# A Data Transmission Method with Spectral Switches via Electroabsorption
## 3 Results  
Now we can proceed to study the modulated light intensity under the applied electric field. First, we consider a uniform unit spectral intensity (spectrum) in the wavelength range from 826 nm to 856 nm, as shown in Figure 4. [PERSON]'s law [21] is  
\[I(\lambda,d)=I(\lambda,0)\ \exp[-\alpha(\lambda)\cdot d], \tag{1}\]  
where \(I(\lambda,0)\) and \(I(\lambda,d)\) are the incident intensity and the final one after propagating distance \(d\), respectively, and \(\alpha(\lambda)\) is the absorption coefficient in Figure 3. Figure 5 shows the natural log of \(I(\lambda,d)\) for \(d\) = 150 \(\mu\)m. The log function here makes the whole range of \(I(\lambda,d)\) seen more clearly. Figure 4: The spectral distribution of a unit uniform spectrum. Figure 3: The absorption spectra \(\alpha(\lambda)\) of the quantum well waveguide for the s-polarization mode as a function of the electric field applied perpendicular to the layers. (i) 1.6 \(\times\) 10\({}^{4}\) V/cm and (ii) 10\({}^{5}\) V/cm [20]. The solid line and dashed line correspond to the two applied voltage values respectively. The circle markers on the lines are used for cubic spline interpolation. Now we turn our attention to how to use this effect to generate the spectral switch and use it to perform the data transmission task. Let us first use another type of spectrum, the normalized Gaussian one, in the form  
\[S(\lambda,0)=\exp\left[-\left(\frac{\lambda-\ \lambda_{c}}{\sigma_{\lambda}} \right)^{2}\right], \tag{2}\]  
where \(\lambda_{c}\) and \(\sigma_{\lambda}\) are the center wavelength and the spectral bandwidth, respectively. Here we use the symbol \(S(\lambda,0)\) to differentiate from the \(I(\lambda,0)\) used in Figure 4. It is plotted in Figure 6 for \(\lambda_{c}\)= 843 nm and \(\sigma_{\lambda}\)= 5 nm. When this Gaussian spectrum is incident to the same electroabsorption waveguide and travels the distance \(d\), its spectral intensity again is \(S(\lambda,d)=S(\lambda,0)\ \exp[-\alpha(\lambda)\cdot d]\),  
Figure 5: The natural log of \(I(\lambda,d)\) for \(d\) = 150 \(\upmu\)m corresponding to the two \(\alpha(\lambda)\) curves in Figure 3. (i) \(1.6\times 10^{4}\) V/cm and (ii) \(10^{5}\) V/cm. Figure 6: The spectral distribution of a Gaussian spectrum. where the normalized spectrum for the two different applied field values (see Figure 3) is plotted in Figure 7a,b, respectively. As seen in the figure, the spectral shift is a red shift (the peak moves to the right of the original incident peak) in Figure 7a, whereas it is a blue shift (the peak moves to the left of the original incident peak) in Figure 7b. Thus, the spectral shift can be controlled by the magnitude of the applied field. This behavior is called a spectral switch (SS); it appears in different schemes or occasions and has been studied in detail [7, 22]. One of the SS applications is utilized in information encoding and transmission in free space [3, 23]. Here, it can be used to transmit data in free space or on the chip scale because a waveguide device and light source of this sort can be fabricated and integrated on a single chip [18]. The scheme goes as follows. Consider a set of binary digital data (as shown in the first row of Figure 8) that needed to be transmitted through an electroabsorption device such as the one in \[I(\lambda,d)=I(\lambda,0)\ \exp[-\alpha(\lambda)\cdot d], \tag{1}\]0 Using the spectral shift manipulation by controlling the magnitude of the applied field as in Figure 3, we can designate blue shift and red shift as a bit of \"1\" or \"0\", respectively. The notations B and R are used to indicate the blue shift and red shift in the third row of Figure 8, starting with the word \"spectrum\". By properly adjusting the magnitude of the applied voltage (the bottom row of Figure 8) the blue shift or red shift in the spectrum peak can be controlled accordingly, as seen in \[I(\lambda,d)=I(\lambda,0)\ \exp[-\alpha(\lambda)\cdot d], \tag{1}\]1 The data can then be transmitted and detected or decoded by a receiver.