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The experimental distinction is concrete. A 1962 gallium arsenide p-n junction laser used top and bottom contacts, parallel polished faces, and current pulses with the device in liquid nitrogen. An infrared image converter recorded the radiation pattern; a spectrometer measured narrowing above laser threshold. Comparing the same device below and above laser threshold supplied a control. Pulsed, cooled operation did not demonstrate continuous operation at room temperature.^[ref]

Zhores I. Alferov's 1970 team photolithographically patterned stripe double heterostructure lasers on silver-covered copper plates. He reports sustained laser emission at room temperature; Fig. 4 shows the device structure. Independently, Izuo Hayashi, Morton B. Panish and collaborators demonstrated continuous double heterostructure laser operation with diamond heat sinks.^[ref]

The below-threshold comparison tests the onset of stimulated emission; continuous operation additionally requires sustained removal of waste heat. Neither observation alone measures the separate band offsets, optical overlap, or every loss mechanism. The schematic above therefore explains a design principle rather than reconstructing the historical apparatus.

A double heterostructure laser electrically pumps its central layer for stimulated emission. Band offsets confine charge carriers; refractive index contrast confines the optical normal mode.^[ref]

For an original bookkeeping model, let $R$ be the injected pair rate per unit area, $d$ the active-layer thickness, $N$ its excess pair number density, $\tau$ a recombination lifetime, and ${\tau }_e$ an escape time. Before appreciable stimulated emission, supposeChoose two otherwise identical devices with ${\tau }_e=\tau$ and ${\tau }_e=9\tau$. The resulting steady state populations are $R\tau /(2d)$ and $9R\tau /(10d)$: improved confinement raises the population by a factor $1.8$ at fixed injection. This linear model assumes equal excess electron and electron hole densities, fixed lifetimes, and no laser gain clamping.

Optical confinement enters separately. For a chosen optical normal mode, define $0<\Gamma \le 1$ as its gain-overlap factor with the active layer. With material optical gain $g$, internal loss ${\alpha }_i$, and mirror loss ${\alpha }_m$, a simple laser threshold condition isFor stipulated losses ${\alpha }_i+{\alpha }_m=3$ in inverse-length units, $\Gamma =1/2$ requires $g=6$, whereas $\Gamma =3/4$ requires $g=4$. This calculation varies optical overlap only; the preceding population calculation varies carrier escape only. Their combination explains the usefulness of controlling both the energy band profile and the optical normal mode.

Herbert Kroemer proposed the double heterostructure laser in 1963; he did not participate in its 1970 experimental realization.^[ref] Zhores I. Alferov describes his group's independent 1963 proposal and later experimental program.^[ref]

Consider an original one-dimensional effective mass model with $V(x)=0$ for $|x|<a$ and $V(x)=V_0>0$ outside. Take the same positive effective mass $m^{\ast }$ everywhere, an abrupt interface, and no interactions. The wavefunction represents a transverse envelope; free motion parallel to the layer is outside this calculation. A double heterostructure laser need not be thin enough for this quantization to dominate its operation.

Set $s=x/a$, $ϵ={\hslash }^2/(2m^{\ast }{a}^2)$, $z_0^2=V_0/ϵ$, $z^2=E/ϵ$ and $w=\sqrt{z_0^2-z^2}$. The time-independent Schrödinger equation becomesHere $u(s)$ denotes the dimensionless potential; a bound state has $0<z<z_0$. Matching the wavefunction and its derivative at $s=1$ givesFor the even bound state, the interior solution is $A\cos (zs)$ and the exterior solution is $A\cos z{e}^{-w(|s|-1)}$. For the odd bound state, replace $\cos (zs)$ by $\sin (zs)$ and $\cos z$ by $\mathrm{sgn}(s)\sin z$. The physical wavefunction is $\psi (x)=\varphi (x/a)/\sqrt{a}$.

Wavefunction normalization includes both exterior tails, not just the active layer. Direct integration givesThe first two terms are the interior integral; the last is the total exterior integral. Thus the interior probability is $P_{\mathrm{in}}=A^2[1\pm \sin (2z)/(2z)]$, with the upper sign for even parity.

Choose $z_0=2$. There is one even root in $(0,\pi /2)$ and one odd root in $(\pi /2,2)$; higher branches start beyond $z_0$. Each left-hand side increases on its stated interval while $\sqrt{4-z^2}$ decreases, proving uniqueness there. Numerically,These are calculated values of the chosen finite square well. The excited bound state lies closer to the barrier and has a longer exterior tail: being bound does not mean having unit probability inside the well.

This model demonstrates electronic confinement, not optical refractive index confinement or a complete laser. Unequal effective masses, band bending, interface disorder and interactions require a more detailed model. In particular, continuity of the ordinary derivative above uses the chosen constant effective mass assumption.

An optical waveguide confines an optical normal mode transversely while permitting longitudinal propagation. A higher-refractive index layer between lower-index layers provides a simple dielectric realization. In a double heterostructure laser, overlap of the guided field with the carrier-rich active layer improves useful optical gain.

A double heterostructure laser places a lower-band gap active layer between wider-band gap layers with suitable type-I band alignment. The band offsets confine injected electrons and electron holes in the same small volume, increasing their overlap and reducing escape. Usually the active layer also has larger refractive index, so the same sandwich forms an optical waveguide. Optical confinement increases the gain-overlap factor $\Gamma$, while carrier confinement lowers the injection needed to reach the required quasi-Fermi-level splitting. These two distinct mechanisms reduce threshold current and heating. A band gap difference alone does not establish the sign of both confinement barriers; suitable band offsets are essential.

A double heterostructure laser sandwiches a narrow-band gap active layer between wider-band gap cladding layers. In a type-I band alignment, the conduction band edge is lower and the valence band edge higher in the active layer. Electrons therefore see an energy well, and electron holes also see a well because their excitation energy increases when the valence band edge decreases. Both carrier populations remain concentrated where stimulated emission occurs.

The active layer also normally has the higher refractive index, forming an optical waveguide. The optical normal mode overlaps the injected carriers strongly, and the wider-band gap cladding has less interband absorption at the emitted photon energy. Carrier confinement reduces leakage, while optical confinement reduces the required pump current and hence heating.

Writing $\Gamma$ for the fraction of the optical normal mode overlapping the active layer, the threshold condition is $\Gamma g={\alpha }_i+{\alpha }_m$, with internal and mirror losses ${\alpha }_i,{\alpha }_m$. A larger overlap and a higher carrier number density at a given current both lower the threshold current. The figure shows composition-induced offsets; a working junction also has band bending under bias, which is omitted to make the confinement mechanism visible.