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Optical Modulators and SHG: Principles & Applications

Learn about longitudinal, transverse, traveling-wave fields, Pockels effect, modulation techniques, phase modulation, and applications in Q-switching and interferometry. Explore the math behind phase modulation, spectroscopy, Pound-Drever-Hall locking, electro-optic and acousto-optic effects, SHG, phase-matching, and more.

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Optical Modulators and SHG: Principles & Applications

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  1. Modulators & SHG (a) Longitudinal field; (b) Transverse field; (c) Travelling-wave field.

  2. Pockels Effect in ADP

  3. The index ellipsoid

  4. The Longitudinal Modulator Output field Input field

  5. Amplitude modulation (Transverse) Inserting a quarter-wave Plate provides a static bias to point B providing a near linear response

  6. Application: Q-switching

  7. Phase modulation

  8. Phase modulation Mach-Zehnder Interferometer with a phase modulator In one arm Optical fibre version of the same interferometer

  9. Phase modulation: the maths 1 The input & output light fields And the voltage on the crystal is:

  10. Phase modulation: the maths 2 Expanding the cosine: And using the Bessel function identity: Gives for the output field – a series of side-bands

  11. Amplitude 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.

  12. Pound-Drever-Hall Locking

  13. The detected signal The 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

  14. The Lock Signal

  15. Electro-optic deflection - 1

  16. Electro-optic deflection - 2 With a given maximum voltage V to scan N spots requires 2N times the half-wave voltage

  17. Electro-optic deflection - 3

  18. Acousto-optic effects The sound waves modulate the reflector which in turn Doppler shifts the optical wave.

  19. Acousto-optic applications

  20. Acousto-optic deflection

  21. Acousto-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.

  22. SHG – 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

  23. Symmetry & Kleinman

  24. Second Harmonic Generation

  25. SHG: more maths Now insert the following and take a 1D plane wave: where and similarly for 2ω

  26. SHG: and yet more.. Now assuming a small variation of A with z, and using

  27. SHG: so finally…

  28. Phase-matching

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