What influences the efficiency for nonlinear optical devices?  Conversion of light to a different frequency is a wave-wave interaction process governed by the optical nonlinear coefficient, the "nonlinear susceptibility" of the material. From the power series expansion of the susceptibility χ as a function of electric field, usually either the second order χ⁽²⁾ or the third order χ⁽³⁾ term is employed for practical devices. This yields respectively, processes that interact 3 waves (second harmonic generation or sum or difference frequencies of 2 waves) or 4 waves (third harmonic generation, frequency shifting to the sum or difference of 3 waves, and degenerate four-wave mixing (FWM) yielding a phase conjugate wave at the same frequency). Three things are essential in an efficient device: 1) a large nonlinear coefficient to couple the interacting waves but not accompanied by significant linear absorption of any of the interacting waves, 2) a means to keep the generated wave in phase (travelling at the same phase velocity) with the driving polarization for the generated wave, produced by the interaction of the source waves, over a significant interaction length, called "phase matching" and 3) a way to keep the waves confined transversely through the interaction length by a wave guiding structure or by focusing, which is limited by diffraction.

Materials for degenerate nonlinear optics:

It is known that metal and semiconductor nanocomposites have large nonlinear susceptibilities χ⁽²⁾ and χ⁽³⁾. A nanocomposite of metal nanoparticles has a third-order susceptibility 1,000 times that of bulk materials. For silver (Ag) nanoparticles in fused silica   χ⁽³⁾ ~ 10^-7 esu, nearly 7 orders of magnitude larger than fused silica itself. But, this large enhancement has only been observed in degenerate four-wave mixing experiments. The reason for this is that field enhancement is wavelength specific. In metallic nanoparticles this wavelength is near the surface plasmon energy, about 3eV in Ag. Because all four waves are on resonance, field enhancement enters into the nonlinear wave equations with a high power.

Really, degenerate FWM experiments are less efficient than what is predicted solely by the susceptibility. The nonlinear coefficient divided by the linear absorption  χ⁽³⁾/α provides a more accurate measure of the overall efficiency. For metal nanocomposites χ⁽³⁾/α ~ 10^-12 to 10^-11 esu. On the other hand, semiconductors have less loss. Large χ⁽³⁾in semiconductors occurs near conduction to valence band transitions and can be tuned by choice of the band gap and by the size of the nanoparticles (e.g. by quantum confinement). This requires a narrow size distribution of nanoparticles to obtain the largest χ⁽³⁾. Our LAM process generates a narrow size distribution.

The limits of field enhancement:

In addition to high absorption, very fast (~10^-15) decoherence and and decay routes have been shown to frustrate enhancement schemes. Runaway fluorescence losses have been observed in silver nanoparticles, that may be related to white light generation.

Non-degenerate nanocomposites for nonlinear optics:

Nonlinear materials to enhance second-harmonic and third-harmonic generation of a femtosecond laser pulse require new design principles. An enhanced nonlinear material that resonates the q^th harmonic requires a material that will resonate all the q-1, q-2, ..., 2, 1 subharmonics. It must also satisfy the appropriate symmetry conditions, set by the particular harmonic order. For instance, second harmonic generation is more restrictive than third-harmonic generation, because an asymmetric material is required to satisfy angular momentum conservation. 2 l=1 photons cannot radiate an l=1 photon without any additional angular momentum. This is typically accomplished in a biaxial crystal like Calcite, BBO, or z- cut quartz, but also can be accomplished using silver nanoparticles.

Wild, new frontiers:

Our results have shown THG enhancement of femtosecond lasers may require unique solutions, because of the large group velocity mismatch between the pump pulse and the harmonic pulse. One effect of this is that THG is highly interface sensitive. It may be that quasi phase matching is a naive approach, so enhancing third-harmonic effects means designing materials materials that will manipulate how pulses travel in a material. Click here to open up a .pdf presentation that describes interface THG generation, and how it is used to study nanocomposite optical materials (5Mb, Requires Acrobat 6.0).

Interface THG may also become a useful diagnostic for designing subharmonic nonlinear resonators. We are now developing a phase sensitive diagnostic that will allow us to measure the efficiency of each, successive energy step.

Research Goals:

1.The development of efficient, nanoparticle-based nonlinear optical materials for second and third-harmonic generation

2.A better understanding of 'runaway' effects in field enhancement schemes.

3.Optical diagnostics that relate nonlinear performance to electron transport at the nanoscale.