How can a green laser pointer come from an infrared laser?

Many green lasers use a nonlinear crystal to frequency-double the invisible infrared output of a neodymium laser, halving the wavelength to produce visible green light.

Why is phase matching needed?

Because the fundamental and converted waves usually travel at different speeds in a dispersive medium, they fall out of step and the conversion cancels itself; phase matching keeps them synchronized so the converted wave grows along the crystal.

Harmonic Generation and Frequency Conversion

Second-order nonlinearities let crystals double or mix optical frequencies, converting laser light to new wavelengths through phase-matched processes.

Definition

Nonlinear optical processes mediated by the second-order susceptibility in which two optical waves combine to produce a wave at the sum, difference, or doubled frequency, requiring phase matching for efficient coherent conversion.

Scope

This topic covers the second-order nonlinear processes that generate light at new frequencies. It includes second-harmonic generation, sum- and difference-frequency generation, optical parametric amplification and oscillation, and the all-important condition of phase matching, achieved through birefringence or quasi-phase-matching in periodically poled crystals, that allows the converted wave to grow coherently. It also touches on higher harmonics. It explains how lasers are shifted in wavelength and how tunable and entangled-photon sources are built.

Core questions

How does a crystal double the frequency of laser light?
What is phase matching and why is it essential?
How are sum- and difference-frequency generation and parametric amplification related?
How does periodic poling achieve quasi-phase-matching?

Key concepts

second-harmonic generation
sum-frequency generation
difference-frequency generation
optical parametric oscillation
phase matching
quasi-phase-matching
periodically poled crystals
frequency doubling

Key theories

Second-harmonic and three-wave mixing: Through the second-order susceptibility two photons combine into one at the sum frequency, or one splits into two; second-harmonic generation is the special case of frequency doubling, and difference-frequency and parametric processes generate tunable output.
Phase matching: Efficient conversion requires the interacting waves to stay in phase as they propagate; this is arranged by exploiting birefringence to equalize phase velocities or by periodically reversing the nonlinearity to achieve quasi-phase-matching.

Clinical relevance

Frequency doubling produces the green light of neodymium-based surgical and ophthalmic lasers from infrared output, and second-harmonic generation in tissue provides label-free contrast in nonlinear microscopy of collagen and other ordered structures.

History

Franken and colleagues observed the first optical second harmonic in 1961 by focusing a ruby laser into quartz. Armstrong, Bloembergen, and co-workers soon developed the theory of phase matching and nonlinear interactions, and quasi-phase-matching in periodically poled crystals later made efficient conversion widely practical.

Key figures

Peter Franken
Nicolaas Bloembergen
John Armstrong

Seminal works

boyd2020
franken1961

Frequently asked questions

How can a green laser pointer come from an infrared laser?: Many green lasers use a nonlinear crystal to frequency-double the invisible infrared output of a neodymium laser, halving the wavelength to produce visible green light.
Why is phase matching needed?: Because the fundamental and converted waves usually travel at different speeds in a dispersive medium, they fall out of step and the conversion cancels itself; phase matching keeps them synchronized so the converted wave grows along the crystal.