Nonlinear Optics: Doing the Impossible with Light

September 2009
Topics: Optoelectronics
Nonlinear optics describes an optical system in which the energy of the system does not directly correspond to the output of the system.
Optics lab

Shining a Light Outside the Box

Have you ever been told to "think outside the box"? If you're an optical engineer or scientist, then linear optics might be your box. And what's outside the linear optics box? Well, nonlinear optics, of course! Over the past half-century, nonlinear optics (NLO) has enabled breakthrough developments in laser design, slow light, and remote sensing, to name a few. It offers the promise of further breakthroughs during the next half-century. At MITRE, for example, we are experimenting with NLO to pursue major improvements in such areas as quantum computing, quantum cryptography, and remote sensing.

What Is Nonlinear Optics?

The concept of linear vs. nonlinear is a mathematical one. Simply put, an effect is called linear if the response varies linearly with the input. For example, sales tax is a linear function of the amount spent. If you buy twice as much stuff, you pay twice as much tax. By contrast, income tax is nonlinear; if your income doubles, you pay more than twice as much tax. Social Security tax is also nonlinear, but in the other direction; as your income increases, your Social Security tax eventually saturates, meaning that it stops increasing. Often, nonlinear systems have a domain in which they are effectively linear, like Social Security below the tax cap.

For optical systems, the mathematical relationship in question is usually between the electric field of the light and a material's polarization—the amount that the electrons are moved around by the light. The polarization is important because as the light acts on matter and creates this polarization, matter acts back on the light. This interaction is responsible for all major optical effects, including reflection, refraction, and absorption. To behave linearly basically means that any light output from an interaction can be described as a multiple of the light input. A multiple smaller than one means absorption, larger than one means amplification, and a complex multiple means a change of phase.

When the polarization of light behaves nonlinearly with the incoming electric field, it can make for dramatic changes in the wavelength of the light. While wavelength-changing may sound mundane, the resulting effects can be profound. For example, the lasers used in green laser pointers naturally produce invisible infrared light. But by using "frequency doubling crystals" that operate on NLO principles, the lasers can efficiently convert that invisible infrared light into the green beam you observe.

Other Nonlinear Optics Applications

Perhaps the most dramatic and irreplaceable application of nonlinear optics is the generation of entangled photon pairs, a unique feature of quantum mechanics. Researchers are hoping that entangled photons will be the key to designing incredibly fast supercomputers and unbreakable codes.

Another area that may be presently undergoing a revolution due to NLO is "slow light," the family of techniques used to slow light down to a tiny fraction of its normally blistering speed. Over the past several years, a community of researchers has pursued this goal of slowing down light in order to develop the next generation of Internet infrastructure: an all-optical network.

Another NLO application—more pedestrian but still crucial—is developing a more extreme cousin of the photochromic sunglasses that darken in bright light. This will aid warfighters who are finding themselves increasingly exposed to high-power lasers, both friendly and hostile. Such laser-proof glasses would appear transparent at low light but would completely saturate (like Social Security tax) when exposed to the blinding light of a laser, becoming opaque.

Nonlinear Challenges

If nonlinear optics is so great, why isn't it used more? The first reason is simply because it's hard. Most linear optics can be represented cleanly with simple mathematical systems. If you know how a system will respond to a little light, then you know how it will respond to a lot.

More important, you can often describe complicated inputs as combinations or "superpositions" of several simple inputs. This superposition principle is one of the most fundamental tools of physics and engineering, but it does not work for nonlinear systems. As a result, otherwise simple problems often cannot be solved analytically, requiring costly and time-consuming simulation to explore. As nonlinear effects are often counterintuitive, engineers typically choose to exhaust their linear options before turning to nonlinear approaches.

The other major challenge to NLO is that it typically requires a large amount of optical energy, posing challenges in providing the proper levels of power, efficiency, and safety. Researchers are thus attempting to find or develop nonlinear devices that operate at smaller optical intensities. One promising possibility comes from the previously mentioned field of slow light. By slowing down light, it is possible to pack more energy within a nonlinear device, thereby increasing the effective energy and enhancing the nonlinear effect.

A History of the Impossible

Nonlinear optics has a long history of making impossible optical tasks possible. It has done so by quietly enabling new and unanticipated capabilities, and by operating outside the standard linear engineering paradigm. As new nonlinear materials that demonstrate these effects at ever-lower intensity are developed, we will see NLO appear more and more in the imaging and sensing world. As this happens, we can expect dramatic developments, just as NLO has provided over the last several decades in other fields.

——by Michael Stenner

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