Optics: What is phase matching, and mode locking

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Phase matching, also known as velocity matching, is a condition in nonlinear optics where the phases of interacting waves are synchronized to maximize energy transfer. Mode locking is a technique used in lasers to produce short pulses of light by locking different longitudinal modes of the laser cavity in phase. When phases are not matched, the efficiency of energy transfer decreases, leading to less effective laser operation. Understanding these concepts requires a foundational knowledge of wave interactions and laser physics. A simple explanation may be elusive due to the complexity of the underlying principles.
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The other day in lecture my professor mentioned the words mode locking and phase matching (same as velocity matching apparently) while on the topics of lasers. However, i can't find anything that can provide a simple explanation of what they are. Is there anyone who would know how to explain in simple terms what they are? Thank you in advance
 
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That will be because there is no "simple explanation" of what they are, whatever that means.
You should start from a picture of what you are doing and what happens normally - i.e. when the phases are not matched etc.

It sounds to me like you missed a lecture.
 

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