Abstract
Before it is put to use, a laser beam is generally transformed in some way. The most common type of transformation is that which occurs when the beam is simply made to propagate in free space or through a suitable optical system. Since this produces a change in the spatial distribution of the beam (e.g., the beam may be focused or expanded), we shall refer to this as a spatial transformation of the laser beam. A second type of transformation, also rather frequently encountered, is that which occurs when the beam is passed through an amplifier or chain of amplifiers. Since the main effect here is to alter the beam amplitude, we shall refer to this as amplitude transformation. A third, rather different, case occurs when the wavelength of the beam is changed as a result of propagating through a suitable nonlinear optical material (wavelength transformation or frequency conversion). Finally the temporal behavior of the laser beam can be modified by a suitable optical element. For example, the amplitude of a cw laser beam may be temporally modulated by an electro-optic or acousto-optic modulator or the time duration of a laser pulse may be increased (pulse expansion) or decreased (pulse compression) using suitably dispersive optical systems or nonlinear optical elements. This fourth and last case will be referred to as time transformation. It should be noted that these four types of beam transformation are often interrelated. For instance, amplitude transformation and frequency conversion often result in spatial and time transformations occurring as well.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
We use 2ε0 dE 2 rather than dE 2 (as often used in other textbooks) to make d conform to increasingly accepted practice.
- 2.
The quantity P NL also contains a term at frequency ω = 0 which leads to development of a dc voltage across the crystal (optical rectification).
- 3.
It should be noted that for this intersection to occur at all it is necessary for n e (2ω, 90 ∘ ) to be less than n o (ω), otherwise the ellipse for n e (2ω) (see Fig 12.7) will lie wholly outside the circle for n o (ω). Thus n e (2ω, 90 ∘ ) = n e (2ω) < n o (ω) < n o (2ω), which shows that crystal birefringence n o (2ω) − n e (2ω) must be larger than crystal dispersion n o (2ω) − n o (ω).
- 4.
More generally, interactions in which the polarizations of the two fundamental waves are the same are termed type I (e.g., also e ω + e ω → o2ω), and interactions in which the polarization of the fundamental waves are orthogonal are termed type II.
- 5.
Techniques of this type to produce shorter pulses by first imposing a linear frequency chirp followed by pulse compression have been extensively used in the field of radar (chirped radars) since World War II.
References
R. W. Boyd, Nonlinear Optics (Academic Press, New York, 1992).
A. Yariv, Optical Electronics fourth edn. (Holt Rinehart and Winston, New York, 1991), Chaps. 9 and 12.
O. Svelto, Self-Focusing, Self-Steepening and Self-Phase-Modulation of Laser Beams, in Progress in Optics, ed. by E. Wolf (North-Holland, Amsterdam 1974), Vol. XII, pp. 3–50.
A. E. Siegman, New Developments in Laser Resonators, in Laser Resonators ed. by D. A. Holmes, Proc. SPIE, 1224, 2–14 (1990).
A. E. Siegman, Defining and Measuring Laser Beam Quality, in Solid State Lasers-New Develpments and Applications, ed. by M. Inguscio and R. Wallenstein (Plenum, New York 1993) pp 13–28.
L. M. Franz and J. S. Nodvick, Theory of Pulse Propagation in a Laser Amplifier, J. Appl. Phys., 34, 2346–2349 (1963).
P. G. Kriukov and V. S. Letokhov, Techniques of High-Power Light-Pulse Amplification, in Laser Handbook, ed. by F. T. Arecchi and E. O. Schultz-Dubois (North-Holland, Amsterdam, 1972), Vol. l, pp. 561–595.
W. Koechner, Solid-State Laser Engineering, fourth edn. (Springer, Berlin 1996), Chap. 4.
D. Strickland and G. Mourou, Compression of Amplified Chirped Optical Pulses, Opt. Commun., 56, 219–221 (1985).
G. Mourou, The Ultra-High-Peak-Power Laser: Present and Future, Appl. Phys. B, 65, 205–211 (1997).
M. D. Perry et al., The Petawatt Laser and its Application to Inertial Confinement Fusion, CLEO ‘96 Conference Digest (Optical Society of America, Whashington) paper CWI4.
Proceedings of the International Conference on Superstrong Fields in Plasmas, ed. by M. Lontano, G. Mourou, F. Pegoraro, and E. Sindoni (American Institute of Physics Series, New York 1998).
R. J. Mears, L. Reekie, I. M. Jauncey, and D. N. Payne, Low Noise Erbium-Doped Fiber Amplifier at 1. 54 μm, Electron. Lett., 23, 1026–1028 (1987).
Emmanuel Desurvire, Erbium-Doped Fiber Amplifiers (John Wiley and Sons, New York, 1994).
R. L. Byer, Optical Parametric Oscillators, in Quantum Electronics, ed. by H. Rabin and C. L. Tang (Academic, New York, 1975), Vol. 1, Part B, pp. 588–694.
P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, Generation of Optical Harmonics, Phys. Rev. Lett. 7, 118 (l961).
J. A. Giordmaine and R. C. Miller, Tunable Optical Parametric Oscillation in LiNbO3 at Optical Frequencies, Phys. Rev. Lett. 14, 973 (1965).
J. A. Giordmaine, Mixing of Light Beams in Crystals, Phys. Rev. Lett. 8, 19 (1962).
P. D. Maker, R. W. Terhune, M. Nisenhoff, and C. M. Savage, Effects of Dispersion and Focusing on the Production of Optical Harmonics, Phys. Rev. Lett. 8, 21 (l962).
F. Zernike and J. E. Midwinter, Applied Nonlinear Optics (Wiley, New York, 1973), Sec. 3.7.
D. Grischkowsky and A. C. Balant, Optical Pulse Compression Based on Enhanced Frequency Chirping, Appl. Phys. Lett. 41, 1 (1982).
G. P. Agrawal, Nonlinear Fiber Optics, second edn. (Academic, San Diego, 1995) Chapter 2.
E. B. Treacy, Optical Pulse Compression with Diffraction Gratings, IEEE J. Quantum Electron. QE-5, 454 (1969).
Reference [22] Chapter 6.
R. L. Fork et al., Compression of Optical Pulses to Six Femtosecond by Using Cubic Phase Compensation, Opt. Lett., 12, 483–485 (1987).
M. Nisoli, S. De Silvestri and O. Svelto, Generation of High Energy 10 fs Pulses by a New Compression Technique, Appl. Phys. Letters, 68, 2793–2795 (1996).
R. Szipöcs, K. Ferencz, C. Spielmann, F. Krausz, Chirped Multilayer Coatings for Broadband Dispersion Control in Femtosecond Lasers, Opt. Letters, 19, 201–203 (1994).
M. Nisoli et al., Compression of High-Energy Laser Pulses below 5 fs, Opt. Letters, 22, 522–524 (1997).
M. Pessot, P. Maine and G. Mourou, 1000 Times Expansion-Compression Optical Pulses for Chirped Pulse Amplification, Opt. Comm., 62, 419–421 (1987).
O. E. Martinez, 3000 Times Grating Compressor with Positive Group Velocity Dispersion: Application to Fiber Compensation in \(1.3 - 1.6\,\mu \mathrm{m}\) Region, IEEE J. Quantum Electron., QE-23, 59–64 (1987).
B. E. Lemoff and C. P. J. Barty, Quintic-Phase-Limited, Spatially Uniform Expansion and Recompression of Ultrashort Optical Pulse, Opt. Letters, 18, 1651–1653 (1993).
Detao Du et al., Terawatt Ti:Sapphire Laser with a Spherical Reflective-Optic Pulse Expander, Opt. Letters, 20, 2114–2116 (1995).
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Svelto, O. (2010). Laser Beam Transformation: Propagation, Amplification, Frequency Conversion, Pulse Compression and Pulse Expansion. In: Principles of Lasers. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-1302-9_12
Download citation
DOI: https://doi.org/10.1007/978-1-4419-1302-9_12
Published:
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-1301-2
Online ISBN: 978-1-4419-1302-9
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)