Classical behaviour of CW Optical Parametric Oscillators

1
Classical behaviour of CW Optical Parametric
Oscillators

• T. Coudreau
• Laboratoire Kastler Brossel, UMR CNRS 8552 et
  Université Pierre et Marie Curie, PARIS, France
• also with Pôle Matériaux et Phénomènes
  Quantiques, Fédération de Recherche CNRS 2437 et
  Université Denis Diderot , PARIS, France

2
Definition
Introduction

• An Optical Parametric Oscillator is a device that
  can
• generate two coherent waves (signal and idler)
  from a pump wave.
• It consists in
• an active medium
• an optical cavity, Fabry Perot resonator, in
  which resonates one, two or three frequencies

Signal (?1)
Pump (?0)
Idler (?2)
3
History
Introduction

• First realised in 1965 Giordmaine Miller,
• Phys. Rev. Lett 14, 973 (1965)
• Important development 1965 - 1975 as a tunable
  source of coherent radiation
• Outdated between 1975-1990 due to the occurrence
  of dye lasers
• Renewal since the 1990s due to
• improvements in laser sources and crystals
• quantum properties

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Outline
Introduction

• Introduction
• Definition
• History
• Basic principles
• Optical non linearities
• Second order non linearity
• Energy conservation and phase matching
• Classical Operation
• Singly resonant OPO
• Doubly resonant OPO
• Triply resonant OPO
• Conclusion

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Optical nonlinearities
Basic Principles
An electric field applied to an atomic medium
displaces the dipole
-
-

As the electric field becomes large, one gets
6
Second order non linearity
Basic Principles
In a non centrosymetric medium, one can get a non
zero
Lithium Niobate
Molecule
A
D
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Second order non linearity
Basic Principles

• With a pump wave at frequency ?0, on can get two
  kinds of behaviour
• Second Harmonic Generation (SHG) where a wave at
  frequency 2?0 is generated
• Parametric down-conversion where two waves at
  frequencies ?1 and ?2 are generated

?0
?2
2?0
?1?2
?0
?1
?1
?0
?2
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Energy and momentum conservation
Basic Principles

• Two conditions must be fulfilled
• Energy conservation
• which must be always fulfilled exactly
• Momentum conservation
• which has to be fulfilled exactly only in the
  case of an infinite medium, the useful condition
  being

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Phase matching
Basic Principles
Momentum conservation is often called phase
matching the generated signal and idler remain
in phase with the waves generated before in the
crystal. If , the phase shift is ? after
a length called the coherence length.
Output power
Pump ? signal, idler
Signal, idler ? Pump
?k?0
Crystals length
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Realisation of phase matching
Basic Principles
The natural birefringence of the crystal is
generally used to ensure phase matching
Extraordinary axis
Ordinary axis
Input light
Index of refraction
Frequency
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Influence of temperature
Basic Principles
The phase matching depends on the crystal
temperature (and angle)
Type II
Type I
Signal
Signal
Idler
Idler
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Quasi phase matching
Basic Principles

• The previous solution is not always chosen
• the most efficient nonlinear coefficient is not
  always used
• some wavelength regions are not reachable
• One can revert the sign of the non linearity
  after a length lc.

Single pass output power
Crystals length
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Parametric down-conversion basic eqns
Basic Principles
where ?i2 is a number of photons and is a
field envelope These equations can be solved
analytically in terms of elliptic functions.
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Notations
Basic Principles
For a weak efficiency, we have a linear variation
of the amplitudes
The variation depends on the relative phase !
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Laser vs OPO
Basic Principles

• Laser
• The pump creates a population inversion which
  generates gain through stimulated emission
• The system depends on the pump intensity
• OPO
• No population inversion, i.e. the medium is
  transparent
• The system depends on the pump amplitude

Signal (?1)
Pump (?0)
Idler (?2)
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Different kind of cw OPOs
Classical operation
Frequency tuning difficulty
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Singly Resonant OPO
Classical operation
Only the signal (or idler) wave resonates inside
the cavity.
Coupling mirror
is the free space round trip length is the
crystal length is the amplitude reflection
coefficient

• Usual assumptions
• Good cavity with
• close to resonance with
• Finally, one gets

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SROPO - Basic properties
Classical operation

• Pump threshold

which corresponds to optical powers on the order
of 1W
4

• Behaviour above threshold

Mean pump intensity constant
Signal field at resonance
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SROPO - Output Power
Classical operation
The output power is given by the implicit equation
100 conversion efficiency at
times above threshold
E. Rosencher, C. Fabre JOSA B 19 1107 (2002)
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SROPO - Frequency tuning
Classical operation

• There is a linear variation of the frequency (for
  small variations of
• ).The SROPO is
• tunable like a standard laser
• has a bandwidth limited by phase-matching,
  and/or mirror bandwidth

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Doubly Resonant OPO
Classical operation
Signal and pump Doubly resonant Pump
enhanced singly resonant
Signal and idler Doubly resonant
Similar to a SROPO Specific behaviour
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PESROPO - Basic Properties
Classical operation
The pump threshold power is diminished with
respect to the SROPO case
but the pump-cavity detuning, ?0, must be taken
into account. The output power is also modified
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PESROPO - Frequency tuning
Classical operation
As in a SROPO, the frequency depends linearly on
the cavity length. However, the cavity length
region is limited by the pump resonance width.
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DROPO - Basic Properties
Classical operation
The system forces the signal and idler detunings
?1 ?2 ?
with
Output power
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DROPO - Frequency tuning (1)
Classical operation
Since we have ?1 ?2, the round trip phases are
equal (modulo 2?) which gives for the signal
frequency
As opposed to the previous case, the variation
depends on the distance to frequency degeneracy
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DROPO - Frequency tuning (2)
Classical operation
m
m1
The resonance width is the signal resonance width
which is very narrow it is almost impossible
to tune by length without mode hops
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Triply Resonant OPO
Classical operation
The threshold is again lower than for a DROPO
It can be below 1 mW !
The output intensity now obeys a second degree
equation the system can be monostable,
bistable or even chaotic...
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TROPO - Stability
Classical operation
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TROPO - Frequency tuning
Classical operation
The behaviour is similar to a DROPO with a
limitation due to the pump resonance width.
m m1 m2 ...
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Frequency of emission
Conclusion

• OPOs draw their advantage from their very broad
  tunability since it is not limited by the
  proximity of a resonance in the active medium.
  What then limits this tunability ?
• The nonlinear coefficient and the reflection
  coefficients of the mirrors
• Phase matching which can be varied using
  temperature (or orientation)
• Recycling of one or more waves inside the cavity
• The system oscillates on frequency corresponding
  to the lowest threshold and only on this
  frequency (in a cw laser) as an homogeneously
  broadened laser.

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Summary
Conclusion
Triply resonant
Singly resonant
Doubly resonant
Threshold 100s mW Tuning like a laser
Threshold 100s µW Tuning by mode hops
Threshold 10s mW Tuning by mode hops
Pump enhanced singly resonant
Threshold 100s mW Tuning like a laser
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Conclusion
Conclusion

• The OPO
• is a coherent source of radiation
• can be tuned over large domains of wavelength
• can have a very low threshold
• can have a very small linewidth