### Coupled Lasers

July 18, 2014

When doing experiments, scientists strive to isolate the object under study. It's no use trying to measure small magnetic fields when you haven't taken the precaution of using Helmholtz coils to null the Earth's magnetic field. If you're a chemist looking for trace concentrations of ions, you had better use deionized water for your analysis, and not tap water.

My first introduction to how one physical system can interfere with another was in my elementary school days when I was experimenting with radio circuits. If two inductor-capacitor (LC) oscillators operating at nearly the same frequency are placed close to each other, the magnetic field of each inductor will influence the other. This magnetic coupling causes the frequencies of the oscillators to "lock" onto the same oscillation frequency.

Synchronization of three coupled oscillators. The data are from a computer simulation by the author, rendered using Gnumeric)

This effect, called injection locking is put to good use in laser engineering when high powered lasers are injection-locked to more precise, lower power lasers. In this case, the so-called "master" laser's low noise signal is injected into the optical resonator of the larger, "slave," laser through a partially-transparent mirror. As with the LC oscillator example, above, the laser wavelengths need to be close, but higher power in the master oscillator allows injection-locking when there's a considerable wavelength difference between the master and slave lasers.

As I wrote in a previous article (Coupled Oscillators, November 15, 2011), the first observation of coupled oscillators was by Christiaan Huygens, who observed this effect for pendulums, which are mechanical oscillators. Huygens, who was the inventor of the pendulum clock, quite accidentally noticed that two pendulum clocks, mounted on the same structure, would eventually synchronize in a state in which their pendulums would swing in exactly opposite directions.[1]

Huygens called the effect, odd sympathy, since the pendulums synchronized 180° out of phase. There are a few online examples of coupled pendulums.[2-3] It's easy to think that this synchronization is caused by a momentum transfer of one pendulum to the other through the shared mounting, but the actual reason is somewhat more elusive.

Scientists from the Georgia Tech did a further study of Huygens' pendulums in 2002, and they found that the synchrony is caused by the friction at the pendulum pivot. When the pendulums are swinging with the same amplitude in opposite directions, the pivot friction is minimized, and the system prefers that lowest energy state.[4] Coupling of oscillators can improve their frequency precision.[5]

A type of pendulum with some physics of its own.

A Foucault pendulum at the City of Arts and Sciences, Valencia, Spain.

(Photo by Daniel Sancho, via Wikimedia Commons.)

Recent research by scientists from the Vienna University of Technology (Vienna, Austria) and Princeton University (Princeton, New Jersey) has shown that coupled lasers can show the paradoxical behavior that additional energy can switch them off, while a reduction of energy can switch them on. Under the same excitation, the lasers would each emit light when isolated, but they switch each other off when coupled. This switching effect opens the possibility for a different type of optical logic circuit.[6-8]

The idea for such a device came from a theoretical observation by Hakan Türeci, an assistant professor of electrical engineering at Princeton University, who developed a mathematical model of the complex interactions that exist in semiconductor lasers of micrometer and nanometer dimension.[9] The model incorporates non-Hermitian matrices that allow for asymmetries in a system's function. These asymmetries arise from quantum effects appearing at such small scales.[7]

In closely coupled miniature lasers, these quantum effects allow for a spatial manipulation of the optical gain of the laser medium; that is, an area of optical amplification can be adjacent to an area of optical loss. A collaboration was formed between Princeton and the Vienna University of Technology in an attempt to make such small lasers more efficient.[7] In 2012, computer simulations by this research team showed the possibility of a laser system that will shuts off when supplied with additional energy.[10]

Such a phenomenon happens at so-called exceptional points, which are points in the parameter space of these lasers where a resonant mode with gain coincides with another with loss in both position and their width.[6] Says Stefan Rotter, a professor at the Vienna University of Technology,
"We were puzzled when we first discovered the effect in computer simulations... Usually, there is a simple relationship between the amount of energy which is pumped into a laser and the brightness of the beam emitted by it... Once a critical threshold is reached, the laser starts to emit light, and the more energy is put in, the brighter the laser beam gets."[8]
To prove the theory, they built small, coupled, quantum cascade lasers, which emit at terahertz frequencies. This is a rather long wavelength for an optical system, and that allows the coupling to occur.[8] As shown in the electron micrograph, the two lasers are nearly touching, being separated by a distance just 2% of the diameter of the lasers themselves.

Electron micrograph of two microdisk quantum cascade lasers, coupled by their micrometer proximity.

(Vienna University of Technology image.)

In operation, electrical current is supplied to one laser, which starts to emit light. When electrical current is supplied to the other, that laser doesn't turn on; instead, this action causes the other laser to turn off.[7] For this effect to occur, an absorbing layer must be placed on the lasers to dissipate part of the light.[8] Says Princeton's Hakan Türeci, "Loss is something you normally are trying to avoid... In this case, we take advantage of it and it gives us a different dimension we can use – a new tool – in controlling optical systems."[7]

Gain map of coupled lasers.

(Vienna University of Technology image.)

Such research could be important in the design of "lab-on-a-chip" devices, which use the optical signatures of tagged molecules for analysis. This phenomenon might allow such sensors to detect chemical species at very low concentrations.[7] It can be used, also, for electro-optical switches, and for optical computing devices.[8] Says Türeci, "Our approach provides a whole new set of levers to create unforeseen and useful behaviors."[7]

This research was funded by the Vienna Science and Technology Fund, the Austrian Science Fund, the Defense Advanced Research Projects Agency (DARPA); and the National Science Foundation (NSF) through its support of the Mid-Infrared Technologies for Health and the Environment Center (MIRTHE) at Princeton.[7]

### References:

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