Intense laser beams bring nonlinearity to light

From frequency shifting to spectroscopic analysis, nonlinear optical effects have revolutionized the way we interact with light.

Jan 1st, 2003
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Ed note: A new series of "Back to Basics" starts this month that reviews the field of nonlinear optics. Besides revolutionizing laser technology, nonlinear optics are finding increasing use in a broad range of applications. This first article provides a general overview, including the origin of nonlinear optics, topics of research, and some of the more widespread applications. Future articles will examine the underlying physics of nonlinear optics, while also highlighting key applications, such as frequency shifting, parametric oscillation, and stimulated scattering phenomena.

Perhaps the most startling of all the effects made possible by an intense laser beam are those that result from changes in an optic caused by the beam itself. In the familiar realm of linear optics, a light beam can be deflected, absorbed, and so on, but its wavelength remains the same. Intense beams of light, however, can interact with a material to produce entirely new wavelengths, as well as other unexpected phenomena—and not all of them are benign.

In this realm of nonlinear optics (NLO) there are problems as well as opportunities. Currently, the NLO problems found in optical fibers have the most widespread consequences, placing constraints on the performance of high-speed networks.

First light

Nonlinear optics refers to a specific class of effects—those that occur when the energy in an electric field applied to a material under illumination approaches the energy that binds its electrons to its molecules. The electric field can come from the illumination itself (an intense laser beam) or it may be applied separately.

A few consequences of NLO have been known since the 19th centur, such as those that occur when a high DC voltage is applied to an illuminated dielectric. But it took the extreme fields of high-power lasers to bring NLO phenomenon to light. Second-harmonic generation (SHG) was first demonstrated in 1961, when researchers focused a pulsed ruby laser into quartz and produced coherent ultraviolet (UV) light .

The prospects for generating new coherent wavelengths were obvious, and within a few years all of today's most significant NLO effects had been discovered, including the generation of higher-order harmonics, stimulated scattering, self-focusing, and nonlinear absorption. Nonlinear optics covers a wide domain, and it is not possible to mention all of its effects in a brief review. A few important examples follow.

Spectroscopy of life

The spectroscopy of nonlinear absorption phenomena has brought about a revolution in biological analysis. The basic idea of multiphoton absorption is to excite a sample to high energy levels without using UV. Many organic molecules can withstand high irradiance in the infrared, but are easily dissociated by UV.

At high intensities, however, virtual energy states in the material can be excited by infrared photons, and these intermediate states can then further absorb infrared photons to reach the final state of excitation in a stepwise fashion. Analysis of these states provides important information about a variety of processes in the life sciences, as evidenced by the number of Nobel prizes awarded for research based on these techniques.

Multiphoton confocal laser imaging is one such technique. A high-peak-power, tunable laser can excite resonances in a wide variety of substances, even living tissue (see Fig. 1). Scanning a microscope along different axes builds up an image of the sample, and correlation of the fluorescence with the laser pulses allows investigation of ultrafast processes in proteins.

FIGURE 1. Multiphoton absorption of infrared photons can be used to excite dyes in living cells without exposing them to harmful ultraviolet. Here the division of an embryo of c. elegans, a worm widely studied in genetic research, is captured in detail.
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Every silver lining has a cloud

Data rates that now exceed 1 Tbit/s leave little margin for error in optical networking. Nonlinear optical effects cause four main problems in optical fibers, all resulting from the long reach of a fiber network and the confinement of the optical signal in the micron-sized fiber core.

Stimulated Brillouin scattering (SBS) generates a backward-traveling wave in silica fiber at 1.55 µm. Once the threshold for SBS is exceeded, the intensity of this wave grows exponentially as the pump level increases. This threshold value might be a low as 1 mW.

Stimulated Raman scattering (SRS) is a particular problem for wavelength-division multiplexing (WDM) systems, as it takes signal power from shorter wavelengths and adds it to the longer data wavelengths in the WDM comb. Because SRS occurs when different channels are simultaneously transmitting a '1' (that is, a pulse is present), crosstalk results.

As a pulse propagates through a fiber, its leading and trailing edges experience a different index of refraction brought about by the intensity of the pulse itself. This is the phenomenon of self-phase-modulation (SPM). Self-phase-modulation is a significant problem for long-haul networks that rely on optical amplifiers.

When at least three beams are transmitted in a fiber, the process of four-wave mixing generates a new beam at a different frequency. In the case of WDM, a very large number of beams can be generated. The frequencies of these beams usually match those of the input, so data integrity is not only reduced by loss of power from a signal, but also by the addition of this power to other signals as noise.

Put this way, it's simple

Light does not simply "pass through" a dielectric material such as glass. The electric field of the light wave is absorbed by the dielectric and sets into oscillation the electron clouds of its molecules. The displacement of the electrons from the molecular nuclei gives rise to polarization. It is the oscillation of the polarization itself that generates the light that is transmitted through the material.

Polarization is proportional to the electric field. In one dimension, this is P ∝ χE, where the complex susceptibility χ contains all of the information about the optical properties of a material—its index of refraction (the real part), and its absorption (the imaginary part).

To examine the nonlinear response of a dielectric, it is helpful to expand the electric field as a power series: E + E2 + E3 +··· . The electric field of light is a harmonic function, such as Ecos(ωt), and trigonometric identities allow the polarization to be represented (still in one dimension for the sake of clarity) as:

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Physically, this means that when light enters a material, the electron cloud oscillates not only at the same frequency as the applied field, but also at multiples of that frequency. However, the coefficients for these higher frequencies ... χ(2), χ(3), and so on, are so weak that the only light transmitted is usually at the same frequency as the incident beam.

FIGURE 2. Intense light incident on a nonlinear crystal overwhelms the linear response of its polarization. The resulting output contains harmonics of the frequency of the incident beam.
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If the incident beam exceeds some threshold irradiance, additional wavelengths then appear (see Fig. 2). This is the case of a single intense beam. With more than one beam, the equation for polarization must be modified to take into account incident beams at different wavelengths, which gives rise to some of the richest nonlinear optical phenomena.

As a very rough rule of thumb, nonlinear optical processes become apparent when the irradiance exceeds 1 W/mm2. The efficiency of a particular NLO effect varies greatly from dielectric to dielectric, depending on their crystalline structure. Crystalline materials that lack inversion symmetry are necessary for use in SHG.

The coefficient for SHG efficiency of a crystal arises from its second order susceptibility. Although this efficiency is important, it is not the only consideration in choosing a crystal for SHG. Durability, availability, and optical quality, as well as other properties are also essential.

The cutting edge of NLO

Organic NLO materials have nonlinear coefficients that for some processes are orders of magnitude greater than traditional crystals, allowing the use of lower power, less expensive lasers. The optical quality of these materials is a drawback. Someday, however, microscopic structures of organic compounds may help make practical devices from today's leading edge of research.

Applications of "optical phase conjugation" can appear almost magical—the phase conjugate mirror (PCM), for example, which produces a time-reversed reflection of an incoming beam. A beam that has passed through a distorting medium and is then reflected by a PCM back through the same medium will have the distortion removed. Other OPC effects, such as holographic motion pictures, appear equally dramatic.

Some NLO phenomena are inherently quantum mechanical and cannot be studied using a classical approach. "Squeezed light" and "entangled light" are such phenomena. Entangled light appears to defy the limitations of relativity by demonstrating that two distant photons are in instantaneous communication between about their states of polarization.

The goal of devices based on "optical bistability" is to control light using only light. It is possible to use optical bistability to construct an all-optical transistor. Optically bistable devices have two different outputs for the same input, and can switch rapidly between them.

FIGURE 3. Solitons can interact through nonlinear optical processes to reduce their losses even further. Here the collision of two solitons is depicted. Such solitons can translate through thousands of kilometers of fiber with no loss without the need for amplification.
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A soliton pulse is a uniquely nonlinear phenomenon that relies on two different effects (such as SPM and dispersion) that individually distort the pulse. But taken together, the effects can maintain the pulse shape in time and space through the distorting medium (see Fig. 3). Solitons are the subject of intense research in optical networking.

Next month's article looks at the physical origin of nonlinear optics in more detail.

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