or FWHM) are  || = 7° in the plane of the junction and  ⊥ = 35° perpendicular to the junction. In the top row of the fig- ure, (a, b), where the assumed beam has no astigmatism, the phase distribution at the laser’s front facet is uniform. In the middle row, (c, d), the astigmatic distance (defined as an equivalent dis- tance in free space between horizontal and vertical beam waists) is z = 10 m, resulting in a slightly wider beam along the X-axis, and a divergent phase front whose peak-to-valley variation (i.e., from the edge to the center of the beam) is ~120°. In the bottom row, (e, f), the assumed astigmatism is z = 25 m. Again the beam is broader (in the hori- zontal direction) than the one without astigmatism, and the phase distribution exhibits a peak-to-valley variation of ~190°. The elliptical cross-section of the beam emerging at the front facet of the laser is responsible (through diffraction) for  || being much smaller than  ⊥ . The cause of astigmatism is the non-uni- form gain profile (along the X-axis) within the active region of the laser. As the gain is strongest near the cavity’s central axis, the beam, while propagating in the cavity along Z , experiences a “gain focusing” effect toward this axis—a direct consequence of stronger amplification on-axis than in the wings. 2 Consequently, a divergent phase profile automatically evolves for countering this tendency of the beam to collapse to the center. We will have more to say about this property in the following section. Another interesting property of a diode laser beam is its polar- ization state, which is typically linear, having E-field parallel to the plane of the junction. This property may be traced back to the fact that, for light polarized parallel to the junction (i.e., E || ) the gain is somewhat greater than that for perpendicularly polarized light (hereinafter E ⊥ ). The guided mode associated with E ⊥ is slightly broader in the Y-direction than the mode associated with E || . Since a broad mode has less overlap with the gain layer than a more compact mode, it stays behind while the compact mode surpasses the threshold and begins to lase. Moreover, confine- ment of electrons and holes to a thin (quantum well) active layer makes it easier for E || (relative to E ⊥ ) to stimulate the excited elec- trons and holes into surrendering their photons and returning to the ground state. In practice a combination of both effects is re- sponsible for promoting the selection of E || polarization over E ⊥ . Origin of diode laser astigmatism The non-uniformity of the gain profile along X has a focusing ef- fect on the guided mode that is countered automatically by a di- vergent phase front imposed on the beam as it propagates along the Z-axis of the cavity. An easy demonstration is provided by The Optics of Semiconductor Diode Lasers Masud Mansuripur and Ewan M.Wright R obert N. Hall, born in New Haven, Connecticut in 1919, joined General Electric’s Research and Development Center after graduating from the California Institute of Tech- nology. In 1962, having realized that a semiconductor junction could sup- port population inversion, Hall built the first semiconductor injection laser. This device, based on a specially de- signed p-n junction, operated when an electric current injected the electrons directly into the junction, thus allow- ing for highly efficient generation of coherent light from a compact source. Today, diode lasers based on Hall's original idea are used, among other places, in CD and DVD players, laser printers, and fiber-optic communication systems. 1 In this article we describe the basic features of the beam of light emitted by a diode laser, and discuss methods to analyze and manipulate this beam. Collimation and beam-shaping with a pair of cylindrical lenses will be shown to be a simple and flexible method that may be applied not only to diode lasers but also to beams emerging from optical fibers. Characteristics of diode lasers A semiconductor diode laser shown schematically in Fig. 1 con- sists of a gain layer (only a few ten nanometers thick), surround- ed by guiding layers for confining the laser mode. The guiding layers’ index of refraction is somewhat greater than that of the surrounding regions (substrate and cladding), thus permitting confinement by total internal reflection. The electrical current is injected through the positive electrode, a metallic stripe several microns wide, and collected at the base-plate on the opposite side of the junction (ground electrode). The population inversion and optical gain are strongest beneath the positive electrode, tapering off laterally with an increasing distance from the electrode’s cen- ter line along Z. In gain-guided lasers, this tapering off of the gain is responsible for lateral beam confinement. (By contrast, in in- dex-guided lasers the regions adjacent to the guiding stripe are se- lectively etched away, then replaced by a lower-index cladding material.) In general, the gain layer is highly absorptive in regions that are not directly underneath the electrode and, therefore, ex- perience weak pumping or no pumping at all. The guiding layers are essentially transparent, except for losses due to scattering at impurities and at the interfaces. The substrate and the cladding are also highly transparent. Figure 2 shows plots of intensity and phase at the front facet of a single-transverse-mode diode laser ( o = 980 nm). The assumed beam divergence angles (full-width-at-half-maximum intensity 57 Optics & Photonics News ■ July 2002 Figure 1. A semiconductor diode laser consisting of an ac- tive layer surrounded by guiding layers for confinement of the laser mode.The electrical current, injected through the positive electrode, is collected on the opposite side of the junction by the ground electrode. Guiding Layers Ground Electrode Gain Medium Substrate Cladding Positive Electrode Y X Z ENGINEERING July 2002 ■ Optics & Photonics News 57