Chapter 5. Mid-size-gap antennas
5.4 Results and discussions
5.4.1 Trap-enhanced bias field
the analyze between the p
5.4. Results and discussions
5.4.1 Trap-enhanced bias field
Before presenting the experimental data, w lti-GaAs:As antennas with numerical results which will be compared with the corresponding measured results. The measured THz waveforms for SI-GaAs will also be shown without any explanation of numerical simulation.
e analyze our mu
For multi-GaAs:As antennas, Figure 5.4 shows on a logarithmic scale the simulated bias field E (x) as a function of position x for four different G in the absence of pump pulses excitation. E
+
b
ach Eb(x) in Fig. 5.4 is near the edge of the anode (0≤ ≤x 10 mμ ) and at depth z=0.1 mμ . As seen in this figure, the Eb(x) established G, one can find much
stronger E (x) with the larger G. Besides, one common feature in all the cases is that the Eb(x) will grow very rapidly if x approaches the anode ( ~ 0x ). For instance, Eb(x) reaches field strength of as high as 103 kV/cm at x 0.5 m
near the anode are highly nonuniform. For different values of
b
μ
< in the case of
0.5 mm
.
G= This gap-dependent strong bias field is a consequence of the PC antennas with larger G being applied by larger bias voltage.
Because the absorption coefficient of the PC material is about 106 m-1, the main absorption range of pump pulses is from z= to 0 z=2 m,μ and is relatively much smaller than the antenna’s gap size. Thus, for a given x, Eb is uniform along the ithin this absorption r is somewhat similar to the distribution of the magnetic field genera agnetic bar. Provided that the length of a magnetic bar is 20 cm, then the m ield will be uniform near the bar.
5.4.2 Evolutions of p in antenn
z-direction w ange. This
ted from a m agnetic f
arameters as
Next we study the variations of some physical parameters with time at specific pump depth z and pump fluence F. As an example, Fig. 5.5 shows the calculated
(
n x, )t , Δ( , )x t , E x t , and s( , ) E x t( , ) for the case of G=0.5 mm. As can be seen from Fig. 5.5(a), at x=0.12 mmthe photo-excited electron concentration n exhibits a maximum peak which is the signature of an edge illumination. After excitation, both the photo-excited electron and hole are subjected to Es and thus move in opposite directions since both possess opposite charges. Of importance, the carrier separation leads to two positive peaks in Δ as depicted in Fig. 5.5(b) where one peak locates at around the gap center and the other peak is near the anode. Obviously, the magnitude ral peak. The large peak has
of the peak near the anode is much larger than that of the cent
a magnitude of 102 of the small peak. This extremely large peak arises from the combination of three mechanisms: the first is that electron mobility is much larger
le it cond i e enhanced bias f anode speeds up
the movement of electron near the anode, and the third is that large amounts of electrons are absorbed by the anode.
The space-charge bias-field screening
than ho mobil y, the se s that th ield near the
phenomenon associated with the two Δ peaks is demonstrated in Fig. 5.5(c). We can see from this figure that the nonuniform bias field E diminishes from its initial value E to a lower value with t. This behavior originates from the mechanism that the small
s b
Δ peak at gap center produces an
opposite field canceling out the original field between the gap center and anode, while the large Δ peak near the anode creates a strong opposite field that screens the original enhanced bias field near the anode. The near-field THz radiation E was obtained from the solution of Eq. (5.2.12), with the result presented in Fig. 5.5(d). It is clear that inasmuch as the electron and bias field have extreme values near the anode, the maximum E also occurs in the vicinity of the anode.
Let us turn to what is the key to the understanding of gap-dependent TH waveform, the variations of Δ and E
z
s with t at specific z and x near the anode.
Substituting four different values of G into the calculations, we obtain the t dependence of Δ and E at x = 0.01 mm and s z=0.1 mμ as shown in Fig. 5.6. For
each G, one sees that the quantity Δ increases from 0 to 1.6 10 cm× 15 −3 with t. For different G the larger the G, the larger the , Δ. The increase of Δ with t is related to the fast decrease in Es, which is also plotted in Fig. 5.6. The result of Fig. 5.6 indicates that the decreasing amount of Es is proportional to G within certain time duration. In other words, it implies that an antenna with larger G also has a larger space-charge screening effect that significantly influents THz radiation waveforms Er , as we will show in the following.
5.4.3 THz radiation waveforms and spectra
According to Eq. (5.2.13), we calculated temporal THz fields Er and corresponding Fourier-transformed amplitudes Er spectra using four different values of G, and the results of these calculations are given in Fig. 5.7(a) and 5.7(b), respectively. For comparison, we present the measured E from multi-GaAs:Asr +
antennas and their corresponding Er in Fig. 5.7(c) and Fig. 5.7(d). The measured THz waveforms and spectra for SI-GaAs antennas are shown in Fig. 5.7(e) and Fig.
5.7(f). Here we first analyze the measured data for the multi-GaAs:As+ case. In Fig.
5.7(c), each measured waveform contains a dominant pos nd a negative peak followe ly varying tail. The dimensionless param ter Er was obtained e, so that the maximum amp
itive peak a
d by a slow e
by normalizing individual waveform to its maximum amplitud
litude of Er is equal to one. In the time domain, the analysis for these waveforms can be characterized in terms of four quantities: the positive peak widths (full width of the positive peak at half maximum)δp, and the negative peak widths (full width of the
negative peak at half minimum)δ , and the negative tail with duration of Γ , and the n
negative value −Erminof the negative peak. In the frequency domain, we concentrate on the frequency bandwidth fΔ of the spectrum (full width of the spectrum at half maximum).
Examining the measured positive and negative peaks in Fig. 5.7(c), it is worth noting that the inequality δp > δn is always satisfied at different values of G. In
detail, we observe that the measured δp values are fixed to about 0.33 ps which is less than that reported from Grischkowsky et al. (δp~ 0.38 ps) [14]. Furthermore, for different G the measured values of δn are also different, and range irregularly between 0.30 to 0.27 ps without an explicit dependence. For each G, one can see from Fig. 5.7(c) that a relatively ng negative tail with duration ~ 3.7 p
y
lo Γ s follows
the negative peak, and is more obvious than those found in other similar experiments [15-16].
Let us now to anal ze the simulated data. In Fig. 5.7(a), we found that the me
return y
asured feature that δp > δn can also be fulfilled by the simulated data. Besides, the simulated data can reproduce the measured long negative tails. Quantitatively, the simulated δp, δn, and Γ are about 0.25, 0.18, and 0.8 ps, respectively. While further simulating the model by varying F, we found that the numerical solution gives the result of δp > δn at large enough ( F >10 J / cmμ 2), but a reverse result, δp <
δn, will be obtained at small F (<10 J / cmμ 2). In addition, the simulated positive peak Ermaxwill vary in a nonlinear way that obeys the scaling rule F as the case of small or large-gap antennas. On the other hand, as F increases, the negative value E−
at various
min
r of the simulated negative peak exhibits an increasing trend since a larger F will excite larger carrier concentration and thus acquire larger space-charge field screening effect.
5.4.4 Dependence of the negative peak on gap size
Also found in Fig. 5.7 is the phenomenon that the value of −Ermin varies with G, as well as the bandwidth fΔ . The dependences of both the simulated r and fΔ
orm min= ( G), which is also plotted in The increasing trend in −Ermin reflects the variation of
on can be obtained from Figs. 5.6(a) and 5.6(b). In Fig. 5.8 we compare these simulated dependences with the measured ones obtained from Figs. 5.7(c) and 5.7(d).
As can be seen, as G increases from 0.02 to 0.5 mm the measured −Ermin increases monotonically from 0.46 to 0.58, and depends in a strongly nonlinear way on G. The nonlinear dependence of the measured −Ermin on G can be described by a saturation function with the f
G
0.45G0.198+0.24)/(1+0.14 Er
−
.8. Δ , and enables f
Fig. 5
Δ to exhibit an increasing trend similar to r. In detail, the measured ff Δ increases nonlinearly from 1.2 to 1.6 THz with increasing G. These fΔ values are close to those reported by Grischkowsky et al. [17] (Δf ~ 1.32 THz) and M. Tani et a 18]
(Δf ~ 1.63 THz). What is especially interesting is that such large
l. [
Δ are much larger f than those obtained from some large-aperture SI-GaAs antennas ( fΔ ~ 0.27 THz) [19], as well as some small-aperture SI-GaAs or multi-GaAs:As+ antennas ( fΔ ~ 1 THz) [20]. This larger fΔ is a reflection of a narrow negative peak in Fig. 5.5(c) and
5.5(d), and it is just favorable for applications such as THz medical or security imaging requiring broader spectra.
Compared to the measured data in Fig. 5.8, one can perceive that either the simulated −Ermin or fΔ vary with G in a manner similar to the measured ones. Fits to the simulated −Ermin yield a saturation function by the form −Ermin =
6.66G) as plotted in Fig. 5.8. The values of
(4.42G+0.43)/(1+ the simulated −Ermin
agree well with the measured results, while the simulated fΔ was found to be larger than the measured ones. This inconsistency is because our simulation neglect some pulse broadening factors such as the THz pulse dispersion in optical elements, and the strong diffraction property of the THz beam optics. In addition, we also ignore the antenna effect in the 100- m-wideμ transmission lines where the field traveling in the x-direction is reflected and transmitted into free space (or into the substrate) at the
edge of th due to he large impedance mismatch between the metal and the semiconductor. This antenna effect might be one of the reasons why the ex ntal pulse width of THz radiation is broader than that of theoretical one. However reasonable to guess the overall characteristics of the THz radiation is determined by the THz field generated in the photoconductive gap and the antenna effect only broadens the pulse shape without changing qualitative characteristics of the THz
e line t
perime , it is
radiation. We think na effect is worthy to be investigated further in future project.
According to the above numerical study, it implies that the underlying mechanism giving rise to the increasing trend in −Ermin is that −Ermin s /
− is proportional to the space-charge screening effect. Therefore an antenna with
larger G will create a stronger space-charge field screening effect leading to larger
min
Er
− and fΔ .
On the contrary, in the case of SI-GaAs antenna, −Ermin decreases linearly from 0.64 to 0.47, and Δf also decreases monotonically from 1.77 to 1.41 THz. Obviously, the curves of Δf versus G vary in a manner similar to those of −Erminversus G for bot
sing different PC or. Figure 5(a)
plo
both ends of the curve together with linear relationships h kinds of PC materials.
Bias field and pump fluence dependencies
Next we study how the peak THz amplitude E
5.4.5
rmax
varies with the bias field Eb and
fluence uF G fact
pump materials and varying the
ts the Eb dependencies of Ermax
from SI-GaAs and multi-GaAs:As+ antennas with three different figures for G. As seen in this figure, the data reveals linear variations in the case of G .02 mm. In the case of G = 0.5 and 1 mm, it is worth noting that nonlinear behaviors occur at
= 0
appearing in the middle parts of the curves. Such nonlinear behaviors become more cm and 9 kV/cm, wh
obvious in the case of multi-GaAs:As+ antennas between 6 kV/
ere the amplitude reduction is probably owing to the heating effect within the antennas. This implies that an even higher THz radiation power may be acquired under good cooling apparatus in the pumping area of the sample. Besides, the multi-GaAs:As+ antenna has the advantage of enduring a nominal bias field of as high as 8 kV/cm without causing any electrical damage to itself under photoexcitation. By contrast, the bias field applied to the SI-GaAs antenna has to be constrained below the threshold of 4 kV/cm to prevent electrical damage to the devices.
The F dependencies of Ermax
are plotted in Fig. 5(b) where the Ermax
increases monotonically with the increase of F for each material and G. We also found that the antenna with a larger G possesses higher Ermax
for each material, and the Ermax
of a multi-GaAs:As+ antenna is lower than that of a SI-GaAs antenna in the measurable range (i.e. 0 ~ 70 J/cmμ 2) with the same G. Nevertheless, we perceive that the Ermax
from SI-GaAs antennas reveals slightly saturated trends at a high F, leading to a reverse consequence that if F is over 70 J/cmμ 2 the Ermax from multi-GaAs:As +
antennas will be expected to be higher than the SI-GaAs cases, according to the theoretical curves obtained from the fit to experimental data using the scaling rule [15].
In the following, we employ the scaling rule to interpret the observations in Fig. 5.
It is known that the scaling rule relates Ermax
to both Eb and F by the form
In this notation, nL is the refractive index, e
q R
μ is the electron mobility, A refers to
pump spot area, and hν is the photon energy.
As described in the aforementioned experimental conditions, the diameter of our
pump spot area stays at about 0. 7.8 10 mm× −3 2.
For the cases of G=0.02, lues of A are equal to the gap area
4 2
3.1 10 mm× − in the former case, but equal to the pump spot size 7.8 10 mm× −3 2 in the latter two cases as indicated in
0.02-mm-gap antenna is proportional to
ve the same value of A, the value of Erma
1 mm, corresponding to an area of 0.5, and 1 mm, the va
Fig. 1. According to Eq. (1) and (2), the Ermax
of a A, and thus has a lower value either in the bias
or pump fluence dependence since its value of A s smaller than the other two cases. As a matter of fact, although the latter two cases ha
i
x of a 1-mm-gap antenna is higher than that of a 0.5-mm-gap antenna rather than
having the same value of Ermax. The reason is because the strength of the
above, if one appl field to each antenna, the larger the G, the ear the anode. Thus the E
ies the same nominal bias
higher the Eb n rmax
of a 1-mm-gap antenna w is higher than that of a 0.5-mm-gap antenna with a lower E according to Eq. (2).
In Eq. (1) and (2), the n and e
ith a higher Eb
b
L μ show involvement with the optical and electrical properties of PC materials. Due to ion implantation, the values of n for a multi-GaAs:As
L
+ antenna are larger than that of a SI-GaAs antenna, and the effective
μe of a multi-GaAs:As+ antenna is estimated to be about 1500 cm / Vs less than 2 that of a SI-GaAs antenna (μe~ 3000 cm / Vs ). According to Eq. (3), a larger n and 2 smaller e
L
μ correspond to a larger D and F , leading to the Es rmax of a multi-GaAs:As +
antenna being lower than a specific F but becoming higher than a specific F at the same G. Here we take the 0.5-mm-gap antennas as an example to account for the F dependencies. In Fig. 5(b) the fit to the experimental data yields that D = 15.6, Fs = 870.5μJ/cm2 for a multi-GaAs:As+ antenna, and D = 10.2, Fs= 550.5μJ/cm2for a SI-GaAs antenna. We substitute these values into Eq. (1), and thus obtain the corresponding theoretical curves as plotted by the dashed lines of Fig. 5(b). According
these two fits for G = 0.5 mm, it can be seen that the E
to rmax
of a multi-GaAs:As+ antenna is lower than that f a SI-G o aAs antenna if F <70 J/cmμ 2, but becomes higher if F>70 J/cmμ 2. Similar phenomenon has also been found in our
large-aperture GaAs:As+ antennas [19], and hence we believe that the mid-size-gap multi-GaAs:As+ antennas will benefit from high pump fluence as well.
5.5 Conclusions
We have presented a combined experimental and theoretical study of gap-size dependent effects on THz radiation.
Experimentally, we used four multi-GaAs:As+ and four SI-GaAs mid-aperture antennas with different bias voltages and gap sizes to observe their bipolar THz waveforms in an optical pump-probe experiment. At fixed pump fluence and nominal bias field, with the increase of gap size of antennas, we observe t the
and on and the abso inimum
antennas, whereas they increase monotonically for mu
n that from a SI-GaAs antenna at a large gap size.
The
hat both b width of THz radiati lute value of THz waveform m decrease linearly for SI-GaAs
lti-GaAs:As antennas resulting in a consequence that the bandwidth from a +
multi-GaAs:As+ antenna is larger tha
bandwidths of the THz radiations from our antennas are considerably larger compared to other small or large-aperture antennas. In the dependencies of bias field and pump fluence on the peak THz amplitude, the measured data and associated theoretical prediction curves indicate that the multi-GaAs:As+ antenna benefits from
its higher reachable bias fields, and can generate even higher THz power, probably at high pump fluence, in comparison with SI-GaAs antennas.
Theoretically, we adopted a rigorous model incorporating trap-enhanced bias fields with a set of electromagnetic wave and drift-Poisson equations to interpret our experimental discovery. The numerical simulations demonstrate the carrier and field dynamics under pump pulses propagation within antennas, and also reproduce the THz waveforms which account for the experimental observations, including:
increasing trends in both the negative value of the negative peak of terahertz waveform and the bandwidth, larger peak widths, as well as long waveform tails. Our numerical study indicates that an antenna with larger G has a higher trap-enhanced bias field near the edge of the anode, resulting in larger space-charge screening effect and bandwidth.
The results will help us understand the mechanisms responsible for gap-dependent THz radiations, and also enable the researchers to realize how to obtain what they need by controlling suitable experimental conditions.
Refer
C. Fattinger and D. Grischkowsky, Appl. Phys. Lett. 53, 1480 (1988).
P. U. Jepsen and S. R. Keiding, Opt. Lett. 20, 807 (1995).
[14] N. Katzenellenbogen and D. Grischkowsky, Appl. Phys. Lett. 58, 222 (1991).
ences
[1] T. Hattori, K. Tukamoto, and H. Nakatsuka, J. Japan. App. Phys. 40, 4907 (2001).
[8] E. J. Rothwell and M. J. Cloud, Electromagnetics, CRC Press New York, 100 (2001).
[9] J. W. Goodman, Introduction to Fourier Optics, McGraw-Hill, New York (1996).
. A. Liu, M
[11] M. Tani, S. Matsuura, K. Sakai, and S. Nakashima, Appl. O
[12] M. B. Ketchen, D. Grischkowsky, T. C. Chen, C-C. Chi, I. hl. Du Hala, J-M. Halbout, J. A. Kash, and G. P. Li, Appl. Phys. Lett.
[13] Q. Wu and X.-C. Zhang, Appl. Phys. Lett. 67, 3523 (1995).
[15] C. Baker, C. E. Norman, IEEE J. Quantum Electron. 59, 121 (2002).
[16] T. A. Liu, M. Tani, and C. L. Pan, J. Appl. Phys. 93, 2996 (2003).
[17] J. Lloyd-Hughes, E. Castro-Camus, M. D. Fraser, C. Jagadish, and M. B.
Johnston, Phys. Rev. B 70, 235330 (2004).
. Tani, S. Matsuura, K. Sakai, and S. Nakashima, Appl. Opts. 36, 7853 (1997)
[18] M .
990).
[19] E. Sano and T Shibata, IEEE J. Quantum Electron. 26, 372 (1 [20] G. Rodriguez and A. J. Taylor, Opt. Lett. 21, 1046 (1996).
ig. 5.1: Geometry for calculating the far-THz field Er(t).
x
'F is the point on the
antenna’s surface,
x
is the observation point,r '
is the relative vector ofx
' with respect to x,r '
is the distance from 'x
to , x ˆz is the normal to the surface, and ds is the differential area on the surface.Fig. 5.2: The experimental setup for THz radiation from mid-size-gap photoconductive antennas.
PD1
PD2 HWP
mode-locked
Delay line
Antenna
EO c Ti:Sapphire laser
LIA
rystal
BS
V G
ig. 5.3: Schematic representation of DC-biased PC antennas excited by femtosecond l to 10
mm and 0.1 mm, respec ions are indicated by a
red circ ate a uniform
illumi n asymmetric
illumi F
laser pulses. The transmission line length L and width W are equa tively. The illuminated reg
ular spot. The left and right diagrams illustr nation for gap size G = 0.02 or 0.1 mm, and a nation for G = 0.2 or 0.5 mm, respectively.
Fig. 5.4: Simulated bias field Eb(x) as a function of position x at depth z=0.1 mμ for multi- GaAs:As+ antennas with gap sizes G of 0.02 (blue), 0.1 (green), 0.2 (red), and 0.5 mm (black).
Fig. 5.5: Simulation results. (a) electron concentration n x t( , ) , (b) negative logarithmic function of the net-charge concentration, −log[ ( , )]Δ x t , (c) space-charge field E x t , and (d) near-field THz radiation E(x,t) as a s( , ) function of the time delays t and gap position x at pump depth z=0.1 mμ for multi-GaAs:As+ antenna with gap size of 0.5 mm. The values of the large
Fig. 5.5: Simulation results. (a) electron concentration n x t( , ) , (b) negative logarithmic function of the net-charge concentration, −log[ ( , )]Δ x t , (c) space-charge field E x t , and (d) near-field THz radiation E(x,t) as a s( , ) function of the time delays t and gap position x at pump depth z=0.1 mμ for multi-GaAs:As+ antenna with gap size of 0.5 mm. The values of the large