Fiber Optic Tutorials
Lateral Structures of Semiconductor Junctions
This is a continuation from the previous tutorial - semiconductor junction structures. The junction structure of a device determines the carrier and optical field distributions in the vertical direction perpendicular to the junction plane of a device. The carrier and optical field distributions in the transverse directions parallel to the junction plane are determined by the lateral structure. The lateral structure of a surface-emitting device can have either a broad active area, formed with little or no lateral restrictions on the injected current, or a small active area, formed by restricting the current flow into a confined area, as...
Semiconductor Junction Structures
This is a continuation from the previous tutorial - spontaneous emission in semiconductors. A semiconductor junction device can have either a homostructure or a heterostructure. A basic homostructure simply consists of a p-n homojunction. There are a number of different heterostructures, but the two basic concepts are the single heterostructure (SH), which consists of a single heterojunction, and the double heterostructure (DH), which consists of two heterojunctions. When the layer between the junctions of a DH is thin enough, the structure becomes a quantum well (QW) because of the quantum size effect in the thin layer. An electrically pumped...
Spontaneous Emission in Semiconductors
This is a continuation from the previous tutorial - optical gain in semiconductors. The spontaneous emission spectrum of a semiconductor can be explicitly related to the absorption and gain spectra of the semiconductor. By using (13-32) [refer to the optical gain in semiconductors tutorial] to eliminate \(\rho(\nu)\) in (13-28) [refer to the band-to-band optical transitions in semiconductors tutorial], we find \[\tag{13-41}R_\text{sp}(\nu)=\frac{8\pi{n}^2\nu^2}{c^2}\alpha_0(\nu)f_\text{c}(E_2)[1-f_\text{v}(E_1)]\] Using (13-33), (13-34) [refer to the optical gain in semiconductors tutorial], and (13-41), we can express the spontaneous emission spectrum \(R_\text{sp}(\nu)\) in terms of the absorption spectrum \(\alpha(\nu)\) and the gain spectrum \(g(\nu)\) as follows: \[\tag{13-42}R_\text{sp}(\nu)=\frac{8\pi{n}^2\nu^2}{c^2}\frac{\alpha(\nu)}{\text{e}^{(h\nu-\Delta{E}_\text{F})/k_\text{B}T}-1}=\frac{8\pi{n}^2\nu^2}{c^2}\frac{g(\nu)}{1-\text{e}^{(h\nu-\Delta{E}_\text{F})/k_\text{B}T}}\] In the...
Optical Gain in Semiconductors
This is a continuation from the previous tutorial - band-to-band optical transitions in semiconductors. By following a line of reasoning similar to that used in the optical absorption and amplification tutorial while associating \(R_\text{a}(\nu)\) with \(N_1W_{12}(\nu)\) and \(R_\text{e}(\nu)\) with \(N_2W_{21}(\nu)\), we can write down the absorption and gain coefficients contributed by direct band-to-band transitions in a semiconductor as \[\tag{13-30}\alpha(\nu)=\frac{h\nu}{I(\nu)}[R_\text{a}(\nu)-R_\text{e}(\nu)]=\frac{c^2}{8\pi{n}^2\nu^2\tau_\text{sp}}[f_\text{v}(E_1)-f_\text{c}(E_2)]\rho(\nu)\] and \[\tag{13-31}g(\nu)=\frac{h\nu}{I(\nu)}[R_\text{e}(\nu)-R_\text{a}(\nu)]=\frac{c^2}{8\pi{n}^2\nu^2\tau_\text{sp}}[f_\text{c}(E_2)-f_\text{v}(E_1)]\rho(\nu)\] respectively. By definition, \(g(\nu)=-\alpha(\nu)\). The relations in (13-30) and (13-31) are valid for carriers in either an equilibrium state or a quasi-equilibrium state because their validity follows from that of the relations in (13-26) and (13-27) [refer to...
Band-to-band optical transitions in semiconductors
This is a continuation from the previous tutorial - radiative recombination in semiconductors. In the discussion of the characteristics of optical transitions between the energy levels of an individual atom or molecule in the optical transitions for laser amplifiers tutorial, each active atom or molecule is considered a separate system in the sense that it has its own energy levels and it can reside in a particular state independently of the states of other active atoms or molecules. For the electrons and holes in a semiconductor, the situation is quite different. The states of all of the valence electrons in...