Backward phase-matching for nonlinear optical generation in negative-index materials.

Area of Science:

• Nonlinear optics
• Metamaterials science
• Plasmonics

Background:

• Metamaterials exhibit unique electromagnetic properties beyond natural materials.
• Backward phase-matching in nonlinear metamaterials involves counter-propagating fundamental and harmonic waves in negative-index media.
• This phenomenon was predicted a decade ago but lacked definitive optical experimental confirmation.

Purpose of the Study:

• To experimentally confirm backward phase-matching at optical frequencies.
• To investigate nonlinear metamaterials for unconventional optical effects.
• To explore the potential of plasmonic waveguides in achieving phase-matching conditions.

Main Methods:

• Optical measurements utilizing nonlinear plasmonic waveguides.
• Exploitation of two distinct modes to achieve phase-matching.
• Characterization of mode refractive indices for fundamental and harmonic waves.

Main Results:

• Demonstration of backward phase-matching in a nonlinear plasmonic waveguide.
• Observed refractive indices of 3.4 and -3.4 for fundamental and harmonic waves, respectively.
• Achieved peak conversion efficiency at ~780 nm excitation wavelength, confirming phase-matching conditions k(2ω) = 2k(ω) and n(2ω) = -n(ω).

Conclusions:

• The study provides the first definitive optical experimental confirmation of backward phase-matching.
• The results validate theoretical predictions and highlight the potential of metamaterials in nonlinear optics.
• Coherent harmonic waves were observed propagating in the direction opposite to the fundamental light.