{"uid":"cap_H-pfsOIozwnqF-Vvpq3M3","slug":"rectangular-pec-waveguide-complete-te-tm-complex-modal-fields-0b0d0acd","name":"Rectangular PEC Waveguide Complete TE/TM Complex Modal Fields","description":"Resolve complete propagating or evanescent electromagnetic mode fields of a supplied ideal guide.","url":"https://detect.halowerk.com/v1/F-TD2000-GEO-INDUSTRY-B009/rectangular-pec-waveguide-complete-te-tm-complex-modal-fields?utm_source=zero.xyz","method":"POST","headers":{},"bodySchema":{"type":"object","properties":{"artifact":{"type":"object","required":["waveguide"],"properties":{"waveguide":{"type":"object","required":["data","claim"],"properties":{"data":{"type":"object","required":["width","height","frequency_hz","relative_permittivity","relative_permeability","modes","queries"],"properties":{"modes":{"type":"array","items":{"type":"object","required":["type","m","n"],"properties":{"m":{"type":"integer","maximum":8,"minimum":0},"n":{"type":"integer","maximum":8,"minimum":0},"type":{"enum":["TE","TM"]}},"additionalProperties":false},"maxItems":8,"minItems":1},"width":{"type":"number","maximum":100,"minimum":0.000001},"height":{"type":"number","maximum":100,"minimum":0.000001},"queries":{"type":"array","items":{"type":"array","items":{"type":"number","maximum":1000,"minimum":0},"maxItems":3,"minItems":3},"maxItems":8,"minItems":1},"frequency_hz":{"type":"number","maximum":10000000000000,"minimum":1000},"relative_permeability":{"type":"number","maximum":10000,"minimum":0.01},"relative_permittivity":{"type":"number","maximum":10000,"minimum":0.01}},"additionalProperties":false},"claim":{}},"additionalProperties":false}},"additionalProperties":false}}},"responseSchema":null,"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.003","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"probe","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.003/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.003","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.003","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_u5Dzx2yPo2dF4kduUZm8X","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.003","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Computes complete propagating and evanescent TE and TM electromagnetic mode field distributions at specified spatial query points inside a rectangular perfect-electric-conductor waveguide filled with a homogeneous medium.","exampleAgentPrompt":"I need the complete complex electric and magnetic field components for the TE10 and TM11 modes in a rectangular PEC waveguide that is 22.86 mm wide and 10.16 mm tall, operating at 10 GHz in air (relative permittivity 1.0, relative permeability 1.0), evaluated at the three spatial points [0.005, 0.003, 0.0], [0.010, 0.005, 0.01], and [0.015, 0.008, 0.02].","exampleUseCases":[{"title":"X-band waveguide mode field mapping","prompt":"Can you compute the full TE10 mode field distribution at five points along the cross-section of a standard X-band waveguide (22.86 mm × 10.16 mm) filled with air at 9.5 GHz? Give me the complex field values at positions [0.005,0.003,0],[0.010,0.005,0],[0.015,0.008,0],[0.020,0.003,0],[0.011,0.005,0.01]."},{"title":"Evanescent mode analysis below cutoff","prompt":"I need to check whether the TE20 mode in a 10 mm × 5 mm rectangular PEC waveguide at 12 GHz with relative permittivity 2.2 and relative permeability 1.0 is propagating or evanescent, and get its complex field values at query points [0.002,0.001,0],[0.005,0.002,0.005],[0.008,0.004,0.01]."},{"title":"Dielectric-loaded waveguide multi-mode fields","prompt":"Compute the complex modal fields for TE11 and TM11 modes simultaneously in a rectangular guide 15 mm wide and 8 mm tall, filled with a dielectric of relative permittivity 4.0 and relative permeability 1.5, at 20 GHz, evaluated at points [0.003,0.002,0],[0.007,0.004,0.005],[0.012,0.006,0.01]."}],"resultDescription":"Returns complex-valued electromagnetic field components (Ex, Ey, Ez, Hx, Hy, Hz) for each requested mode at each spatial query point, covering both propagating modes (above cutoff) and evanescent modes (below cutoff), along with mode classification and cutoff frequency information.","failureModes":["TM modes with m=0 or n=0 are physically invalid and will be rejected (TM modes require both m≥1, n≥1)","Query points outside the waveguide cross-section bounds will produce errors or undefined results","Frequency below the minimum 1000 Hz threshold or above 10 THz will be rejected","Mode indices exceeding maximum value of 8 will be rejected","Degenerate mode pairs or zero-field configurations may produce numerical edge cases","Invalid or missing claim field will cause authentication/authorization failure"],"whenToPreferThis":"Use this endpoint when you need analytically exact complex field distributions for rectangular PEC waveguides with uniform dielectric fill, covering multiple modes simultaneously and arbitrary spatial query points. It handles both propagating and evanescent regimes in one call, making it ideal for waveguide design, field mapping, coupling analysis, and modal decomposition tasks requiring precise complex-valued field data.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-11-04T06:41:09.627Z","isFirstParty":false,"canonicalSlug":"rectangular-pec-waveguide-complete-te-tm-complex-modal-fields-0b0d0acd"}