WOLFRAM|DEMONSTRATIONS PROJECT

Modeling a One-Cycle THz Radiation Waveform Moving through Biological Tissue

​
waveform & spectrum
parameters of THz signal
amplitude,
E
o
(a.u.)
4.
center frequency,
f
C
(THz)
0.1
vibration mode,
v
b
1.7
optic penetration, δ (​
-1
mm
​)
1.
acquisition time,
t
a
(ps)
5.6
number of data points, n
40
delay time,
t
d
(ps)
0.75
peak position,
p
o
(ps)
5
time range, t (ps)
10
phase angle, θ (°)
30.
relaxation time,
t
r
(ps)
2.5
range of frequency, f (THz)
1
noise
0.0005
This Demonstration models a THz radiation waveform of one cycle moving through air and through biological tissue. The goal is to understand the unique characteristics of THz radiation and its interaction with biological tissue, to assist in the analysis of experiments involving radiation through a biological medium. We seek information about peak intensity, reflection, oscillations, resonant absorptions, position of surface, thickness, interface, and interface index. In the frequency domain, this central frequency of this waveform occurs at about 0.1 THz, for a bandwidth of 1 THz. These signal parameters apply for intended applications, including cancer detection. You can select parameters for THz signals in various one-cycle patterns, to tease out the dominant characteristics.
Gaussian sinusoidal pulses of THz radiation have been commonly used in these simulations. Their source is a continuous wave (CW) signal or ultra-short optical pulses of a femtosecond laser. The Gaussian envelope can be characterized by the pulse's central frequency
f
C
and the ratio of central frequency to bandwidth (quality factor)
q
. In these applications, ultra-short THz pulses are used. The radiation is characterized by an electric field amplitude
E(x,t)
and a carrier wave of the form
i(kx-ωt)
e
. We use phasor notation in a slowly varying envelope approximation. This can be modified by varying the amplitude and time factor to form a pulse with a distorted shape. We can compare the results of the pulse distortion obtained using an inverse fast Fourier transform (IFFT) and direct calculations in the time domain. Pulse duration can be measured in several ways by applying different clipping levels, such as
1/e
,
1/
2
e
, or full width at half maximum, and calculating these in terms of either the electric field or the power.