# Rectangular PEC Waveguide Complete TE/TM Complex Modal Fields

> Rectangular PEC Waveguide Complete TE/TM Complex Modal Fields is a paid API for AI agents from detect.halowerk.com, paid per call via x402, $0.003/call, status unknown (last checked 2026-11-04).

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.

## Facts

- Endpoint: POST https://detect.halowerk.com/v1/F-TD2000-GEO-INDUSTRY-B009/rectangular-pec-waveguide-complete-te-tm-complex-modal-fields?utm_source=zero.xyz
- Price: $0.003/call
- Payment: x402
- Status: unknown
- Last checked: 2026-11-04
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/rectangular-pec-waveguide-complete-te-tm-complex-modal-fields-0b0d0acd
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_H-pfsOIozwnqF-Vvpq3M3

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability rectangular-pec-waveguide-complete-te-tm-complex-modal-fields-0b0d0acd -d '<json body>'
```

Example prompt: 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].

## When to prefer this

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.

## Known failure modes

- 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

## How this service works

Resolve complete propagating or evanescent electromagnetic mode fields of a supplied ideal guide.

## Output

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.

## Request schema (JSON Schema)

```json
{
 "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
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/rectangular-pec-waveguide-complete-te-tm-complex-modal-fields-0b0d0acd/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from detect.halowerk.com](https://www.zero.xyz/host/detect.halowerk.com/llms.txt)