Fano lines in the reflection spectrum of directly coupled systems of waveguides and cavities: Measurements, modeling, and manipulation of the Fano asymmetry

We measured and analyzed reflection spectra of directly coupled systems of waveguides and cavities. The observed Fano lines offer insight on the reflection and coupling processes. Very different from side-coupled systems, the observed Fano line shape is not caused by the termini of the waveguide but by the coupling process between the measurement device fiber and the waveguide. Our experimental results and analytical model show that the Fano parameter that describes the Fano line shape is very sensitive to the coupling condition. A movement of the fiber well below the Rayleigh range can lead to a drastic change of the Fano line shape.

Figure 1

A schematic representation of the sample and experimental setup. The green membrane structure represents the sample. In the barrier waveguide (middle line defect), three cavities have been created by shifting the holes around the waveguide in a tapered way. The shift of the green holes is $S1=0.0124a$, the shifts of the red and blue holes are 2/3 $S1$ and 1/3 $S1$, and $a$ is the lattice constant. The red cone next to the sample represents a polarization maintaining lensed fiber used to couple light into the membrane.

Figure 2

Reflection spectrum of a direct coupled waveguide and multiple-cavity system. Black square, measured spectrum; red line, calculated spectra taking into account the reflection of the waveguide; blue dotted line, calculated spectra ignoring reflection of the waveguide facet. The calculations were performed without taking into account the lossy Fabry-Perot cavity between the fiber tip and photonic crystal chip.

Figure 3

Schematic of the optical system including coupled cavities directly coupled to waveguides. A lensed fiber as a measurement device is also taken into account in the system.

Figure 4

Reference reflection spectrum. The black squares represent the experimental data and the red line is the fit from our theoretical model. Panels (b)–(d) are zoomed in from panel (a).

Figure 5

Tuned reflection spectrum. The black squares represent the experimental data and the red line is the fit from our theoretical model. Panels (b)–(d) are zoomed in from panel (a).

Figure 6

Reflection spectra of a Fano resonance at different air gap sizes. The black squares represent experimental data and the red lines represent fits from the model. (a) $\mathrm{\Delta }$. (b) $\mathrm{\Delta }+100\mathrm{nm}$. (c) $\mathrm{\Delta }+300\mathrm{nm}$. (d) $\mathrm{\Delta }+500\mathrm{nm}$.