L1 ⚛ L1-494 ⊙ Testnet

LED and Laser Rate Equations

Semiconductor Physics · Optoelectronic devices

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⬇ L1-494.md

# ⚛ L1 Principle — LED and Laser Rate Equations **ID:** `L1-494` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Semiconductor Physics — *Optoelectronic devices* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** N S time trajectories > **📡 Carrier:** electron · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554142 --- ## 🧠 1. Introduction **LED and Laser Rate Equations** is a **nonlinear inverse problem** whose unknown lives in **N S time trajectories** space, within the **Optoelectronic devices** sub-domain of **Semiconductor Physics**. Measurements consist of electrons collected by an electron detector via a **electroluminescence modulation** sensing mechanism. The forward operator applies, in order: E · carrier rate operator; E · photon rate operator; D · time · implicit operator; O · LI modulation operator. Observations are corrupted by additive Gaussian noise. Well-posed for typical semiconductor lasers; threshold bifurcation well-resolved; multi-mode regimes need spatial extension. ## ⚙ 2. Forward Model Physical chain: **x** → E · carrier rate → E · photon rate → D · time · implicit → O · LI modulation → **y** (detector). ``` y = `O.LI_modulation` `D.time.implicit` `E.photon_rate` `E.carrier_rate` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `E.carrier_rate` | E · carrier rate operator | | `E.photon_rate` | E · photon rate operator | | `D.time.implicit` | D · time · implicit operator | | `O.LI_modulation` | O · li modulation operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Semiconductor Physics | | Sub domain | Optoelectronic devices | | Carrier | electron | | Problem class | nonlinear_inverse | | Solution space | N_S_time_trajectories | | Noise model | gaussian | | Integration axis | time | | Difficulty delta | 3 | | L dag | 3.3 | ## 📡 4. Measurement Model Well-posed for typical semiconductor lasers; threshold bifurcation well-resolved; multi-mode regimes need spatial extension. | Metric | Value | |---|---| | Metric | LI_relative_error | | Secondary | modulation_bandwidth_error | ## 📏 5. Operating Range (Ω) **Center problem class:** `laser_rate_parameter_inversion` · **Forward operator:** `rate_eq_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | T k | — | 298 | | I ma | — | 20 | | V um3 | — | 100 | | N tr cm3 | — | 1000000000000000000 | | Lambda nm | nm | 850 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | T k | — | 200 – 400 | | I ma | — | 0.1 – 1000 | | V um3 | — | 1 – 10000 | | N tr cm3 | — | 100000000000000000 – 10000000000000000000 | | Lambda nm | nm | 400 – 1550 | ## 🎯 6. Tolerance (ε) **Center tolerance:** L-I relative error <= 0.03 | Metric | Range | |---|---| | Li relative error | 0.01 – 0.4 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **LI_relative_error**, with κ = `100` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x774268abb12879adc3f1f27401fb91cce67f6065f3dd6600fc0f7d9afc4adced` - **Chain tx hash:** `0x97d42d45519fb670b38c993e1743df8e600dccb76be2725224c60a2b69206446` - **Chain block:** `41554142` --- ## File Mapping This bundle consists of: `L1-494.md`, `L1-494.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-494.md` | Source of truth — edit this | Human or LLM | | `L1-494.json` | Structured metadata for the registry | LLM regenerates from the sections above | **Prompt for your LLM after editing this Markdown:** > Read the attached Markdown. Regenerate the sibling `.json` so every field matches. > Preserve the schema documented in the rows above. > Output each file in its own fenced code block tagged with the filename. > Output only the JSON object. _This Markdown was auto-synthesized from the catalog row for `L1-494`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-494.md).
Regenerate L1-494.json so every field matches the Markdown.
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📋 JSON metadata

{
  "artifact_id": "L1-494",
  "chain_block": 41554142,
  "chain_hash": "0x774268abb12879adc3f1f27401fb91cce67f6065f3dd6600fc0f7d9afc4adced",
  "chain_tx_hash": "0x97d42d45519fb670b38c993e1743df8e600dccb76be2725224c60a2b69206446",
  "domain": "Semiconductor Physics",
  "hardness_fn": {
    "delta": 3,
    "kappa": 100,
    "metric": "LI_relative_error",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
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      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "LI_relative_error",
    "regime": "Well-posed for typical semiconductor lasers; threshold bifurcation well-resolved; multi-mode regimes need spatial extension.",
    "secondary": "modulation_bandwidth_error"
  },
  "physics_fingerprint": {
    "L_DAG": 3.3,
    "carrier": "electron",
    "difficulty_delta": 3,
    "domain": "Semiconductor Physics",
    "integration_axis": "time",
    "noise_model": "gaussian",
    "primitives": [
      "E.carrier_rate",
      "E.photon_rate",
      "D.time.implicit",
      "O.LI_modulation"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "electroluminescence_modulation",
    "solution_space": "N_S_time_trajectories",
    "sub_domain": "Optoelectronic devices",
    "title": "LED and Laser Rate Equations"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "rate_eq_forward"
    ],
    "allowed_omega_dimensions": [
      "I_mA",
      "T_K",
      "V_um3",
      "lambda_nm",
      "N_tr_cm3"
    ],
    "allowed_problem_classes": [
      "laser_rate_parameter_inversion"
    ],
    "center_spec": {
      "epsilon_fn_center": "L-I relative error \u003c= 0.03",
      "forward_operator": "rate_eq_forward",
      "input_format": "measurement_only",
      "omega": {
        "I_mA": 20,
        "N_tr_cm3": 1000000000000000000,
        "T_K": 298,
        "V_um3": 100,
        "lambda_nm": 850
      },
      "problem_class": "laser_rate_parameter_inversion"
    },
    "epsilon_bounds": {
      "LI_relative_error": [
        0.01,
        0.4
      ]
    },
    "omega_bounds": {
      "I_mA": [
        0.1,
        1000
      ],
      "N_tr_cm3": [
        100000000000000000,
        10000000000000000000
      ],
      "T_K": [
        200,
        400
      ],
      "V_um3": [
        1,
        10000
      ],
      "lambda_nm": [
        400,
        1550
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Optoelectronic devices",
  "title": "LED and Laser Rate Equations"
}

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