{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:T66O2YRLHAV4ES2OFSMCE36WWR","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"316a02b471a1c5fb7c62d31d9a36a9f74d7ccfced061f374e082c548b1adb86a","cross_cats_sorted":["physics.optics"],"license":"","primary_cat":"physics.comp-ph","submitted_at":"2003-07-30T11:36:58Z","title_canon_sha256":"4b730f73ed6fcff01f18163b6a31eb661c276c3524c9a46e00e0c0f7d613d576"},"schema_version":"1.0","source":{"id":"physics/0307150","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"physics/0307150","created_at":"2026-05-18T03:24:21Z"},{"alias_kind":"arxiv_version","alias_value":"physics/0307150v1","created_at":"2026-05-18T03:24:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.physics/0307150","created_at":"2026-05-18T03:24:21Z"},{"alias_kind":"pith_short_12","alias_value":"T66O2YRLHAV4","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"T66O2YRLHAV4ES2O","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"T66O2YRL","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:d5029fb046413c31b6819b0c5b7adae8c98110cac05362283fb71b9919679da1","target":"graph","created_at":"2026-05-18T03:24:21Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We propose a method derived from the simple plane wave expansion that can easily solve the interface problem between vacuum and a semi-infinite photonic crystal. The method is designed to find the complete set of all the eigenfunctions, propagating or evanescent, of the translation operators $\\{{\\bf T_R} \\}$, at a fixed frequency. With these eigenfunctions and their eigenvalues, the transmitted and reflected waves can be determined. Two kinds of applications are presented for 2D photonic crystals. The first is a selection rule for determine the normal direction of the vacuum-photonic crystal i","authors_text":"Tzong-Jer Yang, Young-Chung Hsue","cross_cats":["physics.optics"],"headline":"","license":"","primary_cat":"physics.comp-ph","submitted_at":"2003-07-30T11:36:58Z","title":"A novel view of plane wave expansion method in photonic crystals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"physics/0307150","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:19bc1e3f7d152bcdeece22c85499de0f457a259da5dd5a580a67c9bc5cbc4240","target":"record","created_at":"2026-05-18T03:24:21Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"316a02b471a1c5fb7c62d31d9a36a9f74d7ccfced061f374e082c548b1adb86a","cross_cats_sorted":["physics.optics"],"license":"","primary_cat":"physics.comp-ph","submitted_at":"2003-07-30T11:36:58Z","title_canon_sha256":"4b730f73ed6fcff01f18163b6a31eb661c276c3524c9a46e00e0c0f7d613d576"},"schema_version":"1.0","source":{"id":"physics/0307150","kind":"arxiv","version":1}},"canonical_sha256":"9fbced622b382bc24b4e2c98226fd6b45a322dd7934eb7faeaea19bf7a3b4dae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9fbced622b382bc24b4e2c98226fd6b45a322dd7934eb7faeaea19bf7a3b4dae","first_computed_at":"2026-05-18T03:24:21.013005Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:24:21.013005Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5s5yKRzg7d0ChfTxc4gY1EXmaYSg+I0gLz+/+QFQolZDktsxPApGSV/Uklxj+w/utpM2Ir9jTwcVQZoXiCUgBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:24:21.013807Z","signed_message":"canonical_sha256_bytes"},"source_id":"physics/0307150","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:19bc1e3f7d152bcdeece22c85499de0f457a259da5dd5a580a67c9bc5cbc4240","sha256:d5029fb046413c31b6819b0c5b7adae8c98110cac05362283fb71b9919679da1"],"state_sha256":"6e7219cd1a34724282f51574616d2763436a9b94a9fc660092969a049b005e6f"}