# Detailed Analysis on Nonlinear Optics and Important Nonlinear Processes

NONLINEAR OPTICS

Nonlinear optics or NLO refers to the branch of optics that studies light’s properties in a nonlinear medium. In nonlinear media, the polarization density (P) interacts non-linearly with the light’s electric field (E). Generally, the non-linearity of light can be examined at extremely high light intensities (values of atomic electric fields, usually 108 V/m), as produced by lasers. A vacuum is estimated to become a nonlinear media after crossing the Schwinger limit. The superposition principle cannot be applied to nonlinear optics.

## History of Nonlinear optics

Maria Goeppert Mayer was the first person to observe the nonlinear optical effect during two-photon absorption in 1931. However, this theory remained unexplored until 1961. In 1961, Bell labs conducted experiments for observing two-photon absorption. Simultaneously, Peter Franken et al. from the University of Michigan discovered second-harmonic generation. Both of these advances occurred soon after Theodore Maiman developed the first laser. However, certain properties of nonlinear optics were brought to light before the construction of the laser. Bloembergen’s monograph “nonlinear optics” was the first to describe and establish the basic theory for several nonlinear optics processes.

## What are nonlinear optical processes?

Nonlinear optics further explains the nonlinear response of properties such as polarization, frequency, wavelength, path or phase of the incident light, interaction with different media, etc. Such nonlinear interactions lead to several optical phenomena:

## Frequency-mixing processes

Second-harmonic generation (shg), or frequency doubling: SHG refers to the process of light generation with a frequency two times the original light (or half the wavelength). In this process, two photons are destroyed for producing a single photon having doubled frequency.

Third-harmonic generation (thg): THG refers to the process of light generation with a frequency three times that of the original light (or one-third the wavelength). In this process, three photons are destroyed for producing a single photon, having tripled be frequency.

High-harmonic generation (hhg): HHG refers to the process of light generation with frequencies several times more than the original (generally 100 to 1000 times greater).

Sum-frequency generation (sfg): The process of summation of two separate frequencies to generate light having the resultant frequency is called SFG.

Difference-frequency generation (dfg): The process of subtracting two separate frequencies to generate having the resultant frequency is called DFG.

Optical parametric amplification (opa): OPA refers to the process of signal input amplification by utilizing a higher-frequency pump wave and simultaneously creating an idler wave.

Optical parametric oscillation (opo): OPO refers to the process of signal and idler wave generation in a resonator with the help of a parametric amplifier (without any signal input).

Optical parametric generation (opg): OPG is similar to parametric oscillation, but it does not include a resonator and incorporating an extremely high gain instead.

Half-harmonic generation: It is a particular case of opg or opo. In this, the idler and the signal degenerate in a single frequency.

Spontaneous parametric down-conversion (spdc): SPDC refers to the process of vacuum fluctuation amplification belonging to the low-gain regime.

Optical rectification (or): OR refers to the process of the creation of quasi-static electric fields.

• Interaction of nonlinear light-matter with plasmas and free electrons.

Other nonlinear processes

Optical Kerr effect, that depicts intensity-dependent refractive index.

Kerr effect: The Kerr effect (sometimes referred to as Quadratic electro-optic effect) refers to the change in the refractive index of a medium influenced by an applied electric field.
• Self-focusing occurs as a result of the optical Kerr effect (and possibly higher-order nonlinearities). It produces a spatial variation in the refractive index due to spatial variation in the intensity.
• Kerr-lens mode-locking (klm): KLM refers to using the self-focusing mechanism to a mode-lock laser.
• Self-phase modulation (spm): SPM generally refers to the effect produced because of the optical Kerr effect. It produces a temporal variation in the refractive index due to the temporal variation in the intensity.
• Optical solitons: OS refers to an equilibrium solution for either a spatial mode (spatial soliton) or optical pulse (temporal soliton) that remains unchanged during propagation. This happens as a result of the equilibrium maintained between the Kerr effect and dispersion.

Cross-phase modulation (xpm): In XPM, a certain wavelength of light may influence the phase of a different wavelength of light due to the optical Kerr effect.

Four-wave mixing (fwm): FWM is created from other nonlinearities.

Cross-polarized wave generation (xpw): XPW refers to the effect that generates a wave having the polarization vector orthogonal to the input wave.

Raman amplification

Modulational instability.

Optical phase conjugation: This refers to the reversal of the propagation direction and phase of a given beam of light.

Stimulated Brillouin scattering: This refers to the photon interaction with acoustic phonons.

Multi-photon absorption: This refers to the transferring of energy into a single electron by the absorption of two or more photons simultaneously.

Multiple photoionizations: This refers to the exclusion of several bound electrons by one single photon near-simultaneously.

Optical chaos: This refers to the laser instabilities observed in several nonlinear optical systems.

Nonlinear Optics Related processes:

The processes in which the medium observes a linear interaction of light, but are affected by various other causes:

Pockels effect: In this, the medium’s refractive index is influenced by a static electric field. This is found in electro-optic modulators.

Acousto-optics: In this, the medium’s refractive index is influenced by acoustic waves (ultrasound). This is used in acousto-optic modulators.

Molecular nonlinear optics

The early observations on nonlinear optics and mediums primarily concentrated on the inorganic solids. With time as more studies related to nonlinear optics came up, the field of molecular nonlinear optics was investigated.

The early approaches that were used to improve nonlinear properties or nonlinearities comprise the processes of

• Expanding chromophore π-systems.
• Expanding conjugation in 2D.
• Altering bond length alternation.
• Engineering multipolar charge distributions.
• Inducing intramolecular charge transfer.

In recent years, several novel directions were deviced for light manipulation and improved nonlinearity. Some of those proposals included cascading of second-order nonlinearity microscopically, combining rich density of states with bond alternation, twisting chromophores, etc. The illustrious benefits of molecular nonlinear optics have resulted in it being used significantly in the field of biophotonics that includes biosensing, bioimaging, phototherapy, etc.

Molecular nonlinear optics is based on the theory of the sum-over-states (SOS) model. The interaction of a single isolated molecule with radiation is studied by the first-order perturbation theory. The resultant expressions for the nonlinear molecular hyperpolarizabilities and linear polarizability are dependent on the properties of the transition moments of electric dipoles and the molecular states for light-induced transitions between them.

Nonlinear optical pattern formation

When optical fields are transmitted through nonlinear Kerr media, they may display some form of pattern formation. This happens due to the amplification of spatial and temporal noise by the nonlinear medium. This effect is termed as optical modulation instability. Optical modulation instability has been perceived in both photonic lattices, photo-refractive along with photo-reactive systems. Reaction induced optical nonlinearity increases in refractive index for the photo-reactive systems.

Optical phase conjugation

Nonlinear optical processes have made it possible to reverse the direction of propagation and phase variation of a light beam. The reversed beam is termed a conjugate beam (hence, the name optical phase conjugation) of the original. This technique is also referred to as wavefront reversal of time-reversal. The instrument that produces such conjugated beams is known as a phase-conjugate mirror (PCM).

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