Linear and Nonlinear Photoinduced Deformations of Cantilevers

Glassy and elastomeric nematic networks with dye molecules present can be very responsive to illumination, huge reversible strains being possible. If absorption is appreciable, strain decreases with depth into a cantilever, leading to bend that is the basis of micro-opto-mechanical systems (MOMS). Bend actually occurs even when Beer’s law suggests a tiny penetration of light into a heavily dye-doped system. We model the nonlinear opto-elastic processes behind this effect. In the regime of cantilever thickness giving optimal bending for a given incident light intensity, there are three neutral surfaces. In practice such nonlinear absorptive effects are very important since heavily doped systems are commonly used.

Figure 1

(a) A cantilever bending towards its side illuminated by a spot (P. Palffy-Muhoray). (b) Radiation penetration with linear absorption length $d$ giving light-induced bend.

Figure 2

The decay in reduced light intensity with depth for various reduced incident intensities $\alpha$.

Figure 3

Number fraction $n_c(x)$ of dye molecules converted to cis against reduced depth $x/d$ for various reduced incident light intensities, $\alpha =I_0/I_c$. Increasing $\alpha$ extends the conversion to greater depths because of photo bleaching of the surface layers. Reduced geometric bend strain for $\alpha =5$, 10 are straight lines. For cantilevers of thickness $w=w*=10.053d$ and $w=12.5d$, respectively, there are three and two intersections (neutral surfaces) with the photo-strain curves.

Figure 4

Curvature reduced by $1/d$ against reduced cantilever thickness $w/d$ for various incident reduced light intensities $\alpha$. For high intensities, bleached surface layers let light penetrate more deeply, and hence a significant fraction of the cantilever has its natural length contracted. Bend occurs even for cantilevers much thicker than the linear penetration depth $d$.

Figure 5

Neutral surfaces for fixed incident light intensity $\alpha =5$ as cantilever thickness $w$ changes. At the $w$ maximizing curvature, a third neutral surface appears from the rear face; at greater $w$, a neutral surface is lost at the front face.