分支光波导数值模拟
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摘要
随着集成光学技术的发展，诸多具有不同结构，功能各异的光波导器件应运而生。单纯通过实验来设计光波导器件是很费时费力的，通过计算机辅助设计的手段，对光波导器件进行预设计，不但可以克服以上困难，同时能直观完备地反映光波导器件的特性，准确快速地达到预期的设计要求。于是出现了用数值分析方法来分析集成光波导。其中，光束传播法就是分析光波导器件的一种好方法。
本文对二维有限差分光束传播法(FD-BPM)建立了理论模型。在此模型的基础上，我们分析了光波导中光场的传输特性，并对影响其传播的因素进行了详细的分析和讨论，并将计算结果和有关文献报道的结果进行了对比研究。
首先，我们简单介绍了光波导理论：平板光波导的波动方程及分支光波导的制备。然后我们在Maxwell方程的基础上，根据慢包络近似理论，在折射率截面为n(x，z)的条件下，利用有限差分近似来代替偏微分方程，推出了有限差分光束传播法计算所需要的公式。因为我们所能模拟的空间是有界情况，所以我们需要建立一种人为的边界条件来模拟无界的情况。这里我们介绍了透明边界条件。接着我们建立了FD-BPM在分析分支光波导器件时所需的理论模型。并利用计算机模拟出了脊形波导、Y形分支波导、多分支波导及X形分支波导的光场传播图。然后我们详细分析了影响光场传输和BPM计算精度的因素。例如：Y分支的夹角对Y型分支波导光传输效率的影响，参考折射率的选择、计算窗口的大小、格点间距值、折射率差的变化对BPM计算精度的影响。
结果表明，利用FD-BPM方法对折射率变化不大的器件进行模拟，其结果是精确的。为我们进一步分析光波导器件特性打下了良好基础。
With the development of integrated optics, all kinds of optical wave-guide devices with different function and structure have appeared. Designing wave-guide completely by experimental method is complicated, while design a wave-guide with CAD method can not only overcome such difficulty but also analyze the characters of optical wave-guide and thus lead to a quick designation. Then numerical algorithms are used to analyze integrated optical wave-guide and beam propagation method is a good method which is widely used.
This paper build a theoretical model based on two dimensional FD-BPM. On this basis, we analyzed the trait of optical field in optical wave-guide and factors influencing the propagation, and furthermore compared the results with those in related papers.
First, we simply introduced the optical wave-guide theory: the fluctuation equations of planar wave-guide and the preparation of embranchment wave-guide . Then based on Maxwell equations and in the paraxial limit we deduced the formula needed in calculating FD-BPM. The refractive index section was n(x,y). Because the space we simulated has its boundary, we needed to found a man-made condition to simulate the space that has no boundary. Here we introduced the Transparent Boundary Condition(TBC). Then we found the theory model when we study the embranchment wave-guide using FD-BPM. And we simulated the optical field's propagation of the ridge wave-guide, Y-type embranchment wave-guide, more embranchment wave-guide and X-type embranchment wave-guide. After this we studied the factors influencing the propagation of optical field and the precision of calculating BPM. For example, we studied the influence of angle to the propagation efficiency of Y-type embranchment and influence of calculation window size, selection of reference refractive index, the interval between dots, the difference of refractive index to the calculation of BPM.
The result showed that it was precise when we used FD-BPM to simulate the apparatus that the refractive index value change was small. It was favorable to our further study.
本文对二维有限差分光束传播法(FD-BPM)建立了理论模型。在此模型的基础上，我们分析了光波导中光场的传输特性，并对影响其传播的因素进行了详细的分析和讨论，并将计算结果和有关文献报道的结果进行了对比研究。
首先，我们简单介绍了光波导理论：平板光波导的波动方程及分支光波导的制备。然后我们在Maxwell方程的基础上，根据慢包络近似理论，在折射率截面为n(x，z)的条件下，利用有限差分近似来代替偏微分方程，推出了有限差分光束传播法计算所需要的公式。因为我们所能模拟的空间是有界情况，所以我们需要建立一种人为的边界条件来模拟无界的情况。这里我们介绍了透明边界条件。接着我们建立了FD-BPM在分析分支光波导器件时所需的理论模型。并利用计算机模拟出了脊形波导、Y形分支波导、多分支波导及X形分支波导的光场传播图。然后我们详细分析了影响光场传输和BPM计算精度的因素。例如：Y分支的夹角对Y型分支波导光传输效率的影响，参考折射率的选择、计算窗口的大小、格点间距值、折射率差的变化对BPM计算精度的影响。
结果表明，利用FD-BPM方法对折射率变化不大的器件进行模拟，其结果是精确的。为我们进一步分析光波导器件特性打下了良好基础。
With the development of integrated optics, all kinds of optical wave-guide devices with different function and structure have appeared. Designing wave-guide completely by experimental method is complicated, while design a wave-guide with CAD method can not only overcome such difficulty but also analyze the characters of optical wave-guide and thus lead to a quick designation. Then numerical algorithms are used to analyze integrated optical wave-guide and beam propagation method is a good method which is widely used.
This paper build a theoretical model based on two dimensional FD-BPM. On this basis, we analyzed the trait of optical field in optical wave-guide and factors influencing the propagation, and furthermore compared the results with those in related papers.
First, we simply introduced the optical wave-guide theory: the fluctuation equations of planar wave-guide and the preparation of embranchment wave-guide . Then based on Maxwell equations and in the paraxial limit we deduced the formula needed in calculating FD-BPM. The refractive index section was n(x,y). Because the space we simulated has its boundary, we needed to found a man-made condition to simulate the space that has no boundary. Here we introduced the Transparent Boundary Condition(TBC). Then we found the theory model when we study the embranchment wave-guide using FD-BPM. And we simulated the optical field's propagation of the ridge wave-guide, Y-type embranchment wave-guide, more embranchment wave-guide and X-type embranchment wave-guide. After this we studied the factors influencing the propagation of optical field and the precision of calculating BPM. For example, we studied the influence of angle to the propagation efficiency of Y-type embranchment and influence of calculation window size, selection of reference refractive index, the interval between dots, the difference of refractive index to the calculation of BPM.
The result showed that it was precise when we used FD-BPM to simulate the apparatus that the refractive index value change was small. It was favorable to our further study.
引文
[1] Felt M.D and Fleck J.A. "Light Propagation in Graded-index Optical Fibers". Appl.Opt. 1978, vol. 18, No.10.pp.3990～3998
[2] M.D.Feit and J.A.Fleck, Jr,"Computation of mode properties in optical fiber waveguide by a propagating beam method",Appl.Opt. 1980,Vol. 19,No.7,pp. 1154-1163
[3] J.Van Roey, J,Van der Donk,and P.E.langasse,"Beam Propagation Method: analysis and assessment" J.Opt. Soc. Amer, 1981,Vol.71,pp.803
[4] B.M.Nymand and P.R.Pruncnal,"The modified beam propagation method",IEEE Quantum electron, 1989,Vol.7,No6,pp.931-936
[5] D.Yevick and B.Hermansson," Efficient beam propagation techniques",IEEE Quantum electron., 1990,Vol 26,pp 109-112
[6] C.L.Xu,W.p. Huang and S.K.Chaudhuri,"Efficient and accurate vector mode calculations by beam propagation method", Journal of lighwave technology., 1993, Vol. 11 No.7, pp 1209-1215
[7] Y. Chung and N.Dagli, "Explicit finite difference beam propagation method: Application to semiconductor rib waveguide Y-junction analysis", Electron Lett. 1990,Vol.26,No. 11 ,pp711-713
[8] Y. Chung and N.Dagli, "An assessment of finite difference beam propagation method", IEEE J.Quantum electron. 1990,Vol26,1335-1339
[9] R. Scarmozzino and R.M.Osggod,Jr., "Compassion of finite-difference and Fourier-transformsolutions ",J.Opt. Soc. Amer. A, 1991,Vol 18,No5,pp.727-731
[10] T.B.Koch,JB.Davies and D.Wickramasinghe, "Finite element/Finite fifference propagation algorithm for integrated optical device",Electron. Lett., 1989,Vol.25,No.5,pp514-516
[11] R.Klein and A.Neyer, Silicon Micromatching for Micro-Replication Technologies,Electron. Lett., 1994, Vol.30(20); pp: 1672-1673
[12] 蔡伯荣，《集成光学》．北京．电子科技大学出版社．1990
[13] 郭长志，《半导体激光模式理论》．北京．人民邮电出版社 1989
[14] 陈益新等．《集成光学——理论和技术》．上海．上海交通大学出版社．1985．193
[15] Motamed M E. Micro-optoelectromechanical system. Optical Engineering. 1994.33(11): 3305-3517
[16] Gravesen Peter. Microfluidics-A review. J. Micromech. Microeng., 1993,3(1): 168:182
[17] Laskoskie C. Ti-LiNbO_3 Waveguide Serrodyne Modulator with Ultrahigh Sideband Suppression for Fiber Optic Gyroscope.J.of Light wave Technology, 1989;7(4):600:606
[18] Chio Y A.Environmentally robust Fiber Optic Gyro Component Development and Productization. SPIE, 1991; 1985: 182-185
[19] G.Ronald Hadley, "Multistep method for wide-angle beam propagation", Optics Letters. 1992,Vol. 17,No.24,pp 1743-1745
[20] Junji Yamauchi,Jun shibayayama, "Wide-angle propagating beam analysis based on the generalized
douglas scheme for variable coefficient",Optics Letters, 1995,Vol 20, pp7-9
[21] David Yevick, "Forward wide-angle light propagation in semiconductor rib waveguide", Optics Letters, 1995,Vol.20,pp7-9
[22] H.E.Hernandez-Figueroa, "Simple Nonparaxial Beam-Propagation Method for Integrated Optics", Journal of lightwave technology, 1994,vol. 12,pp644-649
[23] Jun Shibayama, Member, OSA,Kenji Matsubaru, "Efficient Nonuniform Schemes for Paraxial and Wideangle Finite-Difference Beam Propagation Method", Journal of Lightwave Technology, 1999, Vol 17, No.4, pp301-303
[24] H.J.W.M.Hoekstra, G.J.M.Krijnen and P.V. Lambeck. "New formulation if the beam propagation method based on the slowly varying envelope approximation:,Optics Communications ,Vol.97,1993,pp301-303
[25] G.Ronald Hadley, "wide-angle beam propagation using Pade approximant operators",Optics Letters, 1992,Vol 17 ,No .20 ,pp 1426-1428
[26] G.A.Baker, Essentials of Pade Approximants(Academic,New York, 1975)
[27] 巨振乐，付君眉，“宽角光束传播法在集成光学中的应用”，半导体光电，Vol．18，1997，No．3，pp：187-189
[28] E.E.Kriezis,Member, IEEE,and Antonis G.Pagatikis, :A Three-Dimensional Full vectorial Beam Propagation Method for z-Dependent Structures", IEEE Journal of Quantum Electronics, 1997,Vol.33
[29] 巨振乐，付君眉，“改进的宽角光束传播法”，半导体光电，1998,Vol19，No．3，pp184-186
[30] Lizhong Sun and Gar Lam Yip, "Modified finite-difference beam-propagation method based on the Douglas scheme", Optics Letter, 1993,Vol. 18,No. 15,pp 1229-1231
[31] Huang W P, Xu C L," A wide-angle vector beam propagation method",IEEE Phtonics Technology Letters., 1992,Vol.4,No. 10,pp 1118-1120
[32] L.Thylen, "The beam propagation method: an analysis of its applicability," Opt. Quantum Electron., 1983,Vol. 15,pp433
[33] J.Van Roy, J.van der Donk ,and P.E.Lagasses,"Beam propagtion method: Analysis and assessment," J.Opt. Soc.Amer, 1983,Vol.71,pp803
[34] E.O.Brigham,The Fast Fourier Transformation. Englewood Cliffs, NJ,Prentice Hall, 1974,pp163-164
[35] M.D.Feit and J.A.Fleck,Jr, "Mode properties of optical fibers",1981,Vol.20,No.5,pp848-856
[36] H.A.Haus,in Waves and Fields in Optoeletronics. Englewood Cliffs,NJ:Prentice Hall, 1984,pp99-103
[37] W.H.Press,B.P. Flannnery, S.A.Teuldsky, and W.T. Vetterling,Numerical Recipes: The Art of Scientific Computing. New York:Cambridge Univ. 1986,pp40-41
[38] Liu P L,LiBJ,IEEE J Q E, 1993;29;2385-2389
[39] Liu P L,Yang S L ,Yuan D M.IEEE J Q E, 1993;29:1205-1210
[40] Deng H, Jin G H, Harari J et al.J Lightwave Technology, 1998;16;915-922
[41] Caccavale F, Segato F, Mansour I.J Lightwave Technology, 1997;15;1294-1300
[42] Chou H F ,Lin C F ,Wang G C.J Lightwave Technology, 1998;16;1686-1693
[43] Koch T B, Mara R,Davies J B.Beam propagation method using z-transient variatuional principle,in Proc 16th European Conf Opt Commun(ECOC), 1 Amsteram,The Netherland, 1990:163-166
[44] Schulz D,Glingener C,Bludszuweit M et al J Lightwave technology, 1998,Vol(16),pp:1336-1341
[45] Cucinotta A,Selleri S,Vincetti I,IEEE Photon Technol Lrtt, 1999,Vol(11),pp:209-211
[46] Yasumoto K,Maeda. H, and Morita. S, "Numerical Analysis of Transitions and Discontinuties in Optical Waveguide",Asia-Pacific microwave Conference Proc, 1996,pp647-650
[47] G.R.Hardley, "Transparent Boundary Condition for the Beam Propagation Method", IEEE J.Quantuam Electronic, 1992,Vol.28,No. 1,pp364-370
[48] Hadley G R "Transparent Boundary condition for beam propagation",Opt Lett, 1991,16(9),pp624-626
[49] Hadley G R "Transparent Boundary condition for beam propagation",IEEE,J Quantum Electron, 1992, 28(1) ,pp363-370
[50] Ma F, Xu C L,Huang W P, "Wide-angle full vectorial beam propagation method. IEE Pro Optoeletron,1996,143(2);139-143
[51] Rappaport C.M. Perfectly matched absorbing boundary conditions based on anisotropic lossy mapping of space. IEEE Microwave Guided Wave Lett, 1995,5(3):90-92
[52] Collins M D. Higher-order Pade approximations for accurate and stable elastic parabolicequations with application to interface wave propagation. J Acoust Soc Amer, 1991, 89(3): 1050-1057
[53] JU Zheng-le,FU Jun-mei,FENG En-xin. Modified wide-angle beam propagation method[J]. Semi conductor Optoelectronics, 1998,19(12):25-28
[54] P L Liu,S L Yang,D M Yuan. The semivetorial beam propagation method[J].IEEE J.Quantum Electron, 1993,29(11 ): 1205-1211
[55] 李庆扬，王能超，易大义，《数值分析》．华中科技大学出版社．1982
[56] E E Kriezis,Antonis G Papagiannakis. A three-dimensional full vectorial beam propagation method for z-dependent structures[J].IEEE.J.Quantum Electronics, 1997,33(5):321-326
[57] LI Qing-yang, WANG Neng-chao,YI Da-yi. Numerical Simulations[M].Wuhan: Express of huaZhong University of Science and Technology, 1998.(in Chinese)
[58] 赵策洲．半导体导波光学器件理论及技术．北京：国防工业出版社．1998．pp：58-59
[59] Laznicka O M, Suchoski P G.. Intertial-Grade Fiber Optic Cyro Utilizing an Advanced Intergrated Optical Circuit with Beat Detection.SPIE, 1991; 1985:182-185
[60] Handrich E.Flight Demonstration of Fiber Optic Gyros AHRS. Symposium Gyro Technology, 1989:11.1-11.8
[61] Lefevre H C.Fiber Optic Opic Gyro Production at Photonics. SPIE, 1991 ;1585:42-47
[2] M.D.Feit and J.A.Fleck, Jr,"Computation of mode properties in optical fiber waveguide by a propagating beam method",Appl.Opt. 1980,Vol. 19,No.7,pp. 1154-1163
[3] J.Van Roey, J,Van der Donk,and P.E.langasse,"Beam Propagation Method: analysis and assessment" J.Opt. Soc. Amer, 1981,Vol.71,pp.803
[4] B.M.Nymand and P.R.Pruncnal,"The modified beam propagation method",IEEE Quantum electron, 1989,Vol.7,No6,pp.931-936
[5] D.Yevick and B.Hermansson," Efficient beam propagation techniques",IEEE Quantum electron., 1990,Vol 26,pp 109-112
[6] C.L.Xu,W.p. Huang and S.K.Chaudhuri,"Efficient and accurate vector mode calculations by beam propagation method", Journal of lighwave technology., 1993, Vol. 11 No.7, pp 1209-1215
[7] Y. Chung and N.Dagli, "Explicit finite difference beam propagation method: Application to semiconductor rib waveguide Y-junction analysis", Electron Lett. 1990,Vol.26,No. 11 ,pp711-713
[8] Y. Chung and N.Dagli, "An assessment of finite difference beam propagation method", IEEE J.Quantum electron. 1990,Vol26,1335-1339
[9] R. Scarmozzino and R.M.Osggod,Jr., "Compassion of finite-difference and Fourier-transformsolutions ",J.Opt. Soc. Amer. A, 1991,Vol 18,No5,pp.727-731
[10] T.B.Koch,JB.Davies and D.Wickramasinghe, "Finite element/Finite fifference propagation algorithm for integrated optical device",Electron. Lett., 1989,Vol.25,No.5,pp514-516
[11] R.Klein and A.Neyer, Silicon Micromatching for Micro-Replication Technologies,Electron. Lett., 1994, Vol.30(20); pp: 1672-1673
[12] 蔡伯荣，《集成光学》．北京．电子科技大学出版社．1990
[13] 郭长志，《半导体激光模式理论》．北京．人民邮电出版社 1989
[14] 陈益新等．《集成光学——理论和技术》．上海．上海交通大学出版社．1985．193
[15] Motamed M E. Micro-optoelectromechanical system. Optical Engineering. 1994.33(11): 3305-3517
[16] Gravesen Peter. Microfluidics-A review. J. Micromech. Microeng., 1993,3(1): 168:182
[17] Laskoskie C. Ti-LiNbO_3 Waveguide Serrodyne Modulator with Ultrahigh Sideband Suppression for Fiber Optic Gyroscope.J.of Light wave Technology, 1989;7(4):600:606
[18] Chio Y A.Environmentally robust Fiber Optic Gyro Component Development and Productization. SPIE, 1991; 1985: 182-185
[19] G.Ronald Hadley, "Multistep method for wide-angle beam propagation", Optics Letters. 1992,Vol. 17,No.24,pp 1743-1745
[20] Junji Yamauchi,Jun shibayayama, "Wide-angle propagating beam analysis based on the generalized
douglas scheme for variable coefficient",Optics Letters, 1995,Vol 20, pp7-9
[21] David Yevick, "Forward wide-angle light propagation in semiconductor rib waveguide", Optics Letters, 1995,Vol.20,pp7-9
[22] H.E.Hernandez-Figueroa, "Simple Nonparaxial Beam-Propagation Method for Integrated Optics", Journal of lightwave technology, 1994,vol. 12,pp644-649
[23] Jun Shibayama, Member, OSA,Kenji Matsubaru, "Efficient Nonuniform Schemes for Paraxial and Wideangle Finite-Difference Beam Propagation Method", Journal of Lightwave Technology, 1999, Vol 17, No.4, pp301-303
[24] H.J.W.M.Hoekstra, G.J.M.Krijnen and P.V. Lambeck. "New formulation if the beam propagation method based on the slowly varying envelope approximation:,Optics Communications ,Vol.97,1993,pp301-303
[25] G.Ronald Hadley, "wide-angle beam propagation using Pade approximant operators",Optics Letters, 1992,Vol 17 ,No .20 ,pp 1426-1428
[26] G.A.Baker, Essentials of Pade Approximants(Academic,New York, 1975)
[27] 巨振乐，付君眉，“宽角光束传播法在集成光学中的应用”，半导体光电，Vol．18，1997，No．3，pp：187-189
[28] E.E.Kriezis,Member, IEEE,and Antonis G.Pagatikis, :A Three-Dimensional Full vectorial Beam Propagation Method for z-Dependent Structures", IEEE Journal of Quantum Electronics, 1997,Vol.33
[29] 巨振乐，付君眉，“改进的宽角光束传播法”，半导体光电，1998,Vol19，No．3，pp184-186
[30] Lizhong Sun and Gar Lam Yip, "Modified finite-difference beam-propagation method based on the Douglas scheme", Optics Letter, 1993,Vol. 18,No. 15,pp 1229-1231
[31] Huang W P, Xu C L," A wide-angle vector beam propagation method",IEEE Phtonics Technology Letters., 1992,Vol.4,No. 10,pp 1118-1120
[32] L.Thylen, "The beam propagation method: an analysis of its applicability," Opt. Quantum Electron., 1983,Vol. 15,pp433
[33] J.Van Roy, J.van der Donk ,and P.E.Lagasses,"Beam propagtion method: Analysis and assessment," J.Opt. Soc.Amer, 1983,Vol.71,pp803
[34] E.O.Brigham,The Fast Fourier Transformation. Englewood Cliffs, NJ,Prentice Hall, 1974,pp163-164
[35] M.D.Feit and J.A.Fleck,Jr, "Mode properties of optical fibers",1981,Vol.20,No.5,pp848-856
[36] H.A.Haus,in Waves and Fields in Optoeletronics. Englewood Cliffs,NJ:Prentice Hall, 1984,pp99-103
[37] W.H.Press,B.P. Flannnery, S.A.Teuldsky, and W.T. Vetterling,Numerical Recipes: The Art of Scientific Computing. New York:Cambridge Univ. 1986,pp40-41
[38] Liu P L,LiBJ,IEEE J Q E, 1993;29;2385-2389
[39] Liu P L,Yang S L ,Yuan D M.IEEE J Q E, 1993;29:1205-1210
[40] Deng H, Jin G H, Harari J et al.J Lightwave Technology, 1998;16;915-922
[41] Caccavale F, Segato F, Mansour I.J Lightwave Technology, 1997;15;1294-1300
[42] Chou H F ,Lin C F ,Wang G C.J Lightwave Technology, 1998;16;1686-1693
[43] Koch T B, Mara R,Davies J B.Beam propagation method using z-transient variatuional principle,in Proc 16th European Conf Opt Commun(ECOC), 1 Amsteram,The Netherland, 1990:163-166
[44] Schulz D,Glingener C,Bludszuweit M et al J Lightwave technology, 1998,Vol(16),pp:1336-1341
[45] Cucinotta A,Selleri S,Vincetti I,IEEE Photon Technol Lrtt, 1999,Vol(11),pp:209-211
[46] Yasumoto K,Maeda. H, and Morita. S, "Numerical Analysis of Transitions and Discontinuties in Optical Waveguide",Asia-Pacific microwave Conference Proc, 1996,pp647-650
[47] G.R.Hardley, "Transparent Boundary Condition for the Beam Propagation Method", IEEE J.Quantuam Electronic, 1992,Vol.28,No. 1,pp364-370
[48] Hadley G R "Transparent Boundary condition for beam propagation",Opt Lett, 1991,16(9),pp624-626
[49] Hadley G R "Transparent Boundary condition for beam propagation",IEEE,J Quantum Electron, 1992, 28(1) ,pp363-370
[50] Ma F, Xu C L,Huang W P, "Wide-angle full vectorial beam propagation method. IEE Pro Optoeletron,1996,143(2);139-143
[51] Rappaport C.M. Perfectly matched absorbing boundary conditions based on anisotropic lossy mapping of space. IEEE Microwave Guided Wave Lett, 1995,5(3):90-92
[52] Collins M D. Higher-order Pade approximations for accurate and stable elastic parabolicequations with application to interface wave propagation. J Acoust Soc Amer, 1991, 89(3): 1050-1057
[53] JU Zheng-le,FU Jun-mei,FENG En-xin. Modified wide-angle beam propagation method[J]. Semi conductor Optoelectronics, 1998,19(12):25-28
[54] P L Liu,S L Yang,D M Yuan. The semivetorial beam propagation method[J].IEEE J.Quantum Electron, 1993,29(11 ): 1205-1211
[55] 李庆扬，王能超，易大义，《数值分析》．华中科技大学出版社．1982
[56] E E Kriezis,Antonis G Papagiannakis. A three-dimensional full vectorial beam propagation method for z-dependent structures[J].IEEE.J.Quantum Electronics, 1997,33(5):321-326
[57] LI Qing-yang, WANG Neng-chao,YI Da-yi. Numerical Simulations[M].Wuhan: Express of huaZhong University of Science and Technology, 1998.(in Chinese)
[58] 赵策洲．半导体导波光学器件理论及技术．北京：国防工业出版社．1998．pp：58-59
[59] Laznicka O M, Suchoski P G.. Intertial-Grade Fiber Optic Cyro Utilizing an Advanced Intergrated Optical Circuit with Beat Detection.SPIE, 1991; 1985:182-185
[60] Handrich E.Flight Demonstration of Fiber Optic Gyros AHRS. Symposium Gyro Technology, 1989:11.1-11.8
[61] Lefevre H C.Fiber Optic Opic Gyro Production at Photonics. SPIE, 1991 ;1585:42-47