Kogelnik and Li (1966) and Marcuse (1972) introduced the real-argument Hermite-Gauss beams in connection with laser beams and resonators. The real-argument Hermite-Gauss beams are another series of higher-order solutions to the paraxial wave equation in the Cartesian coordinate system. This series of eigenfunctions forms an orthonormal set. The fundamental Gaussian beam is the lowest-order, (m, n) = (0, 0), mode in this set, where m and n are the mode numbers in the x and y directions, respectively. In this chapter, the real-argument Hermite-Gauss beams are treated. As for the other paraxial beams, the reactive power of the real-argument Hermite-Gauss beams vanishes. The source in the complex space required for the full-wave generalization of the real-argument Hermite-Gauss beams is obtained. The basic full real-argument Hermite-Gauss wave produced by the complex space source is derived. The real and the reactive powers of the basic full real-argument Hermite-Gauss waves are evaluated. As for the other basic full Gaussian waves, the reactive power is infinite. The characteristics of the real power are discussed. The real power increases as kw₀ is increased, reaching the limiting value of the paraxial beam. For a fixed kw₀, the real power decreases as the mode orders increase.

Chapter Contents:

• 1 Real-argument Hermite-Gauss beam
• 1.1 Paraxial beam
• 1.2 Time-averaged power
• 2 Real-argument Hermite-Gauss wave
• 3 Real and reactive powers
• Appendix AA: Evaluation of the integral Im (x,z)
• Appendix AB: Complex space source
• References

Inspec keywords: electromagnetic wave propagation

Other keywords: basic full real-argument Hermite-Gauss wave; Cartesian coordinate system; orthonormal set; resonators; paraxial wave equation; full-wave generalization; eigenfunctions; fundamental Gaussian beam; higher-order solutions; mode numbers; reactive powers; paraxial beams; real-argument Hermite-Gauss beams; laser beams

Subjects: Electromagnetic waves: theory; Electromagnetic wave propagation