Terahertz (THz) physics — electromagnetic radiation in the frequency band 0.1-10 THz (wavelengths 30 µm - 3 mm, photon energies 0.4-40 meV), the 'terahertz gap' bridging microwave electronics (≲ 300 GHz) and mid-infrared photonics (≳ 30…
terahertz-physics
Photon energy: E = h·f
The Planck-Einstein relation E = h·f specifies the quantum energy of a single photon of frequency f, with h = 6.626·10⁻³⁴ J·s Planck's…
Drude plasma frequency: ω_p = √(n_e·e²/(ε₀·m_e))
The plasma frequency ω_p = √(n_e·e²/(ε₀·m_e)) — the natural collective oscillation frequency of a free-electron gas of density n_e — is the…
Cherenkov angle: cos(θ_C) = 1/(β·n)
The Cherenkov cone condition cos(θ_C) = 1/(β·n) specifies the angle (relative to particle velocity) at which coherent electromagnetic…
Photon-energy anchor: E(1 THz) / h = 10¹² Hz
Sympy-exact witness of the Planck-Einstein relation at 1 THz. Setup: E = h·f as a two-symbol product. Identity: dividing by h and setting…
Plasma-freq √-scaling: ω_p(4·n_e)/ω_p(n_e) = 2
Sympy-exact witness of the plasma-frequency density-quadrupling identity. Setup: ω_p = √(n_e·e²/(ε₀·m_e)) as a four-symbol function. …
Cherenkov anchor: cos(θ_C)(β·n=2) = 1/2; θ_C = π/3
Sympy-exact witness of the Cherenkov cone-angle canonical anchor. Setup: cos(θ_C) = 1/(β·n) — a two-symbol rational function. Identity:…
THz time-domain spectroscopy E(t) <-> Ê(omega) Fourier-pair; FFT framework
THz time-domain spectroscopy framework (Fattinger-Grischkowsky 1989 Appl Phys Lett 54, 490; Auston-Cheung-Smith 1984). Setup: THz-TDS…
Drude-conductivity pole sigma(omega) = sigma_0/(1 - i omega tau); meromorphic
Drude-conductivity dispersion framework (Drude 1900 Annalen der Physik 1, 566). Setup: free-electron response to AC electric field σ(ω) =…
Dielectric loss tangent tan delta = eps''/eps'; condition-number perturbation
Dielectric loss tangent framework (Debye 1929 Polar Molecules). Setup: complex permittivity ε(ω) = ε'(ω) - i ε''(ω) with real and imaginary…
Theorem: int_R e^{-t^2/2} dt - sqrt(2 pi) = 0 (Gaussian Fourier-pair zero-omega)
Theorem (THz Gaussian Fourier-pair canonical): the Gaussian pulse E(t) = e^{-t²/2} has Fourier transform Ê(ω) = √(2π)·e^{-ω²/2} - the…
Theorem: sigma(omega = 0) - sigma_0 = 0 (Drude DC conductivity limit)
Theorem (Drude-DC canonical): substituting ω = 0 into σ(ω) = σ_0/(1 - i ω τ) gives σ(0) = σ_0/1 = σ_0 exactly. Canonical sympy pin:…
Theorem: tan delta(eps'' = 0) = 0 (lossless-dielectric loss-tangent vanishing)
Theorem (loss-tangent-lossless canonical): tan δ = ε''/ε'; at ε'' = 0 (lossless dielectric) tan δ = 0/ε' = 0 identically. Canonical sympy…
THz-TDS (Fattinger 1989)
Fattinger-Grischkowsky 1989 photoconductive THz-time-domain-spectroscopy; modern coherent-THz + asynchronous-optical-sampling at 100s of…
QCL (Faist 1994)
J Faist 1994 quantum-cascade-laser; modern THz-QCL Williams 2007 + room-T QCL above 250K Khalatpour 2021.
THz imaging (Tonouchi 2007)
M Tonouchi 2007 'Cutting-edge terahertz technology' Nature Photonics review; medical + security + non-destructive applications.
Photoconductive antenna (Auston 1984)
Auston 1984 LT-GaAs photoconductive switch; modern Cs-LT-GaAs + InGaAs/InAlAs detectors; 100s of THz bandwidth.
THz metamaterials (Padilla 2006)
W J Padilla 2006 SRR + ELC THz-metamaterials; modern dynamic + tunable + active control via graphene-gating Lee 2012.
THz vibrational (Walther 2003)
M Walther 2003 collective-mode THz-spectroscopy in DNA + proteins; modern ATR + waveguide-THz biomolecule sensitivity.
Auston switch (1984)
D Auston 1984 photoconductive-antenna + Mourou-Knox 1986 fs-laser-pulse; modern modern foundational + 2024 InGaAs-PCA broadband 5 THz.
THz-TDS (Fattinger-Grischkowsky 1989)
C Fattinger-D Grischkowsky 1989 THz-TDS; modern modern foundational text + 2024 commercial THz-TDS + medical imaging cancer-margin.
QCL (Köhler-Faist 1994)
J Faist 1994 + Köhler 2002 THz-QCL quantum-cascade-laser; modern modern foundational text + 2024 RT-QCL room-temperature 4 mW operation.
THz imaging (Pickwell-Wallace 2003)
E Pickwell-V P Wallace 2003 + Tonouchi 2007 medical-imaging; modern modern foundational text + 2024 endoscopic-THz + skin-cancer…
THz vibrational (Walther 2003)
M Walther 2003 + Williams 2012 THz-vibrational fingerprinting; modern modern foundational text + 2024 polymorph + protein-low-frequency…
Strong-field THz (Hirori 2011)
H Hirori 2011 + 2024 LiNbO3-tilted-pulse THz; modern modern foundational + GV/cm strong-field nonlinear-THz electron-emission FE…