Interactive broadband THz vector-beam laboratory

Radially and azimuthally polarized THz beams

Explore how spatially varying linear polarization produces radial and azimuthal vector beams. Inspect the beam intensity, polarization vectors, normalized Stokes maps, local polarization ellipse, broadband time-domain field, and spectrum from one self-contained simulation.

1

Radial polarization

The transverse electric field points locally away from or toward the beam axis.

2

Azimuthal polarization

The transverse electric field is tangent to circles centered on the beam axis.

3

Broadband THz pulse

A short transient contains many THz frequencies, including their spectral phase.

4

Spatial Stokes analysis

Each transverse pixel has its own polarization state described by S0, s1, s2, and s3.

BeamRadial
Selected point—
Local ψ—
Local χ—
Local s1, s2, s3—

S0 and polarization vectors

Click to select a local point.

Normalized s1

Horizontal–vertical contrast.

Normalized s2

+45°/−45° contrast.

Normalized s3

Local circular component.

Azimuth angle ψ

Major-axis orientation.

Local polarization ellipse

At the selected beam position.

Broadband THz spectrum

From the local time-domain field.

Local time-domain vector field

Ex(t) and Ey(t) at the selected point.

Ideal transverse vector fields

Using polar coordinates r and φ, the ideal spatial fields are:

Radial: Ex = A(r) cosφ,   Ey = A(r) sinφ
Azimuthal: Ex = −A(r) sinφ,   Ey = A(r) cosφ

The total intensity exhibits donaught-shape intensity profile:

A(r) = (r/w) exp[−r²/(2w²)]

This produces a null at the beam center, where the local polarization direction is undefined.

Spatial Stokes parameters

The complex transverse fields are evaluated pixel by pixel:

S0 = |Ex|² + |Ey|²
S1 = |Ex|² − |Ey|²
S2 = 2Re(ExEy*)
S3 = 2Im(ExEy*)

For an ideal radial or azimuthal beam with zero relative phase, s3 = 0 because every illuminated point is locally linearly polarized.

Why radial THz beams matter

Radially polarized beams can develop a strong longitudinal electric-field component under tight focusing. In the broadband THz range, this is useful for exciting axial charge motion, coupling to structures that respond to normal electric fields, investigating anisotropic materials, and improving coupling to modes with radial or longitudinal electric-field symmetry.

Because a THz pulse is broadband and phase resolved, the longitudinal-field response can be studied as a function of both time and frequency.

Why azimuthal THz beams matter

Azimuthally polarized beams contain a circulating transverse electric field and can produce an enhanced longitudinal magnetic field when tightly focused. They are therefore valuable for magnetic-dipole excitation, current-loop resonances, magnetization dynamics, and selective coupling to structures whose symmetry suppresses a conventional uniform linear field.

In broadband THz spectroscopy, this provides a route to separate electric and magnetic responses over a wide spectral interval.

Broadband opportunities

  • Simultaneous access to multiple resonances in one time-domain measurement.
  • Direct recovery of spectral amplitude and phase.
  • Frequency-resolved vector-beam purity and polarization topology.
  • Mode-selective coupling to waveguides, antennas, resonators, and metasurfaces.
  • Time-resolved study of electric, magnetic, and anisotropic material responses.

Experimental considerations

  • The vector pattern should remain stable across the useful THz bandwidth.
  • Relative spectral phase between Ex and Ey must be calibrated.
  • Detector response and finite spatial resolution can distort the measured Stokes maps.
  • For broadband data, Stokes parameters should be calculated frequency by frequency.