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This is a brief tutorial on prism and multiple-prism pulse compression, and compressors, provided from a historical perspective. Prismatic pulse compressors for femtosecond, and ultrafast tunable lasers, were first introduced, *via a single-prism configuration*, in 1983 by Dietel *et al.* [1]. Multiple-prism pulse compressor arrays followed in 1984 [2]. Independently, the generalized multiple-prism dispersion theory applicable to prismatic pulse compression was introduced by Duarte and Piper in 1982 [3] and then extended to second order derivatives in 1987 [4]. A double-prism pulse compressor in a femtosecond laser cavity is depicted in Fig. 1.

The principles of prism, and multiple-prism, pulse compression are described and discussed by Duarte [5] and Diels and Rudolph [6]. Briefly: to a first approximation the linewidth, or bandwidth, of tunable laser emission is inversely proportional to the dispersion provided by the intracavity elements. Large dispersion leads to narrow linewidth emission. Very small overall dispersion results in very large bandwidth, and via Heisenberg's Uncertainty Principle, in very short pulses [5]. It turns out that prismatic arrays can be configured, at will, to either yield very high intracavity dispersion, very small intracavity dispersion, or even substract dispersion [3-6]. The linewidth equation, and the generalized prism dispersion equations, are available in PDF format. The various terms, comprising these equations, are explained in [5]. This reference also includes detailed figures describing the geometry of prismatic pulse compressors.

Additive, and compensating, multiple-prism arrays introduced in [3] are illustrated in Fig. 2. In the compensating configuration, shown in Fig. 2(b), the second prism substracts dispersion from the first prism. More generalized multiple-prism additive, and compensating, configurations are depicted in Fig. 3. Again, in the compensating array shown in Fig. 3 (b), the second prism substracts dispersion from the first prism.

Further developments include the introduction of a fiber prism-pair pulse compressors, by Kafka and Baer [8], and the use of prismatic arrays for pulse compression in semiconductor lasers [9]. In general, the effect of minute intracavity beam deviations and geometrical perturbations on intracavity dispersion, and hence pulse compression, has been described theoretically by Duarte [10] and verified experimentally in femtosecond lasers by Osvay *et al.* [11]. A recent historical account of prismatic dispersion in pulse compression is given in [12] and a thorough study of dispersion control with prism pairs was performed by Arissian and Diels [13]. A survey of multiple-prism array applications is given in [14].

More on theory: multiple-prism beam expanders and arrays were described in matrix form in 1989 [15]. The multiple-prism dispersion theory was given in 4 X 4 matrix form in 1992 [16]. These matrix equations are applicable either to prism pulse compressors or multiple-pism beam expanders. These results are nicely reviewed and summarized in *Tunable Laser Optics* [5].

A comprehensive unified and generalized higher-order multiple-prism dispersion theory, applicable to pulse compression, is now available [17]. In this paper, generalized dispersion derivatives are given, up to the 5th order, in a mathematical framework that allows the expression of even higher derivatives, up to the *N*th order, as needed. The latest reviews and updates on this subject are given in invited papers [18, 19].

- W. Dietel
*et al.*, Intracavity pulse compression with glass: a new method of generating pulses shorter than 60 fs,*Opt. Lett.*8, 4-6 (1983). - R. L. Fork
*et al.*, Negative dispersion using pairs of prisms,*Opt. Lett.*9, 150-152 (1984). - F. J. Duarte and J. A. Piper, Dispersion theory of multiple-prism beam expander for pulsed dye lasers,
*Opt. Commun.*43, 303-307 (1982). - F. J. Duarte, Generalized multiple-prism dispersion theory for pulse compression in ultrafast dye lasers,
*Opt. Quantum Electron.*19, 223-229 (1987). - F. J. Duarte,
*Tunable Laser Optics*, 2nd Edition (CRC, New York, 2015). - J. C. Diels and W. Rudolph,
*Ultrashort Laser Pulse Phenomena*, 2nd Ed. (Elsevier Academic, New York, 2006). - F. J. Duarte and J. A. Piper, Generalized prism dispersion theory,
*Am. J. Phys.*51, 1132-1134 (1983). - J. D. Kafka and T. Baer, Prism-pair dispersive delay lines in optical pulse compression,
*Opt. Lett.*12, 401-403 (1987). - L. Y. Pang, J. G. Fujimoto, and E. S. Kintzer, Ultrashort-pulse generation from high-power diode arrays by using intracavity optical nonlinearities,
*Opt. Lett.*17, 1599-1601 (1992). - F. J. Duarte, Prismatic pulse compression: beam deviations and geometrical perturbations,
*Opt. Quantum Electron.*22, 467-471 (1990). - K. Osvay
*et al.*, Measurement of non-compensated angular dispersion and the subsequent temporal lengthening of femtosecond pulses in a CPA laser,*Opt. Commun.*248, 201-209 (2005). - F. J. Duarte, Equations for multiple-prism dispersion were derived earlier,
*Laser Focus World*42 (9), 11 (2006). - L. Arissian and J-C. Diels, Carrier to envelope and dispersion control in a cavity with prism pairs,
*Phys. Rev. A.*75, 013814 (2007). - F. J. Duarte (Ed.),
*Tunable Laser Applications*, 2nd Ed. (CRC, New York, 2009) Chapter 13. - F. J. Duarte, Ray transfer matrix analysis of multiple-prism dye laser oscillators,
*Opt. Quantum Electron.*21, 47-54 (1989). - F. J. Duarte, Multiple-prism dispersion and 4 x 4 ray transfer matrices,
*Opt. Quantum Electron.*24, 49-53 (1992). - F. J. Duarte, Generalized multiple-prism dispersion theory for laser pulse compression: higher order phase derivatives,
*Appl. Phys. B*96, 809-814 (2009). - F. J. Duarte, Tunable organic dye lasers: physics and technology of high-performance liquid and solid-state narrow-linewidth oscillators,
*Progress in Quantum Electronics*36, 29-50 (2012). - F. J. Duarte, Tunable laser optics: applications to optics and quantum optics,
*Progress in Quantum Electronics*37, 326-347 (2013).

Key words: *pulse compresor, prism compression, prism compressor, prism compressors, prism pulse compression, prism pulse compressor, prism pulse compressors,
multiple-prism compression, multiple-prism compressor, multiple-prism compressors, multiple-prism pulse compression, multiple-prism pulse compressor, multiple-prism pulse compressors. *

Published on the *25th of September, 2007*; updated on the *14th of February, 2015.*