| Optical interference is not only the basic physical phenomenon to reveal the wave nature of light,but also the basis of many applications,such as optical coherence tomography,Fourier transform spectrometer,gravitational wave detection.In linear optics,the interference phenomenon is produced by the superposition of two or more beams of light,but the frequency of light remains unchanged;while in nonlinear optics,the superposition of two or more beams can produce new frequency light,such as sum-frequency process or third-harmonic generation.Some recent researches show that the combination of nonlinear effect and interference will produce new interference phenomena and greatly enrich the application of interferometer.For example,the sensitivity of nonlinear interferometers based on parametric amplification is greatly improved compared with traditional linear interferometers,and the nonlinear interferometers based on spontaneous parametric down-conversion(SPDC)can realize infrared imaging with undetected visible photons.Focusing on the combination of second-order nonlinear effect and interference phenomenon,we systematically study a variety of interference phenomena with light from the different second-order nonlinear processes,such as second-harmonic generation(SHG)and SPDC,to reveal the physical mechanism and find the possible new applications of these phenomena,such as frequency conversion of vector beam,phase difference amplification,calibration of zero arm difference position of an interferometer,etc.The main research contents and significance are as follows:1.The frequency conversion based on the second-order nonlinear optical effect can be used as a quantum interface that can connect two quantum communication modules with different working wavelengths.For example,the working wavelength of a rubidium atomic quantum memory is 795 nm while the working wavelength in fiber communication is 1550 nm.The frequency conversion technology enables photons to be transmitted between the two modules based on the sum-frequency generation(SFG)or difference-frequency generation(DFG)processes which require a 1632 nm laser as pump light.Therefore,a cavity that is used to enhance the DFG process is designed and built to obtain the 1632 nm laser beam.To design the cavity,the split-step Fourier method is used to simulate the energy conversion process and efficiency in the DFG process,and the optical waist radius in the cavity is designed based on the simulation results.The highest enhancement factor obtained in the experiment is 17.3,the highest net quantum conversion efficiency is 55%,the highest output power is 300 mW,and the one-hour power stability of the output light is 0.51%.The cavity-enhanced DFG device can be used as a pump light source for future quantum interface experiments.2.Vector beams have attracted much attention recently because of their unique super-diffraction limiting properties.The frequency conversion technology based on the second-order nonlinear effect can be used to expand the waveband of vector beams,for example,UV or mid-infrared where the manufacture of optical elements is not yet mature.Generally,the nonlinear effect only responds to lights with a certain linear polarization,which prevents frequency conversion of vector beams that have non-uniform polarization distribution.A scheme solving how to implement the frequency conversion of cylindrical vector beams based on a polarized Sagnac interferometer is proposed and experimentally verified.The SHG processes of the azimuthally and radially polarized vector beams with a wavelength of 1550 nm are realized,the cylindrical vector beams of 775 nm are generated,and the phenomenon of topological charge doubling is observed.This scheme can be generalized to realize the frequency up-conversion and down-conversion of vector beams based on SFG and DFG.3.The change of interference fringes can reflect the change of phase difference in an interferometer,therefore,an interferometer can be used to measure physical quantities that can cause the change of phase difference.If the phase difference of an interferometer can be amplified,the measurement resolution can be improved.In this paper,a phase difference amplification scheme based on interference of harmonic light is proposed.Experimentally,the phase difference in a Michelson interferometer is amplified by 2 times and 4 times based on the polarized interference of second-harmonic and fourth-harmonic light,respectively.As a result,an optical path difference(OPD)that causes the change of the fundamental interference curve for one cycle can now cause the change of the SH and FH interference curve for 2 and 4 cycles,therefore,the SH and FH interferometers improve the measurement resolution of the OPD by 2 and 4 times.The scheme proposed here can be generalized to the interference of higher harmonic light to realize higher phase difference amplification.4.The nondegenerate SPDC process can produce a pair of photons with frequency correlation characteristics and the two photons can be in the visible and infrared band respectively when a certain phase-matching condition is satisfied.In the nonlinear interferometer based on SPDC,the physical quantities in the infrared band,such as infrared refractive index,infrared spectrum,infrared image,etc.,can be measured by detecting visible photons,which avoids the shortcomings of infrared detector compared with the visible detector in noise performance,detection efficiency,cost performance and so on.In the present dissertation,a nonlinear Michelson interferometer based on the photons from the nondegenerate SPDC process of a PPKTP crystal is built.The center wavelengths of the associated photon pairs are 797 nm and 1540 nm.It is verified that in this interferometer,only the interference fringes formed by 797 nm photons be detected to realize the measurement of the refractive index at 1540 nm of a BBO crystal,and the included angle between the two surfaces of the BBO crystal can be measured by equal-thickness interference.Besides,the equal-inclination interference in the interferometer is also studied.By changing the length of a common path between the PPKTP crystal and the Michelson interferometer,different numbers of equal-inclination interference fringes can be observed.This phenomenon can be used for distance measurement.5.The equal-inclination interference is a basic interference phenomenon where the OPD is dependent on the incident angle of light and therefore the constructive or destructive interference depends on the incident angle.In a circular symmetric optical system,the equal-inclination interference fringes are a series of concentric rings.In this dissertation,one photon in the correlated photon pair generated by a nondegenerate SPDC process is used for single-photon interference in a Michelson interferometer and the interference fringes that are similar to the equal-inclination interference fringes are observed.The interference principle is as follows.In the nondegenerate SPDC process,the frequency of light depends on the incident angle of light,therefore,the constructive or destructive interference depends on the incident angle as well,and the interference fringes are also a series of concentric rings.In this dissertation,this kind of interference is called angular-frequency spectrum(AFS)interference because the dependence of frequency on angle comes from the special AFS.The analytical expression of angular frequency spectrum interference is deduced theoretically,and the equivalent wavelength is defined based on the formula of equal-inclination interference to quantitatively describe the fringe distribution of AFS interference.The experimental and theoretical results are consistent,and both reflect that the AFS interference has an ultra-short equivalent wavelength,based on which the AFS interference is expected to be used to improve the calibration accuracy of the equal arm position of the interferometer.6.The commonly used method to measure the AFS or tuning curve of an SPDC process is measuring the spectrums or center wavelengths corresponding to different spatial Fourier modes with a spectrometer,where the spatial Fourier modes are filtered by a movable pinhole.In this dissertation,a measurement method of the tuning curve in a nondegenerate SPDC process is proposed,which only needs to analyze the interference pattern without scanning using a pinhole.The method is to insert a grating before the detector in the setup of the above AFS interference,and the comet-tail-like interference fringes can be observed.The comet-tail-like fringes have a parabolic envelope.In this dissertation,the approximate expression of the tuning curve and its relationship with the parabolic envelope are both derived.Based on this relationship,the tuning curve can be deduced by measuring the parabola envelope of the fringe.The innovations of this dissertation are as follows:1.The scheme to realize the SHG process of vector beams based on a polarized Sagnac interferometer is proposed and experimentally verified.This scheme can be generalized to the SFG and DFG processes of vector beams and can be used to expand the waveband of vector beams.2.The scheme of phase difference amplification of nonlinear interferometer based on harmonic generation is proposed and experimentally verified.Based on this scheme,the phase resolution of interferometers is expected to greatly improve.3.The quasi-isoclinic interference phenomenon of special angular-frequency spectrum photons generated by the SPDC process is observed and explained theoretically.The property of ultrashort equivalent wavelength of the interference fringes is expected to be used to improve the calibration accuracy of the zero arm difference position of interferometers.4.We experimentally observed and explained the comet-tail-like interference fringes in angular frequency spectrum interference.Based on these fringes,a scheme to estimate the tuning curves of SPDC by measuring the parabolic envelope of fringes is proposed,which is verified experimentally. |
