Frequency Generation and Solitonic Decay in ThreeWave Interactions

Abstract

We consider experimentally three-wave resonant nonlinear interactions of fields propagating in nonlinear media. We investigate the spatial dynamics of two diffractionless beams at frequency omega1, omega2 which mix to generate a field at the sum frequency omega3. If the generated field at omega3 can sustain a soliton, it decays into solitons at omega1, omega2. We report the experimental evidence of the transition from steady frequency wave generation to solitonic decay in nonlinear optics.

Frequency Conversion Based on Three-Wave Parametric Solitons

“…(9) where the independent coordinates are, instead of Ǐ 1 = Ǐ and Ǖ, the two spatial variables Ǐ 1 and Ǐ 2 . In order to clearly distinguish this situation, involving the interaction between three spatial beams, from the previous cases involving short temporal pulses, and to maintain the same notation used in (Baronio et al, 2009), we name the longitudinal spatial coordinate Ǐ 1 = z and the transverse spatial coordinate Ǐ 2 = x. Moreover, we also set in this case A 1,2,3 = φ 1,2,3 .…”

“…Here we describe the set-up which led to the first experimental demonstration of laser beam reshaping by means of the three-wave ZM soliton effect in optics (Baronio et al, 2009). To be precise, Fig.…”

“…In order to provide the experimental demonstration of the above discussed nonlinear dynamics, Ref. (Baronio et al, 2009) considered the optical spatial non-collinear scheme with type II second harmonic generation (SHG) in a birefringent KTP crystal. Two orthogonally polarized beams at frequency nj1 =nj 2 =nj=1064nm, e E λ and o E λ , were injected into the nonlinear birefringent medium to cross and overlap at the input face of the crystal.…”

“…As the intensities of the input fields were varied in a suitable range (1MW/cm 2 ï 2.5GW/cm 2 ), the TWI linear, frequency conversion, and solitonic regimes in the ordinary KTP plane were experimentally observed as reported in ref. (Baronio et al, 2009). …”

The Three-Wave Resonant Interaction Equations: Spectral and Numerical Methods

“…The focus in the present paper is on the spectral theory of the three-wave interaction equation with the purpose of numerically integrating the spectral equation for both vanishing and non vanishing boundary values. In particular we apply spectral techniques to recently found theoretical and experimental results on the three-wave resonant interaction processes [25][26][27][28][29][30][31][32][33][34].…”