Crossed NbTiN Nanowire Optical Detector — FDTD Study
I built and simulated a crossed-nanowire optical detector model in Tidy3D FDTD, using orthogonal NbTiN detector elements inside a multilayer SiO₂ and gold optical stack. The completed V1 run records electric-field distributions and directional flux near 1.55 µm. The crossed geometry was intended to reduce polarization dependence, but the surviving simulation uses only one incident linear polarization — so polarization insensitivity remains a design goal rather than a demonstrated result.
Summary
- Physics & Modeling
- Major project
- In development
Evidence on file
My contribution
I built the Tidy3D FDTD model: the multilayer optical stack, the crossed NbTiN nanowire geometry, the plane-wave source, four field monitors and two flux monitors. I ran V1 to completion and post-processed the stored field datasets into the |E|² maps on this page.
Everything here is numerical. No device was fabricated, nothing was measured electrically, no photon counting took place, and no detection efficiency was calculated.
Project overview
Why I built this
How does a crossed pair of orthogonal NbTiN nanowires interact with an incident optical field near 1.55 µm, and what additional simulation would be required to establish polarization-independent response?
The second half of that question is the honest part. The geometry was chosen with polarization insensitivity in mind, and V1 shows what the field does around it — but showing what the field does under one polarization is not the same as showing the response does not depend on polarization.
What I modelled
Read out of setup-v1.hdf5 rather than from the filenames. Positions are the box centres along z, in micrometres, with the stack built from four dielectric and metal boxes plus the two detector elements. Every box has a 0.21 × 0.21 µm lateral footprint unless stated.
- NbTiN, 0.11 × 0.21 × 0.009 µm — 110 × 210 × 9 nm — centred at z = 0.009 µm, long axis along y.
- NbTiN, 0.21 × 0.11 × 0.008 µm — 210 × 110 × 8 nm — centred at z = 0.042 µm, long axis along x. Orthogonal to the lower wire.
- A non-dispersive medium: permittivity 2.8175, conductivity 0.8898. Not a dispersive superconductor model.
- SiO₂ layer, 0.254 µm thick, centred at z = −0.199 µm.
- Gold layer, 0.254 µm thick, centred at z = 0. Johnson & Christy dispersive model.
- SiO₂ layer, 0.030 µm thick, centred at z = 0.028 µm.
- SiO₂ layer, 0.110 µm thick, centred at z = 0.096 µm.
- The file gives these boxes no functional names, so neither does this page. They are SiO₂ and gold layers, not a mirror, cavity or reflector — nothing in the setup assigns those roles.
- Several boxes overlap in z and the solver resolves that by structure priority. Each is reported as the file states it rather than as a pre-resolved stack-up.
Why crossed nanowires
The crossed geometry was built around the expectation that coupling to a straight nanowire can depend on the incident polarization relative to the wire orientation. Placing two detector elements at right angles was therefore intended to reduce that dependence.
In this model that is the lower wire running along y and the upper wire running along x, separated by 33 nm of stack.
That is an argument from geometry, and geometry is not evidence. A symmetric arrangement makes polarization independence plausible; it does not make it true. The response depends on the fields that actually reach each wire, which is set by the whole stack — the layers above and below, the separation between the wires, the materials, and how each wire sits relative to the standing-wave pattern.
What would settle it is a controlled comparison: the same geometry, the same mesh, the same monitors, run under at least two orthogonal incident polarizations, with a detector-relevant quantity compared between them. V1 does not contain that comparison.
Simulation setup
The configuration as stored in setup-v1.hdf5, with the solver figures taken from the V1 run log.
| Setting | Value |
|---|---|
| Domain | 0.35 × 0.35 × 3 µm, centred at (0, 0, 0.35). The 0.21 × 0.21 µm structure footprint does not fill it. |
| Boundaries | Periodic in x and y; PML in z, 12 layers each side. |
| Symmetry | None — (0, 0, 0). |
| Source | PlaneWave at z = 0.55 µm, size 0.25 × 0.25 µm, propagating in −z. Normal incidence: angle_theta = 0, angle_phi = 0. |
| Polarization | pol_angle = 0 — a single linear polarization. This is the whole of the polarization coverage in V1. |
| Pulse | GaussianPulse, freq0 = 193.616 THz (λ ≈ 1.5484 µm), fwidth = 12.491 THz, roughly 1.45–1.66 µm. num_freqs = 3. |
| Materials | SiO₂ and gold as dispersive PoleResidue models; NbTiN as a non-dispersive medium, permittivity 2.8175, conductivity 0.8898. |
| Grid | AutoGrid in all three axes, 10 steps per wavelength minimum, max scale 1.4, at λ = 1.55 µm, with a local override box around the nanowires. |
| Mesh | 49 × 47 × 132 cells — 3.086 × 10⁵ points. |
| Run | 8.5324 × 10⁴ time steps at 7.0377 × 10⁻¹⁸ s, Courant 0.99, shutoff 1 × 10⁻⁵. |
| Outcome | Completed in 2.55 s of solver time, diverged = false. Tidy3D 2.11.2. |
Real V1 results
V1 completed successfully. V2 exists as a draft, and the artefacts say nothing about why, so neither does this page.
Everything below this point comes from that completed run — the field maps and the flux numbers are read out of results-v1.hdf5, not redrawn or estimated.
Tidy3D model view with the version menu open: V1 marked Success, V2 marked Draft. The structure list shows the four SiO₂ and gold boxes and the two NbTiN nanowires.
The V1 Setup view: the plane-wave source, the four field monitors and the two flux monitors positioned around the stack.
The V1 Results workspace, listing the stored monitor datasets from the completed run.
Field distribution through the stack
Two orthogonal cross-sections through the domain, both recorded at 1.55 µm. The field monitors store a single wavelength with all six field components; these maps are |Ex|² + |Ey|² + |Ez|², computed from the stored components.
Completed V1 FDTD result. Electric-field intensity |E|² through the x–z cross-section at approximately 1.55 µm.
Completed V1 FDTD result. Electric-field intensity |E|² through the y–z cross-section at approximately 1.55 µm.
Field around the nanowire plane
Completed V1 FDTD result. Electric-field intensity |E|² in the plane of the upper NbTiN nanowire at approximately 1.55 µm — a horizontal slice at z = 0.042 µm, recorded by a monitor spanning 0.205 × 0.115 µm at that height.
This shows where field intensity sits in that plane at one wavelength and one polarization. It is not an absorption map, an efficiency map or a detector-response map: no such quantity was calculated from this run.
What the flux monitors record
Two flux monitors, each 0.21 × 0.21 µm and each storing five wavelengths — 1.50, 1.525, 1.55, 1.575 and 1.60 µm. One sits below the stack at z = −0.65 µm with its normal facing +z; the other sits above the source at z = +0.95 µm.
The lower monitor reads −0.1543 to −0.1571 across the band and the upper reads +0.0516 to +0.0497. These are raw directional monitor flux. The sign follows the monitor surface-normal / flux-direction convention; it does not represent negative optical power. They are not reflectance, transmittance, absorptance or efficiency, and they are not converted into percentages here — doing any of that needs an incident-power normalisation that this run does not document. Their magnitudes do not sum to one, which is what you would expect of unnormalised values.
What V1 does not prove
The completed run establishes a field solution for one configuration. Four things it is not, each of which names the evidence that would be needed.
- Only one incident linear polarization is present — pol_angle = 0. Establishing independence needs the same geometry run under at least one orthogonal polarization and the two compared.
- No validated per-wire normalised absorption was calculated. That needs monitors designed to integrate absorbed power in each NbTiN element, and a documented incident-power normalisation.
- FDTD field and flux data describe electromagnetic energy. Superconducting photon-detection efficiency depends on bias current, hotspot formation and the device electronics, none of which is modelled here.
- No device was fabricated and nothing was measured. This is a simulation.
What I would test next
The shortest path from what exists to a claim the evidence could support. None of this has been run.
- 01
Rerun V1 under the orthogonal polarization
Identical geometry, mesh, monitors and source — only pol_angle changed. Anything else that moves makes the comparison meaningless.
- 02
Compare a detector-relevant normalised metric between the two
Power absorbed in each NbTiN wire, total NbTiN absorption, and the difference between polarization states. This needs absorption monitors and an incident-power normalisation that V1 does not have.
- 03
Compare any V2 geometry against V1 under identical conditions
If the geometry changes, the two runs have to share source, mesh and monitors or the difference cannot be attributed to the geometry.
- 04
Run mesh convergence around the thin NbTiN elements
The wires are 8 and 9 nm thick on a grid set by 10 steps per wavelength at 1.55 µm. Whether the result is converged at that resolution is a question the run does not answer.
What I learned
I started out thinking crossed nanowires made the detector polarization-insensitive by construction. Two elements at right angles, symmetric by inspection — what else would you need?
Building the model and looking at what it actually contains changed the question from a design argument to an evidence one. A crossed geometry makes polarization independence plausible. Demonstrating it needs a controlled comparison: the same structure under different incident polarizations, with a detector-relevant quantity measured for each. V1 has one polarization in it, so whatever it shows, it cannot show that.
The second lesson is about what a field map is. The |E|² maps on this page are real solver output and they show where electromagnetic energy concentrates — that is genuinely useful, and it is not a measurement of detector efficiency. Getting from one to the other means integrating absorbed power in the right volumes, normalising against the incident power, and then adding the superconducting physics that decides whether an absorbed photon produces a count. Each of those is a separate step, and a picture of a bright region skips all of them.
Evidence
Related work
I designed a computational nanophotonics study around a simple question: can an optical metasurface remain useful after realistic fabrication defects are introduced? The model is a 6 × 6 periodic supercell of TiO₂ nanodisks on glass, with missing disks, radius and height variation, and positional jitter. Instead of optimising only a perfect geometry, I designed the Tidy3D FDTD workflow around robustness — transmission, reflection, diffraction, field behaviour, and a quantitative defect-sensitivity metric. I also iterated through earlier Tidy3D models and completed multiple solver runs. Those development runs used earlier geometry and wavelength settings, so I treat them as evidence of the simulation workflow rather than validation of the final visible-band defect-tolerance study.
I developed a multi-element broadband optical-delivery model in Ansys Zemax OpticStudio and evaluated it across multiple wavelengths, field angles, and three saved configurations. The prescription uses fused silica and CaF₂ elements with multiple powered and AR-coated surfaces. Native analyses include configuration-matrix spot diagrams, polychromatic diffraction encircled energy, and wavefront evaluation. The design concept included polarization preservation as an objective, but the saved evidence here does not contain a polarization-specific metric, so I do not present that behavior as demonstrated.
I developed two related sequential optical models in Ansys Zemax OpticStudio to study how a microlens could direct broadband solar illumination toward a small rectenna microcell plane. The models explore different lenslet geometries, wavelength ranges, and field angles. Native OpticStudio outputs include 3D layout, optical-path-difference analysis, and saved 850-nm wavefront results. Because the two prescriptions and pupil conditions differ, I treat their results as evidence of design exploration rather than a controlled before-and-after performance comparison.