Twenty watts of terahertz Terahertz radiation, also known as submillimeter radiation, is the latest frontier in the electromagnetic spectrum. Coherent sources produce electromagnetic waves extending from wavelengths of 100,000 km to 0.1 µm, but until recently the region between around 100 and 300 µm had no good coherent sources. Such terahertz waves have a range of potential applications, especially in biomedicine, where they can be used to analyze surface proteins of living tissues to provide instant “biopsies” for diseases such as skin cancers. Current methods of producing teraherz radiation, however, yield a limited average power of only about 1 mW. A pulse of light from a femtosecond laser, for example, can accelerate electrons to high-peak-power pulses, but the total amount of radiation from each pulse is low, and so is average power output. Now, a collaborative effort among three national laboratories— Brookhaven (Upton, NY), Lawrence Berkeley (Berkeley, CA), and the Thomas Jefferson National Accelerator Facility (Newport News VA), commonly called the Jefferson Lab— has achieved an average output of 20 W using relativistic electrons from a linear accelerator, or linac (Nature 2002, 420, 153).

Terahertz radiation coming through a window from the free-electron laser is reflected by a mirror onto the detector array of a pyroelectric camera to produce this false-color, real-time video image. (Jefferson Lab)

The new method begins with the production of a picosecond-long pulse of electrons generated by exposing gallium arsenide to a femtosecond laser. The electrons are then fed into the 30-mlong linac at the Jefferson Lab’s free-electron laser (FEL) to boost their energy to 40 MeV. The accelerated electrons are bent by a magnetic field into a 1-m arc. As they are accelerated through this curve, they radiate in the terahertz range.

Although the number of electrons in each pulse is comparable to that produced by existing techniques, the amount of energy each electron radiates increases as the fourth power of the relativistic factor, or of the energy. For 40-MeV electrons, this means a 200,000-fold increase in power over subrelativistic electrons. With a repetition rate of 37 MHz, the Jefferson Lab’s FEL linac produces a 5-mA current and a 20-W radiation output.

The efficiency of the entire system is greatly enhanced because after the electrons radiate, they are fed back into the accelerator to decelerate them back down to 10 MeV. Thus, about threequarters of the energy of the electrons is fed back into the power supply, reducing total power input by a factor of 4.

“Of course, a 30-m-long accelerator is not a practical source for medical diagnostics,” says Gwyn P. Williams of the Jefferson Lab, one of the researchers. “But we are currently looking at what the minimum parameters needed for adequate power are. We expect that we will be able to reduce accelerator length to 2 to 3 m and perhaps the cost to that of an MRI scanner.” The team is now working with Advanced Energy Systems (Medford, NY) to develop a compact system for commercialization.

Such a terahertz scanner could detect skin cancer on a patient without a biopsy and substitute spectral analyses for biopsies in endoscopic procedures such as colonoscopies. (Terahertz radiation does not penetrate tissue well, so it cannot probe for diseases located much below the surface.) Because terahertz radiation does penetrate cloth and paper easily, other possible applications include security scanners.

Chaos in the engine One of the fastest ways to reduce fossilfuel use is to increase the energy efficiency of machines, and one of the less-efficient machines is the internal combustion engine—despite a century of development. One cause of this inefficiency is the stroketo- stroke variation in the power supplied by each piston. Because the crankshaft can absorb only a set amount of power at a given rotation rate, variations in the energy generated by each piston cause wasted power, which goes into engine noise. Eliminating such variability would increase engine efficiency by about 10% and save enormous amounts of fuel each year. Researchers at the Technical Institute of Lublin (Poland) have found clues to how this stroke variability develops, clues that may aid in reducing it . Using a fiber-optic-based pressure measurement system, they obtained continuous recordings of pressure in a single piston with high time resolution. They showed that in certain types of operation, the variation of pressure in the cylinder became chaotic. Chaotic variability, although not random, is characterized by a strongly nonperiodic variability that is difficult to control by any conventional feedback mechanism.

In an internal combustion engine, the variation of pressure (p) in the cylinder becomes chaotic at a critical value of the ignition advance angle, as shown by this pressure-time series. (Technical University of Lublin, Poland)

The key parameter in the onset of chaos, the Lublin team discovered, was the ignition advance angle, defined as the difference in the angular position of the crankshaft between the time that the spark ignites combustion and the time of maximum compression. The larger the advance angle, the higher the torque and the larger the efficiency of the energy conversion, other factors being equal. But the team found that larger advance angles also led to increased variability and eventually to chaotic functioning that cut efficiency.

At an advance angle of 5°, which is less than that generally used for low-speed operation, compression is wholly repeatable and variability is small. At 20°, somewhat more than the typical angle, instabilities set in and periodically change the peak pressure by 50% or more. True chaotic behavior occurs at 30°, an angle that can be reached in high-speed operation or acceleration, with peak pressure as much as triple the average value. Pressure variation at this point exhibits the strange attractor behavior--which lacks regular oscillation--that is characteristic of chaotic systems.

Improving engine efficiency requires achieving a larger advance angle without setting off chaotic behavior. "There are a number of ways of reducing the chaotic behavior,"explains Grzegorz Litak, one of the researchers. "You can use a higher spark energy, swirl the incoming air faster, or use direct gasoline injection. Unfortunately, all of these solutions are expensive.

"Efforts to optimize engine functioning to avoid the chaotic regime will be particularly important if hybrid engines, which feed energy to an electric motor, become popular. Such engines can operate continuously at an ideal engine speed, thus allowing parameters such as the advance angle to remain at the most efficient levels.

In the past few years, researchers have accomplished this trick by using two-photon polymerization with femtosecond lasers. This approach uses liquid resins that are transparent to infrared light but polymerize and become solids when exposed to ultraviolet (UV) light. When femtosecond laser pulses are focused on these resins, the intensity in the focal point is so high that molecules can rapidly absorb two photons, enough to create radicals that set off polymerization. No polymerization occurs outside the focal point, so one can freely generate three-dimensional patterns by moving the laser's focal point.

Scanning electron microscope images of a microcapsule used for drug delivery and a microscale Venus statuette, both fabricated by means of two-photon polymerization with femtosecond lasers. (Laser Zentrum Hannover, e.V.)

Unfortunately, the commercial resins used in these experiments do not have the optical, mechanical, or thermal priorities desired for many applications, including photonic crystals, because they are relatively heat-sensitive and not very transparent.

A group of German researchers at Laser Zentrum Hannover (Germany) and the Fraunhofer Institut fur Silicatforschung (Wurzburg, Germany) have overcome this limitation. They did so by fabricating three-dimensional submicrometer structures in an inorganic.organic hybrid material that can be designed to have many of the desirable characteristics of glass (Optics Lett. 2003, 28, 301).

Inorganic.organic hybrid polymers consist of resins and silicates intermixed at the molecular level by a sol-gel process. They have high optical transparency and high chemical resistance, and they are mechanically and thermally stable in their solid form. The research team, using a commercial hybrid called Ormocer, inscribed the three-dimensional pattern with a Ti:sapphire laser operating at a wavelength of 780 nm, a pulse length of 50 fs, and an 80-MHz repetition rate.

Normally in photolithography, the smallest size of a feature is limited by the wavelength of the light used. However, because the two-photon process only functions above a sharp threshold in intensity, it is possible to create structures with resolutions far smaller than the 780-nm wavelength of the light. Only a small volume of material around the peak intensity of the focal point is polymerized, which enabled a resolution of about 200 nm.

As a demonstration, the team created a micrometer-scale statuette and a photonic crystal array. To speed the fabrication process, which took about 5 min, the researchers polymerized only the outer surface of the statuette. After that, the surrounding resin was washed away and the inside polymerized with a burst of UV light. For practical applications, fabrication rates can be increased by orders of magnitude by using more sensitive polymerization initiators.

"The great advantage of the hybrid materials is their flexibility," says Boris Chichkov of the Laser Zentrum team. "You can change the index of refraction and maximize transparency for telecommunication applications, or the biocompatibility for medical applications. In addition, the materials used are inexpensive, so the range of applications should be great."

Stock physics The stock market in recent years has acted to transfer huge sums of wealth from small investors to certain big investors. Much of this wealth transfer occurred when the large investors sold their huge holdings at high prices long before small investors learned that a company's books were cooked. The small investors then sold their stocks at vastly lower prices. Why do the big fish (who own most of the shares) get out safely, but when the little fish try to flee, the stock price plummets in their stampede? A statistical study of stock trading by Fabrizio Lillo and Rosario N. Mantegna from the University of Palermo, Italy, and J. Doyne Farmer from the Santa Fe Institute (NM) provides a partial quantitative answer (Nature 2003, 421, 129). The team was examining the more general issue of how a single stock trade of a given size affects the price of that stock. To do so, it analyzed trading data from 1995 to 1998 for the 1,000 stocks with the largest market values on the New York Stock Exchange and found that the impact of a given trade on the price of a stock increased more slowly than linearly with the size of the trade. This tendency became more pronounced for the biggest trades. The largest trades typically involved 1,000 times as much money as the smallest trades but moved the stock price only about 8 to 10 times as far. This means that across the stock market, if a huge investor sells $10 million worth of shares in a single transaction and causes the price to fall by 2%, 1,000 investors each selling only $10,000 in stock can cause the stock to plummet by 90%, even though they have withdrawn the same total cash amount. So it is easy for big investors to get out of a stock without heavy losses, but impossible for small investors to do so if many of them sell at the same time. Similarly, in a rising market, a single large investor can easily buy in early without making the stock soar, but small investors trying to get on board cannot do so at the bottom because their buying sends the stock into the stratosphere.

Price shift, LP, versus normalized transaction size, (t), for buy orders initiated in 1996, where each curve represents a set of stocks homogeneous in market capitalization, increasing from low-(A) to high-capitalization (T)--such as Coca Cola, General Electric, and Exxon (a). The same data collapse onto a single curve when replotted on axes modified by the mean capitalization, C, raised to a power (b).

"There is not a one-to-one correspondence of the size of an order and the size of the transaction because several small orders can get bundled together," cautions Farmer, "but large orders tend to have less impact per share than small ones."