{"corpus_id":122778100,"paper_sha":"757bca928e5ed93357bee68e14690057ccbe86d3","doi":"10.1103/PHYSREV.128.1761","arxiv_id":null,"pmid":null,"pmcid":null,"mag_id":2072758696,"dblp_id":null,"acl_id":null,"title":"Theory of Second Harmonic Generation of Light","year":1962,"publication_date":"1962-11-15","venue":"","journal":{"name":"Physical Review","pages":"1761-1775","volume":"128"},"journal_issn":null,"journal_title":null,"publication_types":[],"pubmed_pub_types":null,"s2_fields_of_study":["Physics"],"reference_count":0,"citation_count":266,"influential_citation_count":4,"is_open_access":false,"arxiv_categories":null,"arxiv_license":null,"arxiv_journal_ref":null,"mesh_headings":null,"chemicals":null,"comments_corrections":null,"source_flags":1,"s2_open_access_pdf_url":null,"s2_open_access_landing_url":null,"s2_open_access_license":null,"s2_open_access_status":null,"pmc_open_access_pdf_url":null,"pmc_open_access_landing_url":null,"pmc_open_access_license":null,"pmc_open_access_status":null,"unpaywall_open_access_pdf_url":null,"unpaywall_open_access_landing_url":null,"unpaywall_open_access_license":null,"unpaywall_open_access_status":null,"abstract":"A theory is given for the generation of second harmonic light in crystals analogous to the classical theory of crystal optics. Optical activity and absorption are neglected, but the anisotropy is treated rigorously. An approximate treatment is also given, valid for most crystals, which retains the essential effects of the anisotropy and neglects the minor effects. All coherence effects are treated exactly, and special attention is given to the case of index matching. An exact solution is given for the second harmonic waves produced in and outside the medium when the fundamental beam enters the medium at a plane surface. A brief discussion is given of the effects of the finite aperture of the beam. The theory is applied to recent experiments on KDP and quartz, and values are given for the second-order polarization coefficients of these materials. Finally, the theory is given for second harmonic generation by focused beams based upon the diffraction theory of an ideal focus.","claims":[{"public_id":"cl_3bb123f98ce02456019dd6890f277d00","status":"active","text":"A theory for second harmonic generation by focused beams is developed based on the diffraction theory of an ideal focus.","confidence":0.9,"contributors":[{"id":171,"public_id":"b9tnx83g25","public_label":"eunsjani (b9tnx83g25)","roles":["extraction"],"url":"https://sah.borca.ai/u/b9tnx83g25"},{"id":2,"public_id":"4715169a40","public_label":"AK (4715169a40)","roles":["review"],"url":"https://sah.borca.ai/u/4715169a40"},{"id":17,"public_id":"322360f1c1","public_label":"Killer Whale (322360f1c1)","roles":["review"],"url":"https://sah.borca.ai/u/322360f1c1"}],"url":"https://sah.borca.ai/claims/cl_3bb123f98ce02456019dd6890f277d00"},{"public_id":"cl_6901e69dab956afec698f2d4eaacfd5b","status":"active","text":"A theory for second harmonic generation in anisotropic crystals is developed that treats anisotropy rigorously and all coherence effects exactly, while neglecting optical activity and absorption.","confidence":0.95,"contributors":[{"id":171,"public_id":"b9tnx83g25","public_label":"eunsjani (b9tnx83g25)","roles":["extraction"],"url":"https://sah.borca.ai/u/b9tnx83g25"},{"id":2,"public_id":"4715169a40","public_label":"AK (4715169a40)","roles":["review"],"url":"https://sah.borca.ai/u/4715169a40"},{"id":17,"public_id":"322360f1c1","public_label":"Killer Whale (322360f1c1)","roles":["review"],"url":"https://sah.borca.ai/u/322360f1c1"}],"url":"https://sah.borca.ai/claims/cl_6901e69dab956afec698f2d4eaacfd5b"},{"public_id":"cl_6d9564bbb9d92897eadb463db8a1f38c","status":"active","text":"An approximate treatment valid for most crystals is derived that retains the essential effects of anisotropy and neglects the minor effects.","confidence":0.9,"contributors":[{"id":171,"public_id":"b9tnx83g25","public_label":"eunsjani (b9tnx83g25)","roles":["extraction"],"url":"https://sah.borca.ai/u/b9tnx83g25"},{"id":2,"public_id":"4715169a40","public_label":"AK (4715169a40)","roles":["review"],"url":"https://sah.borca.ai/u/4715169a40"},{"id":17,"public_id":"322360f1c1","public_label":"Killer Whale (322360f1c1)","roles":["review"],"url":"https://sah.borca.ai/u/322360f1c1"}],"url":"https://sah.borca.ai/claims/cl_6d9564bbb9d92897eadb463db8a1f38c"},{"public_id":"cl_33354a8df38c715f913c83447c7cc3ba","status":"active","text":"An exact solution is given for the second harmonic waves produced in and outside the medium when the fundamental beam enters the medium at a plane surface.","confidence":0.95,"contributors":[{"id":171,"public_id":"b9tnx83g25","public_label":"eunsjani (b9tnx83g25)","roles":["extraction"],"url":"https://sah.borca.ai/u/b9tnx83g25"},{"id":2,"public_id":"4715169a40","public_label":"AK (4715169a40)","roles":["review"],"url":"https://sah.borca.ai/u/4715169a40"},{"id":17,"public_id":"322360f1c1","public_label":"Killer Whale (322360f1c1)","roles":["review"],"url":"https://sah.borca.ai/u/322360f1c1"}],"url":"https://sah.borca.ai/claims/cl_33354a8df38c715f913c83447c7cc3ba"},{"public_id":"cl_ed8887384aa2d56cb9a9de62e7c854fe","status":"active","text":"Applying the theory to KDP and quartz yields values for the second-order polarization coefficients of these materials.","confidence":0.95,"contributors":[{"id":171,"public_id":"b9tnx83g25","public_label":"eunsjani (b9tnx83g25)","roles":["extraction"],"url":"https://sah.borca.ai/u/b9tnx83g25"},{"id":2,"public_id":"4715169a40","public_label":"AK (4715169a40)","roles":["review"],"url":"https://sah.borca.ai/u/4715169a40"},{"id":17,"public_id":"322360f1c1","public_label":"Killer Whale (322360f1c1)","roles":["review"],"url":"https://sah.borca.ai/u/322360f1c1"}],"url":"https://sah.borca.ai/claims/cl_ed8887384aa2d56cb9a9de62e7c854fe"}],"concepts":[{"public_id":"co_0769f80e1660a75527d06b53c82b5afb","status":"active","name":"second harmonic generation","description":"The nonlinear optical process by which crystals generate light at twice the frequency of the incident fundamental beam.","types":["phenomenon","method"],"aliases":["SHG"],"contributors":[{"id":171,"public_id":"b9tnx83g25","public_label":"eunsjani (b9tnx83g25)","roles":["extraction"],"url":"https://sah.borca.ai/u/b9tnx83g25"},{"id":2,"public_id":"4715169a40","public_label":"AK (4715169a40)","roles":["review"],"url":"https://sah.borca.ai/u/4715169a40"},{"id":17,"public_id":"322360f1c1","public_label":"Killer Whale (322360f1c1)","roles":["review"],"url":"https://sah.borca.ai/u/322360f1c1"}],"url":"https://sah.borca.ai/concepts/co_0769f80e1660a75527d06b53c82b5afb"},{"public_id":"co_1f344f7bf9f0ec1ef5a8b55a4e280ca8","status":"active","name":"focused beams","description":"Converging laser beam geometry for which a separate second harmonic generation theory is derived using diffraction theory.","types":["configuration"],"aliases":[],"contributors":[{"id":171,"public_id":"b9tnx83g25","public_label":"eunsjani (b9tnx83g25)","roles":["extraction"],"url":"https://sah.borca.ai/u/b9tnx83g25"},{"id":2,"public_id":"4715169a40","public_label":"AK (4715169a40)","roles":["review"],"url":"https://sah.borca.ai/u/4715169a40"},{"id":17,"public_id":"322360f1c1","public_label":"Killer Whale (322360f1c1)","roles":["review"],"url":"https://sah.borca.ai/u/322360f1c1"}],"url":"https://sah.borca.ai/concepts/co_1f344f7bf9f0ec1ef5a8b55a4e280ca8"},{"public_id":"co_26167a44b2bd6ead6408fd491c5c2b4b","status":"active","name":"diffraction theory of an ideal focus","description":"The wave-optics framework describing the focusing of a beam to an ideal focal point, used as the basis for the focused-beam SHG theory.","types":["theoretical framework"],"aliases":[],"contributors":[{"id":171,"public_id":"b9tnx83g25","public_label":"eunsjani (b9tnx83g25)","roles":["extraction"],"url":"https://sah.borca.ai/u/b9tnx83g25"},{"id":2,"public_id":"4715169a40","public_label":"AK (4715169a40)","roles":["review"],"url":"https://sah.borca.ai/u/4715169a40"},{"id":17,"public_id":"322360f1c1","public_label":"Killer Whale (322360f1c1)","roles":["review"],"url":"https://sah.borca.ai/u/322360f1c1"}],"url":"https://sah.borca.ai/concepts/co_26167a44b2bd6ead6408fd491c5c2b4b"},{"public_id":"co_26204c19923a443073fadc043e587c70","status":"active","name":"anisotropy","description":"The directional dependence of optical properties in crystals, treated rigorously in the developed theory.","types":["physical property"],"aliases":[],"contributors":[{"id":171,"public_id":"b9tnx83g25","public_label":"eunsjani (b9tnx83g25)","roles":["extraction"],"url":"https://sah.borca.ai/u/b9tnx83g25"},{"id":2,"public_id":"4715169a40","public_label":"AK (4715169a40)","roles":["review"],"url":"https://sah.borca.ai/u/4715169a40"},{"id":17,"public_id":"322360f1c1","public_label":"Killer Whale (322360f1c1)","roles":["review"],"url":"https://sah.borca.ai/u/322360f1c1"}],"url":"https://sah.borca.ai/concepts/co_26204c19923a443073fadc043e587c70"},{"public_id":"co_433aeb8d47907d39c77d29648a597b3c","status":"active","name":"quartz","description":"A crystalline material to which the theory is applied alongside KDP to extract second-order polarization coefficients.","types":["material"],"aliases":[],"contributors":[{"id":171,"public_id":"b9tnx83g25","public_label":"eunsjani (b9tnx83g25)","roles":["extraction"],"url":"https://sah.borca.ai/u/b9tnx83g25"},{"id":2,"public_id":"4715169a40","public_label":"AK (4715169a40)","roles":["review"],"url":"https://sah.borca.ai/u/4715169a40"},{"id":17,"public_id":"322360f1c1","public_label":"Killer Whale (322360f1c1)","roles":["review"],"url":"https://sah.borca.ai/u/322360f1c1"}],"url":"https://sah.borca.ai/concepts/co_433aeb8d47907d39c77d29648a597b3c"},{"public_id":"co_4aad29242824c2966e24a46129ff60b7","status":"active","name":"index matching","description":"The condition in which the phase velocities of the fundamental and second harmonic waves are equal, given special treatment in the theory.","types":["phenomenon"],"aliases":["phase matching"],"contributors":[{"id":171,"public_id":"b9tnx83g25","public_label":"eunsjani (b9tnx83g25)","roles":["extraction"],"url":"https://sah.borca.ai/u/b9tnx83g25"},{"id":2,"public_id":"4715169a40","public_label":"AK (4715169a40)","roles":["review"],"url":"https://sah.borca.ai/u/4715169a40"},{"id":17,"public_id":"322360f1c1","public_label":"Killer Whale (322360f1c1)","roles":["review"],"url":"https://sah.borca.ai/u/322360f1c1"}],"url":"https://sah.borca.ai/concepts/co_4aad29242824c2966e24a46129ff60b7"},{"public_id":"co_6ced1851378274e8ea3f121360531e82","status":"active","name":"second-order polarization coefficients","description":"Material parameters that quantify the nonlinear optical response of a crystal at second order, measured here for KDP and quartz.","types":["material parameter"],"aliases":[],"contributors":[{"id":171,"public_id":"b9tnx83g25","public_label":"eunsjani (b9tnx83g25)","roles":["extraction"],"url":"https://sah.borca.ai/u/b9tnx83g25"},{"id":2,"public_id":"4715169a40","public_label":"AK (4715169a40)","roles":["review"],"url":"https://sah.borca.ai/u/4715169a40"},{"id":17,"public_id":"322360f1c1","public_label":"Killer Whale (322360f1c1)","roles":["review"],"url":"https://sah.borca.ai/u/322360f1c1"}],"url":"https://sah.borca.ai/concepts/co_6ced1851378274e8ea3f121360531e82"},{"public_id":"co_84e1ddd6f84c8fb7bbf5e884b3c8a15d","status":"active","name":"optical activity","description":"The rotation of the polarization state of light by chiral media, explicitly neglected in the developed theory.","types":["phenomenon"],"aliases":[],"contributors":[{"id":171,"public_id":"b9tnx83g25","public_label":"eunsjani (b9tnx83g25)","roles":["extraction"],"url":"https://sah.borca.ai/u/b9tnx83g25"},{"id":2,"public_id":"4715169a40","public_label":"AK (4715169a40)","roles":["review"],"url":"https://sah.borca.ai/u/4715169a40"},{"id":17,"public_id":"322360f1c1","public_label":"Killer Whale (322360f1c1)","roles":["review"],"url":"https://sah.borca.ai/u/322360f1c1"}],"url":"https://sah.borca.ai/concepts/co_84e1ddd6f84c8fb7bbf5e884b3c8a15d"},{"public_id":"co_892b07e201ec17bedf5a468cd0c1ff97","status":"active","name":"KDP","description":"A nonlinear optical crystal to which the developed second harmonic generation theory is applied and for which polarization coefficients are reported.","types":["material"],"aliases":[],"contributors":[{"id":171,"public_id":"b9tnx83g25","public_label":"eunsjani (b9tnx83g25)","roles":["extraction"],"url":"https://sah.borca.ai/u/b9tnx83g25"},{"id":2,"public_id":"4715169a40","public_label":"AK (4715169a40)","roles":["review"],"url":"https://sah.borca.ai/u/4715169a40"},{"id":17,"public_id":"322360f1c1","public_label":"Killer Whale (322360f1c1)","roles":["review"],"url":"https://sah.borca.ai/u/322360f1c1"}],"url":"https://sah.borca.ai/concepts/co_892b07e201ec17bedf5a468cd0c1ff97"},{"public_id":"co_9bac8b65f8a8081b6d47ef5ffdcb6033","status":"active","name":"fundamental beam","description":"The input light beam at the original frequency that enters the crystal and drives second harmonic generation.","types":["physical entity"],"aliases":[],"contributors":[{"id":171,"public_id":"b9tnx83g25","public_label":"eunsjani (b9tnx83g25)","roles":["extraction"],"url":"https://sah.borca.ai/u/b9tnx83g25"},{"id":2,"public_id":"4715169a40","public_label":"AK (4715169a40)","roles":["review"],"url":"https://sah.borca.ai/u/4715169a40"},{"id":17,"public_id":"322360f1c1","public_label":"Killer Whale (322360f1c1)","roles":["review"],"url":"https://sah.borca.ai/u/322360f1c1"}],"url":"https://sah.borca.ai/concepts/co_9bac8b65f8a8081b6d47ef5ffdcb6033"},{"public_id":"co_9e8eb8ea1dc800cff35a32df1799a6e7","status":"active","name":"crystal optics","description":"The classical theoretical framework for describing light propagation in anisotropic optical crystals, used here as the analogy for the developed theory.","types":["theoretical framework"],"aliases":[],"contributors":[{"id":171,"public_id":"b9tnx83g25","public_label":"eunsjani (b9tnx83g25)","roles":["extraction"],"url":"https://sah.borca.ai/u/b9tnx83g25"},{"id":2,"public_id":"4715169a40","public_label":"AK (4715169a40)","roles":["review"],"url":"https://sah.borca.ai/u/4715169a40"},{"id":17,"public_id":"322360f1c1","public_label":"Killer Whale (322360f1c1)","roles":["review"],"url":"https://sah.borca.ai/u/322360f1c1"}],"url":"https://sah.borca.ai/concepts/co_9e8eb8ea1dc800cff35a32df1799a6e7"},{"public_id":"co_b29290ab15d504ce5bf7daf1b5dbb3c1","status":"active","name":"coherence effects","description":"Phase relationship effects between the fundamental and harmonic waves that determine constructive or destructive interference in the output.","types":["phenomenon"],"aliases":[],"contributors":[{"id":171,"public_id":"b9tnx83g25","public_label":"eunsjani (b9tnx83g25)","roles":["extraction"],"url":"https://sah.borca.ai/u/b9tnx83g25"},{"id":2,"public_id":"4715169a40","public_label":"AK (4715169a40)","roles":["review"],"url":"https://sah.borca.ai/u/4715169a40"},{"id":17,"public_id":"322360f1c1","public_label":"Killer Whale (322360f1c1)","roles":["review"],"url":"https://sah.borca.ai/u/322360f1c1"}],"url":"https://sah.borca.ai/concepts/co_b29290ab15d504ce5bf7daf1b5dbb3c1"},{"public_id":"co_c9e21e6c8ce2b53bff7b061ae0acb8c5","status":"active","name":"plane surface","description":"A flat interface at which the fundamental beam enters the nonlinear crystal medium, used as the boundary condition for the exact solution.","types":["boundary condition"],"aliases":[],"contributors":[{"id":171,"public_id":"b9tnx83g25","public_label":"eunsjani (b9tnx83g25)","roles":["extraction"],"url":"https://sah.borca.ai/u/b9tnx83g25"},{"id":2,"public_id":"4715169a40","public_label":"AK (4715169a40)","roles":["review"],"url":"https://sah.borca.ai/u/4715169a40"},{"id":17,"public_id":"322360f1c1","public_label":"Killer Whale (322360f1c1)","roles":["review"],"url":"https://sah.borca.ai/u/322360f1c1"}],"url":"https://sah.borca.ai/concepts/co_c9e21e6c8ce2b53bff7b061ae0acb8c5"}],"external_ids":{"DOI":"10.1103/PHYSREV.128.1761","ArXiv":null,"PubMed":null,"PubMedCentral":null,"MAG":2072758696,"DBLP":null,"ACL":null},"open_access":{"is_open_access":false,"pdf_url":null,"landing_url":"https://sah.borca.ai/papers/122778100","source":null,"pdf_url_source":null,"license":null,"reason":"pdf_url_not_indexed"},"reference_availability":{"status":"unknown","references_indexed":false,"full_text_available":false,"full_text_source":null,"count_basis":"semantic_scholar_metadata","extraction_status":"not_applicable","reason":null},"source":{"provider":"episteme2","base_corpus":"semantic_scholar_dump","freshness_mode":"unknown","basis":["semantic_scholar_metadata","postgres_metadata"],"limits":["paper metadata is based on indexed upstream scholarly datasets","claims and concepts are available only for extracted papers","absence of claims or concepts means no extracted graph data is available in this response"],"status":"available","degraded":false,"degraded_reasons":[],"diagnostics":{"status":"available","degraded":false,"degraded_reasons":[],"metadata_status":"available","graph_status":"available","abstract_status":"available"},"source_flags":1},"paper_id":631368,"paper_uid":"75d69842-45e4-4c28-883c-0e98d82704ec","canonical_identity":{"paper_id":631368,"paper_uid":"75d69842-45e4-4c28-883c-0e98d82704ec","identity_status":"available","lookup_basis":"semantic_scholar_external_id","compatibility_path":"corpus_id"},"url":"https://sah.borca.ai/papers/122778100"}