ScienceWeek

APPLIED PHYSICS: ON EXTREME NONLINEAR OPTICS

The following points are made by H.C. Kapteyn et al (Physics Today 2005 March):

1) Laser technology -- the ability to generate intense and coherent light with controllable properties -- is one of the most significant enabling achievements of 20th century science. Because atoms interact through the electromagnetic force, researchers can probe -- and in some cases control -- the properties and dynamics of atomic, molecular, or condensed matter systems with unprecedented precision simply by applying external, controlled electromagnetic fields.

2) In recent years, nonlinear-optical techniques that convert one frequency of light to another have played an increasingly pivotal role in that technology -- a role second in significance only to that of the laser itself. Optical frequency doubling or parametric amplification, for instance, converts laser light into coherent radiation tunable over the near-IR, visible, and near-UV regions of the spectrum. Recent years have also seen the development of ultrashort-pulse technologies. The uncertainty principle dictates that a very short pulse of light must have broad spectral bandwidth. However, generating such a short pulse also requires that the colors in that broad spectrum have a well-defined phase relationship with each other; that is, the coherence must span the entire spectrum. More generally, control over broad-spectrum coherence makes it possible to implement the optical analog of an arbitrary waveform generator, a device that can sculpt the shape of a light pulse over time and precisely manipulate atomic or molecular dynamics.

3) By taking concepts of nonlinear optics and ultrashort pulse generation to an extreme limit, one can generate coherent light at even shorter wavelengths using a process called high-harmonic generation (HHG). This process shifts femtosecond laser light from the near-IR (1-2 eV) to the extreme-UV (tens to hundreds of eV) and soft x-ray (up to a keV) regions of the spectrum. The EUV is a difficult region of the spectrum for nonlinear optics because traditional frequency-conversion techniques generally rely on crystalline solids as the nonlinear medium, and solids are not transparent in the EUV. Nevertheless, good reasons are driving the development of new light sources in that spectral range: Short-wavelength light is ideal as a structural and chemical spectroscopic probe and as a tool for nanoscale lithography. Synchrotron sources were originally developed to address such applications, but those machines are large and have limited access.

4) High-harmonic generation produces tunable, laserlike light with high spatial and temporal coherence from an assembly of components small enough to sit on a tabletop. Moreover, the physics of the process differs radically from traditional nonlinear optics because it is intimately linked to the attosecond time domain. The quantum dynamics of the atom-field interaction determines the wavelength range, efficiency, coherence properties, and pulse duration of the generated light.[1-5]

References (abridged):

1. K. C. Kulander, K. J. Schafer, J. L. Krause, in Super-Intense Laser-Atom Physics, vol. 316, B. Piraux, A. L'Huillier, K. Rzazewski, eds., Plenum Press, New York (1993), p. 95; P. B. Corkum, Phys. Rev. Lett. 71, 1994

2. M. Ferray et al., J. Phys. B 21, L31 (1988) [CAS]; A. McPherson et al., J. Opt. Soc. Am. B 4, 595 (1987)

3. S. Backus et al., Rev. Sci. Instrum. 69, 1207 (1998)

4. J. Zhou et al., Phys. Rev. Lett. 76, 752 (1996)

5. A. Rundquist et al., Science 280, 1412 (1998)

Physics Today http://www.physicstoday.org

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MATERIALS SCIENCE: DISORDERED MATERIALS AND NONLINEAR OPTICS

The following points are made by Sergey E. Skipetrov (Nature 2004 432:285):

1) Optical frequency converters are widely used to generate coherent light at frequencies at which laser light is unavailable. Standard devices can have a very high efficiency (close to 100%), but they employ pure, sizeable -- and hence expensive -- nonlinear single crystals, and require careful adjustments. Recent work(1) demonstrates that efficient optical frequency conversion can be achieved in disordered polycrystalline materials, which are, by contrast, rather cheap to fabricate and require hardly any control. This finding is likely to mark a significant step towards large-scale applications of nonlinear optics in everyday life.

2) Suppose that light of some frequency (say, the red light of a ruby laser, at 4.3 x 10^(14) hertz) is shone onto a nonlinear crystal (a material that is not centrosymmetric). The vibrating electric field of the laser beam excites oscillations of the electrons bound in the atoms of the material. The electrons, in their turn, re-emit light at the "fundamental" (original) frequency but also at a frequency that is double the original value (8.6 x 10^(14) hertz, in this example; ultraviolet light). This "second harmonic" appears because of the anharmonicity and the asymmetry of the electric potential seen by the electrons in the crystal. This is the simplest optical frequency converter.

3) But nonlinear frequency conversion is efficient only if the second-harmonic waves generated by different atoms interfere constructively -- or, at least, do not extinguish each other because they are out of phase. This "phase-matching" condition is a manifestation of momentum conservation and is of paramount importance for all nonlinear wave-mixing processes. In the first report of the generation of optical harmonics by Franken et al.(2), for example, the nonlinear process was not phase-matched and the resulting signal was weak -- so weak, it is said, that the editorial staff of Physical Review Letters mistook it for irrelevant noise and carefully removed the tiny spot it produced on the photographic plate.

4) The condition of phase matching requires that the two waves, the fundamental and the second harmonic, should travel with the same velocity. But the speed of a wave is a monotonically decreasing function of frequency (for so-called normal dispersion), so phase matching cannot be obtained "for free". The most common approach has been to make use of a particular type of crystal, one that is birefringent. In such a crystal, the polarization of the light (the orientation of its electric-field vector) and its direction of propagation influence the speed of the wave. So for some special choice of polarization and direction, phase matching can be achieved.

5) Could there be an easy, cheap solution to the phase-matching puzzle in isotropic materials? The possibility that random structures might be appropriate had already been noted(3,4), and now it seems that a competitive alternative to the traditional approach might indeed be provided by the "random" quasi-phase-matching introduced by Baudrier-Raybaut et al(1), and explored theoretically as "stochastic" quasi-phase-matching by Morozov and Chirkin(5). Baudrier-Raybaut et al(1) used a polycrystalline disordered sample, consisting of a large number of single-crystal domains with random orientations, random shapes and random sizes. The frequency-converted waves generated by different domains --be they second-harmonic waves or "difference-frequency" waves from the mixing of two incoming waves, achieve random phases and interfere neither constructively nor destructively.

References (abridged):

1. Baudrier-Raybaut, M., Ha dar, R., Kupecek, Ph., Lemasson, Ph. & Rosencher, E. Nature 432, 374-376 (2004)

2. Franken, P. A., Hill, A. E., Peters, C. W. & Weinreich, G. Phys. Rev. Lett. 7, 118-119 (1961)

3. Miller, R. C. Phys. Rev. 134, A1313-A1319 (1964)

4. Dewey, C. F. & Hocker, L. O. Appl. Phys. Lett. 26, 442-444 (1975)

5. Morozov, E. Yu. & Chirkin, A. S. Quantum Electronics 34, 227-232 (2004)

Nature http://www.nature.com/nature

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ON NONLINEAR OPTICS, SOLITONS, AND MATTER WAVES.

Notes by ScienceWeek:

The term "nonlinear optics" refers to the study of the optical properties of matter subjected to intense electromagnetic fields. In order for nonlinearity to be exhibited, the external field should not be negligible compared to the internal fields of the atoms and molecules composing the material. Lasers are capable of generating external fields of sufficient intensity for nonlinearity to occur, and the field of nonlinear optics has developed largely as a result of the invention of the laser. In general, in nonlinear optics, the induced electric polarization of the medium is not a linear function of the strength of the external electromagnetic radiation, which leads to phenomena more complicated than phenomena occurring in linear optics.

The following points are made by M.C. Downer (Science 2002 298:373):

1) In the first nonlinear optics experiment, Franken et al. (1) focused a 3-joule red ruby laser pulse into a quartz crystal to generate a few nanojoules of ultraviolet light at exactly twice the incident frequency. The photographic recording of the signal was so weak that the editor mistook it for a blemish and erased it before publication. The memory of nonlinear optics might have been erased, too, except that since then, a series of breakthroughs has increased the efficiency of many nonlinear optical frequency conversion processes by orders of magnitude, transforming them into useful tools for science and technology.

2) In the 1960s, researchers discovered a class of crystals, now standard in laser laboratories, that could convert pulses one-thousandth as strong as Franken's ruby pulse to another color with as much as 50% efficiency simply by matching the index of refraction of the input and output frequencies (2). In the 1990s, a new class of synthetic nonlinear optical multilayer structures was developed and commercialized that efficiently converted still weaker, fixed-frequency beams from small solid-state lasers to tunable visible and infrared radiation for applications in materials processing, remote sensing of environmentally sensitive gases, and interferometry (3).

3) Along an independent line, chemists discovered in the 1970s that another notoriously weak nonlinear optical process, spontaneous Raman scattering, used to fingerprint molecular vibrations (4), could be enhanced dramatically by attaching molecules to rough metal surfaces or metal nanoparticles (5). With this approach, Raman spectra of single molecules can now be measured. Benabid et al (6) recently reported a breakthrough in the nonlinear optics of molecular gases that adds a new milestone to these historical examples. After pressurizing the hollow core of a meter-long glass photonic-crystal fiber with hydrogen gas, they demonstrated that green laser pulses propagating through the core with microjoule energy -- two orders of magnitude weaker than previous demonstrations in gases -- convert efficiently (30%) to red pulses by stimulated Raman scattering from the hydrogen stretch vibration. Reductions in fiber loss and laser line width, and an increase in fiber length, should lower the threshold energy for gas-phase stimulated Raman scattering even further.

References (abridged):

1. P. Franken, A. E. Hill, C. W. Peters, G. Weinrich, Phys. Rev. Lett. 7, 118 (1962).

2. V. G. Dmitriev, G. G. Gurzadyan, D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals (Springer-Verlag, New York, ed. 3, 1999).

3. M. Fejer, IEEE J. Quantum Electron. 28, 2631 (1992).

4. C. V. Raman, K. S. Krishnan, Indian J. Phys. 2, 399 (1928).

5. A. Otto, in Light Scattering in Solids IV, M. Cardona, G. Guntherodt, Eds. (Springer, Berlin, 1984), p. 289.

6. F. Benabid et al., Science 298, 399 (2002).

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