Download properties of laser beams

PROPERTIES OF LASER BEAMS
 Laser beam is generated in a specific wave length by the
interaction of electromagnetic wave with the active medium.
 To represent this emission line we draw
the radiation intensity as a function of
wave length or frequency.
 Also we assumed that the emission of the exited atom is
focused at one frequency νo called the Resonance
Frequency.
 In reality the absorption and emission process does not
happened at single frequency νo but at band of frequency ∆
ν represent the width of the emission line.
 This width of the emission line depends in many factors we
are gowning to discuss.
 Emission line is described by plotting spontaneous emission
radiation intensity as a function of frequency (or
wavelength), for the specific lasing transition
1. Monochromaticity
• The theoretical limit to this monochromaticity arises
from zero-point fluctuations
• In another word frequent changes in amount, value, or
level.
• However, this limit generally corresponds to a very low
value for the oscillating bandwidth ∆ν
• In many cases, technical effects, such as vibrations and
thermal expansion of the cavity, determine the laser
linewidth ∆ν.
This property is due to the following two
circumstances:
A) Only an em wave of frequency ν (one
wavelength) given by Eq. (1.1.1) can be amplified.
B) Since a two-mirror arrangement forms a resonant
cavity, oscillation can occur only at the resonance
frequencies of this cavity.
To get much narrower laser linewidth than the usual
line width of the transition 2—> 1, as observed in
spontaneous emission we have to control the this
circumstances. The degree of monochromaticity
required depends of course on the given
application.
• The narrowest laser linewidths are needed for only
the most sophisticated applications in metrology and
fundamental measurements in physics (e.g.,
gravitational wave detection).
• For more common applications, such as
interferometric measurements of distances, coherent
laser radar, and coherent optical communications, the
required monochromaticity falls in the 10-100 kHz
range.
• A monochromaticity of ~1 MHz is typically needed for
much of high- resolution spectroscopy, and it certainly
suffices for optical communications using WDM.
• For some applications, of course, laser
monochromaticity is not relevant; this is the case in
important applications such as laser material working
and most applications in the biomedical field.
2. Coherence:
There are two types of coherence, spatial and temporal
By definition the difference between phases of the two
fields at time t = 0 is zero. If this difference remains zero
at any time t > 0, we say that there is a perfect
coherence between the two points. If such coherence
occurs for any two points of the em wave front, we then
say that the wave has perfect spatial coherence.
• To define temporal coherence, we now consider the
electric field of the em wave, at a given point, at times
t and t + τ.
• The phase difference between the two fields remains
the same for any time τ, we say that there is a
temporal coherence over a time t.
• If this occurs for any value of τi,
the em wave is said to have perfect
temporal coherence.
• It is important to point out that the two concepts of
temporal and spatial coherence are indeed
independent of each other. In fact examples can be
given of a wave with perfect spatial coherence but
only limited temporal coherence (or vice versa).
3. Directionality:
This property is a direct consequence of the fact that the active
medium is placed in a resonant cavity.
According to Huyghens's principle the wave front at some plane P
behind the screen can be obtained by the superposition of the
elementary waves emitted by each point of the aperture. We thus
see that, on account of the finite size D of the aperture, the beam
has a finite divergence θd. Its value can be obtained from
diffraction theory. For an arbitrary amplitude distribution, we
obtain
where β is a numerical coefficient of the order of
unity whose exact value depends on how both the
divergence θ and coherence area Sc are defined.
The output beam of a laser can be made diffraction
limited.
4.Brightness
We define the brightness of a given source of em
waves as the power emitted per unit Surface area
per unit solid angle
let dS be the elemental surface
area at point O of the source (Fig. 1.7a).
The power dP emitted by dS into a solid angle dΩ
around direction OO' can be written as:
where θ is the angle between OO' and the normal
n to the surface. The quantity cosθ ds is projection of
dS on the plane. . The quantity B is called the calle
the source brightness.
• When B is a constant, the source is said to be
isotropic (or a Lambertian source).
• Let us now consider a laser beam
of power P , with a circular cross section of
diameter D and with a divergence 9 (Fig. 1.7b)
Since θ is usually very small, we have cos θ= 1.
Since the area of the beam is equal to πD2/4 and
the emission solid angle is πθ2, then, according
to Eq. (1.4.3), we obtain the beam brightness as:
which is the maximum brightness for a beam of
power P. power of the beam W/cm2or mW/cm2
Example:
Calculate the irradiance of the beam of He Ne
laser of power 5 mw and of area 0.2cm2?
Solution:
Example:
If the power of the beam is 0.5mW find its
irradiance if its radius is 0.2cm?
Solution:
5.Short Pulse Duration
• We can say that, by means of a special technique
called mode locking, it is possible to produce light
pulses whose duration is roughly equal to the
inverse of the linewidth of the laser transition 2→1.
• If the line width is narrow the pulse width is very
short~ 0.1-1 ns some flash lamps can emit light
pulses with a duration of somewhat less than 1 ns.
• On the other hand, the linewidth of some solid state
and liquid lasers can be 103— 105 times greater than
that of a gas laser; in this case much shorter pulses
may be generated (down to ~ 10 fs). Note that the
property of short duration, which implies energy
concentration in time
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Laser Modes
To obtain laser we have to use suitable positive
feedback. Feedback is often obtained by placing the
active material between two highly reflecting
mirrors.
These amplify the em wave as it oscillates between
the mirrors in the presence of the active material.
The presence of the mirrors affects the em wave
inside the cavity and produces two kind of modes
longitudinal modes and transverse modes
Longitudinal modes only specific frequencies are
possible inside the optical cavity of a laser,
according to standing wave condition.
Transverse modes are created in cross section of
the beam, perpendicular to the optical axis of the
laser.
Longitudinal modes (Axial Modes)
Using Fabry-Perot interferometer one can observe that
the output of the laser beam consists of a number of
discrete frequency components. These modes are
known as longitudinal modes or axial modes. These
modes are created inside the optical resonator
between the two mirrors. In a laser system an optical
cavity is created by two mirrors at both ends of the
laser.
These mirrors serve two goals:
• They increase the length of the active medium, by
making the beam pass through it many times.
• They determine the boundary conditions for the
electromagnetic fields inside the laser cavity.
• The axis connecting the centres of these mirrors
and perpendicular to them is called Optical Axis of
the laser. The laser beam is ejected out of the laser
in the direction of the optical axis.
• An electromagnetic wave which moves inside the
laser cavity from right to left is reflected by the left
mirror, and move to the right until it is reflected
from the right mirror, and so on. Thus, two waves
of the same frequency and amplitude are moving
in opposite directions, which is the condition for
creating a standing wave.
• The mean reason to generate the longitudinal modes
inside the cavity is the presence of the Standing waves in
a laser cavity.
• The Standing waves in a laser cavity is formed as a result
of interference of the two waves of same frequency but
have opposite direction of propagation along the two
mirror axis
• Standing waves must fulfil the condition:
L = Length of the optical cavity.
q = Number of the mode, which is equal to the number of
half wavelengths inside the optical cavity. The first
mode contains half a wavelength, the second mode 2
halves (one) wavelength.
lq = Wavelength of mode m inside the laser cavity.
• In fact the number of modes (q) in most lasers is very large. For
Example if the central wavelength is 500nm and the mirror
separation is 25cm , q has a value of 1000000, since q can be any
integer, there are many possible wavelengths within the laser
transition shape.
• Example
• The length of an optical cavity is 25 [cm]. Calculate the
frequencies nm and wavelengths lm of the following modes:
• m =1 , m = 10 , m = 100
, m = 106
The separation between axial modes
• If the First mode is q then
• If the Second mode is q+1 then
It is more convenient to refer to the axial modes by
their frequency
The separation between neighbouring frequencies is
equal to C/2L i.e. dependent only on the
separation between mirrors and independent of
q. For L = 25cm The separation between
neighboring frequencies is 6x108sec-1.
• It is clear that a single mode laser can be made by
reducing the length of the cavity, such that only one
longitudinal mode will remain under the fluorescence
curve with GL>1.
• The approximate number of possible laser modes is
given by the width of the Laser bandwidth divided by
the distance between adjacent modes.
• Example
The length of the optical cavity in He-Ne laser is 30 [cm]. The
emitted wavelength is 0.6328 [μm]. Calculate:
1. The difference in frequency between adjacent
longitudinal modes.
(∆ ν) = C/(2L) = 3*108 [m/s]/(2*0.3 [m]) = 0.5*109 [Hz] = 0.5
[GHz]
2. The number of the emitted longitudinal mode at this
wavelength.
λq = 2L/m
q = 2L/λq = 2*0.3 [m]/0.6328*10-6 [m ] = 0.948*106
which means that the laser operate at a frequency which is
almost a million times the basic frequency of the cavity.
3. The laser frequency
ν= c/λ = 3*108 [m/s]/0.6328*10-6 [m ] = 4.74*1014 [Hz]
Example
The length of the optical cavity in He-Ne laser is 55 [cm].
The Laser bandwidth is 1.5 [GHz]. Find the
approximate number of longitudinal laser modes.
Solution
The distance between adjacent longitudinal modes is:
∆ν= c/(2L) = 3*108 [m/s]/(2*0.55 [m]) = 2.73*108 [m/s] =
0.273 [GHz]
The approximate number of longitudinal laser modes:
N =Laser bandwidth /∆ ν= 1.5 [GHz]/0.273 [GHz] = 5.5≈5
The importance of Longitudinal Optical Modes at the Output of the Laser
• In most high power applications for material processing or
medical surgery, the laser is used as a mean for transferring
the energy to the target. Thus there is no importance for the
longitudinal laser modes.
• In applications where interference of electromagnetic
radiation is important, such as holography or interferometric
measurements, the longitudinal modes are very important.
• In spectroscopic and photochemical applications, a much
defined wavelength is required. This wavelength is achieved
by operating the laser in single mode, and then controlling
the length of the cavity, such that this mode will operate at
exactly the required wavelength. The structure of
longitudinal laser modes is critical for these applications.
• When high power short pulses are needed, mode locking is
used. This process causes constructive interference between
all the modes inside the laser cavity. The structure of
longitudinal laser modes is important for these applications.