1. §9.6 High-Frequency Modulation Considerations Lecture 16 In practice, the modulation signal is often at very high frequencies and may occupy a large bandwidth, such that the wide frequency spectrum of lasers can be efficiently used. In this section, we consider some basic factors limiting the highest usable modulation frequencies in some basic experimental situations. (A) Maximum Modulation Bandwidth : Internal resistance of source : Capacitance of EO crystal Assume:

2. Then voltage drop: EO crystal: Internal Resistance: §9.6 High-Frequency Modulation Considerations when We have Most of voltage is waste ! Capacitor impedance: This can also be obtained from the impedance Resistance impedance: Voltage drop is proportional to its impedance.

3. §9.6 High-Frequency Modulation Considerations The solution: Parallel connect a inductance (L) and a resistance (R L ), and make the circuits resonant to obtain the maximum impedance i.e., or Then the RLC circuits impedance: As long as:Most of voltage will drip across crystal However, above results is subject to the bandwidth limitation. The maximum modulation bandwidth

4. §9.6 High-Frequency Modulation Considerations Electric Power: Consume Power & Peak Retardation EO retardation: Capacitance:

5. §9.6 High-Frequency Modulation Considerations (B) Transit-Time Limitation Transit-Time: the time that light pass through the crystal What happen if Electric field change is comparable with transit-time? Peak retardation at Reduction Factor

6. §9.6 High-Frequency Modulation Considerations For example: KDP crystal Modulation frequency

7. §9.6 High-Frequency Modulation Considerations (C) Traveling-Wave Modulators There is a way to eliminate the transit-time limitation, which makes the optical and modulation filed have a same phase velocity such that a portion of an optical wavefront will exercise the same instantaneous E field through the crystal.

8. §9.6 High-Frequency Modulation Considerations Reduction Factor The same as previous one, except Optical wavefront position at time t ’ Retardation: Modulation field: Phase velocity of modulation field

9. §9.6 High-Frequency Modulation Considerations Transit-time limitation eliminate Modulation frequency

10. Lecture 17 Chapter X Interaction of Light and Sound Highlights 1. Scattering of Light by Sound 3. Bragg Diffraction of Light by Acoustic Waves - Analysis 2. Raman-Nath and Bragg Diffraction Controlling the frequency, intensity and direction of an optical beam Propagation of laser beams in crystals with acoustic waves 4. Deflection of Light by Sound Partially Reflecting Mirror Model Particle Picture

11. §10.1 Scattering of Light by Sound A sound wave consists of sinusoidal perturbation of the density of the material, or strain, that travels at the sound velocity Index of refraction Average Index Distance Diffraction of light by sound waves was predicted by Brillouin in 1922 and demonstrated experimentally some ten years later.

12. §10.1 Scattering of Light by Sound I. Partially Reflecting Mirrors Model Incident optical beam Diffracted beam (A) All the points on a given mirror contribute in phase to the diffraction direction … Optical path difference: AC-BD For example: Interfere constructively condition -----

13. §10.1 Scattering of Light by Sound (B) Diffraction from any two acoustic phase fronts add up in phase in the reflected direction … Incident optical beam  Diffracted beam  s  Moving sound wavefunction  s  For example: Optical path difference: AO+OB Bragg diffraction example

14. §10.1 Scattering of Light by Sound II. Particle Picture of Bragg Diffraction Dual particle-wave nature of light Conservation of momentum Conservation of energy

15. §10.1 Scattering of Light by Sound III. Doppler Derivation of the Frequency Shift The Doppler shift changes sign when the sound wave direction is reversed, so

16. §10.2 Raman-Nath and Bragg Diffraction I. Raman-Nath Diffraction Low sound wave frequency, short interaction length, and Phase grating II. Bragg Diffraction Higher sound wave frequency, longer interaction length, and Raman -Nath +1 +2 III. criterion Raman-Nath Diffraction Bragg Diffraction

17. §10.3 Bragg Diffraction of Light by Acoustic Waves I. Coupled Wave Function Index of refraction modulation Additional electric polarization Wave equation Total field Slow amplitude variation assumption

18. §10.3 Bragg Diffraction of Light by Acoustic Waves At bragg condition Coordinate transform Initial conditions

19. §10.3 Bragg Diffraction of Light by Acoustic Waves II. Diffraction Efficiency Diffraction figure of merit

20. §10.4 Deflection of Light by Sound Incident light Diffracted beam at v s Diffracted beam at v s +  v s Initially Then Deflection of optical beam can be achieved by changing the sound frequency near the Bragg- diffraction condition A B O

21. §10.4 Deflection of Light by Sound Number of resolvable spots example Calculate: