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• PCA application
The PCA can be used as a THz emitter or detector in
pulse laser gated broadband THz measurement systems for time-domain spectroscopy.
Because THz waves penetrate dielectric materials like paper or plastic, are reflected by materials with free electrons like metals and are absorbed by moleculs with certain vibration levels within the terahertz band they have a lot of applications in the fields of time-domain spectroscopy and imaging.
Note: Terahertz radiation is nonionizing. That means it is safe.
• Frequency and wavelength
Frequency and wavelength
The photoconductive antenna can be considered as a dipole of length L which is in resonance with
the electromagnetic wavelength λn inside the semiconductor.
The resonance condition is L = m · λn/2 with m = 1, 2, 3,.. integer.
The wavelength λn in the material with refractive index n can be approximated by λn = λ/n.
Using the wave relation c = λ · f and m = 1 the resonance frequency f of the antenna can be estimated as f = c/(2 · n ·L) with
The refractive index n of GaAs at terahertz frequencies is n = 3.4. With this value the first resonant frequency and wavelength of the antenna with length L can be calculated as follows:
|f (THz)||λ (µm)||L (µm)|
• Focusing the optical beam on the antenna
Focusing the optical beam on the photoconductive antenna
The semiconducting gap in the center of the antenna must be illuminated by a focused laser beam. If we consider a Gaussian beam then the beam width w(z) along the beam axis z and the Raygleigh range zR are
The diameter of the beam width 2·w0 at the focus point z = 0 is
with λ - laser wavelength, fL - focal length of the lens, D - diameter of the laser beam at the focusing lens.
To ensure that the focused beam diamter 2·w0 is somewhat larger then the antenna gap distance g the focal length fL of the focusing lens must be
In case of g = 5 µm, D = 1 mm, and λ = 800 nm the focal length of the lens must be fL ~ 6 mm.
Gaussian beam width w(z) as a function of the distance z along the beam axis. w0 - beam waist; b - depth of focus; zR - Rayleigh range; θ - asymptotic beam divergence.
• THz pulse emission
THz pulse emission
Phase 1: Antenna before illumination
Phase 2: Optical pulse meets the antenna gap
Phase 3: THz pulse emission
• Escape angle of the THz radiation, PCA without substrate lens
Escape angle of the THz radiation
Because of the high refractive index n ~ 3.4 of the semiconductor PCA the outgoing terahertz waves are strongly diffracted at the substrate-air interface. The boundary angle α for the total reflection can be calculated as
α = arcsin(n-1) ~ 17.1 °
Only THz waves emitted in the solid angle Ω with
can escape the substrate. For GaAs with n = 3.4 the escape solid angle is Ω = 0.088 π sr = 0.28 sr. This is only 4.4 % of the forward directed intensity.
• Aplanatic hyperhemispherical lens
Hyperhemispherical silicon lens
To increase the escape cone angle α a hemispherical lens with the same refractive index n as the PCA can be used. To decrease the divergence in air a hyperhemispherical lens with a certain distance d between emitter and lens tip is common. If this distance d is
then the hyperhemispherical lens is aplanatic, that means without spherical and coma aberration.
For a silicon lens with almost the same refractive index n ~ 3.4 as GaAs at
terahertz frequencies the distance is d = 1.29 R with lens radius R. The height h
of the aplanatic hyperhemispherical lens is therefore h = d - t with the thickness t of
the semiconductor PCA.
The length L from lens tip to the virtual focus behind the lens is given by
L = R (n+1)
For silicon is L = 4.4 R. With this hyperhemispherical lens nearly all the forward directed
terahertz intensity can escape the PCA. The collection angle is α = 73.6 ° and the solid angle for the collected THz beam
is Ω= 1.43 π sr = 4.51 sr.
The problem left is the beam divergence, which requires a further focusing element like a lens or mirror.
• Collimating elliptic lens
Collimating elliptic lens
With an elliptical lens (truncated ellipsoid) with refractive index n equal to that of the PCA a collimated THz beam can be realized if the following relations are fulfilled:
Distance d (lens thickness)
Here R is the radius of curvature at the intersection of the ellipsoid with the optical axis. The lens parameters scales with R.
The conic constant k = -1/n2 is related to the standard equation for an aspheric lens:
where the optic axis is presumed to lie in the z direction, and z(r) is the sag—the z-component of the displacement of the surface from the vertex, at distance r from the axis.
The antenna is located at the focal point F1 on the major axis of the truncated ellipsoid. The ellipse is characterized by the following parameters:
The collection angle is
The solid collection angle is
The lens diameter is
For an elliptic collimating silicon lens with n ~ 3.4 the conic constant is k = -0.086, the eccentricity ε = 0.294, the lens diameter D = 2.09 R, the collection angle α = 72.8° and the solid collection angle Ω = 1.41π sr = 4.44 sr.