Introduction to Lasers -...

Introduction to Lasers

OPTI 500 ABCCarl Maes

September 6, 2012

Contents

• Introduction and Motivation • Interaction of Light and Matter• Light Amplification• Basics of Laser Operation• Laser Oscillation and Specific Laser Systems

Introduction & Motivation

• (Laser applications, particular properties of laser radiation, history of laser developments, references)

Borrowed from Thomas Halfmann Laser Physics course

References• Laser Physics, by Simon Hooker and Colin Webb• Laser Material Processing, 4th ed., William Steen and Jyotirmoy Mazumder. Online

at http://www.springerlink.com/content/978‐1‐84996‐062‐5#section=823328&page=1

• Phontonic Simulation Software for Teaching: http://www.st‐andrews.ac.uk/~psst/• Lasers, by Anthony Siegman• Laser Physics, by Milonni and Eberly (2010)• Lasers, by Milonni and Eberly (1988)• Laser Resonators and Beam Propagation, by Hodgson and Weber, online at

http://www.springerlink.com/content/n31g100834x7/• Solid State Lasers, by Koechner• Solid State Lasers, a Graduate Text, Koechner and Bass, online at

http://www.scribd.com/doc/10565960/SolidState‐Lasers‐A‐Graduate‐Text‐koechner‐Mbass

• Laser Electronics, by Verdeyen• Principles of Lasers, by Orazio Svelto• Optical Electronics in Modern Communications, by Yariv

Amplification—General Case

Amplification—a Closer Look

Note the shape of the Gain curve…

Interaction of Light and Matter

Radiative processes: (a) absorption—an incident photon is absorbed while the atomic state is elevated from energy level E1 to E2(b) spontaneous emission—a photon is emitted while the atomic system descends from energy level E2 to E1(c) stimulated emission—an additional photon is emitted when an atomic system is under the action of an incident photon→”light amplification”

Light Amplification—Interaction of Light and Matter

• Light amplification not common in nature—Why?

• Thermal equilibrium between light and matter– Absorption of light much more dominant over gain because of Boltzmann’s Distribution of Matter

• Probability for transitions resulting in emission at optical frequencies at room temperature is about e‐40

TkEE

NN

B

12

1

2 exp

Photonics, 6th edition Yariv and Yeh 13

Figure 5.5 Amplification of a traveling electromagnetic wave in (a) an inverted population (N2 N1) and (b) attenuation in an absorbing (N2 < N1) medium.

Light Amplification

• Requires Population Inversion, N2>N1

• Need some sort of external pump to raise atomic population from lower to upper energy level

Examples of Pumping


Spectral LineshapeGain (or Absorption) Profile

Frequency dependent phase shiftn is index of refraction

Transition Wavelength: Center Wavelength with Finite Spectral Width

Laser Operation• Light Amplification by Stimulated Emission of Radiation• Maximize light amplification/stimulated emission by use of optical resonator

• Stimulates emission along optical axis• Narrows spectral linewidth typically

Pump

Gain Medium Requirements

• Lasing not possible with only two energy levels due to saturation: N1=N2 with maximum pumping so no population inversion

• Solution: Pump to higher energy level that decays to upper lasing level; laser transition between upper and lower lasing energy levels

• Require at least three energy levels to obtain population inversion


Idealized 3‐Level Laser

Photonics, 6th edition Yarivand Yeh

Idealized 4‐Level Laser

Note advantage over 3‐level laser: if decay from E1 to E0 is very rapid, then any nonzero population in E2 results in population inversion!


Figure 5.6 Energy levels and transition rates of a four‐level laser system. (The fourth level, which is involved in the original excitation by the pump, is not shown and the pumping is shown as proceeding directly into levels 1 and 2.) The total lifetime of level 2 is t2, where 1/t2 = 1/tspont + 1/t20, where 1/t20 is the decay rate to the ground state (0).

Energy Levels and Rates

Note: Require tspont > t1 to build population inversion

Threshold and Pumping • Initially active medium is at thermal equilibrium• Pumping increases population into upper lasing level• Higher pumping results in population inversion…but still no

lasing yet• Still higher pumping required to overcome losses

– Optical resonator losses due to transmitted beam– Internal losses due to scattering, absorption, etc.

• Finally, with more pumping, obtain Pump Threshold: laser amplifier gain equals system losses.

• Still higher pumping increases output power; however gain is clamped at threshold value due to gain saturation of population

24

Laser Gain and Threshold

Losses Gain :lasingfor Condition

ln1

4

)()(

:) of linewidth FWHM is recenter whe lineat Gain

)(8

)()(

mediumgain oflength ,ty reflectivi , loss internal ), Lineshapefrequency , refraction ofindex , spopulation ,constant Gain

21threshold

spont2

2

120

spont

2

12

RRl

tNN

g(υ

gt

NN

lRg(υnN

i

i

Gain Saturation• Reduction of population inversion and hence gain due to intense radiation in gain medium

σ(υ)Nγ(υ)

gt

hI

σ τI

NNNI

ININ

N

*

RR

s

Rs

1gg

2*

s

*

1

2

:Note

and )(8

)( where)(

section crossgain ,imerecovery t , Instensity Saturation

where1

)0()(

Population Saturated

2spont

2

**

Photonics, 6th edition Yariv and Yeh

Threshold Pump Power, Pth

Pump Threshold and Efficiency

Minimum pump power required: Must obtain population inversion, N2> N1

ANDMust have sufficient gain (stimulated emission) to overcome losses (mirrors, etc.)

1

αTl

2TAIP

2

g2s 0modeout

2


Figure 6.7 Useful power output (Po) versus mirror transmission T for various values of internal loss Li in an He–Ne 6328 Å laser.(After Reference [3].)

Output Power Dependence on Mirror Reflectivity and Internal Losses

Note: •Optimal value for mirror reflectivity•Internal losses strongly impact output power•Internal loss examples: dirty mirrors, scattering, etc.


Figure 6.1 Schematic drawing of multiple reflections inside a Fabry–Perot cavity and the corresponding partially transmitted beams. E1 isthe first transmitted beam, E2 is the transmitted beam after one round‐trip inside the cavity, E3 is the transmitted beam after two round‐tripsinside the cavity, and so on.

•Optical Resonator acts as a Fabry‐Perot cavity•Low loss modes transmitted only at specific frequencies (longitudinal modes)

Optical Resonator


Figure 6.10 (a) Inhomogeneously broadened Doppler gain curve of the 6328 Å Ne transition and position of allowed longitudinal‐mode frequencies. (b) Intensity versus frequency profile of an oscillating He–Ne laser. Six modes have sufficient gain to oscillate (After Reference [5].)

Note relative width of Gain curve and Resonator Modes

Longitudinal Modes and Gain Profile

Atomic Gain Lineshape Broadening

• Lineshape broadening causes:– Radiative lifetime (spontaneous emission)– Collisions of gas atoms (phase perturbation)– Phonons in solids (shifts linecenter)– Doppler effect (linecenter velocity dependence)– Asymmetric strain in substrate (shifts linecenter)

• Homogenous broadening (all atoms experience same magnitude of effect)

• Inhomogenous broadening (different groups of atoms experience different magnitude of effect

Homogeneous Broadening Below and Above Threshold

Inhomogeneous Broadening Below and Above Threshold

Photonics, 6th edition Yarivand Yeh33

Figure 6.9 (a) Single‐pass gain curves for a homogeneous atomic system (A—below threshold; B—at threshold; C—well above threshold).(b) Mode spectrum of optical resonator. (c) Oscillation spectrum (only one mode oscillates). (d) Single‐pass gain curves for an inhomogeneous atomic system (A—below threshold; B—at threshold; C—well above threshold). (e) Mode spectrum of optical resonator. (f) Oscillation spectrum for pumping level C, showing three oscillating modes.

Summary of Broadening, Saturation, and Threshold Effects on Lasing


Figure 6.39 Pumping–oscillation cycle of a typical laser.

Specific Laser Examples

• Nd:YAG, • Ruby• Erbium• Ti:sapphire• Perhaps most common: laser pointer


Figure 6.46 Energy‐level diagram of Nd3+ in YAG. (After Reference [42].) The unit 1 cm–1 corresponds to = 30 GHz, or h = 1.24 × 10–4 eV.


Figure 6.47 Spontaneous emission spectrum of Nd3+ in YAG near the laser transition at 0 = 1.064 m. (After Reference [43].)


Figure 6.48 Typical continuous solid‐state laser arrangement employing an elliptic cylinder housing for concentrating lamplight onto laser.


Figure 6.50 Fluorescent emission of the 1.06 m line of Nd3+ at 300 K in various glass bases. (After Reference [44].)


Figure 6.51 Nd3+ absorption spectrum for a sample of glass 6.4 mm thick with the composition 66 wt.% SiO2, 5 wt.% Nd2O3, 16 wt.% Na2O, 5 wt.% BaO, 2 wt.% A12O3, and 1 wt.% Sb2O3. (After Reference [44].)


Figure 6.44 Typical setup of a pulsed ruby laser using flashlamp pumping and external mirrors.


Figure 6.40 Energy levels pertinent to the operation of a ruby laser. The unit 1 cm–1 corresponds to v = 30 GHz, or hv = 1.24 × 10–4 eV.(After Reference [38].)


Figure 6.41 Absorption coefficient and absorption cross section as functions of wavelength for E || c and E c. The 300 K data were derived from transmittance measurements on pink ruby with an average Cr ion concentration of 1.88 × 1019 cm–3. (After Reference [39].)


Figure 6.43 Linewidth of the R1 line of ruby as a function of temperature. (After Reference [40].)


Figure 6.45 Spectral output characteristics of two commercial high‐pressure lamps. Output is plotted as a fraction of electrical input tolamp over certain wavelength intervals (mostly 200 Å) between 0.4 and 1.4 m. (After Reference [41].)


Figure 6.55 Energy levels of Ti3+ ions in sapphire crystal showing the effect due to crystal–field, spin–orbit, and Jahn–Teller splitting.


Figure 6.56 Absorption cross section (in units of 10–20 cm2) for the transition 2T2 2E in the Ti:sapphire laser as a function of wavelength(in units of nm). E = polarization of electric field; c = axis of symmetry of crystal. (Data from Reference [52].)


Figure 6.57 Emission spectra of the Ti:sapphire laser. E = polarization of electric field; c = axis of symmetry of crystal. (Data from Reference [52].)


Figure 6.53 Energy levels of Er3+ ion and some dominant transitions. The unit 1 cm–1 corresponds to = 30 GHz, or h = 1.24 × 10–4 eV.

pump

Wikipedia: Kerr‐lens modelocking

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