光折变空间暗孤子分裂的理论和实验研究
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摘要
光折变空间孤子是晶体的光折变非线性严格平衡衍射效应的结果。自从光折变空间孤子的预言和实验观察以来，由于其在低功率和所有横向维的存在以及它们在光束控制、光互连和非线性光学器件等方面的潜在应用已经引起了更多的兴趣。
本论文主要是从理论上利用相干密度法研究了非相干屏蔽灰孤子和非相干屏蔽光伏孤子分裂，利用光束传播法研究与时间有关的开环相干光伏孤子分裂，并从实验上研究非相干光伏孤子分裂，具体结论如下：
1.非相干光伏孤子实验研究
无背景光辐照时，利用振幅掩模穿过一束空间非相干光的方法产生暗迹，将暗迹成像在晶体前表面上，在LiNbO3:Fe晶体内形成偶数序列的非相干暗光伏孤子。实验结果表明，无背景光辐照时可以在非瞬时响应的光折变光伏晶体内形成非相干暗光伏孤子序列，形成的孤子分裂数目与入射宽度和光束相干长度有关。
在给定光束的空间相干长度时，形成孤子数目与入射暗纹的宽度有关，当入射的暗纹宽度较小时，只能形成一个Y结孤子对；随着入射宽度的增加，可以形成偶数序列暗光伏孤子，在晶体前表面入射的暗纹宽度越宽，形成孤子数目越多，这与相干孤子FWHM的变化规律一致。形成多孤子时，位于中心的孤子对灰度最小，其他孤子对与中心距离越远，灰度越大；孤子数目越多，孤子间隔越小，每个孤子的宽度都比N=2时孤子宽度稍微小一点。另外，光束的相干长度对孤子分裂有影响，入射光束的空间相干性越好，相干长度越大，形成孤子所需入射宽度越小。
2.非相干灰屏蔽孤子
利用相干密度法研究非相干屏蔽灰孤子在偏压光折变非线性介质中的传输特性和空间相干性。数值模拟结果表明，可以在偏压SBN晶体内形成非相干屏蔽灰孤子。
当偏压较小时，只能形成非相干的Y结屏蔽灰孤子，对应最低阶的孤子，当外偏压增加时，非相干光束趋于分裂为偶数序列的非相干屏蔽灰孤子；如果给定入射光束灰度，增加外偏压和入射光束宽度也可以产生偶数序列非相干屏蔽灰孤子；或者给定入射光束宽度，通过增加外偏压并减小光束灰度仍可以产生那样的偶数序列非相干灰屏蔽孤子。
非相干屏蔽灰孤子的相干长度在孤子区域变大，孤子最小强度越小，相干长度越大，而远离孤子区域趋于恒定不变。
3.相干暗光伏孤子
利用光束传播法研究在非线性光折变光伏介质中形成的开环暗光伏孤子分裂。数值模拟结果表明，根据初始条件不同，在均匀光束中心形成的暗纹能在光折变光伏非线性材料中分裂为奇数或偶数序列的暗光伏孤子。
对于一个给定的物理系统，多模暗光伏孤子的形成与初始条件和入射光束强度半高宽有关。一方面，奇初始位相光束总是趋于分裂为奇数序列暗光伏孤子，偶初始位相光束趋于分裂为偶数序列暗光伏孤子；另一方面，当入射宽度较小时，只能形成一个基本孤子或Y结孤子对，随着入射宽度的增加，入射暗光束可以分裂为多暗光伏孤子，入射暗纹宽度越大，形成的孤子数目越多，当有更多孤子产生时，相邻孤子间隔变小，远离中心的孤子可见度下降。
4.非相干屏蔽光伏孤子
利用相干密度法研究非相干屏蔽光伏暗孤子和灰孤子在有偏压的光折变光伏晶体内的传输特性及空间相干性，数值模拟结果表明可以在偏压光折变晶体内形成非相干屏蔽光伏暗孤子和灰孤子。
非相干屏蔽光伏暗孤子的形成依赖初始入射条件和入射暗纹宽度。在奇或偶初始条件下，通过增加入射暗纹宽度可以在晶体内形成奇、偶数序列的非相干屏蔽光伏孤子，入射暗纹宽度越大，形成孤子数目越多；当形成多孤子分裂时，相邻孤子之间的间隔越小，远离中心的孤子对可见度下降。对于给定物理系统和确定的孤子分裂数，入射暗纹宽度越大，相邻孤子间隔越小。
非相干屏蔽光伏灰孤子的形成依赖非相干光束灰度和入射暗纹宽度。在偶初始条件下，如果入射的非相干光束的灰度或者入射光束的强度半高宽较小时，只能形成一个Y分裂，而如果非相干光束的强度半高宽或光束灰度增大时可以在晶体内形成偶数序列的非相干灰屏蔽光伏孤子。
通过对非相干灰屏蔽光伏孤子的相干长度研究发现，非相干孤子的相干长度在孤子区域及附近变化剧烈，特别是中心孤子对，在暗槽内部相干长度增加，而在中心处相干长度急速下降，而相干长度在远离中心的孤子区域是增加的，孤子的强度越小，相干长度越大。
此外，通过研究在有偏压光折变光伏晶体中的非相干屏蔽光伏孤子特性，发现当晶体内的光伏效应可以忽略时，非相干屏蔽光伏孤子的物理系统就转变为非相干屏蔽孤子的物理系统，非相干屏蔽光伏孤子变为非相干屏蔽孤子；而如果去掉外偏压，此时非相干屏蔽光伏孤子的物理系统变为非相干光伏孤子分裂的物理系统，非相干屏蔽光伏孤子变为非相干光伏孤子。
Photorefractive (PR) spatial solitons is the result of PR effect balanced thediffraction. Since the prediction and the observation of PR spatial solitons, it hasattracted more attention in the formation and characters of PR spatial solitons owingto the potential application in beam steering and manipulating light by light, all-optical switching, optical interconnects and optical nonlinear devices et al.
In this paper, I theoretically studied the multiple incoherent gray screeningsolitons splitting and incoherent screening-photovoltaic dark (gray) solitons splittingby using of coherent density method. I investigate the time-dependent coherentphotovoltaic spatial solitons splitting under open-circuit conditions using beampropagation method. In addition, I experimentally study the incoherent photovoltaicsolitons splitting in LiNbO3:Fe crystal without background light. The detailedconclusions as follow:
1. Experimental study on incoherently photovoltaic solitons
A dark stripe is generated when the partially spatially incoherent beam passesthrough amplitude mark without background illumination. The dark stripe is imagedinto the front face of the crystal. The even-number sequence of incoherent darkphotovoltaic solitons is generated. The experimental results indicate that theincoherent photovoltaic soliton sequence can be generated in non-instantaneousnonlinearity photorefractive photovoltaic crystal and that the number of solitons isdependent on the initial input width of the dark stripe and the coherence length of thebeam.
For a fixed beam’s spatial coherence, the number of solitons is dependent to theinitial input width of the dark stripe. Only a Y-junction solitons pair can be observedwhen the input width is small. With the increasing of the initial input width, theeven-number sequence of dark photovoltaic solitons is generated. The more solitonsare formed for wider initial input dark stripe, which is similar to coherent solitonsplitting. When more solitons are generated, the separations between adjacent dark solitons become smaller and the grayness of solitons is grayer as their transversedistance from the center increases. In addition, the coherence length of the incoherentbeam affects the number of solitons splitting. The bigger the coherence length of thebeam, the smaller the input width of the dark stripe needed.
2. Incoherent screening grey solitons
We study the propagation properties and spatial coherence of multiple incoherentscreening grey soliotns in biased photorefractive media by using the coherent densitymethod. The numerically studies results demonstrate that even-number sequence ofmultiple incoherent gray screening solitons is possible.
We find that when the external voltage is small, only an incoherent Y-junctionscreening soliton is generated, corresponding to the lowest order in the even-numberincoherent screening soliton sequence. When the external voltage is increased, theincoherent gray beam splits into an even-number sequence of multiple gray screeningsoliton. For a fixed beam’s grayness, increasing the external voltage and the full widthhalf maximum of the beam’s intensity can produce such an even-number sequence ofmultiple incoherent gray screening solitons. Moreover, for a fixed full width at halfmaximum of the initial input beam’s intensity, increasing the external voltage anddecreasing the beam’s grayness still produces such an even-number sequence ofmultiple incoherent gray screening solitons.
In addition, we find that the coherence length of multiple incoherent grayscreening solitons becomes higher around the soliton regions and that the smaller theminimum intensity of multiple incoherent gray screening solitons, the bigger itscorrelation length. We also find that the correlation length is changeless far away fromthe solitons.
3. Incoherent dark photovoltaic solitons
We study the formation of the multiple dark photovoltaic solitons splitting inphotorefractive photovoltaic nonlinear media under open-circuit condition by using ofbeam propagation method. The simulated results indicate that a single dark stripe onan otherwise uniform optical beam can be split into odd (or even) number sequence ofdark photovoltaic solitons in the photovoltaic photorefractive nonlinear media according to different initial conditions.
We find that for a given physical system, the formation of multiple darkphotovoltaic solitons is depended on the initial input conditions as well as on the fullwidth at half maximum (FWHM) of the input beam’s intensity. On one hand, anodd-phase input beam always tends to split into the odd-number sequence of multipledark photovoltaic solitons, whereas the even-phase input beam tends to split into theeven-number sequence of multiple dark photovoltaic solitons. On the other hand,when the initial input width of the dark stripe is small, it only can form a foundationalsolitons or a Y-junction solution pair. With the increasing of the input width of thedark stripe, it can split into multiple dark photovoltaic solitions. The wider the inputwidth of the dark stripe, the more the number of solitons is generated. When moresolitons are generated, the separations between adjacent solitons become smaller andthe visibility of the solitons far away from the center decrease.
4. Incoherent screening-photovoltaic solitons
We study the propagation properties and the spatial coherences of the incoherentdark and gray screening-photovoltaic spatial solitons in biased photorefractive-photovoltaic crystals by using the coherent density method. The results of numericalsimulation demonstrate that the incoherent screening-photovoltaic dark (or gray)solitons can be generated in biased photorefractive photovoltaic crystal.
For the incoherent screening-photovoltaic spatial dark solitons, formation of it isdependent on the initial input conditions as well as the initial input width of the darkstripe. Under the odd or even initial conditions, the odd or even number sequence ofincoherent screening-photovoltaic solitons is generated throught increasing theintensity FWHM of the optical beam. The wider the input width of the dark stripe, themore the number of incoherent dark screening-photovoltaic solitons is generated.When the more incoherent solitons are generated, the separations between adjacentdark solitons become smaller and the solitons far away from the center become lessvisible. For a given physical system and splitting number, the separations betweenadjacent dark solitons decrease with the increasing of width of the dark stripe.
For the incoherent gray screeing-photovoltaic solitons, its formation is effected by the incoherent beam’s grayness and the FWHM of the incoherent beam’s intensity.Under even initial conditions, if the incoherent beam’s grayness or FWHM of theincoherent beam intensity is small, only a Y-junction soliton is generated. Withincreasing of the grayness of the incoherent beam or FWHM of the incoherent beam’sintensity, the incoherent multiple gray screening-photovoltaic solitons can be formedin the biased photorefractive-photovoltaic crystal.
The coherence length of the incoherent beam is invariable far away from thesoliton region; however the coherence length is tempestuously changed, in particular,the coherence length of the incoherent beam becomes higher within the center solitonpair, with a depression an the center.
In addition, we study the characters of the dark and gray incoherent screening-photovoltaic spatial solitons in biased photorefractive-photovoltaic crystals. We foundthat it translates into the dark incoherent screening soliton splitting when the bulkphotovoltaic effect is neglectable and the dark incoherent photovoltaic solitonsplitting when the external bias field is absent.
本论文主要是从理论上利用相干密度法研究了非相干屏蔽灰孤子和非相干屏蔽光伏孤子分裂，利用光束传播法研究与时间有关的开环相干光伏孤子分裂，并从实验上研究非相干光伏孤子分裂，具体结论如下：
1.非相干光伏孤子实验研究
无背景光辐照时，利用振幅掩模穿过一束空间非相干光的方法产生暗迹，将暗迹成像在晶体前表面上，在LiNbO3:Fe晶体内形成偶数序列的非相干暗光伏孤子。实验结果表明，无背景光辐照时可以在非瞬时响应的光折变光伏晶体内形成非相干暗光伏孤子序列，形成的孤子分裂数目与入射宽度和光束相干长度有关。
在给定光束的空间相干长度时，形成孤子数目与入射暗纹的宽度有关，当入射的暗纹宽度较小时，只能形成一个Y结孤子对；随着入射宽度的增加，可以形成偶数序列暗光伏孤子，在晶体前表面入射的暗纹宽度越宽，形成孤子数目越多，这与相干孤子FWHM的变化规律一致。形成多孤子时，位于中心的孤子对灰度最小，其他孤子对与中心距离越远，灰度越大；孤子数目越多，孤子间隔越小，每个孤子的宽度都比N=2时孤子宽度稍微小一点。另外，光束的相干长度对孤子分裂有影响，入射光束的空间相干性越好，相干长度越大，形成孤子所需入射宽度越小。
2.非相干灰屏蔽孤子
利用相干密度法研究非相干屏蔽灰孤子在偏压光折变非线性介质中的传输特性和空间相干性。数值模拟结果表明，可以在偏压SBN晶体内形成非相干屏蔽灰孤子。
当偏压较小时，只能形成非相干的Y结屏蔽灰孤子，对应最低阶的孤子，当外偏压增加时，非相干光束趋于分裂为偶数序列的非相干屏蔽灰孤子；如果给定入射光束灰度，增加外偏压和入射光束宽度也可以产生偶数序列非相干屏蔽灰孤子；或者给定入射光束宽度，通过增加外偏压并减小光束灰度仍可以产生那样的偶数序列非相干灰屏蔽孤子。
非相干屏蔽灰孤子的相干长度在孤子区域变大，孤子最小强度越小，相干长度越大，而远离孤子区域趋于恒定不变。
3.相干暗光伏孤子
利用光束传播法研究在非线性光折变光伏介质中形成的开环暗光伏孤子分裂。数值模拟结果表明，根据初始条件不同，在均匀光束中心形成的暗纹能在光折变光伏非线性材料中分裂为奇数或偶数序列的暗光伏孤子。
对于一个给定的物理系统，多模暗光伏孤子的形成与初始条件和入射光束强度半高宽有关。一方面，奇初始位相光束总是趋于分裂为奇数序列暗光伏孤子，偶初始位相光束趋于分裂为偶数序列暗光伏孤子；另一方面，当入射宽度较小时，只能形成一个基本孤子或Y结孤子对，随着入射宽度的增加，入射暗光束可以分裂为多暗光伏孤子，入射暗纹宽度越大，形成的孤子数目越多，当有更多孤子产生时，相邻孤子间隔变小，远离中心的孤子可见度下降。
4.非相干屏蔽光伏孤子
利用相干密度法研究非相干屏蔽光伏暗孤子和灰孤子在有偏压的光折变光伏晶体内的传输特性及空间相干性，数值模拟结果表明可以在偏压光折变晶体内形成非相干屏蔽光伏暗孤子和灰孤子。
非相干屏蔽光伏暗孤子的形成依赖初始入射条件和入射暗纹宽度。在奇或偶初始条件下，通过增加入射暗纹宽度可以在晶体内形成奇、偶数序列的非相干屏蔽光伏孤子，入射暗纹宽度越大，形成孤子数目越多；当形成多孤子分裂时，相邻孤子之间的间隔越小，远离中心的孤子对可见度下降。对于给定物理系统和确定的孤子分裂数，入射暗纹宽度越大，相邻孤子间隔越小。
非相干屏蔽光伏灰孤子的形成依赖非相干光束灰度和入射暗纹宽度。在偶初始条件下，如果入射的非相干光束的灰度或者入射光束的强度半高宽较小时，只能形成一个Y分裂，而如果非相干光束的强度半高宽或光束灰度增大时可以在晶体内形成偶数序列的非相干灰屏蔽光伏孤子。
通过对非相干灰屏蔽光伏孤子的相干长度研究发现，非相干孤子的相干长度在孤子区域及附近变化剧烈，特别是中心孤子对，在暗槽内部相干长度增加，而在中心处相干长度急速下降，而相干长度在远离中心的孤子区域是增加的，孤子的强度越小，相干长度越大。
此外，通过研究在有偏压光折变光伏晶体中的非相干屏蔽光伏孤子特性，发现当晶体内的光伏效应可以忽略时，非相干屏蔽光伏孤子的物理系统就转变为非相干屏蔽孤子的物理系统，非相干屏蔽光伏孤子变为非相干屏蔽孤子；而如果去掉外偏压，此时非相干屏蔽光伏孤子的物理系统变为非相干光伏孤子分裂的物理系统，非相干屏蔽光伏孤子变为非相干光伏孤子。
Photorefractive (PR) spatial solitons is the result of PR effect balanced thediffraction. Since the prediction and the observation of PR spatial solitons, it hasattracted more attention in the formation and characters of PR spatial solitons owingto the potential application in beam steering and manipulating light by light, all-optical switching, optical interconnects and optical nonlinear devices et al.
In this paper, I theoretically studied the multiple incoherent gray screeningsolitons splitting and incoherent screening-photovoltaic dark (gray) solitons splittingby using of coherent density method. I investigate the time-dependent coherentphotovoltaic spatial solitons splitting under open-circuit conditions using beampropagation method. In addition, I experimentally study the incoherent photovoltaicsolitons splitting in LiNbO3:Fe crystal without background light. The detailedconclusions as follow:
1. Experimental study on incoherently photovoltaic solitons
A dark stripe is generated when the partially spatially incoherent beam passesthrough amplitude mark without background illumination. The dark stripe is imagedinto the front face of the crystal. The even-number sequence of incoherent darkphotovoltaic solitons is generated. The experimental results indicate that theincoherent photovoltaic soliton sequence can be generated in non-instantaneousnonlinearity photorefractive photovoltaic crystal and that the number of solitons isdependent on the initial input width of the dark stripe and the coherence length of thebeam.
For a fixed beam’s spatial coherence, the number of solitons is dependent to theinitial input width of the dark stripe. Only a Y-junction solitons pair can be observedwhen the input width is small. With the increasing of the initial input width, theeven-number sequence of dark photovoltaic solitons is generated. The more solitonsare formed for wider initial input dark stripe, which is similar to coherent solitonsplitting. When more solitons are generated, the separations between adjacent dark solitons become smaller and the grayness of solitons is grayer as their transversedistance from the center increases. In addition, the coherence length of the incoherentbeam affects the number of solitons splitting. The bigger the coherence length of thebeam, the smaller the input width of the dark stripe needed.
2. Incoherent screening grey solitons
We study the propagation properties and spatial coherence of multiple incoherentscreening grey soliotns in biased photorefractive media by using the coherent densitymethod. The numerically studies results demonstrate that even-number sequence ofmultiple incoherent gray screening solitons is possible.
We find that when the external voltage is small, only an incoherent Y-junctionscreening soliton is generated, corresponding to the lowest order in the even-numberincoherent screening soliton sequence. When the external voltage is increased, theincoherent gray beam splits into an even-number sequence of multiple gray screeningsoliton. For a fixed beam’s grayness, increasing the external voltage and the full widthhalf maximum of the beam’s intensity can produce such an even-number sequence ofmultiple incoherent gray screening solitons. Moreover, for a fixed full width at halfmaximum of the initial input beam’s intensity, increasing the external voltage anddecreasing the beam’s grayness still produces such an even-number sequence ofmultiple incoherent gray screening solitons.
In addition, we find that the coherence length of multiple incoherent grayscreening solitons becomes higher around the soliton regions and that the smaller theminimum intensity of multiple incoherent gray screening solitons, the bigger itscorrelation length. We also find that the correlation length is changeless far away fromthe solitons.
3. Incoherent dark photovoltaic solitons
We study the formation of the multiple dark photovoltaic solitons splitting inphotorefractive photovoltaic nonlinear media under open-circuit condition by using ofbeam propagation method. The simulated results indicate that a single dark stripe onan otherwise uniform optical beam can be split into odd (or even) number sequence ofdark photovoltaic solitons in the photovoltaic photorefractive nonlinear media according to different initial conditions.
We find that for a given physical system, the formation of multiple darkphotovoltaic solitons is depended on the initial input conditions as well as on the fullwidth at half maximum (FWHM) of the input beam’s intensity. On one hand, anodd-phase input beam always tends to split into the odd-number sequence of multipledark photovoltaic solitons, whereas the even-phase input beam tends to split into theeven-number sequence of multiple dark photovoltaic solitons. On the other hand,when the initial input width of the dark stripe is small, it only can form a foundationalsolitons or a Y-junction solution pair. With the increasing of the input width of thedark stripe, it can split into multiple dark photovoltaic solitions. The wider the inputwidth of the dark stripe, the more the number of solitons is generated. When moresolitons are generated, the separations between adjacent solitons become smaller andthe visibility of the solitons far away from the center decrease.
4. Incoherent screening-photovoltaic solitons
We study the propagation properties and the spatial coherences of the incoherentdark and gray screening-photovoltaic spatial solitons in biased photorefractive-photovoltaic crystals by using the coherent density method. The results of numericalsimulation demonstrate that the incoherent screening-photovoltaic dark (or gray)solitons can be generated in biased photorefractive photovoltaic crystal.
For the incoherent screening-photovoltaic spatial dark solitons, formation of it isdependent on the initial input conditions as well as the initial input width of the darkstripe. Under the odd or even initial conditions, the odd or even number sequence ofincoherent screening-photovoltaic solitons is generated throught increasing theintensity FWHM of the optical beam. The wider the input width of the dark stripe, themore the number of incoherent dark screening-photovoltaic solitons is generated.When the more incoherent solitons are generated, the separations between adjacentdark solitons become smaller and the solitons far away from the center become lessvisible. For a given physical system and splitting number, the separations betweenadjacent dark solitons decrease with the increasing of width of the dark stripe.
For the incoherent gray screeing-photovoltaic solitons, its formation is effected by the incoherent beam’s grayness and the FWHM of the incoherent beam’s intensity.Under even initial conditions, if the incoherent beam’s grayness or FWHM of theincoherent beam intensity is small, only a Y-junction soliton is generated. Withincreasing of the grayness of the incoherent beam or FWHM of the incoherent beam’sintensity, the incoherent multiple gray screening-photovoltaic solitons can be formedin the biased photorefractive-photovoltaic crystal.
The coherence length of the incoherent beam is invariable far away from thesoliton region; however the coherence length is tempestuously changed, in particular,the coherence length of the incoherent beam becomes higher within the center solitonpair, with a depression an the center.
In addition, we study the characters of the dark and gray incoherent screening-photovoltaic spatial solitons in biased photorefractive-photovoltaic crystals. We foundthat it translates into the dark incoherent screening soliton splitting when the bulkphotovoltaic effect is neglectable and the dark incoherent photovoltaic solitonsplitting when the external bias field is absent.
引文
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