Second-harmonic generation
Frequency doubling means the phenomenon that results from irradiation of certain materials, such as with a laser, high-intensity, under certain conditions, radiation at twice the frequency. This corresponds to a halving of the wavelength. For example, the infrared radiation from a Nd: YAG laser ( = 1064 nm) of the wavelength of green light of 532 nm are generated. It is also possible to frequency tripling, in the example of the Nd: YAG laser with ultraviolet then arises = 354.7 nm
Frequency doubling is often SHG ( second harmonic generation engl. ) abbreviated, the frequency tripling with THG ( third harmonic generation ).
- 3.1 doubling materials
- 3.2 Measurement of laser pulses
- 3.3 microscopy
Physical background
When electromagnetic radiation passes through matter, the electric field of the radiation results in a periodic displacement of the electric charges at the frequency of the radiation. This oscillating shifts generate turn electromagnetic radiation, ie light. When the intensity of the incident light is small, the deflection of the electric charges from the rest position are small. Then behave like harmonic oscillators that are driven at a frequency away from its resonance: The movement includes only the same frequency components as the excitation.
The potential that repels the dipole to its initial position, has approximately the shape of a parabola only for small deflections. For large deflections, it deviates from this, since it is the nuclear charge of neighboring atoms influences. This difference is called non-linearity, since it implies a non- linear relationship between deflection and considerate driving force. Which shape and thickness, the non-linearity has thus depends on the structure of the irradiated light from the material.
The moving charge experiences by the potential of an acceleration in the direction of the zero position. Just for a quadratic potential results from a sinusoidal profile of the speed. In case of deviations, the charge is accelerated in the meantime too slow or too fast. This leads to deviations from the sinusoidal form during the course of the speed and as a result deviations in the electric field of the emitted light, from said charge. In the spectrum of light, this means that not only the incident frequency, but also its harmonics are included to varying degrees. As the efficiency of conversion to the degree of the harmonics decreases greatly, usually only the second ( SHG) or third ( THG ) technically important.
One can interpret this generation of light of higher frequency as the absorption of two or more photons and emission of a photon. However, it is not fluorescent. Unlike the fluorescence emitted light is coherent with the incident. The mechanism is not related to the energy levels of the atoms.
Frequency doubling ( SHG)
If effective for the oscillating dipole potential is not linear, but symmetrical with respect to zero position, then the speed is the same on both sides of the distorted deflection. The resulting movement does not even Fourier coefficients. It can therefore be produced with a potential light only odd harmonics ( three-fold, five-fold, ...). To generate the double frequency so must the nonlinear material used is not centrosymmetric.
The doubled light propagates in the "forward" direction as the incident beam of light: The single-phase to the forward photons are in phase, so that the waves produced by different atoms increase. In other directions, the waves cancel each other out.
Frequency tripling ( THG )
At a sufficiently high intensity of the incident light, the amplitude of the dipole oscillations sufficient to emit light of the three fold frequency. Unlike the frequency doubling is no specific for asymmetry in the arrangement of the atoms involved necessary. However, the high intensity needed and the wide spanned by the tripling wavelength range represent technical hurdles
Basics
The efficiency of frequency doubling, is highly dependent on the strength of the field strength of the electromagnetic wave. During the polarization in the linear optical system depends only on the first-order term, it is at high radiation intensities now also dependent on the other systems and in this case of a plurality of articles:
Where the dielectric susceptibility corresponds.
In the case of frequency doubling is now the second order term to consider () the above equation. When a strong light wave of angular frequency propagating in the z direction in the material, it produces at a given location, a time-dependent radiation field:
That a second-order polarization causes, and the above equation as follows can look like:
With the aid of the trigonometric identity is thus:
It is apparent that the second order polarization contributions from two of: a constant term, according to a static electric field (optical rectification), and a second term which oscillates at twice the frequency. This oscillating polarization produces a secondary radiation in the frequency, in this case one speaks then of frequency doubling in the nonlinear medium.
So that the secondary radiation is irradiated also at the passage through the medium, the refractive index in the propagation direction for the fundamental wave to the index for the second harmonic must be the same:
If this condition is not met, the conversion takes place in the medium while still held, but the light emitted in the different points of the radiation medium is eliminated by destructive interference. With the same refractive index of the propagation velocities of the fundamental wave and the second harmonic are the same, such that a constructive interference occurs. This adjustment is called phase matching.
Since all media show dispersion phase matching condition is generally optically isotropic material is not available. Therefore, the media mostly used are birefringent crystals. In principle, there are three possibilities for phase matching in nonlinear optical media known: the critical, the non-critical and the quasi- phase matching ( QPM of engl quasi phase matching. ). At the critical phase matching in a birefringent material, the crystal axis is selected relative to the optical axis so that the refractive index of ordinary ray of the fundamental wave and the extraordinary ray of the second harmonic coincide. In the case of non-critical phase matching, the property is utilized in some of the media that the refractive index of the fundamental wave and the second harmonic when the temperature changes different variation. For the desired wavelength, there is then a temperature at which the phase matching condition is satisfied. For example, this is achieved for the conversion of light of wavelength 1064 nm, to 532 nm by using an LBO crystal at a temperature of about 140 ° C. In the quasi-phase matching, the ferroelectricity of the common materials such as in non-linear optics, lithium niobate is used. These domains are written in the material in which the periodic changes sign ( periodic poling ). A true phase matching does not take place, however, the individual domains in make their periodicity and wavelength so that overlap the part of the second harmonic waves generated constructive.
Applications
Using the frequency doubling and frequency tripling, a laser that irradiates a non-linear medium generate higher optical frequencies than the emitted laser itself. Since lasers are particularly easy to manufacture with wavelengths in the near infrared, it is often much easier to operate such a laser with frequency doubling or tripling, than to construct a laser in the visible region or near ultraviolet.
The radiation source used solid-state lasers are usually used, for example, Nd: YAG laser, the beam after frequency doubling green, including in green laser pointers. Frequency -doubled Nd: YAG laser also supply green laser beams with up to several watts of radiated power for laser shows as well as in laser projectors.
Frequency doubling is carried out with a nonlinear medium within the laser cavity ( intracavity SHG) or outside. Frequency doubling the resonator has the advantage that where the intensity of the beam, and thus the conversion efficiency is higher. A disadvantage is the hard to reach power and mode stability: Due to the non linear relationship between intensity and frequency conversion (the latter increases with increasing intensity steeply ) power oscillations occur and competing transverse to modes that are difficult to stabilize.
Frequency -doubled laser radiation enter the higher frequency in similarly high beam quality from as the fundamental wave. Because of the relationship between wavelength and minimal focus diameter, the short-wave radiation can be focused fine. Furthermore, it is better absorbed by many materials, so they are better suited for laser micromachining (eg, laser trimming, machining of silicon).
Doubling materials
Materials that are suitable for frequency doubling, subject to some selection conditions. In addition to the general requirement not to be symmetric under inversion, these are particularly relevant for the technical implementation. For high output power, it is advantageous to find a material with the highest possible coefficient. On the other hand, it must be chemically and thermally stable, must not be destroyed by the prevailing conditions in the arrangement so. Moreover, it should be noted that neither the original nor the frequency-doubled light is strongly absorbed. The choice of material is therefore also dependent on the used laser or its wavelength.
All these requirements are best met by specially manufactured for this purpose crystals. Examples include lithium niobate, potassium dihydrogen phosphate, beta - barium borate, and lithium triborate. But also thin films of diethylaminosulfur trifluoride, periodically poled polymers or liquid crystals can be used for frequency doubling.
Measurement of laser pulses
For the measurement of short laser pulses autocorrelators are used that exploit the effect of the frequency doubling.
Microscopy
In microscopy, frequency doubling can be used to make biological structures visible as collagen fibers or myosin in striated muscle. Both structures are similar crystal lattice, the non- centrosymmetric are in the order of the wavelength of the incident light. Benefits can be frequency doubling and frequency tripling with a multiphoton microscope.
Frequency doubling also occurs at surfaces and interfaces. This can be used to detect changes directly to a surface.