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We have performed pseudopotential calculations of the electronic structure of GaAs-Ga~"Al"As (001) square-we11 superlattices for 0.2 & x & 0.5 and computed the optical matrix elements involving transitions from the top heavy-hole state to confined resonances in the conduction band. We show that such transitions are observable and demonstrate explicitly the link between the change in the Bloch component of the superlattice wave function and the change in the transition probability. Of particular interest is the range of composition 0.4-0.45 in which I -like and L-like resonances cross.We have recently performed pseudopotential calculations of the electronic structure of (001) GaAs-Ga~"Al"As superlattices. ' Among the rich variety of states reported, the most novel ones are those lying above the confining barriers. For instance, one of these states is localized mainly in the alloy layers. This new confined state (resonance) has recently been observed in Raman spectra. In this paper we show that optical transitions between such resonances and the valence ground state of the superlattice are observable and present a unique example of the effect of tuning the Bloch component of the superlattice wave function.Our calculations are based on a pseudopotential scheme which is capable of generating the electronic structure of a semiconductor superlattice of period up to 200 A. The Hamiltonian we start with is H = Hp+ V, where H0 describes bulk GaAs and V is a potential determined by the difference in the atomic potentials of the alloy and bulk GaAs. The Schrodinger equation (Ho+ V -E) p = 0 is solved using the expansion p = g",A"» @"» which leads to a set of linear equations (E"» E)+g~n». (4"' » I l Ign». ) =o, (1) n, i @"» are bulk (GaAs) Bloch states, i.e. , solutions of Ho@"» =E"»$"». The superlattice eigenvalues and eigenfunctions are then calculated by direct diagonalization of (1). The wave function components A"~specify the degree of participation of the individual bulk Bloch states in forming the superlattice state. We shall see that the details of the distribution of these coefficients in K space play a decisive role in determining the optical properties of the system.We have calculated the electronic structure of (001) GaAs-Ga1 "Al"As superlattices of period 140 A, at the center of the Brillouin zone, with the aluminum fraction x ranging from 0.2 to 0.5. We have limited our attention to the conduction-band states in the range of energy 1.55-2.01 eV (the zero of energy is the top of GaAs valence band). The results of these calculations are shown in Fig. 1, where the curves labeled 1 and 2 correspond to the I"-like confined states lying below the top of the conventional confining barriers, curve 3 is a I -like resonance, and 4, 5, and 6 are X-related resonances, i.e. , superlattice states lying above the X minimum of the GaAs band structure and made up of bulk X-like Bloch states. A summary of the charge densities along the superlattice axis (z) illustrating the evolution of the Bloch components of the superlattice...

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