The influence of degenerate four-wave mixing （FWM） on the performance of supercontinuum-based multiwavelength optical source has been investigated in detail experimentally and theoretically. Numerical simulation res...The influence of degenerate four-wave mixing （FWM） on the performance of supercontinuum-based multiwavelength optical source has been investigated in detail experimentally and theoretically. Numerical simulation results show that the degenerate FWM effect has a deteriorative influence on the spectral uniformity and the optical signal-to-noise ratio （OSNR） of supercontinuum-based optical source, and by suppressing degenerate FWM effect the performance enhancement of the supercontinuum can be achieved successfully. These results are also confirmed by our experiments. Experimentally, by suppressing degenerate FWM the crosstalk of adjacent channels to the filtered channel can be reduced by as much as 15 dB, and consequently the measured receiver sensitivity at 10 Gbit/s for the filtered optical source is improved from -1.7 to -17.8 dBm.展开更多
This paper presents the nearly degenerate four wave mixing properties of glass doped with semiconductor CdS x Se 1-x ,nonlinear response time of the material obtained by the laser induced transient gratin...This paper presents the nearly degenerate four wave mixing properties of glass doped with semiconductor CdS x Se 1-x ,nonlinear response time of the material obtained by the laser induced transient grating technique,and properties of photoluminescence of the glass and the blue shift in the luminescence spectra with an increasing intensity of input beam as well. The nonlinearity of the material is believed to be due to the band filling in semiconductor microcrystallites.展开更多
The first observation of collisional narrowing by time-resolved degenerate four-wave mixing has been reported. The velocity-changing collision cross section of Na in Ar De obtained is 5.6 × 10^(-15)cm^(2).
It is found that the field of the combined mode of the probe wave and the phase conjugate wave in the process of non-degenerate four-wave mixing exhibits higher-order squeezing to all even orders. The higher-order squ...It is found that the field of the combined mode of the probe wave and the phase conjugate wave in the process of non-degenerate four-wave mixing exhibits higher-order squeezing to all even orders. The higher-order squeezed parameter and squeezed limit due to the modulation frequency are investigated. The smaller the modulation frequency is, the stronger the degree of higher-order squeezing becomes. Furthermore, the hlgher-order uncertainty relations in the process of non-degenerate four-wave mixing are presented for the first time. The product of higher-order noise moments is related to even order number N and the length L of the medium.展开更多
This paper considers the Riemann-Hilbert problem for linear mixed（elliptichyperbolic） complex equations of first order with degenerate curve in a simply connected domain. We first give the representation theorem and...This paper considers the Riemann-Hilbert problem for linear mixed（elliptichyperbolic） complex equations of first order with degenerate curve in a simply connected domain. We first give the representation theorem and uniqueness of solutions for such boundary value problem. Then by using the methods of successive iteration and parameter extension, the existence of solutions for this problem is proved.展开更多
The present paper deals with the mixed boundary value problem for elliptic equations with degenerate rank 0. We first give the formulation of the problem and estimates of solutions of the problem, and then prove the e...The present paper deals with the mixed boundary value problem for elliptic equations with degenerate rank 0. We first give the formulation of the problem and estimates of solutions of the problem, and then prove the existence of solutions of the above problem for elliptic equations by the above estimates and the method of parameter extension. We use the complex method, namely first discuss the corresponding problem for degenerate elliptic complex equations of first order, afterwards discuss the above problem for degenerate elliptic equations of second order展开更多
This paper deals with a class of doubly degenerate parabolic equations, including as particular cases the porous medium equation and the degenerate pLaplace equation （p 〉 2）ut-div（b（x,t,u）｜↓△u｜^p-2↓△u）=f...This paper deals with a class of doubly degenerate parabolic equations, including as particular cases the porous medium equation and the degenerate pLaplace equation （p 〉 2）ut-div（b（x,t,u）｜↓△u｜^p-2↓△u）=f（x,u,t）The initial-boundary value problem in a bounded domain of R^N is considered under mixed boundary conditions. The existence of local-in-time weak solutions is obtained.展开更多
Carrier recovery time is a key parameter that determines the performance of a semiconductor optical amplifier （SOA）. A measurement method of carrier recovery time in SOA based on a nearly degenerate four-wave mixing...Carrier recovery time is a key parameter that determines the performance of a semiconductor optical amplifier （SOA）. A measurement method of carrier recovery time in SOA based on a nearly degenerate four-wave mixing of narrowband amplified spontaneous emission （ASE） spectra is presented. The results show the carrier times are 50.2, 44.6, and 23.6 ps when the injected currents are 120, 180, and 240 mA, respectively, which are in agreement with the nominal values of the sample.展开更多
A new method using degenerate four-wave mixing for one-way imaging through phase distorting medium is presented.The theoretical analysis and experimental results are given.
All-optical regenerators can be used to suppress amplified spontaneous emission(ASE) noise introduced by cascaded erbium doped fiber amplifiers(EDFAs) in optical fiber communication systems and lead to the improvement...All-optical regenerators can be used to suppress amplified spontaneous emission(ASE) noise introduced by cascaded erbium doped fiber amplifiers(EDFAs) in optical fiber communication systems and lead to the improvement of optical receiver sensitivity. By introducing the Q-factor transfer function(QTF), we evaluate the Q-factor performance of degenerate four-wave mixing(DFWM) regenerators with clock pump and reveal the differences between the optimal input powers determined from the static and dynamic power tranfer function(PTF) and the QTF curves. Our simulation shows that the clock-pump regnerator is capable of improving the Q-facor and receiver sensitivity for 40 Gbit/s ASE-degraded return-to-zero on-off keying(RZ-OOK) signal by 2.58 dB and 4.2 d B, respectively.展开更多
We report on a new method to achieve the single-scan polarization-resolved degenerate four-wave mixing(DFWM)spectroscopy in a Rb atomic medium using a vector optical field,in which two pump beams are kept linearly pol...We report on a new method to achieve the single-scan polarization-resolved degenerate four-wave mixing(DFWM)spectroscopy in a Rb atomic medium using a vector optical field,in which two pump beams are kept linearly polarized and a vector beam is employed as the probe beam.As the polarization and intensity of the DFWM signal are closely dependent on the polarization state of the probe beam,a vector probe beam with space-variant states of polarization is able to generate a DFWM signal with space-variant states of polarization and intensity across the DFWM image.Accordingly,the polarization-resolved spectra can be retrieved from a single DFWM image.To the best of our knowledge,this is the first time that the single-scan polarizationresolved spectrum detection has been realized experimentally with a vector beam.This work provides a simple but efficient single-scan polarization-resolved spectroscopic method,which would be of great utility for the samples of poor light stability and fast optical processes.展开更多
Ⅰ. INTRODUCTION By using degenerate four-wave mixing (DFWM) method, the third-order nonlinear optical susceptibility of transparent media can be conventionally measured. Nonlinear properties of media in ground state ...Ⅰ. INTRODUCTION By using degenerate four-wave mixing (DFWM) method, the third-order nonlinear optical susceptibility of transparent media can be conventionally measured. Nonlinear properties of media in ground state are well known, but those in exciting state are less studied. When a medium absorbs incident radiation, a part of population can be excited into high exciting state. In DFWM this resonant enhancement effect can be used to increase the third-展开更多
Ⅰ. INTRODUCTIONIn ordinary degenerate four-wave mixing experiments, parametric amplification is generated, i.e., when an object wave with a certain intensity is incident on a nonlinear medium, backward reflective wav...Ⅰ. INTRODUCTIONIn ordinary degenerate four-wave mixing experiments, parametric amplification is generated, i.e., when an object wave with a certain intensity is incident on a nonlinear medium, backward reflective wave of the very object wave would be展开更多
We report on the enhancement of phase conjugation degenerate four-wave mixing(DFWM) in hot atomic Rb vapor by using a Bessel beam as the probe beam. The Bessel beam was generated using cross-phase modulation based on ...We report on the enhancement of phase conjugation degenerate four-wave mixing(DFWM) in hot atomic Rb vapor by using a Bessel beam as the probe beam. The Bessel beam was generated using cross-phase modulation based on the thermal nonlinear optical effect. Our results demonstrated that the DFWM signal generated by the Bessel beam is about twice as large as that generated by the Gaussian beam, which can be attributed to the extended depth and tight focusing features of the Bessel beam. We also found that a DFWM signal with reasonable intensity can be detected even when the Bessel beam encounters an obstruction on its way, thanks to the selfhealing property of the Bessel beam. This work not only indicates that DFWM using a Bessel beam would be of great potential in the fields of high-fidelity communication, adaptive optics, and so on, but also suggests that a Bessel beam would be of significance to enhance the nonlinear process, especially in thick and scattering media.展开更多
This article deals with the Riemann-Hilbert boundary value problem for quasilinear mixed （elliptic- hyperbolic） complex equations of first order with degenerate rank 0. Firstly, we give the representation theorem an...This article deals with the Riemann-Hilbert boundary value problem for quasilinear mixed （elliptic- hyperbolic） complex equations of first order with degenerate rank 0. Firstly, we give the representation theorem and prove the uniqueness of solutions for the boundary value problem. Afterwards, by using the method of successive iteration, the existence and estimates of solutions for the boundary value problem are verified. The above problem possesses the important applications to the Tricomi problem of mixed type equations of second order. In this article, the proof of HSlder continuity of a singular double integer is very difficult and interesting as in this Section 4 below.展开更多
The present paper deals with oblique derivative problems for second order nonlinear equa- tions of mixed type with degenerate hyperbolic curve, which include the Tricomi problem as a special case. Firstly the formulat...The present paper deals with oblique derivative problems for second order nonlinear equa- tions of mixed type with degenerate hyperbolic curve, which include the Tricomi problem as a special case. Firstly the formulation of the problems for the equations is given, next the representation and estimates of solutions for the above problems are obtained, finally the existence of solutions for the problems is proved by the successive iteration of solutions of the equations and the fixed-point princi- ple. In this paper, we use the complex analytic method, namely the new partial derivative notations, elliptic complex functions in the elliptic domain and hyperbolic complex functions in the hyperbolic domain are introduced, such that the second order equations of mixed type with degenerate curve are reduced to the first order mixed complex equations with singular coefficients, and then the advantage of complex analytic method can be applied.展开更多
基金Project supported by the National Natural Science Foundation of China （Grant No 60577033）, the Specialized Research Fund for the Doctoral Program of Higher Education （Grant No 20050003010） and the Basic Research Foundation of Tsinghua National Laboratory for Information Science and Technology.
文摘The influence of degenerate four-wave mixing （FWM） on the performance of supercontinuum-based multiwavelength optical source has been investigated in detail experimentally and theoretically. Numerical simulation results show that the degenerate FWM effect has a deteriorative influence on the spectral uniformity and the optical signal-to-noise ratio （OSNR） of supercontinuum-based optical source, and by suppressing degenerate FWM effect the performance enhancement of the supercontinuum can be achieved successfully. These results are also confirmed by our experiments. Experimentally, by suppressing degenerate FWM the crosstalk of adjacent channels to the filtered channel can be reduced by as much as 15 dB, and consequently the measured receiver sensitivity at 10 Gbit/s for the filtered optical source is improved from -1.7 to -17.8 dBm.
文摘This paper presents the nearly degenerate four wave mixing properties of glass doped with semiconductor CdS x Se 1-x ,nonlinear response time of the material obtained by the laser induced transient grating technique,and properties of photoluminescence of the glass and the blue shift in the luminescence spectra with an increasing intensity of input beam as well. The nonlinearity of the material is believed to be due to the band filling in semiconductor microcrystallites.
文摘The first observation of collisional narrowing by time-resolved degenerate four-wave mixing has been reported. The velocity-changing collision cross section of Na in Ar De obtained is 5.6 × 10^(-15)cm^(2).
文摘It is found that the field of the combined mode of the probe wave and the phase conjugate wave in the process of non-degenerate four-wave mixing exhibits higher-order squeezing to all even orders. The higher-order squeezed parameter and squeezed limit due to the modulation frequency are investigated. The smaller the modulation frequency is, the stronger the degree of higher-order squeezing becomes. Furthermore, the hlgher-order uncertainty relations in the process of non-degenerate four-wave mixing are presented for the first time. The product of higher-order noise moments is related to even order number N and the length L of the medium.
基金Supported by the National Natural Science Foundation of China (10971224)
文摘This paper considers the Riemann-Hilbert problem for linear mixed（elliptichyperbolic） complex equations of first order with degenerate curve in a simply connected domain. We first give the representation theorem and uniqueness of solutions for such boundary value problem. Then by using the methods of successive iteration and parameter extension, the existence of solutions for this problem is proved.
文摘The present paper deals with the mixed boundary value problem for elliptic equations with degenerate rank 0. We first give the formulation of the problem and estimates of solutions of the problem, and then prove the existence of solutions of the above problem for elliptic equations by the above estimates and the method of parameter extension. We use the complex method, namely first discuss the corresponding problem for degenerate elliptic complex equations of first order, afterwards discuss the above problem for degenerate elliptic equations of second order
基金The NSFC(10371050)and the"985"program of Jilin University.
文摘This paper deals with a class of doubly degenerate parabolic equations, including as particular cases the porous medium equation and the degenerate pLaplace equation （p 〉 2）ut-div（b（x,t,u）｜↓△u｜^p-2↓△u）=f（x,u,t）The initial-boundary value problem in a bounded domain of R^N is considered under mixed boundary conditions. The existence of local-in-time weak solutions is obtained.
基金Project supported by National High Technology Research and Development Program of China (Grant No. 2006AA03Z414)the National Natural Science Foundation of China (Grant No. 60877056)the Science Fund for Distinguished Young Scholars of Hubei Province of China (Grant No. 2006ABB017)
文摘Carrier recovery time is a key parameter that determines the performance of a semiconductor optical amplifier （SOA）. A measurement method of carrier recovery time in SOA based on a nearly degenerate four-wave mixing of narrowband amplified spontaneous emission （ASE） spectra is presented. The results show the carrier times are 50.2, 44.6, and 23.6 ps when the injected currents are 120, 180, and 240 mA, respectively, which are in agreement with the nominal values of the sample.
文摘A new method using degenerate four-wave mixing for one-way imaging through phase distorting medium is presented.The theoretical analysis and experimental results are given.
基金supported by the National Natural Science Foundation of China(No.61671108)the Fundamental Research Funds for the Central Universities(No.ZYGX2014J005)the Program for Changjiang Scholars and Innovative Research Team in University
文摘All-optical regenerators can be used to suppress amplified spontaneous emission(ASE) noise introduced by cascaded erbium doped fiber amplifiers(EDFAs) in optical fiber communication systems and lead to the improvement of optical receiver sensitivity. By introducing the Q-factor transfer function(QTF), we evaluate the Q-factor performance of degenerate four-wave mixing(DFWM) regenerators with clock pump and reveal the differences between the optimal input powers determined from the static and dynamic power tranfer function(PTF) and the QTF curves. Our simulation shows that the clock-pump regnerator is capable of improving the Q-facor and receiver sensitivity for 40 Gbit/s ASE-degraded return-to-zero on-off keying(RZ-OOK) signal by 2.58 dB and 4.2 d B, respectively.
基金Innovation Capability Support Plan of Shaanxi Province(2018TD-018)Shaanxi Provincial Key Research and Development Project(2018ZDCXL-GY-08-05)+2 种基金State Key Laboratory of Transient Optics and Photonics(SKLST201906)Natural Science Foundation of Shaanxi Province(2020JM-432)National Natural Science Foundation of China(11874299,61805200)。
文摘We report on a new method to achieve the single-scan polarization-resolved degenerate four-wave mixing(DFWM)spectroscopy in a Rb atomic medium using a vector optical field,in which two pump beams are kept linearly polarized and a vector beam is employed as the probe beam.As the polarization and intensity of the DFWM signal are closely dependent on the polarization state of the probe beam,a vector probe beam with space-variant states of polarization is able to generate a DFWM signal with space-variant states of polarization and intensity across the DFWM image.Accordingly,the polarization-resolved spectra can be retrieved from a single DFWM image.To the best of our knowledge,this is the first time that the single-scan polarizationresolved spectrum detection has been realized experimentally with a vector beam.This work provides a simple but efficient single-scan polarization-resolved spectroscopic method,which would be of great utility for the samples of poor light stability and fast optical processes.
文摘Ⅰ. INTRODUCTION By using degenerate four-wave mixing (DFWM) method, the third-order nonlinear optical susceptibility of transparent media can be conventionally measured. Nonlinear properties of media in ground state are well known, but those in exciting state are less studied. When a medium absorbs incident radiation, a part of population can be excited into high exciting state. In DFWM this resonant enhancement effect can be used to increase the third-
文摘Ⅰ. INTRODUCTIONIn ordinary degenerate four-wave mixing experiments, parametric amplification is generated, i.e., when an object wave with a certain intensity is incident on a nonlinear medium, backward reflective wave of the very object wave would be
基金National Natural Science Foundation of China(NSFC)(61475125)Natural Science Foundation of Shaanxi Province(2017JQ6066)+1 种基金Education Department of Shaanxi Province(16JK1776)Northwest University Doctorate Dissertation of Excellence Funds(YYB17006)
文摘We report on the enhancement of phase conjugation degenerate four-wave mixing(DFWM) in hot atomic Rb vapor by using a Bessel beam as the probe beam. The Bessel beam was generated using cross-phase modulation based on the thermal nonlinear optical effect. Our results demonstrated that the DFWM signal generated by the Bessel beam is about twice as large as that generated by the Gaussian beam, which can be attributed to the extended depth and tight focusing features of the Bessel beam. We also found that a DFWM signal with reasonable intensity can be detected even when the Bessel beam encounters an obstruction on its way, thanks to the selfhealing property of the Bessel beam. This work not only indicates that DFWM using a Bessel beam would be of great potential in the fields of high-fidelity communication, adaptive optics, and so on, but also suggests that a Bessel beam would be of significance to enhance the nonlinear process, especially in thick and scattering media.
基金Supported in part by the National Natural Science Foundation of China under Grant No.11021161 and 10928102973 Program of China under Grant No.2011CB80800+2 种基金Chinese Academy of Sciences under Grant No.kjcx-yw-s7project grant of "Center for Research and Applications in Plasma Physics and Pulsed Power Technology,PBCT-Chile-ACT 26"Direcci'on de Programas de Investigaci'on,Universidad de Talca,Chile
文摘This article deals with the Riemann-Hilbert boundary value problem for quasilinear mixed （elliptic- hyperbolic） complex equations of first order with degenerate rank 0. Firstly, we give the representation theorem and prove the uniqueness of solutions for the boundary value problem. Afterwards, by using the method of successive iteration, the existence and estimates of solutions for the boundary value problem are verified. The above problem possesses the important applications to the Tricomi problem of mixed type equations of second order. In this article, the proof of HSlder continuity of a singular double integer is very difficult and interesting as in this Section 4 below.
基金Supported by National Natural Science Foundation of China （Grant No. 10971224）
文摘The present paper deals with oblique derivative problems for second order nonlinear equa- tions of mixed type with degenerate hyperbolic curve, which include the Tricomi problem as a special case. Firstly the formulation of the problems for the equations is given, next the representation and estimates of solutions for the above problems are obtained, finally the existence of solutions for the problems is proved by the successive iteration of solutions of the equations and the fixed-point princi- ple. In this paper, we use the complex analytic method, namely the new partial derivative notations, elliptic complex functions in the elliptic domain and hyperbolic complex functions in the hyperbolic domain are introduced, such that the second order equations of mixed type with degenerate curve are reduced to the first order mixed complex equations with singular coefficients, and then the advantage of complex analytic method can be applied.
