In 1704 the great Isaac Newton described in Opticks, using drawings and words, multiple-prism dispersion [1]. In 1813 Brewster introduced compensating prism pairs for beam expansion [2].

In 1982 physicists working on narrow-linewidth tunable lasers, incorporating multiple-prism grating assemblies, derived a generalized multiple-prism grating dispersion equation [3]. The generalized multiple-prism dispersion equation is the first derivative of the generalized prismatic refraction:

In 1987 the second generalized derivative of the multiple-prism refraction (first derivative of the dispersion) was introduced as a design tool for multiple-prism pulse compressors used in femtosecond lasers [4]. Over the years these equations have been successfully used in pulse compression calculations [5] and as a tool in the design of narrow-linewidth prismatic laser oscillators [6]. Additional applications include laser microscopy.

Multiple-prism beam expanders and arrays were described in matrix form in 1989 [7]. The multiple-prism dispersion theory was given in 4 X 4 matrix form in 1992 [8]. These matrix equations are applicable either to prism pulse compressors or multiple-pism beam expanders. These matrix results are nicely reviewed and summarized in Tunable Laser Optics [9].

Recently, Duarte has elegantly constructed a theoretical framework that allows the evaluation of higher generalized derivatives, of multiple-prism dispersion, at will [10]. These higher derivatives can be used to refine the design of multiple-prism pulse compressors and should find further applications in nonlinear optics. On the other hand, this theoretical framework, provides an elegant, and complete, mathematical description of the prismatic arrays first outlined by Newton’s vision more than 300 years ago.

References

1. I. Newton, Opticks (Royal Society, London, 1704).
2. D. Brewster, A Treatise on New Philosophical Instruments for Various Purposes in the Arts and Sciences with Experiments with Light and Colours (Murray and Blackwood, Edinburgh, 1813).
3. F. J. Duarte and J. A. Piper, Dispersion theory of multiple-prism beam expander for pulsed dye lasers, Opt. Commun. 43, 303-307 (1982).
4. F. J. Duarte, Generalized multiple-prism dispersion theory for pulse compression in ultrafast dye lasers, Opt. Quantum Electron. 19, 223-229 (1987).
5. J. C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena, 2nd Ed. (Elsevier Academic, New York, 2006).
6. F. J. Duarte, Tunable Laser Optics (Elsevier-Academic, New York, 2003).
7. F. J. Duarte, Ray transfer matrix analysis of multiple-prism dye laser oscillators, Opt. Quantum Electron. 21, 47-54 (1989).
8. F. J. Duarte, Multiple-prism dispersion and 4 x 4 ray transfer matrices, Opt. Quantum Electron. 24, 49-53 (1992).
9. F. J. Duarte, Tunable Laser Optics (Elsevier-Academic, New York, 2003).
10. F. J. Duarte, Generalized multiple-prism dispersion theory for laser pulse compression: higher order phase derivatives, Appl. Phys. B 96, 809-814 (2009).
11. F. J. Duarte, T. S. Taylor, A. Costela, I. Garcia-Moreno, and R. Sastre, Long-pulse narrow-linewidth dispersive solid-state dye laser oscillator, Appl. Opt. 37, 3987-3989 (1998).

Page published on the 18th of August, 2009

Updated on the 3rd of July, 2010