Spontaneous Pattern Formation Due to Modulation Instability of Incoherent White Light in a Photopolymerizable Medium

Spontaneous pattern formation due to modulation instability was observed in a broad uniform beam of incoherent white light propagating in an optically isotropic, photopolymerizable organosiloxane. Pattern formation originates from intensity-dependent refractive index changes due to polymerization, which cause competition between the natural diffraction (broadening) and self-induced refraction of the beam. Under these nonlinear conditions, weak intensity modulations in the beam, noise, that would be negligible under linear conditions are amplified. The amplified patterns become unstable over time and spontaneously divide into individual self-trapped filaments of white light of essentially identical diameter (76 +/- 3 microm), which propagate through the medium without diffracting. In the case of noise with a weak 1-D periodic modulation, for example, the uniform beam transformed into a 1-D periodic array of self-trapped lamellae, which in turn formed a 2-D array of self-trapped cylindrical filaments. Although the rate of pattern formation varied inversely with optical power (measured from 8.4 to 59.8 mW), the uniform beam always split into discrete filaments, demonstrating that they are the most stable form of light propagation under the nonlinear conditions created by polymerization. Each filament of light retained the spectral composition and incoherence of white light, which showed that the entire polychromatic, incoherent and unpolarized wavepacket collectively participated in pattern formation. These findings are consistent with recent theoretical models of nonlinear white light propagation and with experimental observations of pattern formation in coherent and partially coherent light. Because refractive index changes due to polymerization are permanent, pattern formation imparts microstructure to the organosiloxane. Optical micrographs revealed that, after pattern formation, the initially homogeneous medium consisted entirely of a closely packed array of narrow channel waveguides induced by self-trapped filaments.