8.2 Second-order nonlinear effects: frequency doubling and parametric processes
3 min read•Last Updated on July 22, 2024
Second-order nonlinear effects in optics manipulate light in fascinating ways. These phenomena, like second harmonic generation and optical parametric amplification, allow us to create new frequencies and amplify weak signals using special materials and precise conditions.
These effects have revolutionized laser technology and optical communications. By harnessing nonlinear processes, we can generate tunable light sources, create shorter wavelengths, and develop high-speed modulators for various applications in science and technology.
Second-order Nonlinear Effects
Process of second harmonic generation
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Top images from around the web for Process of second harmonic generation
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Frontiers | Boosting and Taming Wave Breakup in Second Harmonic Generation View original
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Frontiers | Boosting and Taming Wave Breakup in Second Harmonic Generation View original
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Frontiers | Boosting and Taming Wave Breakup in Second Harmonic Generation View original
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Nonlinear optical process doubles the frequency of an input light wave
Converts input wave with frequency ω to output wave with frequency 2ω
Halves the wavelength of the output wave compared to the input wave (1064 nm to 532 nm)
Occurs in nonlinear optical materials with non-zero second-order susceptibility χ(2)
Materials include KDP (potassium dihydrogen phosphate) and BBO (beta barium borate)
Nonlinear polarization P(2) induced in the material proportional to the square of the input electric field E: P(2)=ϵ0χ(2)E2
Nonlinear polarization acts as a source term for the second harmonic wave
Intensity of the second harmonic wave depends on the square of the input intensity and length of the nonlinear material
Doubling the input intensity quadruples the second harmonic intensity
Increasing the interaction length enhances the conversion efficiency
Phase-matching for nonlinear processes
Crucial for efficient second-order nonlinear processes (SHG, parametric amplification)
Ensures generated nonlinear waves maintain fixed phase relationship with input waves throughout the nonlinear material
Phase mismatch Δk is the difference between the wave vectors of the interacting waves
For SHG: Δk=k2−2k1, where k1 and k2 are wave vectors of fundamental and second harmonic waves
Perfect phase-matching occurs when Δk=0
Leads to constructive interference and efficient nonlinear conversion
Methods to achieve phase-matching:
Birefringent phase-matching: Utilizes difference in refractive indices for ordinary and extraordinary waves in birefringent crystals (BBO, LiNbO3)
Quasi-phase-matching (QPM): Periodically modulates sign of nonlinear coefficient to compensate for phase mismatch
Achieved through periodic poling of ferroelectric materials (lithium niobate)
Optical parametric amplification and oscillation
Optical parametric amplification (OPA): Second-order nonlinear process amplifies weak input signal using strong pump wave
Pump photon with frequency ωp splits into signal photon (ωs) and idler photon (ωi)
Energy conservation: ωp=ωs+ωi
Phase-matching conditions must be satisfied for efficient OPA
Optical parametric oscillation (OPO): Extension of OPA incorporating feedback to generate tunable coherent light
Nonlinear crystal placed inside optical cavity resonant at signal or idler frequency (or both)
Above threshold pump power, OPO starts to oscillate, generating signal and idler waves
OPA and OPO generate tunable light sources in infrared and visible regions
Wavelength tuning achieved by adjusting phase-matching conditions (crystal angle, temperature)
Applications of second-order nonlinear effects
Frequency doubling (SHG) generates shorter wavelengths from available laser sources
Doubling 1064 nm Nd:YAG laser generates 532 nm green light
Nonlinear frequency conversion techniques (sum-frequency generation (SFG), difference-frequency generation (DFG)) generate light at specific wavelengths
Applications: quantum optics, spectroscopy, optical frequency metrology