When light is scattered, the great majority of the photons retain the same quantum of energy and same wavelength as their original value. Such elastic scattering can occur through a variety of mechanisms, depending on how the light interacts with matter. A very small fraction of the incident light however—often less than one photon in 106—is scattered at energies that differ from those in the incident beam. These photons have wavelengths that are determined by a change in the energy states of the scattering molecule, and this type of inelastic scattering is called the Raman effect.
While Raman scattering in the most general sense can occur through changes in the vibrational or rotational states of a molecule, the term usually indicates scattering by vibrational states alone, as purely rotational shifts are small and difficult to observe. The spectrum of the Raman lines is a fingerprint of the molecule, and its intensity is proportional to the number of scattering molecules. Raman spectroscopy is an extraordinarily versatile probe used in disciplines ranging across biology, materials science, combustion engineering, and many more (see Fig. 1).
FIGURE 1. A 532-nm laser beam exits the head of the Monterey Bay Aquarium's deep ocean Raman probe at a depth of 10,000 ft. The system is used to study seafloor minerals that have trapped vast amounts of methane and CO2.
Molecules that exhibit strong Raman scattering typically have distributed electron clouds, such as carbon-carbon double bonds. Molecular vibration bends or stretches these bonds and changes the distribution of electrons substantially. In the semiclassical theory that is used to analyze most of nonlinear optics, this results in a change in the polarization susceptibility of the sample and the emission of new wavelengths of light.
Stokes and anti-Stokes
Raman scattering differs from most nonlinear optical phenomena in that the energy state of the material is involved in the process, and a fully quantum-mechanical theory is required to take this into account. The theory assumes that the energy of the incident photons is low compared to the frequency of the first molecular excited state. In this description, changes in the vibrations of the molecular bonds are coupled to coincident changes in the states of the electrons that form the bonds. These changes in energy take place on the order of femtoseconds.
In the most common form of Raman scattering, an incident photon is absorbed by a molecule in its vibrational ground state. The molecule can be thought to change to a more energetic mode of vibration, and then quickly decay to a lower vibrational mode, but one that is still at a higher energy than the ground state. In the process of this decay the molecule loses energy by emitting a photon, resulting in what is called the Stokes wave.
It is also possible for an incident photon to find the molecule already in a vibrationally excited state. In this case, the molecule can absorb the photon and decay all the way back to its ground state. The emitted photon will then have a greater energy than the photon that was absorbed, producing an anti-Stokes wave. In either the Stokes or anti-Stokes case, the difference in energy between the incident photon and the Raman scattered photon is equal to the energy difference of the initial and final vibrational states of the molecule.
The wavelength of the Raman scattered light λS is given by:
1/λS = 1/λI ± 1/λR
where λI is the incident wavelength and λR corresponds to the Raman transition (added to the incident wave for anti-Stokes, subtracted for Stokes). The anti-Stokes wave is always weaker than the Stokes wave, and the ratio of anti-Stokes to Stokes intensity is a measure of temperature of the sample.
Enhancing the signal
Raman scattering was a well-developed field long before the laser was invented. A variety of techniques, such as having the sample molecules adhere to a metallic surface, have been used to enhance the weak Raman signal levels (see Fig 2). Soon after the development of the laser, a greatly enhanced effect—stimulated Raman scattering—was discovered.
FIGURE 2. An image formed from the Raman spectrum of a single walled carbon nanotube, enhanced by close proximity to a metal surface.
When the incident light exceeds a certain threshold in the active material, it can enhance or stimulate the rate of Raman emission through the rest of the sample. This stimulated Raman scattering (SRS) bears a similarity to the stimulated emission of an optically pumped laser. As a rule of thumb, SRS has a gain of several dB/cm of distance in the Raman material. If the pump intensity remains constant, the Raman wave grows exponentially.
SRS can achieve 50% or higher conversion of the pump wavelength to the Stokes line. While light from the spontaneous Raman effect is emitted nearly uniformly in all directions, SRS emits coherent light in a cone aligned along the pump axis. The polarization properties of SRS emission are altered as well.
Another practical difference is the appearance of additional Raman lines at integral multiples of the fundamental Raman energies. These lines are very weak in the spontaneous effect. While still much reduced in strength from the first Stokes transition, multiples of both the Stokes and anti-Stokes line can be readily apparent in SRS.
Cool CARS
Coherent anti-Stokes Raman spectroscopy (CARS) is a technique based on SRS that uses two laser beams to illuminate a sample. The difference in the frequencies of the laser light is tuned to equal to the frequency of a Raman transition. CARS produces the same Raman signals as conventional Raman spectroscopy, but at levels four or five orders of magnitude greater.
The pump beam in CARS excites the molecule to the first virtual Raman level. Now the second laser, a tunable probe beam, stimulates the Stokes transition. The pump then again excites the molecule to a still higher virtual level, but starting from the higher vibrational state. Finally, the molecule decays back to the ground state, emitting an anti-Stokes photon (see Fig. 3).
FIGURE 3. Coherent anti-Stokes Raman spectroscopy is a third-order nonlinear optical effect that combines three wavelengths to produce a fourth. The difference between the pump and probe photon energies is made equal to a Raman transition in the sample.
The coherence of the CARS signal is particularly useful in discriminating the signal amid high levels of noise, as is present for example in the study of flames. This coherence also enables examination of different regions within a sample, such as the local composition and temperatures in plasmas. Because of its minimal heating of the sample, CARS microscopy has been used to image live bacteria and the mitochondria in living cells.
CARS is a good illustration of stimulated scattering as a nonlinear optical phenomenon. Two pump beams (in this case, both the same beam) and a probe beam combine in a nonlinear medium to produce a beam at a new wavelength. The interaction of the four beams is governed by the third order susceptibility tensor, χ(3).
Unwanted effects
Like other nonlinear optical effects, the unintended appearance of the Raman effect can cause problems for some applications. Atmospheric SRS is one of the impediments in the development of lasers as directed energy weapons. Likewise, the coupling of laser light with plasmas is one of the key issues facing inertial fusion. SRS changes the efficiency and location of the deposition of laser energy in the target capsules.
But the most conspicuous problems caused by Raman scattering arise in optical networking. The tight confinement of light in the core of silica fiber causes the signal itself to achieve intensities sufficient to pump a surprising variety of nonlinear optical effects, SRS among them. SRS results in the creation of spurious signals that can interfere in a number of ways with wavelength division multiplexing (WDM) to degrade signal quality.
SRS in silica creates a Stokes wave that is down-shifted from the pump about 100 nm in the band around 1550 nm that is used in long-haul communications. The Stokes wave propagates forwards in the fiber along with the pump wave. If the pump is actually one signal channel of a WDM system, then the Stokes wave can overlap and interfere with another channel at a longer wavelength.
Raman amplification depletes the power of shorter wavelength WDM signals to pump the longer wavelength channels. This results in a reduced signal-to-noise ratio for some channels, and skewed values of the relative signal levels. Curiously enough, SRS can also be part of the solution to nonlinear problems caused by intense signals in WDM.
Raman to the rescue
A distributed Raman amplifier (DRA) uses as its gain medium the very silica fiber that forms the network. A DRA launches a continuous-wave beam from the receiver end of the fiber back towards the transmitter, pumping the Raman transition in the fiber itself and thus providing amplification along the transmission length. This results in a more gradual amplification than in a conventional system in which the signal is launched at its peak level, and can reduce problems caused by other nonlinear effects, such as four-wave mixing.
The spectrum of the gain bandwidth in a Raman amplifier is determined by the pump wavelength. The peak of the Raman gain in long-haul networks is about 100 nm below the pump wavelength; typically several pump sources at wavelengths spaced 20 nm apart are used so as to broaden and smooth the gain. A single amplifier can thereby span a wavelength range of more than 100 nm.
Raman amplification can cover all bands of optical communication, including wavelengths not readily amplified by other means. The broader and flatter gain spectra of these amplifiers can also have lower effective noise. Noise from the pump lasers themselves, however, which must be relatively high-power devices, is a consideration.
The current workhorse for network amplification is the erbium-doped fiber amplifier (EDFA). These amplifiers need less-powerful pumps than Raman devices and are adequate in themselves for many applications. But DRAs can be used together with EDFAs in high-end applications, such as submarine installations and transmission rates at 10 Gbit/s and above, to lengthen the space between regeneration and improve signal quality.
Discrete Raman amplifiers, which pump their own separate coil of optical fiber to provide gain, can be used in optical networking in a fashion similar to EDFAs. One application that may grow in importance is boosting signals in the short-wavelength telecom band between 1480 and 1525 nm, where conventional EDFAs are inefficient. When carriers fill the WDM channels in the longer-wavelength bands, they may still be able to add new capacity in the same fibers if proponents of these amplifiers are correct in their expectations.
Next month's article discusses the role of nonlinear optical phenomena in fiber-based optoelectronic devices.