Optical Mixing.Sum Frequency generation, Difference Frequency Generation.
Optical Mixing
When 2 coherent electromagnetic beams are allowed to move through a non-linear medium in same direction with same speed, The 2 electron beams will interact with each other. The emerging beam from the medium contains radiations of frequencies ω1 + ω2 and ω1 – ω2. This phenomenon is called Optical Mixing.
Sum Frequency Generation
When 2 Electromagnetic waves with angular frequencies ω1 and ω2 are allowed to incident on a non-linear crystal then a new radiation of frequency ω1 + ω2 can be generated due to the interaction between the radiation and crystal, this phenomenon is called Sum Frequency Generation.
Difference Frequency Generation
When 2 Electromagnetic waves with angular frequencies ω1 and ω2 are allowed to incident on a non-linear crystal then a new radiation of frequency ω1 - ω2 can be generated due to the interaction between the radiation and crystal, this phenomenon is called Difference Frequency Generation.
The instantaneous Electric Field having frequency ω1
The instantaneous Electric Field having frequency ω2
When the 2 coherent electromagnetic waves are moving along the same direction through the non-linear crystal the resultant electric field inside the crystal is given by superposition principle.
Resultant Electric field,
Second Order Polarizability is
Because of the interaction between 2 electromagnetic waves at different frequencies with a non-linear crystal, there are Optical rectification, Second Harmonic generation, Sum Frequency Generation, and Difference Frequency Generation but because of the phase matching condition all this radiation do not come out simultaneously.
[Optical rectification]
Phase matching Condition to get sum Frequency Generation and Difference Frequency Generation
In the case of Sum Frequency Generation the emerging wave has a frequency ω1 + ω2, If k1 and are k2 the wave vectors of the waves with frequency ω1 and ω1 respectively. The phase matching condition for Sum Frequency Generation is
In the case of Difference Frequency Generation the emerging wave has a frequency ω1 - ω2, If k1 and k2 are the wave vectors of the waves with frequency ω1 and ω1 respectively. The phase matching condition for Difference Frequency Generation is
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