modulators & shg (a) longitudinal field; (b) transverse field; (c) travelling-wave field
TRANSCRIPT
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Modulators & SHGModulators & SHG
(a) Longitudinal field; (b) Transverse field; (c) Travelling-wave field.
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Pockels Effect in ADPPockels Effect in ADP
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The index ellipsoidThe index ellipsoid
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The Longitudinal ModulatorThe Longitudinal Modulator
Input field
Output field
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Amplitude modulation (Transverse)Amplitude modulation (Transverse)
Inserting a quarter-wavePlate provides a staticbias to point B providinga near linear response
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Application: Q-switchingApplication: Q-switching
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Phase modulationPhase modulation
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Phase modulationPhase modulation
Mach-Zehnder Interferometer with a phase modulatorIn one arm
Optical fibre version of the same interferometer
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Phase modulation: the maths 1Phase modulation: the maths 1
The input &output lightfields
And the voltageon the crystal is:
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Phase modulation: the maths 2Phase modulation: the maths 2
And using the Bessel function identity:
Expanding the cosine:
Gives for the output field – a series of side-bands
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Amplitude Spectrum of the OutputAmplitude Spectrum of the Output
The output of the phase modulator consists of a series of sidebands spaced by the modulation frequency Ω and whose relative magnitude is given appropriate Bessel function ratio.
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Pound-Drever-Hall LockingPound-Drever-Hall Locking
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The detected signalThe detected signalThe ratio of the reflected beam to the incident beam gives F.For a lossless symmetric cavity we get the following result where Φ represents the phase after one round trip, i.e.
The error signal is obtained by picking out the term going at
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The Lock SignalThe Lock Signal
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Electro-optic deflection - 1Electro-optic deflection - 1
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Electro-optic deflection - 2Electro-optic deflection - 2
anglesmallnd
nri
rr
)1(
With a given maximum voltage V to scan N spots requires 2N times the half-wave voltage
3
0
03
1/ 2 //
/ 2
/ ;
rn V d VN
D V
dL D V
L r n
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Electro-optic deflection - 3Electro-optic deflection - 3
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Acousto-optic effectsAcousto-optic effects
The sound
waves modulate
the reflector
which in turn
Doppler shifts
the optical wave.
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Acousto-optic applicationsAcousto-optic applications
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Acousto-optic deflectionAcousto-optic deflection
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Acousto-optic applicationsAcousto-optic applications
The key feature is to scan the frequency without moving the beam. The double pass through the phase plate rotates the plane of polarisation by 90° allowing the PBS deflect the return beam.
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SHG – the susceptibility tensorSHG – the susceptibility tensor
For ADP or KDP, the crystal symmetry gives only the following non-zero for SHG.
Furthermore, Or if Kleinman’s conjecture is invoked all are equal
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Symmetry & KleinmanSymmetry & Kleinman
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Second Harmonic GenerationSecond Harmonic Generation
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SHG: more mathsSHG: more mathsNow insert the following and take a 1D plane wave:
where and similarly for 2ω
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SHG: and yet more..SHG: and yet more..Now assuming a small variation of A with z, and using
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SHG: so finally…SHG: so finally…
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Phase-matchingPhase-matching