Modern nonlinear spectroscopy opens principally new opportunities of data obtaining (except for the information about new nonlinear parameters of a sample) being a tradition for the linear spectroscopy – the data on the spectral lines position and structure, scattering cross-section, molecular levels of energy and transition probabilities. Though the nonlinear spectroscopy generally works with an unlimited number of new parameters – nonlinear sensitivity of various orders, in fact in the majority of methods (for example, nonlinear polarization spectroscopy, two-photon absorption spectroscopy (TPA), coherent anti-Stokes Raman Scattering (CARS)) resonances in cubic nonlinear sensitivity are investigated which has become one of the most important characteristics of material media. Cubic nonlinear sensitivity X(³) is a 4th-grade tensor, non-zero in centrally symmetric media: liquids, gases, amorphous and crystalline solids.

When two time- and space-matched light waves: E(v_p), higher frequency v_p (pumping wave) and E(v_s), lower frequency v_s (Stokes wave) drop on the nonlinear medium with the 3rd-order X(³) with non-zero nonlinear sensitivity, their interaction cause electromagnetic field jitter at frequency v_p - v_s. In case of their resonance with oscillations of a certain chemical bond of media v_p - v_s = v_vib induced scattering of the second photon of pumping wave E(v_p) on the phased oscillation v_vib with generation of new wave ECARS (2v_p - v_s), anti-Stokes wave with frequency (2v_p - v_s), higher pumping frequency v_p and Stokes frequency v_s is observed.

Coherent anti-Stokes Raman Scattering (CARS) is an induced process of Raman (combination) scattering when molecular oscillations are phased by the external radiation and scatter this radiation to the anti-Stokes area.

Advantages of CARS:

• The signal level in CARS spectroscopy may exceed the level obtained in the spontaneous Raman spectroscopy 10⁴-10⁵ times
• The fact that anti-Stokes wave frequency ν_as » ν_p, ν_s, i.e. it is the highest one, allows one to use filters cutting incidence laser radiation as well as possible fluorescence
• Low divergence of the beam allows obtaining of qualitative spatial separation from the fluorescence background for chemiluminescent samples or heat radiation in flames, discharges
• Basic contribution to the anti-Stokes radiation generation goes from a small near-focus volume of two laser beams. So it is enough to use samples containing a low quantity of a substance. Besides, owing to this fact spatial distribution of molecules on certain vibration-rotation levels with a high spatial resolution can be investigated
• A high spectral resolution can be obtained without any spectrometer. In CARS of collinear geometry, the Doppler width of ninety-degree spectroscopy of spontaneous scattering is ν_p / ν_p-ν_s times reduced

Energy level diagram shows that CARS includes the interaction of four waves with frequencies: pumping v_pump; Stokes component v_s; probing wave v_probe; anti-Stokes component v_CARS on oscillatory resonance v_vib. Pumping frequency and probing wave frequency – is the same frequency ν_pump = ν_probe, set by the pumping laser.

CARS is usually compared to the induced Raman scattering, and also to spontaneous Raman scattering. CARS combines the advantages of a strong signal of the induced scattering with a wide application area of Raman spectroscopy. The intensity of the induced Raman scattering is a few orders higher than the intensity of spontaneous Raman scattering, however, it is observed only when the intensity is higher than the threshold one, which depends on a media absorbance and the derivative of polarizability. The observance of the induced scattering is limited only by the strongest in Raman scattering lines of high-density materials.

In contrast to Raman scattering when the light is scattered in all directions, anti-Stokes signal keeps the direction, set by the incident waves, and at special conditions stimulates other photons to scatter in the same direction accumulating the signal coherently. Like laser radiation, the photons of anti-Stokes signal are phased with each other, scatter in a phase-matched direction, and are therefore easy – detectable. Unlike the microscopy based on linear processes of radiation and imaging, where signal intensities are linearly connected with the laser power, CARS signal is generated on the basis of the 3rd-order nonlinear processes and has more complicated nonlinear dependences on the intensity of incident radiation. CARS signal is proportional to the squared pumping wave intensity and directly proportional to the Stokes wave intensity as well as to all squared contributions to tensor X(³), so that X(³) includes summed responses of all molecules in a zone of interaction in focal waist of laser radiation, and correspondingly CARS is proportional to the squared concentration of molecules contributing to X(³). It allows using CARS (at certain conditions, along with the selective and non-invasive method) for quantitative measurements of chemical substance concentration in a sample.

It seems that the Raman spectroscopy and CARS should have the same sensitivity, as the same molecular transitions are used by them. However a CARS signal is much more intensive (~105) than a spontaneous Raman signal, which cubically depends on excitation power, possesses an accumulation effect in the direction of phase synchronism and its properties are close to the properties of laser signals. It allows the substantial time reduction of signal accumulation (down to units of a microsecond per pixel) and non-destructive real-time analysis, which is almost impossible in other types of imaging – confocal fluorescent microscopy or Raman microscopy.

CARS signal is generated in the direction distinguished by the phase synchronism condition. In a collinear case CARS signal directionally coincides with the direction of laser radiation. CARS signal propagating in the forward direction with the exciting radiation is F-CARS (Forward CARS). F-CARS signal consists of resonant and non-resonant signals. Non-resonant signal (background) is the result of transitions remote from the resonance, for which signals are coherently summed up as well. Resonant amplitude has a phase shift of π radian from the resonance, while non-resonant part of a signal has no phase shift. Due to this fact CARS, spectral line has the form of the Fano profile which is shifted relative to Raman signal. Non-resonant background is usually low and depends on the nature of the investigated object. However, at low concentration of the substance a resonance part of the signal decreases and non-resonant background turns to be a major issue. Sensitivity is limited by the difference between the resonant and non-resonant parts of CARS signal.

One of the ways of reduction of non-resonant background at CARS signals registration is polarization-sensitive detection (Р-CARS), using the difference of polarization of resonant and non-resonant signals. It allows the enhancing of the contrast and improving CARS imaging quality.

When CARS is detected in a backward direction (Epi CARS), non-resonant signal is absent. But E-CARS signal intensity is not high compared to F-CARS signal, as E-CARS signal is generated from a very small volume due to the destructive interference. E-CARS is sensitive to small objects (dimensions of which are less than the optical wavelength), being directly in focus.

In certain conditions when a sample is a strongly-scattering one or when a sample is dried F-CARS signal may scatter in backward direction giving a strong E-CARS signal.