Optical-to-THz Frequency Down-Conversion

Utilizing Two-Dimensional Plasmons

S. Manabe1,2, T. Otsuji1,2, and A. Satou1,2

1
Research Institute of Electrical Communication, Tohoku University, Sendai, Japan
2
Research Organization of Electrical Communication, Tohoku University, Sendai, Japan

Abstract—We theoretically study the carrier frequency gate-to-channel voltage swing as follows:
down-conversion from optical signals to terahertz signals utilizing
߲݊ ߲
two-dimensional plasmons in an InGaAs-channel high-electron- ‫ ۓ‬൅ ሺ݊‫ݒ‬ሻ ൌ ‡ሺ‫ܩ‬௱ఆ ݁ ି௜οఆ௧ ሻ
mobility transistor (InGaAs-HEMT). We demonstrate that the ۖ ߲‫ݐ‬ ߲‫ݔ‬
ۖ ߲‫ݒ‬ ߲‫߶߲ ݁ ݒ‬ ‫ݒ‬
down-conversion can be implemented by the so-called photonic
൅‫ݒ‬ െ ൌെ (1)
‫ݐ߲ ۔‬ ߲‫ݔ߲ ݉ ݔ‬ ߬
double-mixing functionality in the HEMT utilizing the plasmonic
hydrodynamic nonlinearities and that the double-mixing
ۖ
ۖ ‫ܥ‬൫ܸ௚ െ ܸ௧௛ െ ߶൯
conversion gain can be enhanced by orders of magnitude with the
‫ە‬ ݊ൌ
help of the plasmon-resonance effect. ݁
where n(x,t), v(x,t) are carrier density and the velocity, ߶(x,t) is
I. INTRODUCTION potential in the channel, e is the elementary charge, m is the
electron effective mass, ߬ is the momentum relaxation time, C
T HE seamless convergence of fiber networks and
wireless networks are required for future high-capacity
communication networks, together with the use of higher
is the capacitance per unit area, ܸ௚ ǡ ܸ௧௛ are the gate and
threshold voltages, and ‫୼ܩ‬ஐ is the photoelectron generation rate.
wireless carrier frequencies in the millimeter-wave We assume that the photogenerated electrons as a photomixed
(MMW)/terahertz (THz) bands1. One of key technologies for signal is injected into the channel from a photoabsorption layer
the implementation of such networks is a carrier-frequency below the channel layer, which is similar to the HEMT
down-converter from optical data signals to MMW/THz data integrated with a uni-traveling-carrier photodiode structure [4],
signals. We have studied the so-called photonic double-mixing while the RF signal ܸோி ݁ ି௜ఠೃಷ ௧ is applied to the gate (see Fig.
functionality of graphene FETs and InGaAs 1(a)). We adapt the same boundary conditions as in [5], i.e.,
high-electron-mobility transistors (InGaAs-HEMTs) to zero ac potential at the source and zero ac current at the drain.
perform the down-conversion of the 1.5-m bands to the MMW In these conditions, the fundamental plasmon frequency is
bands2,3,4. The photonic double-mixing consists of two mixing written as
functionalities: the photomixing of an optical carrier signal and
an optical subcarrier signal generating a difference-frequency ߨ‫ݏ‬ ߨ ݁ሺܸ௚ െ ܸ௧௛ ሻ
RF signal, and the mixing of this RF signal and another RF ߱௣௟ ൌ ൌ ඨ (2)
ʹ‫ܮʹ ܮ‬ ݉
signal, generating an IF signal. To extend the RF/IF bands
further to the THz bands, the limitation of the operation where s is the velocity of plasma wave and L is the channel
frequency bandwidth by the electron transit time must be length. Parameters of the HEMT were chosen in such a way
overcome. that the fundamental plasmon frequency, pl/2, becomes 0.9
In this work, we investigate theoretically the utilization of THz. Assuming weak amplitudes of both photomixed and RF
two-dimensional (2D) plasmons in an InGaAs-HEMT channel signals, we can apply a perturbation theory to Eq. (1) as
for the THz double-mixing. We show that the hydrodynamic follows:
nonlinearities of the 2D plasmons result in the generation of the
double-mixed THz-IF signal and that the plasmon-resonance ‫ ݒ‬ൌ ‫ݒ‬଴ ൅ ‫ݒ‬ଵ ൅ ‫ݒ‬ଶ ൅ ‫ڮ‬
൜ (3)
effect can enhance the double-mixing conversion gain. ߶ ൌ ߶଴ ൅ ߶ଵ ൅ ߶ଶ ൅ ‫ڮ‬
where v0 and 0 are steady-state electron velocity and channel
II. ANALYTICAL MODEL potential, vn and n are n-th order perturbation terms (n = 1, 2,
Here, we extended the hydrodynamic model in [5] to describe ͐). In this study, we assume source-to-drain is not biased (v0 =
the mixing of a photomixed signal with the frequency, , and 0, 0 = 0). The first-order terms further consist of harmonically
an RF signal with the frequency, RF, by the hydrodynamic oscillating components with frequencies  and Ȱ RF: ‫ݒ‬ଵ ൌ
nonlinearities of the 2D plasmons. The carrier transport along ‡ሾ‫୼ݒ‬ஐ ݁ ି௜୼ஐ௧ ൅ ‫ݒ‬ோி ݁ ି௜ఠೃಷ ௧ ሿ and ߶ଵ ൌ ‡ሾ߶୼ஐ ݁ ି௜୼ஐ௧ ൅
the channel is described by the hydrodynamic equations ߶ோி ݁ ି௜ఠೃಷ ௧ ሿ , whereas the second-order terms consist of
together with the relationship between the carrier density and components oscillating with frequencies 2, 2RF, +RF,
dm = |-RF|, together with second-order correction to the
steady state. Extracting only the double-mixing components
with the frequency dm from the latter, we obtain the following
equations for the amplitudes of the double-mixing components,
‫ݒ‬ௗ௠ and ߶ௗ௠ , from Eq. (1):

Fig. 1. Schematic view of the plasmonic THz double-mixing

        

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 ߲‫ݒ‬ௗ௠ ͳ ߲ ‫כ‬
݅߱ௗ௠ ߶ௗ௠ െ ൫ܸ௚ െ ܸ௧௛ ൯ ൌെ ቂ‫ כ ߶ ݒ‬൅ ‫ݒ‬ǼȐ ሺ߶ோி െ ܸோி ሻቃ
൞ ߲‫ݔ‬ ʹ ߲‫ ݔ‬ோி ୼ஐ (a)
ͳ ݁ ߲߶ௗ௠ ͳ ߲ (4)
൬݅߱ௗ௠ ൅ ൰ ‫ݒ‬ௗ௠ െ ൌെ ሺ‫ כ ݒ ݒ‬ሻ
߬ ݉ ߲‫ݔ‬ ʹ ߲‫ ݔ‬ோி ǼȐ
Equation (4) forms a set of second-order ordinary differential
equations with respect to the coordinate x, which can be solved
by applying the above-mentioned boundary conditions, and the
double-mixed signal ߶ௗ௠ with the frequency, ߱ௗ௠ ൌ
ȁȟȳ െ ߱ோி ȁ is obtained.
III. RESULTS AND DISCUSSION
Figures 2(a) and (b) show log-plots of the ac potential
amplitude at the drain, dm, with the frequency dm = |-RF|,
as a function of the photomixed and RF frequencies with
(b)
different momentum relaxation times in the channel,  = 1 ps
and 0.27 ps. The amplitude is normalized by the amplitude of
the applied ac gate voltage, VRF. First, it is clearly seen that the
double-mixed output is generated by the hydrodynamic
nonlinearities in a wide range of the frequencies. Especially,
distinct peaks of the double-mixed signal are seen at dm =
|-RF| = npl (n = 1, 3, …), suggesting double-mixed output
has plasmon-resonance effect the same as for one signal input
shown in [5]. Second, the peak value increases with the longer
momentum relaxation time as we can see in Fig. 2(b). This
figure clearly shows the double-mixed output also has peaks at
 = npl, RF = npl (n = 1, 3, …), suggesting that we can
receive the benefit of the plasmon-resonance effect even if the (c)
frequency of the output is far from plasmon frequency. Since
RF and dm are fixed value depending on a wireless
communication system where double-mixing is applied, this
result suggests that the plasmon frequency should be set either
one of these frequencies (, RF, and dm) to take advantage
of the enhancement of the double-mixing conversion gain by
orders of magnitude with help of plasmon-resonance effect.
In Fig. 2(c), we set the channel length L = 200 nm, which is
shorter than the case in Fig. 2(a), with  = 0.27 ps, so that the pl
/2 becomes 1.1 THz. As expected, one can see the resonant
peaks in Fig. 2(c) at 1.1 THz. This result shows that the peak
frequencies can be controlled by the channel length.
Fig. 2. Log-plots of the normalized amplitude of the double-mixed signal,
IV. SUMMARY dm/VRF, as a function of the photomixed and RF frequencies,  and RF,
with (a) L = 250 nm and ȫ = 0.72 ps, (b) L = 250 nm and  = 0.72 ps, and
We studied theoretically the plasmonic THz double-mixing, (c) L = 200 nm and  = 0.72 ps. Dotted lines correspond to (a) dm =
which utilizes the hydrodynamic nonlinearities of 2D plasmons |-RF| = npl (n=1,3,…) in (a),  = RF = npl in (b), dm = pl in (c).
in a HEMT channel. We demonstrated that the plasmonic
hydrodynamic nonlinearities generate the double-mixed signal
and the plasmon-resonance effect increases the amplitude of
the double-mixed signal resonantly if either of the photomixed, REFERENCES
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