Harmonic generation (HG, also called multiple harmonic generation) is a nonlinear optical process in which photons with the same frequency interact with a nonlinear material, are "combined", and generate a new photon with times the energy of the initial photons (equivalently, times the frequency and the wavelength divided by ).
In a medium having a substantial nonlinear susceptibility, harmonic generation is possible. Note that for even orders (), the medium must have no center of symmetry (non-centrosymmetrical). [1]
Because the process requires that many photons are present at the same time and at the same place, the generation process has a low probability to occur, and this probability decreases with the order . To generate efficiently, the symmetry of the medium must allow the signal to be amplified (through phase matching, for instance), and the light source must be intense and well-controlled spatially (with a collimated laser) and temporally (more signal if the laser has short pulses). [2]
A special case in which the number of photons in the interaction is , but with two different photons at frequencies and .
A special case in which the number of photons in the interaction is . Also a special case of sum-frequency generation in which both photons are at the same frequency .
A special case in which the number of photons in the interaction is , if all the photons have the same frequency . If they have different frequency, the general term of four-wave mixing is preferred. This process involves the 3rd order nonlinear susceptibility . [3]
Unlike SHG, it is a volumetric process [4] and has been shown in liquids. [5] However, it is enhanced at interfaces. [6]
Nonlinear crystals such as BBO (β-BaB2O4) or LBO can convert THG, otherwise THG can be generated from membranes in microscopy. [7]
A special case in which the number of photons in interaction is . Reported around the year 2000, [8] powerful lasers now enable efficient FHG. This process involves the 4th order nonlinear susceptibility .
Harmonic generation for (5HG) or more is theoretically possible, but the interaction requires a very high number of photons to interact and has therefore a low probability to happen: the signal at higher harmonics will be very low, and requires very intense lasers to be generated. To generate high harmonics (like and so on), the substantially different process of high harmonic generation can be used.
Nonlinear optics (NLO) is the branch of optics that describes the behaviour of light in nonlinear media, that is, media in which the polarization density P responds non-linearly to the electric field E of the light. The non-linearity is typically observed only at very high light intensities (when the electric field of the light is >108 V/m and thus comparable to the atomic electric field of ~1011 V/m) such as those provided by lasers. Above the Schwinger limit, the vacuum itself is expected to become nonlinear. In nonlinear optics, the superposition principle no longer holds.
In optics, an ultrashort pulse, also known as an ultrafast event, is an electromagnetic pulse whose time duration is of the order of a picosecond or less. Such pulses have a broadband optical spectrum, and can be created by mode-locked oscillators. Amplification of ultrashort pulses almost always requires the technique of chirped pulse amplification, in order to avoid damage to the gain medium of the amplifier.
Four-wave mixing (FWM) is an intermodulation phenomenon in nonlinear optics, whereby interactions between two or three wavelengths produce two or one new wavelengths. It is similar to the third-order intercept point in electrical systems. Four-wave mixing can be compared to the intermodulation distortion in standard electrical systems. It is a parametric nonlinear process, in that the energy of the incoming photons is conserved. FWM is a phase-sensitive process, in that the efficiency of the process is strongly affected by phase matching conditions.
Two-photon excitation microscopy is a fluorescence imaging technique that is particularly well-suited to image scattering living tissue of up to about one millimeter in thickness. Unlike traditional fluorescence microscopy, where the excitation wavelength is shorter than the emission wavelength, two-photon excitation requires simultaneous excitation by two photons with longer wavelength than the emitted light. The laser is focused onto a specific location in the tissue and scanned across the sample to sequentially produce the image. Due to the non-linearity of two-photon excitation, mainly fluorophores in the micrometer-sized focus of the laser beam are excited, which results in the spatial resolution of the image. This contrasts with confocal microscopy, where the spatial resolution is produced by the interaction of excitation focus and the confined detection with a pinhole.
An optical parametric oscillator (OPO) is a parametric oscillator that oscillates at optical frequencies. It converts an input laser wave with frequency into two output waves of lower frequency by means of second-order nonlinear optical interaction. The sum of the output waves' frequencies is equal to the input wave frequency: . For historical reasons, the two output waves are called "signal" and "idler", where the output wave with higher frequency is the "signal". A special case is the degenerate OPO, when the output frequency is one-half the pump frequency, , which can result in half-harmonic generation when signal and idler have the same polarization.
Frequency-resolved optical gating (FROG) is a general method for measuring the spectral phase of ultrashort laser pulses, which range from subfemtosecond to about a nanosecond in length. Invented in 1991 by Rick Trebino and Daniel J. Kane, FROG was the first technique to solve this problem, which is difficult because, ordinarily, to measure an event in time, a shorter event is required with which to measure it. For example, to measure a soap bubble popping requires a strobe light with a shorter duration to freeze the action. Because ultrashort laser pulses are the shortest events ever created, before FROG, it was thought by many that their complete measurement in time was not possible. FROG, however, solved the problem by measuring an "auto-spectrogram" of the pulse, in which the pulse gates itself in a nonlinear-optical medium and the resulting gated piece of the pulse is then spectrally resolved as a function of the delay between the two pulses. Retrieval of the pulse from its FROG trace is accomplished by using a two-dimensional phase-retrieval algorithm.
An optical frequency multiplier is a nonlinear optical device in which photons interacting with a nonlinear material are effectively "combined" to form new photons with greater energy, and thus higher frequency. Two types of devices are currently common: frequency doublers, often based on lithium niobate (LN), lithium tantalate (LT), potassium titanyl phosphate (KTP) or lithium triborate (LBO), and frequency triplers typically made of potassium dihydrogen phosphate (KDP). Both are widely used in optical experiments that use lasers as a light source.
Quasi-phase-matching is a technique in nonlinear optics which allows a positive net flow of energy from the pump frequency to the signal and idler frequencies by creating a periodic structure in the nonlinear medium. Momentum is conserved, as is necessary for phase-matching, through an additional momentum contribution corresponding to the wavevector of the periodic structure. Consequently, in principle any three-wave mixing process that satisfies energy conservation can be phase-matched. For example, all the optical frequencies involved can be collinear, can have the same polarization, and travel through the medium in arbitrary directions. This allows one to use the largest nonlinear coefficient of the material in the nonlinear interaction.
Sum-frequency generation (SFG) is a second order nonlinear optical process based on the mixing of two input photons at frequencies and to generate a third photon at frequency . As with any optical phenomenon in nonlinear optics, this can only occur under conditions where: the light is interacting with matter, that lacks centrosymmetry ; the light has a very high intensity . Sum-frequency generation is a "parametric process", meaning that the photons satisfy energy conservation, leaving the matter unchanged:
A frequency comb or spectral comb is a spectrum made of discrete and regularly spaced spectral lines. In optics, a frequency comb can be generated by certain laser sources.
In atomic physics, two-photon absorption (TPA or 2PA), also called two-photon excitation or non-linear absorption, is the simultaneous absorption of two photons of identical or different frequencies in order to excite an atom or a molecule from one state (usually the ground state), via a virtual energy level, to a higher energy, most commonly an excited electronic state. Absorption of two photons with different frequencies is called non-degenerate two-photon absorption. Since TPA depends on the simultaneous absorption of two photons, the probability of TPA is proportional to the photon dose (D), which is proportional to the square of the light intensity (D ∝ I2); thus it is a nonlinear optical process. The energy difference between the involved lower and upper states of the molecule is equal or smaller than the sum of the photon energies of the two photons absorbed. Two-photon absorption is a third-order process, with absorption cross section typically several orders of magnitude smaller than one-photon absorption cross section.
Second-harmonic generation (SHG), also known as frequency doubling, is the lowest-order wave-wave nonlinear interaction that occurs in various systems, including optical, radio, atmospheric, and magnetohydrodynamic systems. As a prototype behavior of waves, SHG is widely used, for example, in doubling laser frequencies. SHG was initially discovered as a nonlinear optical process in which two photons with the same frequency interact with a nonlinear material, are "combined", and generate a new photon with twice the energy of the initial photons, that conserves the coherence of the excitation. It is a special case of sum-frequency generation (2 photons), and more generally of harmonic generation.
Multiphoton intrapulse interference phase scan (MIIPS) is a method used in ultrashort laser technology that simultaneously measures, and compensates femtosecond laser pulses using an adaptive pulse shaper. When an ultrashort laser pulse reaches a duration of less than a few hundred femtosecond, it becomes critical to characterize its duration, its temporal intensity curve, or its electric field as a function of time. Classical photodetectors measuring the intensity of light are still too slow to allow for a direct measurement, even with the fastest photodiodes or streak cameras.
High-harmonic generation (HHG) is a non-linear process during which a target is illuminated by an intense laser pulse. Under such conditions, the sample will emit the high harmonics of the generation beam. Due to the coherent nature of the process, high-harmonics generation is a prerequisite of attosecond physics.
Second-harmonic imaging microscopy (SHIM) is based on a nonlinear optical effect known as second-harmonic generation (SHG). SHIM has been established as a viable microscope imaging contrast mechanism for visualization of cell and tissue structure and function. A second-harmonic microscope obtains contrasts from variations in a specimen's ability to generate second-harmonic light from the incident light while a conventional optical microscope obtains its contrast by detecting variations in optical density, path length, or refractive index of the specimen. SHG requires intense laser light passing through a material with a noncentrosymmetric molecular structure, either inherent or induced externally, for example by an electric field.
Deuterated potassium dihydrogen phosphate (KD2PO4) or DKDP single crystals are widely used in non-linear optics as the second, third and fourth harmonic generators for Nd:YAG and Nd:YLF lasers. They are also found in electro-optical applications as Q-switches for Nd:YAG, Nd:YLF, alexandrite and Ti-sapphire lasers, as well as for Pockels cells.
A parametric process is an optical process in which light interacts with matter in such a way as to leave the quantum state of the material unchanged. As a direct consequence of this there can be no net transfer of energy, momentum, or angular momentum between the optical field and the physical system. In contrast a non-parametric process is a process in which any part of the quantum state of the system changes.
Wide-field multiphoton microscopy refers to an optical non-linear imaging technique tailored for ultrafast imaging in which a large area of the object is illuminated and imaged without the need for scanning. High intensities are required to induce non-linear optical processes such as two-photon fluorescence or second harmonic generation. In scanning multiphoton microscopes the high intensities are achieved by tightly focusing the light, and the image is obtained by beam scanning. In wide-field multiphoton microscopy the high intensities are best achieved using an optically amplified pulsed laser source to attain a large field of view (~100 µm). The image in this case is obtained as a single frame with a CCD without the need of scanning, making the technique particularly useful to visualize dynamic processes simultaneously across the object of interest. With wide-field multiphoton microscopy the frame rate can be increased up to a 1000-fold compared to multiphoton scanning microscopy. Wide-field multiphoton microscopes are not yet commercially available, but working prototypes exist in several optics laboratories.
Stimulated Raman spectroscopy, also referred to as stimulated Raman scattering (SRS) is a form of spectroscopy employed in physics, chemistry, biology, and other fields. The basic mechanism resembles that of spontaneous Raman spectroscopy: a pump photon, of the angular frequency , which is scattered by a molecule has some small probability of inducing some vibrational transition, as opposed to inducing a simple Rayleigh transition. This makes the molecule emit a photon at a shifted frequency. However, SRS, as opposed to spontaneous Raman spectroscopy, is a third-order non-linear phenomenon involving a second photon—the Stokes photon of angular frequency —which stimulates a specific transition. When the difference in frequency between both photons resembles that of a specific vibrational transition the occurrence of this transition is resonantly enhanced. In SRS, the signal is equivalent to changes in the intensity of the pump and Stokes beams. The signals are typically rather low, of the order of a part in 10^5, thus calling for modulation-transfer techniques: one beam is modulated in amplitude and the signal is detected on the other beam via a lock-in amplifier. Employing a pump laser beam of a constant frequency and a Stokes laser beam of a scanned frequency allows for the unraveling of the spectral fingerprint of the molecule. This spectral fingerprint differs from those obtained by other spectroscopy methods such as Rayleigh scattering as the Raman transitions confer to different exclusion rules than those that apply for Rayleigh transitions.
Coherent Raman scattering (CRS) microscopy is a multi-photon microscopy technique based on Raman-active vibrational modes of molecules. The two major techniques in CRS microscopy are stimulated Raman scattering (SRS) and coherent anti-Stokes Raman scattering (CARS). SRS and CARS were theoretically predicted and experimentally realized in the 1960s. In 1982 the first CARS microscope was demonstrated. In 1999, CARS microscopy using a collinear geometry and high numerical aperture objective were developed in Xiaoliang Sunney Xie's lab at Harvard University. This advancement made the technique more compatible with modern laser scanning microscopes. Since then, CRS's popularity in biomedical research started to grow. CRS is mainly used to image lipid, protein, and other bio-molecules in live or fixed cells or tissues without labeling or staining. CRS can also be used to image samples labeled with Raman tags, which can avoid interference from other molecules and normally allows for stronger CRS signals than would normally be obtained for common biomolecules. CRS also finds application in other fields, such as material science and environmental science.
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