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4 The planar waveguide The slab waveguide in the structure of Fig. 8 plays a crucial role in the operation of the device because it controls the overlap of the laser mode with the gain material that drives the stimulated emission and it determines the divergence of the beam on leaving the laser, which is important for coupling into external elements such as fibre. It provides the connection between the gain generated by the gain medium and the amplification experienced by the laser mode. This chapter provides an introduction to optical modes and waveguiding in a passive, planar waveguide, to material and modal gain, and to the optical confinement factor.

2. The units are power per unit area, or energy per unit time per unit area (W m−2 ). 11) Labelling of modes There are solutions of Maxwell’s equations in all three orthogonal directions and these modes are labelled as illustrated in Fig. 6: 10 The electric field is said to be transverse polarised (TE) when the field direction lies in the plane of the slab waveguide, the (x, y) plane. The transverse mode is the solution of Maxwell’s equations along a direction normal to the slab waveguide (the z direction) for TE or TM polarised light.

4 There is a total of 4N electrons in the crystal and these occupy all the bonding states: this is the valence band. The antibonding states are empty: this is the conduction band, separated from the valence band by the energy gap. This diagram suggests that the states at the top of the valance band are similar to atomic p states and those at the bottom of the conduction band are similar to atomic s states. This is not literally true, but it is the case that near the band edges the conduction band states have s-like symmetry (spherical) and the valence band states have p-like symmetry (lobes directed along each of the orthogonal axes).

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