Fadhali- Laser Micromachining 2

7/31/2019 Fadhali- Laser Micromachining 2

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LASER BEAM CHARACTERISTICS

Monochromaticity

Directionality

Coherence

Brightness

Laser

EmissionSpont-

EmissionI


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This property is due to the following two factors. First, only an EM wave of

frequency can be amplified .has a certain range which is called linewidth, this linewidth is decided by

homogeneous broadening factors and inhomogeneous broadening factors,the result linewidth is very small compared with normal lights. Second, thelaser cavity forms a resonant system, oscillation can occur only at theresonance frequencies of this cavity. This leads to the further narrowing ofthe laser linewidth, the narrowing can be as large as 10 orders of

magnitude! So laser light is usually very pure in wavelength, we say it hasthe property of monochromaticity.

hEE /)( 120 =0

Monochromaticity


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For any EM wave, there are two kinds of coherence, namely spatial and

temporal coherence. Lets consider two points that, at time t=0, lie on the

same wave front of some given EM wave, the phase difference of EM waveat the two points at time t=0 is

0. If for any time t>0 the phase difference of

EM wave at the two points remains0, we say the EM wave has perfect

coherence between the two points. If this is true for any two points of thewave front, we say the wave has perfect spatial coherence. In practical thespatial coherence occurs only in a limited area, we say it is partial spatial

coherence. Now consider a fixed point on the EM wave front.

+= )cos( iii tAE Laser radiation is composed of waves at the samewavelength, which start at the same time and keep their relativephase as they advance.

Coherence


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Temporal coherence: Considering the electric field of the em wave, at a

given point P, at times tand t+ . If, for a given time delay , the phasedifference between the two field remains the same for any time t, we say that

there is a temporal coherence over a time . If this occurs for any value of,the em wave is said to haveperfect temporal coherence. If this occurs for a

time delay such that 0 < < 0, the wave is said to havepartial temporal

coherence, with a coherence time equal to 0.

Temporal Coherence is related to monochromaticity.

Spatial Coherence is related to directionality anduniphase wavefronts.


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Directionality

laser

dD

Even for the case of perfect spatial coherence, a beam of finite

aperture has unavoidable divergence due to diffraction. This canbe understood with the help from diffraction theory, for an

arbitrary amplitude distribution, we can have

Dd

=

where andD are the wavelength and the diameter of thebeam, respectively. The factor is a numerical coefficient of

the order of unity whose value depends on the shape of theamplitude distribution and how both the divergence and the

beam diameter are defined.


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The brightness of a light source is defined as the power emitted per unit surface area per

unit solid angle. A laser beam of power P, with a circular beam cross section of diameter

D and a divergence angle and the result emission solid angle is 2, the brightness is

given by:

For the partial spatial coherence, its divergence is greater than the minimum

value set by diffraction. Indeed, for any point P' of the wave front, the

Huygens argument in Fig. 1.6 can be applied only for points lying within the

coherence area Sc around point P'. The coherence area thus acts as a limiting

aperture for the coherent superposition of elementary wavelets. Thus, the

beam divergence can now be written as:

2/1)( cS

=

Divergence:

Gas lasers-0.001rad

solid-state lasers-0.01rad

Brightness


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The maximum brightness for a beam of power P is

PB

2

2

=

In case of limited diffraction


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CW and pulsed operation

The laser can be continuously pumped and hence theoutput power is continuous

It can be operated in pulsed mode using Q-switching

and mode locking techniques


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Short Pulse Duration

Utilizing Q-switch and mode-lock technologies, one canobtain fromps tofs laser pulses.

Generally, the laser pulse duration

0

1~

p

where 0 is the laser linewidth. For gas lasers, it is aboutor less than 1GHz while it is about 300GHz for solid-state

and dye lasers. So from solid-state lasers, we can have

very short laser pulses (10fs).


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Average and peak power

Assume the energy, E , contained in every pulse is constant. Power is just the time rate

of change of the energy flow (energy per unit time). So this leads us to define two

different types of power.

1. Definition of peak power : Rate of energy flow in every pulse.

2. Definition of average power :

Rate of energy flow averaged over one full period (recall that f=1/T ).

Solve both for E and equate:

Rearranging variables allows us to define a new quantity called Duty Cycle, the

fractional amount of time the laser is on during any given period.


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Modes of the laser beam

Laser modes can be classified as

1. Transverse Electromagnetic Modes

They are the electromagnetic distribution developed by the oscillation

inside the cavity (optical resonator)

In many lasers, the symmetry of the optical resonator is restricted by

polarization elements such as Brewster's angle windows. In these lasers,

transverse modes with rectangular symmetry are formed. These modes aredesignated TEMmn with m and n being the horizontal and vertical orders of

the pattern. The intensity at pointx,y is given by:


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o Wave equation looks like harmonic oscillator

o Ex: E =Ee -it

o Separate out z dependence

o Solutions for x and y are Hermite polynomials

Frequencies of transverse modes

Transverse laser modes

0

2

2 =

+ E

c

nE

02

2

=+ xmk

dtxd

02 22

2

2

2

2

2

2

=

+

+

+

+

Ekc

n

y

E

x

E

z

Eik

z

E


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How to make a laser operate in a single basic transverse mode?


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2. Longitudinal modes

These are formed by the standing waves developed inside the cavity resonator

They can be defined as the standing oscillating electromagnetic waves which

are defined by the cavity geometry.


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Focal spot size

It determines the maximum energy density that can be achieved when the laser beam

power is set, so the focal spot size is very important for material processing. When abeam of finite diameter D is focussed by a lens onto a plane, the individual parts of the

beam striking the lens can be imagined to be point radiators of new wave front. The light

rays passing through the lens will converge on the focal plane and interfere with each

other, thus constructive and destructive superposition take place, light energy is

distributed as described in figure below. The central maximum contains about 86% of

the total power.


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The focusing diameter is measured between the points where the intensity has fallen to

1/e 2 of the central peak value. For a rectangular beam with a plane wave front, the

diffraction limited beam diameter, which is the smallest focal diameter, is given by:

For a circular beam

For multi-mode beam TEMplq, the focal spot size is larger than the above two

values. The smallest possible focal sopt size in this case is:

Where f is the lens focal

length, D is the beam

diameter,

There are other factors that affect focal spot size, such as spherical aberration and

thermal lensing effects. Most lenses are made with a spherical shape, but theycannot be of perfect shape, there exist spherical aberration. Lenses in laser systems

transmit or reflect high power laser radiation, laser power variations can cause

shape changes of the lenses, so the focal point will change when the radiation power

changes, thus affect the focal spot size.


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Depth of focus

The laser light is first converged at the lens focal plane, then diverges to wider

beam diameter again. The depth of focus is the distance over which the focused

beam has about the same intensity, it is defined as the distance over which the

focal spot size changes 5%~5%.

f is the lens focal length, D is the unfocussed beam diameter.

Longer depth of focus is preferred, because equal energy density along the beam

is preferred when using the laser to process materials.


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Polarization

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Fadhali- Laser Micromachining 2

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