In recent years, the importance of ''terahertz light'' has increased significantly. Abbreviated THz (Existing in the region between light and radio waves), is a unit of electromagnetic (EM) wave frequency equal to one trillion hertz (1012 Hz). The terahertz is used as an indicator of the frequency of infrared (IR), visible, and ultraviolet (UV) radiation. An EM wave having a frequency of 1 THz has a wavelength of 0.3 millimeters (mm), or 300 micrometers (μm). Wireless transmissions and computer clock speeds are at frequencies far below 1 THz.
Fig.1-1 The spectrum range of electromagnetic waves [ from http://www-ece.rice.edu/]
might someday be developed. At present, the terahertz is of interest primarily to physicists and astronomers [3-8].
Research into the utilization of THz light in imaging technology and new spectroscopic technology is underway around the world [10-11].
THz light can be applied for measurements not only in the semiconductor field, but also in medical diagnoses and materials inspection. There is great potential for its application in a number of other fields as well.[3-8]
Although THz frequencies are potentially very interesting, it took the development of a new technique to generate them to push them into the limelight. Traditionally, THz frequencies were generated by "heat sources" and detected with liquid-helium cooled bolometers, essentially heat detectors.
In order to generate THz radiation, femto-second pulse lasers are the usual light source, such as a Ti-sapphire laser, which is expensive and large size. This laser is not available in usual laboratories and limited the THz applications. So, a compact, inexpensive and the continuous THz source is desirable. Expect the light source of CW THz, we still want to realize the relation between our THz emitters (photoconductive antennas) and the coherence length of the CW THz. Therefore, we can pick up the right emitter to generate the CW THz with longer coherence length.
1.2 Methods of generating THz radiation
During the rapid development of picosecond and femtosecond laser sources in the early 1980，, there are various ways used to generate and
detect ultrashort-pulsed millimeter and submillimeter wave[9]. In our laboratory, we use some kinds of methods to generate and detect THz radiation, such as optical rectification、Resonant THz generation in semiconductor(such as semi-insulating GaAs and low-temperature grown GaAs) with a femtosecond pulse laser and a pair of continuous-wave (CW) laser. Followers are some methods of generation terahertz (THz) radiation.
1.2.1Optical rectification
Optical rectification is a second-order characteristic of nonlinear effect. In the electro-optic medium, the low frequency electric field is produced under intense optical illumination.Optical rectification in a non-absorbing medium is a process in which a laserpulse creates a time-dependent polarization that radiates an electric field which, in the far field, can be written according to ( ) 22P
E tr ∝ ∂∂tr
, where the polarization P follows the pulse intensity envelope.
Fig.1-3 Non-resonant optical rectification with a femtosecond laser pulse It is called rectification because the rapid oscillations of the electric field of the laserpulse are "rectified" and only the envelope of the oscillations remains. In the far-field, this than changes into a pulsehape roughly sketched in the figure.Since the medium is nonabsorbing, the polarization instantanously follows the pulse envelope implying that there is practically no limit on the speed at which the polarization can be switched on and off. The polarization radiates an electrical transient which typically consists of one or one-and-a-half oscillation of the electric field and therefore has a broadband THz frequency bandwidth. Bandwidths as large as 30 THz have been obtained using this generation mechanism.
1.2.2 Photoconductive switch (current surge model)
The mechanism of generation THz radiation from the biased photoconductive switch is generally based on the current surge model.
[12]In this method, if the frequency of the laser is higher than the energy needed to excite electron-hole pairs, THz generation mechanism can occur. THz electromagnetic field is radiated from a transient current which is generated on the surface of a photoconductor. Ultrashort optical pulses generate carriers instantaneously and the carriers are accelerated by the local electric field. The resultant transient current, or current surge, produces an electric field on the surface of the photoconductor and this surface field can be regarded as the source of the THz radiation. And the surface field, at the sametime, partly cancels the bias field applied to the
photoconductor, which is called the near-field screening effect. Fig. 1-4 shows the experimental setup for this method
Fig. 1-4 Resonant THz generation in GaAs with a femtosecond laser pulse.
We suppose to put two electrodes on the top of GaAs wafers which have different emitter structures on it, and we put a voltage across these two electrodes. When we illuminate the region between the two electrodes with a femtosecond laserpulse, the GaAs wafer suddenly becomes conducting where, before excitation, it behaved as an isolator. Under the influence of the applied electric field, a current begins to flow, which shows signs of saturation after approximately 0.5 picoseconds. Such a time-dependent current can also radiate and electrical transient, but with a higher efficiency than with non-resonant optical rectification. The
of 1 THz. This is less than what you would expect, based on the assumption that the frequency contents are determined by the laser pulse duration and that's because it isn't. It's determined by the current which can have a risetime slower that the laser pulse duration.
1.3 Terahertz radiation detection methods
Traditionally, THz frequencies were generated by "heat sources" and detected with liquid-helium cooled bolometers, essentially heat detectors.
Follower we will introduce three kinds of method to detect THz radiation, such as bolometer, photoconductive antenna detection and electro-optic sampling (e-o sampling).
1.3.1 Bolometer
Bolometric detectors have been used for far-infrared (FIR), submillimeter- (submm) and millimeter-wave (mm) astronomy for the past 40 years. A hot electron bolometer is a device, of which the resistance responds to the change of the electron's temperature when it absorbs incident radiation. A traditional bolometer consists of a heat-sensitive detection element mounted inside a heat sink and
physically supported by a thermally conductive physical supporter. The most common systems are helium-cooled Si, Germanium and InSb bolometer. It can measure the power of nW grade, but it losses all the information of phase and frequency. The usual method to get the power of THz radiation is to use Martin-Puplett interferometer, we will introduce the details later.
1.3.2 Photoconductive antenna detection
Since early 80’s, photoconductive (PC) sampling has been widely used to detect THz radiation[1]. Although its high signal to noise ratio, its speed is limited by the resonant character of the antenna structure and the finite carrier lifetime of the photocarriers[2]. Typically, the laser source is divided into two beams (pump and probe beam). When the pump beam illuminates the emitter, THz radiation is generated, then, THz and the synchronous probe beam illuminate the PC-antenna. THz radiation introduce the transient current and probe beam accelerate
1.3.3 Electro-Optic sampling
Recently, since Electro-Optic sampling has high bandwidth and is easy to implement, technique of Electro-Optic sampling became an alternative to PC detection.[9] Here, the Zinc-blende crystal was used to measure THz radiation based on the Pockels effect.[9] When we vary the temporal delay between pump and probe beam , the synchronous probe beam will probe the transient change of refractive index result from THz changing the refractive index. There is a trade-off in this method , thickness plays an important role in it, thick crystal will introduce longer interaction length but reduce the frequency response.
1.4 Objective
Due to the advantages of CW THz system, we want to build a continuous-wave THz system including CW THz source and the detection system. Otherwise, we try to understand the relationship between carry lifetime of the photoconductive antennas and the coherence length of CW THz radiation emitted from the photoconductive antenna. First of all, we use two laser diodes to be the beating source and to illuminate the THz emitter (photoconductive antenna) to generate CW THz. In order to measure the coherence length of the CW THz, we need to use Martin-Puplett interferometer and bolometer for detection. We also want to understand the mechanism of the saturation effect of the Large-Aperture photoconductive antenna
1.5 Organization of this thesis
There are four chapters in this thesis. We introduce the general conception of THz wave in Chap.1,then we give the basic theory of generation THz and the relationship between carry lifefime of the photoconductive antenna and coherence length of CW THz wave in Chap.2. At Chap.3 we give the experiment setup, results and analyses.
Finally, we make some conclusions and the future work.
ChapterⅡ Basic theory of THz wave
In this chapter, we will introduce the basic theory of generation CW THz using photoconductive antenna as the emitter. We also introduce the coherent characteristics of CW THz radiation and the detection system (Martin-Puplett polarization interferometer).
2.1THz wave generated by photoconductive antennas (current surge model)
Photodetectors generally consist of a semiconductor material which has a bandgap energy such that it is sensitive to light in a certain wavelength range.When the photoconductive antenna is illuminated by optical source, where the photon energy is greater than the bandgap of the semiconductor (substrate of the photoconductive antenna). The photon of light can cause the generation of an electron-hole pair which under an applied electric field causes a current to flow. And the expression can be described from the current-surge model.
Initially [12], the radiating source is defined as time-varying parameters, including charge densityρ
(
x,y,z,t)
, current densityJv(
x,y,z,t)
, electric fieldEr(
x,y,z,t)
, and magnetic flux Bv(
x,y,z,t)
. And then, it is necessary to construct Maxwell’s equation before deducing current-surge model.Maxwell’s equation:
t
And then, some non-vector value, V, is induced in the equation.
From (2.6), set Next, the two inhomogeneous wave equations written in terms of A and V could also be deduced from the inhomogeneous Maxwell equations:
From (2.3)
E So that, (2.12) becomes as
J Finally, the two inhomogeneous wave equations expressed in (2.15) and (2.16) are demonstrated. The two equations are used to determine a functional, time dependent form of the radiated electric field in the far
field.
From (2.3), the continuity equation of the free carriers is obtained.
( )
=0 Actually, the current density in the bias photoconductor is strictly a transverse current (parallel to the surface of the photoconductor and perpendicular to the direction of propagation), so that=0
•
∇ Jr
(2.18) Equation (2.17) and (2.18) imply that the charge density dose not vary in time and not contribute to the time-dependent radiated electric field. As a result, from (2.9) the electric field is
( )
A( )
t The solution to the wave equation (2.15) and hence for the vector potential Av leads to the expression for the time-dependent radiated electric field Evrad =( trv, ) at a displacement rv from the center of the vacuum, Jvs is the surface current in the photoconductor evaluated at the retarded time, and d ′a is the increment of surface area at a displacementr r At the same time, the gap between the electrodes of the photoconductor is assumed to be uniformly illuminated by the laser.
Therefore, the surface current Jvs can be assumed to be constant at all points on the surface of the emitter. And then, the radiated electric field can be written as Where A is the illuminated area of the emitter. It is considered that the radiation emitted (and detect) on axis (i.e. x=y=0), and let ⎟
⎠ An expression for the surface current
If we want to know the radiation power of the antenna, we can use a simpler equivalent circuit of the antenna shown in figure 2-1.
(a) (b)
Fig. 2-1 The structure of antenna (a), and the equivalent circuit (b).
Z
C G(t)
V
bThe equivalent circuit equation can be written as: where G(t) is the conductance, C is the capacitance, Z is the radiation impedance.
Solve the equation (2.24), we can get:
] the respective pump powers, h1 and h2 are the external quantum efficiencies, W is the difference frequency, t is the photocarrier lifetime, R is the resistance of the THz load circuit, C is the photomixer capacitance, and e, h, and c are well-known physical constants. Using this CW photomixing equation, we can estimate THz power for the case of shaped pulses. Due to the high peak power of femtosecond pulses, THz intensity generated by the femtosecond pulses can easily exceed that generated by two single mode CW lasers. Another advantage is that the two frequency parts that are to be photomixed are inherently coherent, so that we can bypass the difficulty of phase-locking two ultranarrow band CW lasers.
The current surge model is widely accepted as a model describing the process of THz radiation generation in biased photoconductors.[1] In this method, the surface current density Js(t) of the photoconductive
Here,
σ
s( ) t
is the time-dependent surface conductivity,E
biasandE
surf( ) t
are the static bias field applied to the emitter and the waveform of generated THz radiation field observed on the surface of the emitter, respectively. From the boundary condition of Maxwell’s equations,
surf
( )
E t
is related to Js(t) as( )
0( )
surf
1
sE t η J t
= − ε
+
(2.27) whereη
0 is the impedance of vacuum andε
is the dielectric constant of the emitter medium. Combine (2.26) and (2.27), an expression forsurf
( )
E t
is obtained as0 0
( ) ( )
( ) (1 )
s
surf bias
s
E t t E
t
σ η
σ η ε
= − + +
(2.28)According to the relation between
σ
s( ) t
and the carrier density N(t), we can rewrite the surface field after illumination of the pump pulse is expressed as (assuming that decay of the carrier density due to recombination or trapping is slow and can be neglected in the time window of interest)surf
( )
biassat
E t F E
F F
= − +
(2.29)where
( ) F
∞I t dt
= ∫−∞ (2.30)
is the pump fluence and the saturation fluence ,Fsat(t), is defined as Where R is the reflectance of the emitter and I(t) is the pump intensity.
The electric field of the focused THz pulse,
E
focus( ) t
, has been shown to be proportional to the time derivative of the surface. By assuming the pump light to be Gaussian asIt can be shown that the focused field is proportional to the normalized focused field,
E %
focus( ) t
Finally, the expression for the normalized surface field is obtained as( )
2.2 Photomixing
The basic technique of generation CW THz wave is through photomixing which produces optical intensity beats at THz frequencies by mixing two single-mode lasers or mode beating within a single laser.
The combination of two waves with slightly different frequencies is equivalent to a wave which envelope is modulated by the difference frequency. The intensity-modulated beam will excite the electron-hole pairs in PC antennas then accelerated by the bias voltage applied to the PC antennas. The generated THz frequency is as the same as the optical beating frequency.
When two electric fields with slightly different frequencies propagate collinearly into biased PC antennas, beating signal will be radiated. Set two parallel, scalar electric fields as:
) (
)
( 10 1 1
1 t =E Cos wt+φ E
E2(t)=E20Cos(w2t+φ2) (2.36) Where E10, E20, w1, w2, f1 and f2 are the amplitudes, angular frequencies and constant phases of wave 1 and wave 2, respectively. And the total electric filed is the superposition of the two waves:
) (
) (
) ( ) ( )
(t =E1 t +E2 t =E1Cos w1t+φ1 +E2Cos w2t+φ2
E (2.37)
From the simulated curves of figure 2-2, we can see that the total electric field has the waveform with a slowly various envelope and a fast carrier frequency inside.
-400 -200 0 200 400
Fig. 2-2 The simulated curves of two wave with slightly different
frequencies. The thin curve is the sum of the two waves. The thick curveis the plot of the wave with frequency of (w1- w2)/2
Because the PC antenna has photocarrier lifetime about 1 ps, so it can’t response the faster frequencies. The beating intensity needs to be time averaged:
space, T is the detector response time.
Substituting (2.39) into (2.38), the formula will become simpler:
2 ]} values will decrease rapidly.
Fig. 2-3 The plot of Sinc-function.
When x values larger then p (3.1415), the y values are small enough to ignore it. The laser frequency is about 1015 Hz, but the fast detector response time T is just about 10-12 s. We can ignore these faster terms in equation (2.40), so the equation can be written as:
2 ] The first two terms are the average intensities of wave 1 and wave 2, respectively. W is the difference of angular frequency between two waves.
f is the phase difference of the two waves (figure 2-4).
Fig. 2-4 The beating intensity with an angular frequency of W. In the
simulation, we set I1 equals I2.2.3 Coherence and Martin-puplett interferometor
2.3.1 Carry lifetime and Coherence length
0 5 10 15 20 25
lifetime of photoconductive antenna’s substrate and the coherence length of CW THz wave. First, we assume that the spectrum of the light sources are Gaussian shape. Assume that the line width of the LD (source) are the
same,δw.
Then, we can get the Fourier transform of Ei(ω). We only need the envelope decay term, so the Ei(t) become the last formula of equation (2.32).
Finally, follow the formula below, we can get the intensity beating signal of the CW source.
and the signal in frequency domain I(ω),
1
2 ( 1 2 )2 2 2( 1 2 )2 ( 1 2 )2 ( 1 2 )2
From the rate equation of carrier in the substrate of the photoconductive antennas
R is the reflectivity of the sample. From eq (2.23), we know that radiated THz field is proportional to the derivation of photocurrent with respect to the time Then we take the Fourier transform of the recombination of (2.46), (2.23) and (2.47)
Finally, we find the THz field like this formula
2 2
3.00E+011
Fig. 2-5 CW THz field at frequency domain (a) waveform with different carrier lifetime (b) saturation effect as increasing carrier lifetime(c) waveform with different line-width of the dual-wavelength
Simulation with different carrier lifetime (1, 10 and 100 picosecond), the central frequency of the dual-wavelength system were 3.606*1014 and 3.603*1014 Hz, the corresponding wavelength were about 830nm, and the line width of each laser diode was δw=30MHz. We find that the central frequency of the simulated CW THz radiation field was 0.3 THz, which was equal to the frequency difference of the dual-wavelength system.
Form Fig.2-5(a), we find that the line-width of the radiation with different carrier lifetime were about 84.68MHz, the corresponding
coherence length was above 350cm. As we increase the carrier lifetime of the PC antenna, the calculated amplitude of CW THz radiation waveform increases, but shows the saturation effect. We plot the peak amplitude of the CW THz radiation with carrier lifetime in Fig.2-5(b). It shows much clearer that the peak amplitude of the CW THz radiation saturated when the carrier lifetime is longer than 10picosecond. It also demonstrates that the substrate of the PC antenna with carrier lifetime below 10picosecond performed as the LT-GaAs PC antenna. We changed the linewidth of the dual-wavelength system and the THz waveform was shown in Fig.2-5(c).
The linewidth of the dual-wavelength system was from 30 to 50MHz, and the peak amplitude of the THz radiation was decreasing. From these mathematical analyses, we conclude that the carrier lifetime doesn’t relate to the line-width of the CW THz field, it means that carrier lifetime and the coherence length of the CW THz wave are almost independent.
2.4 Martin-Puplett polarization interferometer
The design of most interferometers used for infrared spectrometry today is based on the two-beam interferometer originally designed by Michelson in 1891. For the electromagnetic field of THz frequency range, Martin-Puplett polarization interferometer is the most usual ones, which is based on a concept originally produced by Martin and Puplett in 1969.
Historically, the Martin-Puplett1 polarizing interferometer has been the
particular importance in astronomical spectroscopy. For example, the modulation efficiency of a polarizing beamsplitter is both high and uniform over a wide spectral range. Martin-puplett interferometer mainly measures the Degree of Coherence function γ(
τ
), the following we will describe the details. The interferometer consisted of a wire grid polarizing beam-splitter rotated 45± relative to the polarization of the incident light wave. The reflected and transmitted light waves are of equal intensity and orthogonally polarized. Retro-reflectors in each arm rotate the polarization of the incident light 180±. The orthogonal transmitted and reflected light waves are recombined at the beamsplitter.A final wire grid polarizer (analyzer) transmits components of the combined outgoing beams with the same polarization. The interferometer
A final wire grid polarizer (analyzer) transmits components of the combined outgoing beams with the same polarization. The interferometer