# A Data Transmission Method with Spectral Switches via Electroabsorption
## 2 Theory  
Electroabsorption is a change in the absorption characteristics of a material in response to an externally applied electric field [18]. The application of an external electric field leads to electron tunneling, which extends the absorption edge into the forbidden gap. The material bandgap energy is thus reduced below that provided by the band tail and Urbach tail. As shown in Figure 1a, we have \(h\
u_{1}>h\
u_{2}\), where \(h\
u_{1}\) and \(h\
u_{2}\) are the two bandgap energies corresponding to the two electric field states (OFF and ON, respectively). This is called the Franz-Keldysh effect, and it shifts the absorption spectrum to longer wavelength, as illustrated in Figure 1b. The applied electric field also results in the absorption broadening and the exciton absorption peak's disappearance. This effect can be used in optical electroabsorption modulators. As shown in Figure 1b, an incident beam at the operating wavelength is transmitted without absorption when the electric field is off. However, the light is absorbed upon electric field application. In comparison with electro-optic modulators which operate based on the refractive-index response to an applied electric field, electroabsorption modulators typically operate at greater speeds and at lower voltages. The electroabsorption effect is more obvious in semiconductor multiquantum-well (MQW) structures [18]. When an electric field is applied in the confinement direction, an additional phenomenon occurs, called the quantum-confined Stark effect (QCSE). There are some merits of QCSE; for example, exciton ionization is inhibited and exciton energy levels remain unbroadened even at high field level. As a result of these MQW properties, the wavelength shift in the absorption peak is greater, and the edge is more abrupt than in bulk semiconductors. Other merits include higher speeds, larger extinction ratios, lower drive voltages and lower chirp. Chirp is defined as the ratio of the increments of the real and imaginary parts of an electroabsorption modulator's complex refractive index, which is an important transmission characteristic. A GaAs/AlGaAs quantum-well waveguide [19; 20] is used as an example. Its data transmission application configuration is illustrated in Figure 2a, and the electric field (denoted as voltage \(V\) in the figure) is perpendicularly applied to the layer plane. Note that the light travels along the plane of the layers (the wave vector \(\stackrel{{\rightarrow}}{{k}}\) in the figure, defined  
Figure 1: The Franz–Keldysh effect. (**a**) The bandgap in the absence of an external electric field (OFF) is reduced in its presence (ON). (**b**) Change in the absorption spectrum caused by the presence of an electric field. The absorption peak moves toward longer wavelengths. C. B. and V. B are conduction band and valence band, respectively. as \(2\pi/\lambda\)). Thus, light can propagate with its polarization either in the plane of the layers (\(p\)) or perpendicular to the plane (s), as indicated in Figure 2a. Additionally, the figure shows a spectral shift controlled by the magnitude of the applied voltage \(V\), which will be explained in detail later. A Gaussian spectral beam is incident on the waveguide from the left. After traveling it and leaving from the right, the outgoing beam will have a different spectral shape depending on the voltage value, as plotted on the right side of the figure. A schematic structure of the waveguide is depicted in Figure 2b. The details can be found in [20]. Two 94 A quantum wells were embedded in a 3.6 \(\upmu\)m-thick superlattice which formed the waveguide core. The sample was doped as a \(p\)-\(i\)-\(n\) diode, which was reverse biased to apply an electric field perpendicular to the quantum wells. It was designed so that a 150 \(\upmu\)m-long sample would exhibit 10 dB modulation depth. The s-polarization mode is inaccessible to light propagating perpendicular to the layers and shows different selection rules [15].