Electromagnetic Realization of Orders-of-Magnitude Tunneling Enhancement in a Double Well System

We report on tunneling enhancement in a periodically perturbed double well system. The double well system was realized by a structure of two optical waveguides. The transfer of light power from one waveguide to the another as induced by the periodic variations of the waveguide geometry was investigated. Our experimental measurements show that, in the presence of periodic perturbation, this transfer of light power can be enhanced by more than 500 times. We use an analogy between electromagnetic wave optics and the quantum wave phenomena to provide an experimental support to the theoretical model of tunneling enhancement of a quantum particle, facilitated by its interaction with auxiliary quantum states.

Figure 1

The schematics of the optical chip with imposed periodic variations of the waveguide width and heaters placed on top of the chip. The dark area stands for the waveguide core embedded in the cladding. The refractive index of the core is $n(x,y)=n_1=1.485$, and the refractive index of the cladding is $n_0=1.445$. The waveguide width is $7\mu \mathrm{m}$ and the distance between waveguides is $15\mu \mathrm{m}$. The thickness of the thin optical layer between waveguides is $0.6\mu \mathrm{m}$ and the total waveguides’ thickness is $2.5\mu \mathrm{m}$. The total length of the waveguide structure is 11 mm and the length of the periodic structure is 7 mm. The input/output regions consisted of two parts: a uniform waveguide structure of two isolated single-mode waveguides (length of 1 mm) and a tapering to a multimode structure with a length of an additional 1 mm.

Figure 2

A picture taken by a camera on the exit facet of the two unperturbed waveguides. The incoming light beam has been directed into the chip and the position of the incoming light was varied such that different modes were preferentially excited: (a) the first almost degenerate pair of trapped optical modes; (b) the fourth-order mode; (c) the sixth-order mode.

Figure 3

A picture taken by a camera on the exit facet of the waveguides when the incoming light beam has been directed into the left waveguide and the periodic variation of the geometry of both waveguides were applied. The amplitude of the waveguide width variations is equal to $0.5\mu \mathrm{m}$ and the period is equal to $80\mu \mathrm{m}$. (a) The left heater is not heated and the right heater is heated by $150°\mathrm{C}$. A significant light power transfer to the right waveguide is obtained. (b) The left heater is heated to $40°\mathrm{C}$ and the right heater is not heated. The light power transfer to the right waveguide is suppressed.

Figure 4

A picture taken by a camera on the exit facet of the waveguides when the incoming light beam has been directed into the left waveguide and the periodic variation of the geometry of the left waveguide were applied. The waveguide variation parameters are the same as in Fig. 3. The right heater was not heated. (a) The left heater temperature is $6°\mathrm{C}$. Most of the light remains in the left waveguide. (b) The left heater temperature is $95°\mathrm{C}$. The fourth-order mode [Fig. 2b] is partially excited. (c) The left heater temperature is $79°\mathrm{C}$. The linear combination of the fifth- and the sixth-order modes is excited.