Download Fabry-Perot Interferometers

Fabry-Perot Interferometers
• The simplest laser cavity is formed by two
plane mirrors
• Such a cavity is a typical Fabry-Perot
interferometer
• Its transmittance is
T = T0 / [1 + Fa sin2(δ/2)]
δ = (2π/λ) 2 n L
for zero angle
To get T = T0 , δ = 2π m, or 1/λ = m /(2nL)
These lasing wavelengths are called longitudinal modes
Spreading in Space
Transverse modes
or transverse electromagnetic modes (TEM)
In theory, they are the solutions
of the differential wave equation
• These different transverse modes are
the solutions of the differential wave
equation under different boundary
conditions
• Here, a qualitative explanation is
provided in the following
– Consider a laser cavity consisting of two
concave mirrors with the same radius
– In this case, we may use Ray Optics to
explain why light may NOT travel in the
central axis
Multiple passes off the optic
axis
Multiple passes off the optic
axis
Multiple passes off the optic
axis
Multiple passes off the optic
axis
Multiple passes off the optic
axis
If the rays are confined into a flat plane, this explains
why there are 2 spots (TEM10 mode)
Multiple passes off the optic
axis
If the rays are NOT confined into a flat plane, it explains
why there are 4 spots (TEM11 mode)
• These transverse modes are
determined by the design of laser cavity
• They are labelled by TEMnm, where
TEM stands for transverse
electromagnetic, and n or m is a
positive integer or zero
• The simplest form is the TEM00 mode
• The frequency of the laser beam is
mixture of TEM modes and longitudinal
modes
Design of laser cavities
TEM00 mode is a Gaussian function which is used
to describe the irradiance distribution in the cross section
of the laser beam, that travels in the z-axis
w(z) is called the beam waist, which is a function
of the z coordinate
−
I = I 0e
2 r '2
w2 ( z )
In cylindrical coordinates
Maximum irradiance
I0 ⇒
w ( z ) = w0
 λz
1 + 
2
 π w0
 z 
= w 0 1 +  
 zR 
w0 ⇒
π w 02
zR =
⇒
λ



2
2
Minimum beam waist
Irradiance distribution
in the cross section
Rayleigh range = zR, at which the beam waist becomes 21/2 w0
The divergence angle →
TanΘ = w(z)/z
For
z >> z R
2
2
z
z
λz
w( z ) = w0 1 + 2 ≈ w0 2 =
zR
zR πw0
w( z )
λz
λ
tan Θ =
≈
=
z
zπw0 πw0
Θ → small
tan Θ ≈ Θ
λ
Θ≈
πw0
This angle is called
the divergence angle
Specification of a laser
• Laser output power
• Pulsed mode or continuous-wave (cw)
mode
• Single or multi-modes
• Divergence angle
• Polarisation of laser light
• Sizes, power consumption, reliability,
operation lifespan, price and etc.
Laser output power
Power (W)
40
30
Pink: laser output
20
Blue: N2 – g2N1/g1
10
Population inversion
0
0
20
40
Applied Voltage (V)
Threshold
60
Saturation in population
inversion
25
25
20
20
Power (W)
Power (W)
Pulsed mode and cw mode
15
10
5
0
15
10
5
0
-5 0 5 10 15 20 25 30 35 40 45 50 55
Time (s)
0
20
40
Time (s)
Pulsed mode is highly desirable in optical communication
in which a laser pulse represent a 1-bit of digital information
60