Nonlinear optics measure phase-velocity distribution

Although it is well understood theoretically that a focused Gaussian beam will present phase-velocity variations across its waist both radially and axially, experimental verification of the effect is difficult due to the tiny difference of the phase velocity (approximately 10–4 times the speed of light in a vacuum, c, even with tight beam focusing). Scientists at Fudan University (Shanghai, China) have developed an approach based on nonlinear optics to reveal the effect experimentally with both high sensitivity and spatial resolution.

The approach uses off-axis sum-frequency generation (SFG) in which two parallel-propagating fundamental beams from a continuous-wave Nd:YVO4 laser operating in TEM00 mode are identically focused into a 150-µm-thick KTP (potassium titanium oxide phosphate) crystal. For a fixed crystal position, the phase mismatches for optimal SFG conversions with coincident and parallel-separated fundamental beams are measured and used to deduce the phase velocity at a certain radial position of a single focused beam. These two-dimensional measurements, capable of resolving the tiny phase-velocity difference of approximately 10–4 c, verify that a superluminal (phase velocity > c) region exists within the beam radius and confocal length. The identification of this phase-velocity distribution has applications in vacuum electron acceleration and in negative-index-of-refraction metamaterials, a direct result of negative phase velocity. Contact Liejia Qian at [email protected].