement of molecules) • Collision Broadening (atomic/molecular collisions) • Radiative Lifetime Broadening (finite lifetime of transitions)

Page 9: Main Requirements of the Laser Optical Resonator Cavity ...gchapman/e894/e894l2j.pdfTransverse Modes • Comes from microwave cavities • Some waves travel off axis, but within cavity

Axial Modes of Laser • Proper phase relationship only signal in phase in cavity • Thus cavity must be integer number of half wavelengths

2pL λ

=

where p = integer • Results in frequency separation of peaks

L2c

=Δν

• Emission from the atomic transitions is a wider Gaussian • Result is axial modes imposed on Gaussian Transition spread

Page 10: Main Requirements of the Laser Optical Resonator Cavity ...gchapman/e894/e894l2j.pdfTransverse Modes • Comes from microwave cavities • Some waves travel off axis, but within cavity

Axial modes within Transition Gaussian • Each axial mode is Gaussian shape narrower than transition peak • eg for L=1 m Argon laser at 514 nm

Hz10x83.510x14.510x00.3cMHz150

210x00.3

L2c 14

7

88

======Δ −λνν

• Thus emission much smaller than 0.0026% of frequency Much narrower than other light sources.

Page 11: Main Requirements of the Laser Optical Resonator Cavity ...gchapman/e894/e894l2j.pdfTransverse Modes • Comes from microwave cavities • Some waves travel off axis, but within cavity

Transverse Modes • Comes from microwave cavities • Some waves travel off axis, but within cavity • Result is Phase changes in repeating paths • These can change shape of output • Get local minimums (nulls) in the output beam shape • Reduce these by narrowing the beam • Called Transverse ElectroMagnetic, TEM

Page 12: Main Requirements of the Laser Optical Resonator Cavity ...gchapman/e894/e894l2j.pdfTransverse Modes • Comes from microwave cavities • Some waves travel off axis, but within cavity

Transverse Modes • Transverse ElectroMagnetic, TEM depend on cavity type • In cylindrical geometry two possible phase reversal orientations • horizontal (q) and vertical (r) • Show these as TEMqr • q and r give number of null's in output beam • Horizontal (q) gives number of vertical running nulls • Vertical (r) gives number of horizontal running nulls • Thus TEM12 has 2 vertical, 1 horizontal nulls • Special mode TEM01* or donut mode • comes from rapid switching from TEM01 to TEM10

Page 13: Main Requirements of the Laser Optical Resonator Cavity ...gchapman/e894/e894l2j.pdfTransverse Modes • Comes from microwave cavities • Some waves travel off axis, but within cavity

General Laser Types • Solid State Laser (solid rods): eg ruby • Gas laser: eg He-Ne • Dye Lasers • Semiconductor Laser: GaAs laser diode • Chemical Lasers • Free Electron Lasers

Page 14: Main Requirements of the Laser Optical Resonator Cavity ...gchapman/e894/e894l2j.pdfTransverse Modes • Comes from microwave cavities • Some waves travel off axis, but within cavity

Gas Lasers • Gas sealed within a tube with brewster windows • electric arc in tube causes glowing of gas • glow indication of pumping • Commonest type He-Ne

Page 15: Main Requirements of the Laser Optical Resonator Cavity ...gchapman/e894/e894l2j.pdfTransverse Modes • Comes from microwave cavities • Some waves travel off axis, but within cavity

He-Ne Laser Energy levels • One type of 3 level laser

Page 16: Main Requirements of the Laser Optical Resonator Cavity ...gchapman/e894/e894l2j.pdfTransverse Modes • Comes from microwave cavities • Some waves travel off axis, but within cavity

Einstein Coefficients and Lasers • Recall the Einstein Emission/Absorption Coefficients • Consider again a 2 level system being pumped by light • A21 is the Einstein spontaneous emission Coefficient • B12 is the Einstein spontaneous absorption coefficient • B21 is the Einstein stimulated emission coefficient • At equilibrium the absorption from pumping equals the spontaneous and stimulated emission.

212212121 BNANBN ρρ +=

• Now recall the Boltzman distribution

[ ]⎟⎠⎞

⎜⎝⎛=⎟

⎠⎞

⎜⎝⎛ −

=KThexp

KTEEexp

NN ν01

0

1

• ν = the frequency of the light • hν = energy in photon • Thus

212112 BAKThexpB ρνρ +=⎟

⎠⎞

⎜⎝⎛

Page 17: Main Requirements of the Laser Optical Resonator Cavity ...gchapman/e894/e894l2j.pdfTransverse Modes • Comes from microwave cavities • Some waves travel off axis, but within cavity

Einstein Coefficients relationships • Solving for the emitted photon energy density

2112

21

BKThexpB

A

−⎟⎠⎞

⎜⎝⎛

ρ

• From Planck's law the photons emitted at a given temperature are:

⎥⎦⎤

⎢⎣⎡ −⎟

⎠⎞

⎜⎝⎛

=1

KThexpc

h83

3

ννπρ

• From these two can solve noting B12 = B21

123123

3

21 Bh8Bch8A

λπνπ

==

• Note absorption to emission increases rapidly with wavelength

Page 18: Main Requirements of the Laser Optical Resonator Cavity ...gchapman/e894/e894l2j.pdfTransverse Modes • Comes from microwave cavities • Some waves travel off axis, but within cavity

Under Lasing Conditions • Spontaneous emission is nil so total emission/unite area is

( ) νρhBNNdxdI

2112 −=

• For a linear beam I = ρ c (energy density times speed) thus

( )c

IhBNNdxdI ν2112 −

=

• Thus the gain is

( )c

hBNNg ν2112 −=

• Or substituting for the spontaneous coefficient

( ) ( )21

212

2

22112

88 πτλ

πνNNcANNg −

=−

=

• Three important implications because we need g>gth to lase (1) For gain N2>N1 (i.e. population inversion) (2) Shorter wavelength the lower the gain Hence much harder to make UV than IR lasers (3) Want short lifetime τ21 for higher gain • But want metastable long τ21 to get population inversion! • Hence tradeoff: τ21 must be short enough for threshold g but long enough for population inversion • More difficult to achieve for CW (continuous) lasers