{"created":"2023-06-19T10:30:13.538136+00:00","id":10446,"links":{},"metadata":{"_buckets":{"deposit":"fb3763d4-4ee2-40fb-af4a-b0935cb3f499"},"_deposit":{"created_by":18,"id":"10446","owners":[18],"pid":{"revision_id":0,"type":"depid","value":"10446"},"status":"published"},"_oai":{"id":"oai:muroran-it.repo.nii.ac.jp:00010446","sets":["41:227"]},"author_link":["58500"],"item_81_date_granted_17":{"attribute_name":"学位授与年月日","attribute_value_mlt":[{"subitem_dategranted":"2021-03-23"}]},"item_81_degree_grantor_10":{"attribute_name":"学位授与機関","attribute_value_mlt":[{"subitem_degreegrantor":[{"subitem_degreegrantor_language":"ja","subitem_degreegrantor_name":"室蘭工業大学"},{"subitem_degreegrantor_language":"en","subitem_degreegrantor_name":"Muroran Institute of Technology"}],"subitem_degreegrantor_identifier":[{"subitem_degreegrantor_identifier_name":"10103","subitem_degreegrantor_identifier_scheme":"kakenhi"}]}]},"item_81_degree_name_11":{"attribute_name":"学位名","attribute_value_mlt":[{"subitem_degreename":"博士（工学）","subitem_degreename_language":"ja"}]},"item_81_description_25":{"attribute_name":"フォーマット","attribute_value_mlt":[{"subitem_description":"application/pdf","subitem_description_type":"Other"}]},"item_81_description_7":{"attribute_name":"抄録","attribute_value_mlt":[{"subitem_description":"光ファイバの断面構造設計には，自動最適化技術が不可欠である．構造最適化は，目的関数を最小化する構造変数の組み合わせを自動で探索することで実施する．構造探索時に目的関数を多数回計算するため，目的関数の算出に用いる分散特性の計算が高速でなければ，実用的な時間で最適化することが困難となる．例えば，群速度ならびに群速度分散であれば，電磁界解析により得られた伝搬定数を波長に関して 1 階微分， 2 階微分することで求まる．伝搬定数算出には，有限差分法や有限要素法に基づく市販の電磁界シミュレータが利用できる．通常は，百万程 度の自由度を有する一般化固有値問題に帰着させる有限要素解析(FEA)を行う．この求めた伝搬定数の微分値は，数値微分である差分法，固有値問題から導いた超越方程式を陰関数定理に基づき微分する方法で算出する．差分法は，複数の波長における位相速度値から多項式補間により微分値を計算するものであり，容易に計算できる．しかしながら，適切な差分間隔が，求める微分値よりも高次の微分値から定まるため，多数の位相速度計算値を用いて差分間隔を決定する必要がある．他方，陰関数定理に基づく方法では，行列式の微分を用いると計算時間が長くなり，左固有ベクトルを用いて超越方程式を導出すると 2 階微分に固有ベクトルの微分が必要となる．このように伝搬定数の微分値計算には，未だ課題が残されていた．一方，Trefftz法を電磁界解析に適用したMultipole Method(MM) は，波動関数を補間関数とするため高精度の位相速度値が求まることが期待でき，同程度の精度のFEAと比較すると，固有値問題の係数行列の次元が小さくなるため，Sakurai Sugiura法 (SSM) により高速に計算可能である．しかしながら，波動関数展開の展開次数を大きくすると電磁界解析精度が低下する問題があった．またSSMに起因するスプリアス解を含んだ位相定数が求まるので，スプリアス解を判別除去する必要がある．さらに MM では，円柱ならびに楕円柱を含む断面構造しか扱えなかった．本論文は，光ファイバの自動最適化設計を目的として，SSMを用いた光ファイバの高速高精度な分散特性解析法について取り纏めたものである．まず伝搬定数の微分値計算法として，SSMにより得た4行4列以下の一般化固有値問題から4次以下の代数方程式を導き，固有値を周波数に関する陽関数として表現し，自動微分を適用することで微分値を得る方法を開発した．またMMの問題点を解消するために，定式化を変更し，波動関数展開の展開次数の増加に伴う精度低下の軽減に成功した．さらにSSMの解に含まれるスプリアス解は，低計算コストである固有値の条件数により，判別除去できることを示した．従来のTrefftz法に課されていた形状の制約を取り除くため，ハイブリッドトレフツ有限要素法にSSMを適用する伝搬特性解析法を開発した．これらの妥当性と有用性は，円や楕円空孔，環状型空孔を有するホーリーファイバの数値解析例により示した．","subitem_description_language":"ja","subitem_description_type":"Abstract"},{"subitem_description":"For optimizing profiles of optical fibers by solving an optimization problem with an objective function including propagation constants, group velocities, or group velocity dispersions, fast and precise numerical methods are required for computing these propagation characteristics. Trefftz methods including the transfer matrix method and the multipole method for computing propagation constants are attractive for designing simple profile of optical fibers due to the advantage of being inherent mesh-free nature and easy imposing the radiation-condition on the guided electromagnetic fields without artificial medium surrounding the cladding over the finite-element method and finite-difference time-domain method. However, four improvements of the Trefftz method were required: (1) there is no fast and precise scheme for computing the differential coefficients of degenerate and nondegenerate propagation constants computed by the Trefftz methods, (2) upper and lower limits of the Fourier-Bessel expansions for the wavefunctions employed in the Trefftz methods may be small for accurately approximating the fields in the complex profile, (3) the Trefftz methods employ the wave-functions for approximating electromagnetic wave fields cannot apply to complex profiles with inhomogeneous media, and (4) because the Sakurai-Sugiura method (SSM) inherently includes spurious solutions of the nonlinear eigenvalue-problem, the low coast criteria in computation for sorting the eigenvalues from results by the SS method was not known . This thesis presented solutions for overcoming above problems of Trefftz method analysis with the SSM solver as follows: (1) a fast and precise scheme to compute the differential coefficients of propagation constants for computing group velocities and group velocity dispersions by making up the explicit forms of eigenvalues from a generalized eigenvalue problem converted from a nonlinear eigenvalue problem given by the Trefftz methods employing the SSM, (2) a refined formulation of the multipole method for relaxing the upper and lower limitations of the number of Fourier-Bessel expansions of electromagnetic fields in optical fibers, (3) a solution based on the hybrid Trefftz finite element method employing the SSM as a nonlinear eigenvalue solver for analyzing complex profiles of photonic optical fibers, and (4) a criterion for selecting the spurious solutions from the eigenvalues computed by the SSM. Numerical results of step-index and holey fibers with circular, elliptic, and ring-shaped cylinders showed that developed solutions remove the problems of the Trefftz methods.","subitem_description_language":"en","subitem_description_type":"Abstract"}]},"item_81_dissertation_number_13":{"attribute_name":"学位授与番号","attribute_value_mlt":[{"subitem_dissertationnumber":"甲第460号"}]},"item_81_identifier_registration":{"attribute_name":"ID登録","attribute_value_mlt":[{"subitem_identifier_reg_text":"10.15118/00010385","subitem_identifier_reg_type":"JaLC"}]},"item_81_subject_9":{"attribute_name":"日本十進分類法","attribute_value_mlt":[{"subitem_subject":"501","subitem_subject_scheme":"NDC"}]},"item_81_text_12":{"attribute_name":"学位の種別","attribute_value_mlt":[{"subitem_text_language":"ja","subitem_text_value":"課程博士"}]},"item_81_text_14":{"attribute_name":"報告番号","attribute_value_mlt":[{"subitem_text_language":"ja","subitem_text_value":"甲第460号"}]},"item_81_text_15":{"attribute_name":"学位記番号","attribute_value_mlt":[{"subitem_text_language":"ja","subitem_text_value":"博甲第460号"}]},"item_81_text_16":{"attribute_name":"研究科・専攻","attribute_value_mlt":[{"subitem_text_language":"ja","subitem_text_value":"工学専攻"}]},"item_81_version_type_24":{"attribute_name":"著者版フラグ","attribute_value_mlt":[{"subitem_version_resource":"http://purl.org/coar/version/c_970fb48d4fbd8a85","subitem_version_type":"VoR"}]},"item_access_right":{"attribute_name":"アクセス権","attribute_value_mlt":[{"subitem_access_right":"open access","subitem_access_right_uri":"http://purl.org/coar/access_right/c_abf2"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorAffiliations":[{"affiliationNameIdentifiers":[],"affiliationNames":[{"affiliationName":""}]}],"creatorNames":[{"creatorName":"對馬, 康雄","creatorNameLang":"ja"},{"creatorName":"TSUSHIMA, Yasuo","creatorNameLang":"en"},{"creatorName":"ツシマ, ヤスオ","creatorNameLang":"ja-Kana"}],"familyNames":[{},{},{}],"givenNames":[{},{},{}],"nameIdentifiers":[{}]}]},"item_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2021-06-23"}],"displaytype":"detail","filename":"A460.pdf","filesize":[{"value":"5.4 MB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"A460","objectType":"fulltext","url":"https://muroran-it.repo.nii.ac.jp/record/10446/files/A460.pdf"},"version_id":"2aea7672-1137-459e-93a2-d6b877859fce"},{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2021-06-23"}],"displaytype":"detail","filename":"A460_summary.pdf","filesize":[{"value":"285.3 kB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"A460_summary","objectType":"abstract","url":"https://muroran-it.repo.nii.ac.jp/record/10446/files/A460_summary.pdf"},"version_id":"eed1da30-34aa-472b-8c05-da30f62c2264"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"jpn"}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourcetype":"doctoral thesis","resourceuri":"http://purl.org/coar/resource_type/c_db06"}]},"item_title":"Sakurai-Sugiura法を用いた光ファイバの分散特性の高速高精度解析に関する研究","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"Sakurai-Sugiura法を用いた光ファイバの分散特性の高速高精度解析に関する研究","subitem_title_language":"ja"}]},"item_type_id":"81","owner":"18","path":["227"],"pubdate":{"attribute_name":"PubDate","attribute_value":"2021-06-23"},"publish_date":"2021-06-23","publish_status":"0","recid":"10446","relation_version_is_last":true,"title":["Sakurai-Sugiura法を用いた光ファイバの分散特性の高速高精度解析に関する研究"],"weko_creator_id":"18","weko_shared_id":-1},"updated":"2024-01-22T01:59:07.173768+00:00"}