Z. Zhu et al. Optics Communications 410 (2018) 389–395
the structure of the entire system, but also improve its performance.
A photonic scheme to simultaneously achieve microwave frequency
down-conversion and tunable microwave phase shift was proposed and
demonstrated in [14]. RF and local oscillator (LO) signals drive two arms
of the DD-MZM, respectively. A FBG reflects the first-order sidebands
of both RF and LO frequency. After optical to electrical conversion,
the IF signal is recovered, and the phase of the IF signal can be
shifted continuously in full 360 degree. However, to realize independent
multichannel phase shifting, multiple lasers or modulators are required,
which increases the complexity of the system.
In this paper, we propose a simple photonic system that can im-
plement frequency down-conversion, multichannel phase shifting, and
zero-IF receiving concurrently. The key devices are a PM in a sagnac
loop and an OBPF, which generate an orthogonal polarized carrier
suppression single sideband (CS-SSB) signal with the frequency shifts
equal to the frequencies of the RF and LO signals. By introducing
phase difference between orthogonal polarized optical sidebands using
a polarization controller (PC), dividing into two polarization directions
via a polarization beam splitter (PBS), and beating at the balanced
photodetector (BPD), frequency down-conversion with improved gain
and independent multichannel phase shifting is achieved. In addition,
zero-IF receiving can be also realized by choosing two quadrature
channels. The proposed method is analyzed theoretically, demonstrated
by simulation, and compared with the conventional two cascaded MZMs
scheme.
2. Principle
2.1. Frequency down-conversion with multichannel phase shifting
Fig. 1 shows the schematic diagram of the proposed frequency
down-conversion with multichannel phase shifting scheme based on
bidirectional use of a PM in a sagnac loop and balanced detection. A
light wave generated from a laser diode (LD) is injected to a polarization
beam splitter (PBS
1
) through a polarization controller (PC
1
) and an
optical circulator (OC). By adjusting PC
1
, the light wave is split into two
orthogonally polarized light waves that are equal in power. The PM is
a commercial traveling-wave modulator with two electric ports, which
are designed to have effective modulation for clockwise direction light
waves at the first electric port (port 1) and have effective modulation for
counter-clockwise direction light waves at the second electric port (port
2) [15]. For the clockwise direction, due to the velocity mismatch, the
optical carrier is only modulated by the RF signal and the modulation
by the LO signal is negligible. For the counter-clockwise direction, the
optical carrier is only modulated by the LO signal and the modulation by
the RF signal is negligible. Since the polarization states of the light waves
from port 1 and port 2 are orthogonal, a 90
◦
polarization rotation (PR) is
introduced by a polarization rotator or a PC. Then, orthogonal polarized
phase modulated signals reach the PBS
1
again, and amplified by the
following erbium-doped fiber amplifier (EDFA). The optical bandpass
filter (OBPF) is used to select upper optical sidebands of the orthogonal
polarized phase modulated signals. The selected optical sidebands are
sent to an optical splitter which is used to divide the optical signals into
N channels. In each channel, a PC, a PBS and a balanced photodetector
(BPD) are used to construct the rest of the photonic microwave phase
shifter, and the phase of the IF signal after the BPD can be tuned easily
by controlling the PC.
According to the bidirectional modulation characteristic of the PM,
the optical signal at the output of the PBS
1
can be written as
𝐸
𝐶𝐾
(𝑡)
𝐸
𝐶𝐶𝐾
(𝑡)
=
2
2
𝐸
𝑐
𝑒
𝑗𝑤
𝑐
𝑡
𝑙
𝑒
𝑗𝑚
𝑅𝐹
cos(𝑤
𝑅𝐹
𝑡)
𝑒
𝑗𝑚
𝐿𝑂
cos(𝑤
𝐿𝑂
𝑡)
(1)
where 𝐸
𝑐
and 𝑤
𝑐
are the amplitude and angular frequency of the optical
carrier, l is insertion loss of the PM, 𝑚
𝑅𝐹
= 𝜋𝑉
𝑅𝐹
∕𝑉
𝜋
represents the
modulation index of the RF signal, 𝑉
𝑅𝐹
is the RF receiving signal voltage
applied to the PM, 𝑉
𝜋
is the half-wave voltage of the modulator, 𝑤
𝑅𝐹
is the angular frequency of the RF receiving signal, 𝑚
𝐿𝑂
= 𝜋𝑉
𝐿𝑂
∕𝑉
𝜋
represents the modulation index of the LO signal, 𝑉
𝐿𝑂
is the LO signal
voltage applied to the PM, 𝑤
𝐿𝑂
is the angular frequency of the LO signal.
Using Jacobi–Anger expansion, Eq. (1) can be approximately rewrit-
ten as
𝐸
𝐶𝐾
(𝑡)
𝐸
𝐶𝐶𝐾
(𝑡)
=
2
2
𝐸
𝑐
𝑒
𝑗𝑤
𝑐
𝑡
𝑙
∞
𝑛=−∞
𝑗
𝑛
𝐽
𝑛
(𝑚
𝑅𝐹
)𝑒
𝑗𝑛𝑤
𝑅𝐹
𝑡
∞
𝑛=−∞
𝑗
𝑛
𝐽
𝑛
(𝑚
𝐿𝑂
)𝑒
𝑗𝑛𝑤
𝐿𝑂
𝑡
(2)
where 𝐽
𝑛
is the (n)th-order Bessel function of the first kind.
As the modulation index is usually small, the second and higher-
order Bessel function are ignored. Eq. (2) can be further simplified as
𝐸
𝐶𝐾
(𝑡)
𝐸
𝐶𝐶𝐾
(𝑡)
=
2
2
𝐸
𝑐
𝑒
𝑗𝑤
𝑐
𝑡
×
𝑙
𝑗𝐽
1
(𝑚
𝑅𝐹
)𝑒
−𝑗𝑤
𝑅𝐹
𝑡
+ 𝐽
0
(𝑚
𝑅𝐹
) + 𝑗𝐽
1
(𝑚
𝑅𝐹
)𝑒
𝑗𝑤
𝑅𝐹
𝑡
𝑗𝐽
1
(𝑚
𝐿𝑂
)𝑒
−𝑗𝑤
𝐿𝑂
𝑡
+ 𝐽
0
(𝑚
𝐿𝑂
) + 𝑗𝐽
1
(𝑚
𝐿𝑂
)𝑒
𝑗𝑤
𝐿𝑂
𝑡
(3)
It can be seen from Eq. (3) that the generated orthogonal polarized
optical signal contains an optical carrier and ±1st order sidebands, as
shown in Fig. 1A and B.
The orthogonal polarized optical signals are amplified by the EDFA
and the upper sidebands are selected by the OBPF, as shown in Fig. 1C.
It can be given as
𝐸
𝑂𝐵𝑃 𝐹
(𝑡) =
2
2
𝐸
𝑐
𝑒
𝑗𝑤
𝑐
𝑡
𝑙𝐺
𝐴
𝑗𝐽
1
(𝑚
𝑅𝐹
)𝑒
𝑗𝑤
𝑅𝐹
𝑡
𝑗𝐽
1
(𝑚
𝐿𝑂
)𝑒
𝑗𝑤
𝐿𝑂
𝑡
(4)
where 𝐺
𝐴
is the gain of the EDFA.
Since the transformation matrix of the PC
𝑛
and PBS
𝑛
is given by
𝑇
𝑃 𝐶−𝑃 𝐵𝑆
=
cos 𝛼 − sin 𝛼𝑒
𝑗𝜃
𝑛
sin 𝛼 cos 𝛼𝑒
𝑗𝜃
𝑛
(5)
where 𝛼 is the angle between the principle state of the light and the
principle axis of the PBS, and 𝜃
𝑛
is the phase difference between the x
and y polarization state induced by the PC
𝑛
. The output optical signal
of the PBS
𝑛
can be written as
𝐸
𝑃 𝐵𝑆−1
(𝑡)
𝐸
𝑃 𝐵𝑆−2
(𝑡)
= 𝑇
𝑃 𝐶−𝑃 𝐵𝑆
𝐸
𝑂𝐵𝑃 𝐹
(𝑡)
=
2
2
𝐸
𝑐
𝑒
𝑗𝑤
𝑐
𝑡
𝑙𝐺
𝐴
cos 𝛼 − sin 𝛼𝑒
𝑗𝜃
𝑛
sin 𝛼 cos 𝛼𝑒
𝑗𝜃
𝑛
𝑗𝐽
1
(𝑚
𝑅𝐹
)𝑒
𝑗𝑤
𝑅𝐹
𝑡
𝑗𝐽
1
(𝑚
𝐿𝑂
)𝑒
𝑗𝑤
𝐿𝑂
𝑡
=
2
2
𝑗𝐸
𝑐
𝑒
𝑗𝑤
𝑐
𝑡
𝑙𝐺
𝐴
cos 𝛼𝐽
1
(𝑚
𝑅𝐹
)𝑒
𝑗𝑤
𝑅𝐹
𝑡
− sin 𝛼𝑒
𝑗𝜃
𝑛
𝐽
1
(𝑚
𝐿𝑂
)𝑒
𝑗𝑤
𝐿𝑂
𝑡
sin 𝛼𝐽
1
(𝑚
𝑅𝐹
)𝑒
𝑗𝑤
𝑅𝐹
𝑡
+ cos 𝛼𝑒
𝑗𝜃
𝑛
𝐽
1
(𝑚
𝐿𝑂
)𝑒
𝑗𝑤
𝐿𝑂
𝑡
(6)
It can be seen from Eq. (6) that two carrier suppression single
sideband (CS-SSB) signals with frequency shift of 𝑤
𝑅𝐹
and 𝑤
𝐿𝑂
and
phase difference of 𝜋 + 𝜃
𝑛
are obtained at the output of one principal
axis of the PBS, and two CS-SSB signals with frequency shift of 𝑤
𝑅𝐹
and
𝑤
𝐿𝑂
and phase difference of 𝜃
𝑛
are obtained at the output of the other
principal axis of the PBS, as shown in Fig. 1D and E. After detected by
a square-law BPD, the photocurrent can be written as
𝐼
𝐵𝑃 𝐷𝑛
(𝑡) = 𝑅
𝐸
𝑃 𝐵𝑆−1
(𝑡)
2
−
𝐸
𝑃 𝐵𝑆−2
(𝑡)
2
= −
1
2
𝑅𝐺
𝐴
𝑙𝐸
2
𝑐
cos
2
𝛼𝐽
2
1
(𝑚
𝑅𝐹
) + sin
2
𝛼𝐽
2
1
(𝑚
𝐿𝑂
)
− sin 2𝛼𝐽
1
(𝑚
𝑅𝐹
)𝐽
1
(𝑚
𝐿𝑂
) cos
(𝑤
𝑅𝐹
− 𝑤
𝐿𝑂
)𝑡 − 𝜃
𝑛
−sin
2
𝛼𝐽
2
1
(𝑚
𝑅𝐹
) − cos
2
𝛼𝐽
2
1
(𝑚
𝐿𝑂
)
− sin 2𝛼𝐽
1
(𝑚
𝑅𝐹
)𝐽
1
(𝑚
𝐿𝑂
) cos
(𝑤
𝑅𝐹
− 𝑤
𝐿𝑂
)𝑡 − 𝜃
𝑛
(7)
where 𝑅 is the BPD responsivity.
In order to suppress the DC components and improve the power of
the IF signal, we set 𝛼 = 45
◦
. Thus, Eq. (7) can be rewritten as
𝐼
𝐵𝑃 𝐷𝑛
(𝑡) = 𝑅𝐺
𝐴
𝑙𝐸
2
𝑐
𝐽
1
(𝑚
𝑅𝐹
)𝐽
1
(𝑚
𝐿𝑂
) cos
(𝑤
𝑅𝐹
− 𝑤
𝐿𝑂
)𝑡 − 𝜃
𝑛
(8)
390