Pub Date : 1900-01-01DOI: 10.1364/domo.1998.dtha.3
S. Brinkmann, T. Dresel, R. Schreiner, J. Schwider
Optical techniques which are well established for the testing of optical surfaces usually suffer from speckle noise caused by the roughness of technical surfaces. For this reason the shape control of technical workpieces is commonly carried out by tactile profilometers. An optical and much faster alternative to mechanical profilometry is grazing incidence interferometry. It suppresses speckle noise by increasing the effective test wavelength from λ to λ/cosϑ, where ϑ is the angle of incidence [1-3]. Diffractive optical elements, containing the shape information of an ideal object in their surface relief, are used as references for the workpiece enabling a null test of the entire mantle surface in a single step. The period p of the diffractive optical elements determines the diffraction angle α=arcsin(λ/p) and hereby the angle of incidence ϑ=π-α, the effective wavelength λeff=p and the sensitivity λeff/2 of the interferometer.
{"title":"Optical Testing of Technical Surfaces with Diffractive Optical Elements","authors":"S. Brinkmann, T. Dresel, R. Schreiner, J. Schwider","doi":"10.1364/domo.1998.dtha.3","DOIUrl":"https://doi.org/10.1364/domo.1998.dtha.3","url":null,"abstract":"Optical techniques which are well established for the testing of optical surfaces usually suffer from speckle noise caused by the roughness of technical surfaces. For this reason the shape control of technical workpieces is commonly carried out by tactile profilometers. An optical and much faster alternative to mechanical profilometry is grazing incidence interferometry. It suppresses speckle noise by increasing the effective test wavelength from λ to λ/cosϑ, where ϑ is the angle of incidence [1-3]. Diffractive optical elements, containing the shape information of an ideal object in their surface relief, are used as references for the workpiece enabling a null test of the entire mantle surface in a single step. The period p of the diffractive optical elements determines the diffraction angle α=arcsin(λ/p) and hereby the angle of incidence ϑ=π-α, the effective wavelength λeff=p and the sensitivity λeff/2 of the interferometer.","PeriodicalId":301804,"journal":{"name":"Diffractive Optics and Micro-Optics","volume":"69 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128336199","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Surface-relief gratings made with anisotropic materials are finding more applications. An example is grooved magneto-optic disks as data storage media. The present work is a reformulation of the couple-wave method, for solving the anisotropic grating problem, that is described in Refs. 1-3. [Since the method essentially is a modal method relying on expanding both the electromagnetic fields and the permittivity function into Fourier series, here it is referred to as the Fourier modal method (FMM).] It originated from the work documented in Refs. 4-7. Recently Lalanne and Morris4, and Granet and Guizal5 simultaneously reformulated the conventional FMM for isotropic gratings in TM polarization. As a result, the convergence of the method for highly conducting metallic gratings was greatly improved. Auslender and Hava6 also reported the same reformulation. The findings of these authors were mathematically justified and summarized in the form of three Fourier factorization rules7. The use of these factorization rules has led to improvement of convergence in two other cases: the C method for gratings with sharp edges8 and the FMM for crossed gratings.9 This conference paper briefly reports yet another successful application of the factorization rules. A detailed exposition will soon appear elsewhere.10
{"title":"Reformulation of the Fourier modal method for surface-relief anisotropic gratings","authors":"Lifeng Li","doi":"10.1364/domo.1998.dma.3","DOIUrl":"https://doi.org/10.1364/domo.1998.dma.3","url":null,"abstract":"Surface-relief gratings made with anisotropic materials are finding more applications. An example is grooved magneto-optic disks as data storage media. The present work is a reformulation of the couple-wave method, for solving the anisotropic grating problem, that is described in Refs. 1-3. [Since the method essentially is a modal method relying on expanding both the electromagnetic fields and the permittivity function into Fourier series, here it is referred to as the Fourier modal method (FMM).] It originated from the work documented in Refs. 4-7. Recently Lalanne and Morris4, and Granet and Guizal5 simultaneously reformulated the conventional FMM for isotropic gratings in TM polarization. As a result, the convergence of the method for highly conducting metallic gratings was greatly improved. Auslender and Hava6 also reported the same reformulation. The findings of these authors were mathematically justified and summarized in the form of three Fourier factorization rules7. The use of these factorization rules has led to improvement of convergence in two other cases: the C method for gratings with sharp edges8 and the FMM for crossed gratings.9 This conference paper briefly reports yet another successful application of the factorization rules. A detailed exposition will soon appear elsewhere.10","PeriodicalId":301804,"journal":{"name":"Diffractive Optics and Micro-Optics","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128358124","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Equipment and techniques were developed at the University of Arizona for fabricating large computer-generated holograms (CGH’s) for measuring aspheric telescope mirrors. A large laser writing machine was built to fabricate binary zone plates onto spherical surfaces up to 1.8 meters in diameter and with focal ratios as fast as f/1. This machine writes 6-µm to 150-µm features with radial position accuracy better than 1 µm rms over the full diameter. The problems of applying and processing photoresist are avoided by writing the patterns using a simple thermochemical technique. Numerous holograms up to 1.2 m across have been successfully written and tested.
{"title":"Fabrication of large circular diffractive optics","authors":"J. Burge","doi":"10.1364/domo.1998.dwd.2","DOIUrl":"https://doi.org/10.1364/domo.1998.dwd.2","url":null,"abstract":"Equipment and techniques were developed at the University of Arizona for fabricating large computer-generated holograms (CGH’s) for measuring aspheric telescope mirrors. A large laser writing machine was built to fabricate binary zone plates onto spherical surfaces up to 1.8 meters in diameter and with focal ratios as fast as f/1. This machine writes 6-µm to 150-µm features with radial position accuracy better than 1 µm rms over the full diameter. The problems of applying and processing photoresist are avoided by writing the patterns using a simple thermochemical technique. Numerous holograms up to 1.2 m across have been successfully written and tested.","PeriodicalId":301804,"journal":{"name":"Diffractive Optics and Micro-Optics","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124752908","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1364/domo.1998.dtud.12
Guo-zhen Yang, Yan Zhang, B. Gu, B. Dong
The wavelet transform (WT) is a relatively useful and powerful technique in many applications, such as signal processing, pattern recognition, data compression, and so on.1-3 It overcomes the disadvantages of the Fourier transform and the Gabor transform, and provides an explicit representation of a signal in both space and frequency domains. Many configurations have been proposed to implement the wavelet transform, however, most of them are based on optical correlator. In this presentation, we present a new scheme to achieve the WT by a computer-generated hologram (CGH) based on the general theory of optical transform.4-6 The for determining the CGH is derived and a computer simulation is presented.
{"title":"Optical Wavelet Transform with Use of A Computer—Generated Hologram","authors":"Guo-zhen Yang, Yan Zhang, B. Gu, B. Dong","doi":"10.1364/domo.1998.dtud.12","DOIUrl":"https://doi.org/10.1364/domo.1998.dtud.12","url":null,"abstract":"The wavelet transform (WT) is a relatively useful and powerful technique in many applications, such as signal processing, pattern recognition, data compression, and so on.1-3 It overcomes the disadvantages of the Fourier transform and the Gabor transform, and provides an explicit representation of a signal in both space and frequency domains. Many configurations have been proposed to implement the wavelet transform, however, most of them are based on optical correlator. In this presentation, we present a new scheme to achieve the WT by a computer-generated hologram (CGH) based on the general theory of optical transform.4-6 The for determining the CGH is derived and a computer simulation is presented.","PeriodicalId":301804,"journal":{"name":"Diffractive Optics and Micro-Optics","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126838624","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Narrowband filters are important optical components that have numerous applications. Conventional interference narrowband filters suffers low peak efficiency due to the roughness of the film coatings especially the roughness of the spacer layers. The minimum linewidths of interference filters are typically 1 nm for the visible regime, while the peak efficiencies are less than 40%. Spectral stability of interference filters is poor because spacer layers absorb water vapors and cause shifting of the peak wavelength. Usually the coatings have to be sandwiched in between two substrates, which are then sealed along the side. In addition, narrowband interference filters are structure-complex; 60 layers are not uncommon for 1 nm interference filters. The large number of layers imposes great difficulty in the use of advanced film deposition techniques such as chemical vapor deposition (CVD) methods.
{"title":"Sub-nanometer linewidth resonant grating filters","authors":"Song Peng, G. Morris","doi":"10.1364/domo.1996.dwa.4","DOIUrl":"https://doi.org/10.1364/domo.1996.dwa.4","url":null,"abstract":"Narrowband filters are important optical components that have numerous applications. Conventional interference narrowband filters suffers low peak efficiency due to the roughness of the film coatings especially the roughness of the spacer layers. The minimum linewidths of interference filters are typically 1 nm for the visible regime, while the peak efficiencies are less than 40%. Spectral stability of interference filters is poor because spacer layers absorb water vapors and cause shifting of the peak wavelength. Usually the coatings have to be sandwiched in between two substrates, which are then sealed along the side. In addition, narrowband interference filters are structure-complex; 60 layers are not uncommon for 1 nm interference filters. The large number of layers imposes great difficulty in the use of advanced film deposition techniques such as chemical vapor deposition (CVD) methods.","PeriodicalId":301804,"journal":{"name":"Diffractive Optics and Micro-Optics","volume":"73 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127019740","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1364/domo.1996.jtub.8
P. Blattner, H. Herzig, K. Weible
The design of first, generation free space laser communication systems is based on laser diodes with output powers in the order of 100 mW [1]. The data rate transmission is in the order of 100 Mbit/s. This leads to terminals with large transmitter and receiver telescope diameters and, consequently, to high terminal mass and dimensions. The optical systems are usually designed with refractive lenses and reflective mirrors. Alternatives are planar diffractive optical elements (DOEs). By relying on diffraction and interference rather than on reflection and refraction, unique and novel properties can be realized. Almost any structure shape, including non–rotationally symmetric aspherics, can be manufactured, which provides all degrees of freedom for the design. Other interesting aspects of DOEs are their low weight, their strong dispersion, and the possibility to make segmented elements, large arrays of elements, beamsplitters, and polarizers. These properties are useful for many applications of DOEs in space, including: filters for image data processing [2], beam shaping [3, 4], and antireflection structures [5, 6]. Furthermore, the combination of refractive and diffractive surfaces (hybrid elements) offers new possibilities for optical design. The negative dispersion of DOEs can be used to compensate the chromatic aberrations of refractive lenses [7, 8]. Hybrid elements can also be used to compensate the temperature induced variations of their mounting system [9, 10]. Diffractive optical elements for space applications must comply with a number of requirements, including mechanical, thermal and optical stability [8]. Suitable techniques for realizing the microstructures in space qualified materials are based on a variety of high resolution lithographic and optical processes [11].
{"title":"Diffractive Optical Elements for Tracking and Receiving in Optical Space Communication Systems","authors":"P. Blattner, H. Herzig, K. Weible","doi":"10.1364/domo.1996.jtub.8","DOIUrl":"https://doi.org/10.1364/domo.1996.jtub.8","url":null,"abstract":"The design of first, generation free space laser communication systems is based on laser diodes with output powers in the order of 100 mW [1]. The data rate transmission is in the order of 100 Mbit/s. This leads to terminals with large transmitter and receiver telescope diameters and, consequently, to high terminal mass and dimensions. The optical systems are usually designed with refractive lenses and reflective mirrors. Alternatives are planar diffractive optical elements (DOEs). By relying on diffraction and interference rather than on reflection and refraction, unique and novel properties can be realized. Almost any structure shape, including non–rotationally symmetric aspherics, can be manufactured, which provides all degrees of freedom for the design. Other interesting aspects of DOEs are their low weight, their strong dispersion, and the possibility to make segmented elements, large arrays of elements, beamsplitters, and polarizers. These properties are useful for many applications of DOEs in space, including: filters for image data processing [2], beam shaping [3, 4], and antireflection structures [5, 6]. Furthermore, the combination of refractive and diffractive surfaces (hybrid elements) offers new possibilities for optical design. The negative dispersion of DOEs can be used to compensate the chromatic aberrations of refractive lenses [7, 8]. Hybrid elements can also be used to compensate the temperature induced variations of their mounting system [9, 10]. Diffractive optical elements for space applications must comply with a number of requirements, including mechanical, thermal and optical stability [8]. Suitable techniques for realizing the microstructures in space qualified materials are based on a variety of high resolution lithographic and optical processes [11].","PeriodicalId":301804,"journal":{"name":"Diffractive Optics and Micro-Optics","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114810350","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1364/domo.1998.dtha.5
M. Goto, M. Imanishi, F. Iwamuro, T. Maihara
The rapid progress of large format infrared detector arrays enables us to take a fairly wide spectrum with a medium resolution by a single exposure, if a coarsely grooved echelle-type grating can be used. To produce such a spectrum onto a square detector array, it is necessary to fabricate a grating with much larger groove separation than those used in visible spectroscopy, which has so far not been available. For instance, if we envision a spectrograph which produces an echelle spectrogram in the 3 to 4 microns, a realistic solution of spectrograph design would be to employ a large-groove grating usable in the orders ranging from 20-th to 30-th, or even higher. Of course, the width of such grooves is beyond the limit of the usual ruling method. We therefore attempted to produce a grating with a 125 μm groove scale by the high precision cutting of an Aluminum alloy directly with a diamond bite. In this report, we present the test result of the machine-cut grating, and make evaluation of the diffraction efficiency by referring to the result of a numerical simulation software. The grating is now incorporated in an astronomical spectrograph which works mainly in 3 μm region (Imanishi et al 1996).
大口径红外探测器阵列的迅速发展，使我们能够在一次曝光下，以中等分辨率获得相当宽的光谱，如果可以使用粗槽梯队型光栅。为了在方形探测器阵列上产生这样的光谱，有必要制造比可见光谱中使用的光栅具有更大的沟槽间距，这到目前为止还没有。例如，如果我们设想一个摄谱仪可以产生3到4微米的梯级光谱图，那么摄谱仪设计的一个现实的解决方案将是使用一个大凹槽光栅，可以在20到30微米的范围内使用，甚至更高。当然，这种凹槽的宽度超出了通常的统治方法的限制。因此，我们尝试用金刚石咬口直接对铝合金进行高精度切割，以生产具有125 μm凹槽尺度的光栅。在本报告中，我们给出了机切光栅的测试结果，并参考数值模拟软件的结果对其衍射效率进行了评价。目前，该光栅已应用于主要工作在3 μm区域的天文光谱仪中(Imanishi et al . 1996)。
{"title":"Evaluation of a diamond-cut large-groove grating for near infrared spectroscopy","authors":"M. Goto, M. Imanishi, F. Iwamuro, T. Maihara","doi":"10.1364/domo.1998.dtha.5","DOIUrl":"https://doi.org/10.1364/domo.1998.dtha.5","url":null,"abstract":"The rapid progress of large format infrared detector arrays enables us to take a fairly wide spectrum with a medium resolution by a single exposure, if a coarsely grooved echelle-type grating can be used. To produce such a spectrum onto a square detector array, it is necessary to fabricate a grating with much larger groove separation than those used in visible spectroscopy, which has so far not been available. For instance, if we envision a spectrograph which produces an echelle spectrogram in the 3 to 4 microns, a realistic solution of spectrograph design would be to employ a large-groove grating usable in the orders ranging from 20-th to 30-th, or even higher. Of course, the width of such grooves is beyond the limit of the usual ruling method. We therefore attempted to produce a grating with a 125 μm groove scale by the high precision cutting of an Aluminum alloy directly with a diamond bite. In this report, we present the test result of the machine-cut grating, and make evaluation of the diffraction efficiency by referring to the result of a numerical simulation software. The grating is now incorporated in an astronomical spectrograph which works mainly in 3 μm region (Imanishi et al 1996).","PeriodicalId":301804,"journal":{"name":"Diffractive Optics and Micro-Optics","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127671411","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1364/domo.1996.jtub.29
S. Song, Suntak Park, El-Hang Lee
We propose a planar integrated optics for Banyan-type 3-D multistage interconnection networks. Result of planar optical experiment on signal and clock beam combination is presented.
{"title":"Planar integrated optics for 3-D multistage interconnection networks","authors":"S. Song, Suntak Park, El-Hang Lee","doi":"10.1364/domo.1996.jtub.29","DOIUrl":"https://doi.org/10.1364/domo.1996.jtub.29","url":null,"abstract":"We propose a planar integrated optics for Banyan-type 3-D multistage interconnection networks. Result of planar optical experiment on signal and clock beam combination is presented.","PeriodicalId":301804,"journal":{"name":"Diffractive Optics and Micro-Optics","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126360068","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Diffractive micro-optical elements gained increasing interest for beam-shaping, e.g., the laser treatment of materials,1 and for illumination systems. The fabrication technologies for diffractive micro-optical elements bring in advance high accuracy and reproducibility, especially of the periodicity of the elements. In monochromatic applications, diffractive micro-optical elements are only restricted by the limits of the fabrication technology.
{"title":"Diffractive diffusers at the fabrication limit","authors":"H. Herzig, W. Singer","doi":"10.1364/domo.1996.jmc.5","DOIUrl":"https://doi.org/10.1364/domo.1996.jmc.5","url":null,"abstract":"Diffractive micro-optical elements gained increasing interest for beam-shaping, e.g., the laser treatment of materials,1 and for illumination systems. The fabrication technologies for diffractive micro-optical elements bring in advance high accuracy and reproducibility, especially of the periodicity of the elements. In monochromatic applications, diffractive micro-optical elements are only restricted by the limits of the fabrication technology.","PeriodicalId":301804,"journal":{"name":"Diffractive Optics and Micro-Optics","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127904793","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1364/domo.1998.dtud.3c
G. Karapetyan
Uniform Fiber Bragg Gratings are wavelength selective reflectors obtained by a periodic modulation of core refractive index along the fiber. They have many applications as narrow-band elements in optical fiber systems. Recently the NG are used for many purposes [1]. For their investigations the numerical solutions of coupled mode are used traditionally. This appoach requires a much machine time, and is not convenient for NG design. Therefore the analytical formulaes for characteristics of NG will be of benefit in NG design, syntezing, and optimization. The first step in solving this problem has been undertake in [2] where the WKB- approximation for solving coupled mode has been used. The drawback of this approximation is that it is not uniform in all frequency interval and is not valid near so called turning points. Then, an unknown phase shift occurs in formulaes which can not be determined within the WKB- approximation, and one needs to evaluate this unknown parameter from qualitative estimations. To avoide these drawbacks of WKB- approximation we elaborated another more suitable method which is valid uniformely in all frequency interval. This method, called R-approximation is the generalization of asymptotic solution of second order differential having one turning point [3] for the case when there are two or more turning points, in the result the analitical formulaes for characteristics of arbitrary NG obtained. R-approximtion is more exact and common than WKB-approximation. The last come to R-approximation by removal from turning points. As an uniform asymtotic formulaes R-approximation has a relative error ~ O(1/H) in all frequency interval, where H=πμN describes the gratings strength, μ-is the depth of effective permittivity modulation, N-is the number of grating periods (for uniform grating the maximum reflectivity is |R|2=th2(H/4)). On the basis of obtained common formulaes a special case of linearly chirped gratings (LCG) is investigated in detail and a designing software “LCG” is created. This software provides all characteristics of LCG versus strength, detuning, and chirping rate, and is a powerfull and convinient tool for designers.
{"title":"New Theoretical Method For Nonuniform Gratings Investigation","authors":"G. Karapetyan","doi":"10.1364/domo.1998.dtud.3c","DOIUrl":"https://doi.org/10.1364/domo.1998.dtud.3c","url":null,"abstract":"Uniform Fiber Bragg Gratings are wavelength selective reflectors obtained by a periodic modulation of core refractive index along the fiber. They have many applications as narrow-band elements in optical fiber systems. Recently the NG are used for many purposes [1]. For their investigations the numerical solutions of coupled mode are used traditionally. This appoach requires a much machine time, and is not convenient for NG design. Therefore the analytical formulaes for characteristics of NG will be of benefit in NG design, syntezing, and optimization. The first step in solving this problem has been undertake in [2] where the WKB- approximation for solving coupled mode has been used. The drawback of this approximation is that it is not uniform in all frequency interval and is not valid near so called turning points. Then, an unknown phase shift occurs in formulaes which can not be determined within the WKB- approximation, and one needs to evaluate this unknown parameter from qualitative estimations. To avoide these drawbacks of WKB- approximation we elaborated another more suitable method which is valid uniformely in all frequency interval. This method, called R-approximation is the generalization of asymptotic solution of second order differential having one turning point [3] for the case when there are two or more turning points, in the result the analitical formulaes for characteristics of arbitrary NG obtained. R-approximtion is more exact and common than WKB-approximation. The last come to R-approximation by removal from turning points. As an uniform asymtotic formulaes R-approximation has a relative error ~ O(1/H) in all frequency interval, where H=πμN describes the gratings strength, μ-is the depth of effective permittivity modulation, N-is the number of grating periods (for uniform grating the maximum reflectivity is |R|2=th2(H/4)). On the basis of obtained common formulaes a special case of linearly chirped gratings (LCG) is investigated in detail and a designing software “LCG” is created. This software provides all characteristics of LCG versus strength, detuning, and chirping rate, and is a powerfull and convinient tool for designers.","PeriodicalId":301804,"journal":{"name":"Diffractive Optics and Micro-Optics","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130048573","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：