Optomechanical Self-Channeling of Light in a Suspended Planar Dual-Nanoweb Waveguide

It is shown that optomechanical forces can cause nonlinear self-channeling of light in a planar dual-slab waveguide. A system of two parallel silica nanowebs, spaced $\sim 100\mathrm{nm}$ and supported inside a fiber capillary, is studied theoretically and an iterative scheme developed to analyze its nonlinear optomechanical properties. Steady-state field distributions and mechanical deformation profiles are obtained, demonstrating that self-channeling is possible in realistic structures at launched powers as low as a few mW. The differential optical nonlinearity of the self-channeled mode can be as much as $10\times {10}^6$ times higher than the corresponding electronic Kerr nonlinearity. It is also intrinsically broadband, does not utilize resonant effects, can be viewed as a consequence of the extreme nonlocality of the mechanical response, and in fact is a notable example of a so-called accessible soliton.

Figure 1

Sketch of the dual-nanoweb fiber structure. Light propagates in the $z$ direction. The electric field of the TE mode and the magnetic field of the TM mode point parallel to the $x$ axis.

Figure 2

Normalized Poynting vector distributions of selected TE self-channeled modes at a power of 100 mW. (a) Even $m=0$ mode and (b) odd $m=0$ mode for $w=200\mathrm{nm}$, $h=300\mathrm{nm}$, $L=70\mu \mathrm{m}$, $\lambda =800\mathrm{nm}$, and $P=100\mathrm{mW}$. (c) Higher-order self-channeled TE mode with two lobes in the $x$ direction ($w=200\mathrm{nm}$). (d) Higher-order self-channeled TE mode with two lobes in each nanoweb in the $y$ direction ($w=400\mathrm{nm}$, $h=300\mathrm{nm}$, $\lambda =600\mathrm{nm}$). (e) Even and (f) odd $m=0$ mode for the asymmetric structure with $w_1=220\mathrm{nm}$ and $w_2=180\mathrm{nm}$, the upper web being thicker.

Figure 3

Power dependence of the modal index and the differential optomechanical nonlinearity. The modal indices converge to the same value at zero power. (a) Even $m=0$ TE mode in a structure with $w=200\mathrm{nm}$, $h=300\mathrm{nm}$, $\lambda =800\mathrm{nm}$, and three different values of width $L$: $60\mu \mathrm{m}$ (dashed line), $70\mu \mathrm{m}$ (solid line), and $80\mu \mathrm{m}$ (dash-dotted line). (b) is the same as (a) for the odd $m=0$ TE mode.

Figure 4

Contours of constant optomechanical nonlinear coefficient ${\gamma }_{\mathrm{om}}$ as a function of gap width $h$ and wavelength (in units of ${10}^6{\mathrm{W}}^{-1}{\mathrm{km}}^{-1}$). The nonlinear coefficient based on the Kerr effect is only $\sim 1{\mathrm{W}}^{-1}{\mathrm{km}}^{-1}$. (a) Nonlinearity of the even $m=0$ TE mode of the dual-nanoweb waveguide with web thickness $w=200\mathrm{nm}$, width $L=70\mu \mathrm{m}$, and optical bias power $P=300\mathrm{mW}$. (b) Nonlinearity of the odd $m=0$ TE mode, red curve showing the cutoff condition for the odd mode at given parameters.