Superlattice Bloch Laser: A Challenge

Abstract

The superlattice Bloch laser (also called Bloch oscillator) exists only as an idea. We discuss this type of laser for two reasons.

Problems

32.1

High frequency limit frequency of a Bloch laser.

• (a) Give a general condition of the high frequency limit of a Bloch laser.

• (b) Determine the high frequency limit of a Bloch laser based on a GaAs/AlAs superlattice with a miniband of a width of 140 meV.

32.2

Large-signal amplitude.

Estimate the large-signal amplitude of a semiconductor superlattice Bloch laser and compare it with $E_\mathrm{c}$,

(a) for $\nu =1$ THz and (b) $\nu =5$ THz. [Hint: choose data of the superlattice described in the text.]

32.3

Estimate the Bloch frequency of a conduction electron in an energy band of GaAs in the case that a static field is applied along the (100) crystal direction and compare it with the Bloch frequency of a miniband electron in a GaAs/AlAs superlattice. [Hint: Bloch oscillations are not observable for bulk GaAs by various reasons: intervalley scattering of electrons and impact ionization are extremely strong for electrons submitted to a strong electric field; furthermore, electrons can reach higher conduction bands.]

32.4

Determine the absolute number of electrons in an active medium of a superlattice Bloch laser described in Sect. 32.1.

32.5

Design a resonator for a superlattice Bloch laser oscillating at 6 THz.

32.6

Estimate the change of the refractive index at the Bloch frequency of the superlattice of a Bloch laser if the laser is switched on.

32.7

Determine the time of onset of laser oscillation of a Bloch laser.

32.8

Relate the high frequency peak-conductivity $\sigma _\mathrm{p}$ and the ohmic conductivity of a superlattice.

32.9

Electric conductivity.

Show the following: Without energy relaxation, a conduction electron (in a crystal) interacting with a static electric field is accelerated and decelerated in turn, but it is, on average, not possible to transfer energy from a field to an electron and vice versa. Electric conduction by materials like copper cables makes use of energy relaxation of the conduction electrons. [Hint: for demonstration, make use of a one-dimensional simple conduction band, separated by an energy gap from the next higher conduction band; see also Fig. 30.3. Assume that the field is not strong enough to cause electron tunneling between the lowest conduction band and the next-higher band or impact ionization.]