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Unit 4 From amplifiers to oscillators,Light amplifiers
Amplifier bandwidth
Gain saturation
From amplifiers to oscillators
The laser
Resonators
Plane-mirror resonators
Spherical-mirror resonators
Cavity modes in cavities with curved mirrors #,From amplifiers to oscillators,the laser: an optical amplifier
a source of light
amplifier : bandwidth and gain saturation
amplifiers with positive feedback
optical oscillators.
laser #,Light amplifiers,Comparing optical amplifiers with electronic amplifiers
Similarities:
both rely on an external power source to supply energy;
both are characterised by a gain coefficient, which is frequency dependent;
both are influenced by noise, gain saturation, and other non-linearities. #,Differences between optical and electronic amplifiers,Phase
The optical amplifier increases the magnitude of the optical field while maintaining its phase.
Phase is not relevant in electronic amplifiers.
Frequency response
In optical amplifiers the basic frequency selection is determined by the energy levels in atoms
Electronic amplifiers rely on electronic circuits made of capacitors, inductors, etc #,Differences between optical and electronic amplifiers,The source of external power
Electronic amplifiers can only be powered by electrical energy
Optical amplifiers can be ‘pumped’ by electrical, optical, chemical, mechanical and even nuclear power sources. #,Amplifier bandwidth,Bandwidth : amplifier’s frequency response
In the optical amplifier
the frequency response is determined by the
frequency dependence of the gain coefficient
The frequency response is proportional to the
lineshape function of the given transition.
#,Amplifier bandwidth,The frequency response is proportional to the
lineshape function of the given transition.
In the case of homogeneous broadening
G() is a Lorentzian function
I→0,Gain saturation,At low power, optical amplify function
I(z) = I(0)exp(Gz)
the exponential growth of the intensity
At high power levels ,this is not correct,
it will produce gain saturation.
#,Gain saturation,The intensity increases
the rate of stimulated emission increases
population from the upper level is reduces
the degree of population inversion is reduced
the gain is also reduced.
#,Gain saturation,The intensity increases in the amplifier,
it stimulates more and more excited atoms to emit photons.
This can only go on as long as the number of stimulating
photons is less than the number of excited atoms.
Once the number of photons overtakes the number of
excited atoms, the exponential growth comes to an end.
#,Gain saturation,The population difference is a function of
the energy density : (ν=ν0)
The saturated gain decreases as the intensity increases
The saturation intensity
#,the gain coefficient
the saturated gain
small-signal gain coefficient
The saturation intensity
#,Gain saturation,From amplifiers to oscillators,Lasers are sources of light.
What is the link between an amplifier and a light source?
The Optical feedback
an optical amplifier with positive feedback
the amplifier between mirrors
Optical cavity or resonator
the initial signal triggers the whole process.
the spontaneously emitted photons
Optical oscillator --Laser
the intensity will quickly build up
and reach a steady-state value.
#,To have stable output from a laser,
two conditions have to be met :
(i) the amplifier gain should be larger than the
losses
(ii) the total phase shift in a round trip of the
radiation should be equal to an integer
multiple of 2.
Both these conditions are related to
the optical cavity or optical resonator. #,Laser,Resonator,an optical cavity or optical resonator
Electro-magnetic theory — Boundary condition
form standing waves
the special wavelength and frequencise
resonant wavelengths
resonant frequencies
plane-mirror, spherical-mirror resonators. #,Plane-mirror resonators,Fabry-Perot resonator (F-P)
The resonant frequencies
m, longitudinal mode
frequency separation between the longitudinal modes,Finesse of the cavity,The intensity distribution of a cavity,
Transmission spectrum :
F -- the finesse of the cavity
The finesse is an important parameter of a cavity
#,Finesse of the cavity,The finesse is an important parameter of a cavity
quantifies the width of a resonant line.
The finesse :
F = /
: width of the resonance
: the separation of the resonant frequencies
for high finesse, highly reflective mirrors,
the spectral response is sharply peaked
for low finesse, the resonances are broad around the resonant frequencies. #,Plane-mirror resonators,Three parameters: characterise the spectral response of Fabry-Perot resonators:
(i) the resonant frequencies:
q = (c/2d)q
(ii) the spacing between the resonant frequencies:
= c/2d
(iii) the width of each resonance:
= / F
F is the finesse of the cavity
#,Kind of open resonator,Stable resonator.
the beam is confined in the cavity even after many reflections
Unstable resonator
the beam leaves the cavity after only a few
reflections
#,Conditions of stabiliry :
Not all unstable resonators are useless.,Some special cavity configurations,Cavity modes in cavities with curved mirrors,q,l,m-- a distinctive standing wave-- a mode.
Each mode -- a specific frequency and intensity distribution in the cavity.
longitudinal or axial modes, q
waves travelling along the optical axis of the cavity.
transverse modes: l, m,Cavity modes in cavities with curved mirrors,l= m = 0 but q 0
The intensity distribution across the beam profile
Gaussian function
-- the lowest beam divergence, highest energy density.
-- for most applications
l 0 or m 0
beam divergence angles, beam profile,Unit 4 From amplifiers to oscillators,Learning outcomes
discuss bandwidth in optical amplifiers
calculate the bandwidth in a homogeneously broadened optical amplifier
discuss gain saturation in optical amplifiers
calculate the saturated gain and the small-signal gain coefficient in optical amplifiers
discuss the laser in terms of an amplifier with feedback
discuss the optical properties of optical cavity
discuss the stability criterion of optical resonators ##,
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