Spotlight Summary by Patricia Segonds
Enhanced Kerr electro-optic nonlinearity and its application in controlling second-harmonic generation
In non-centrosymmetric crystals, third order nonlinear processes are hidden by second order ones. However, third order nonlinearities can be enhanced through the use of cascading, which opens the door to their manipulation.
Second-harmonic generation (SHG) is one of the most widely used second-order conversion processes, for characterization of new nonlinear materials as well as for applications. The main reason for this interest is that the ultraviolet and visible spectral ranges of light can be fully used thanks to SHG, since the generated wavelength is half the one (usually called “fundamental wavelength”) sent into the nonlinear medium. However, the amount of energy generated by SHG is directly controlled by the phase between the nonlinear polarisation of the material and the second harmonic field itself; The required phase relationship, called the phase-matching (PM) condition,,is especially important for applications. PM in bulk nonlinear crystals depends on dispersive parameters of the main refractive indices as functions of the temperature and wavelength. When PM is not possible, quasi phase-matching (QPM), namely the design of a structure in nonlinear crystals where the sign of the nonlinear susceptibility is inverted periodically, has been a very successful alternative.
The authors of this Photonics Research article designed a new kind of structure in a periodically poled LiNbO_{3} (ppLN – the artificial structure with which QPM is realized) nonlinear crystal, to allow simultaneously a cascaded Pockels third-order effect and SHG. With such a scheme, a Kerr electro-optic (EO) nonlinearity was induced, enabling control of SHG by means of an applied external electric field. Such control could be used per se as an application. The authors were also able to measure the magnitude of the enhanced Kerr EO effect in ppLN.
The authors describe the change of the nonlinear phase at the crystal’s exit surface when a e polarised light wave propagates along the x-axis. They considered the application of an external electric field along the y-axis of a ppLN nonlinear crystal with the sign of the nonlinear susceptibility inverted periodically along the z-axis. The consequence is an induced EO nonlinear refractive index that is more than three orders of magnitude higher than the linear and intrinsic Kerr EO effects, so that it effectively determines the total phase shift. In the situation of weak cascaded effects and negligible depletion of the fundamental wave, the induced EO nonlinear refractive index is directly proportional to the third power of the external electric field applied along the y-axis. Then, considering the cascaded Pockels effect and QPM SHG simultaneously, the authors show that the PM condition can be controlled directly by means of the external electric field. The enhanced EO coefficient is more than three orders of magnitude higher than the linear and quadratic EO coefficients, according to the authors.
This prediction is validated experimentally using cascaded EO effect and SHG QPM occurring simultaneously at the fundamental wavelength 1582.1 nm in a ppLN crystal with the domains period of 20.3 microns. The SHG intensity measured as a function of the fundamental wavelength, for increasing values of the external electric field, were recorded at three different temperatures. The experimental results are in complete agreement with the theoretical predictions. The authors show that at 26.3 °C, increasing the value of the external electric field suppresses the efficiency of SHG. When the temperature is lower (24.1°C), the spectrum is mostly shifted to the right with respect to 1582.1 nm, and to left when the temperature is higher (27.6°C). Furthermore, the authors verify from measured phase shifts that the induced EO nonlinear refractive index was directly proportional to the third power of the external electric field.
From these results, an effective control of SHG by an external electric field has been demonstrated. The authors also suggest the possibility of adjusting the fundamental wavelength and temperature, given another ppLN with a different domains period. Finally, they propose the manipulation of other second order conversion processes; currently a very interesting process is that of difference frequency generation (DFG) QPM to generate wavelengths in the mid infrared. This very interesting paper strongly encourages a new use of PPLN nonlinear crystals as electrical controllers of light’s nonlinear phase, independently of the intensity of the light sent into a nonlinear cystal.
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Second-harmonic generation (SHG) is one of the most widely used second-order conversion processes, for characterization of new nonlinear materials as well as for applications. The main reason for this interest is that the ultraviolet and visible spectral ranges of light can be fully used thanks to SHG, since the generated wavelength is half the one (usually called “fundamental wavelength”) sent into the nonlinear medium. However, the amount of energy generated by SHG is directly controlled by the phase between the nonlinear polarisation of the material and the second harmonic field itself; The required phase relationship, called the phase-matching (PM) condition,,is especially important for applications. PM in bulk nonlinear crystals depends on dispersive parameters of the main refractive indices as functions of the temperature and wavelength. When PM is not possible, quasi phase-matching (QPM), namely the design of a structure in nonlinear crystals where the sign of the nonlinear susceptibility is inverted periodically, has been a very successful alternative.
The authors of this Photonics Research article designed a new kind of structure in a periodically poled LiNbO_{3} (ppLN – the artificial structure with which QPM is realized) nonlinear crystal, to allow simultaneously a cascaded Pockels third-order effect and SHG. With such a scheme, a Kerr electro-optic (EO) nonlinearity was induced, enabling control of SHG by means of an applied external electric field. Such control could be used per se as an application. The authors were also able to measure the magnitude of the enhanced Kerr EO effect in ppLN.
The authors describe the change of the nonlinear phase at the crystal’s exit surface when a e polarised light wave propagates along the x-axis. They considered the application of an external electric field along the y-axis of a ppLN nonlinear crystal with the sign of the nonlinear susceptibility inverted periodically along the z-axis. The consequence is an induced EO nonlinear refractive index that is more than three orders of magnitude higher than the linear and intrinsic Kerr EO effects, so that it effectively determines the total phase shift. In the situation of weak cascaded effects and negligible depletion of the fundamental wave, the induced EO nonlinear refractive index is directly proportional to the third power of the external electric field applied along the y-axis. Then, considering the cascaded Pockels effect and QPM SHG simultaneously, the authors show that the PM condition can be controlled directly by means of the external electric field. The enhanced EO coefficient is more than three orders of magnitude higher than the linear and quadratic EO coefficients, according to the authors.
This prediction is validated experimentally using cascaded EO effect and SHG QPM occurring simultaneously at the fundamental wavelength 1582.1 nm in a ppLN crystal with the domains period of 20.3 microns. The SHG intensity measured as a function of the fundamental wavelength, for increasing values of the external electric field, were recorded at three different temperatures. The experimental results are in complete agreement with the theoretical predictions. The authors show that at 26.3 °C, increasing the value of the external electric field suppresses the efficiency of SHG. When the temperature is lower (24.1°C), the spectrum is mostly shifted to the right with respect to 1582.1 nm, and to left when the temperature is higher (27.6°C). Furthermore, the authors verify from measured phase shifts that the induced EO nonlinear refractive index was directly proportional to the third power of the external electric field.
From these results, an effective control of SHG by an external electric field has been demonstrated. The authors also suggest the possibility of adjusting the fundamental wavelength and temperature, given another ppLN with a different domains period. Finally, they propose the manipulation of other second order conversion processes; currently a very interesting process is that of difference frequency generation (DFG) QPM to generate wavelengths in the mid infrared. This very interesting paper strongly encourages a new use of PPLN nonlinear crystals as electrical controllers of light’s nonlinear phase, independently of the intensity of the light sent into a nonlinear cystal.
Article Reference
Enhanced Kerr electro-optic nonlinearity and its application in controlling second-harmonic generation
- Photon. Res. 3(4) 168-172 (2015)
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