Microwave photonic frequency multiplier with 10 times frequency multiplication


Master's Thesis, 2017

136 Pages, Grade: 82


Excerpt

Contents
Chapter 1 Introduction ... 1
1.1 Microwave photonics ... 1
1.1.1 Background ... 1
1.1.2 Microwave photonic link ... 1
1.2 Advantages ... 2
1.3 Research fields and applications ... 2
1.4 Conclusion ... 3
Chapter 2 Optical generation of micro/millimeter wave technology ... 4
2.1 Background ... 4
2.2 Optical Heterodyne ... 5
2.2.1 Optical Injection Locking ... 6
2.2.2 Optical Phase Lock Loop ... 7
2.2.3 Optical injection phase Locking Loop ... 8
2.3 Opto-electronic Oscillator ... 9
2.4 External modulation method ... 11
Chapter 3 Optical external modulator ... 13
3.1 Electro-optic effect ... 13
3.2 Mach-Zehender Modulator ... 13
3.3 Dual Drive MZM ... 15
3.4 Modulation theory ... 17
3.4.1 Double-sideband (DSB) modulation ... 19
3.4.2 Single-sideband (SSB) modulation ... 22
3.4.3 Optical carrier suppressed double-sideband (OCS-DSB) modulation ... 24
3.4.4 Odd-order optical sideband modulation ... 26
3.4.5 Even-order optical sideband modulation ... 28
3.4.6 Linear modulation ... 29
3.5 Conclusion ... 31
Chapter 4 Literature review ... 32
4.1 Introduction ... 32
4.2 Microwave generation with frequency doubled based on one biased MZM ... 32
4.2.1 System structure and principle ... 32
4.2.2 Simulation ... 34
4.2.3 Experiment and conclusion ... 36
4.3 Microwave signal generation based on two cascaded MZMs ... 36
4.3.1 Frequency quadrupling scheme ... 37
4.3.2 Frequency sextupling scheme ... 41
4.3.3 Frequency octupling scheme ... 41
4.3.4 Summary ... 45
4.4 Microwave signal generation based on a Dual-parallel Mach-Zehnder Modulator ... 46
4.4.1 System structure and principle ... 46
4.4.2 Frequency quadrupling scheme ... 47
4.4.3 Frequency sextupling scheme ... 51
4.4.4 Frequency octupling scheme ... 56

4.4.5 Frequency 12-tupler scheme ... 61
4.4.6 Conclusion ... 65
4.5 Frequency octupling scheme based on two parallel DPMZMs ... 66
4.5.1 The system structure and principle ... 66
4.5.2 Simulation ... 68
4.5.3 Conclusion ... 71
4.6 Frequency 10-tupling scheme ... 71
4.6.1 Frequency 10-tupling based on cascaded MZMs ... 71
4.6.2 Frequency 10-tupling based on DPMZM and SBS ... 73
4.6.3 Conclusion ... 75
Chapter 5 Simulation for the MZM or DPMZM in VPI ... 76
5.1 Simulation for MZM ... 76
5.1.1 Even-order optical sidebands ... 76
5.1.2 Odd-order optical sidebands modulation ... 80
5.1.3 Linear optical sidebands ... 83
5.2 How to suppress the first-order optical sidebands ... 85
5.2.1 Modulation theory ... 85
5.2.2 Simulation ... 87
5.3 Photonic frequency multiplication microwave generation based on DPMZM ... 88
5.3.1 Modulation theory ... 88
5.3.2 Simulation analysis ... 89
5.4 Generation of single sidebands based on one MZM and one PM without a coupler ... 93
5.4.1 Basic principle ... 94
5.4.2 Simulation ... 95
5.4.3 Conclusion ... 97
Chapter 6 Microwave signal generation based on two parallel DP-MZMs ... 97
6.1 A scheme for generating frequency 8-tupling microwave based on two DPMZMs ... 97
6.1.1 Basic principle ... 97
6.1.2 Simulation for Frequency 8-tupling microwave generation ... 100
6.2 Frequency 12-tupling microwave generation scheme based on two parallel DP-MZMs ... 101
6.2.1 Basic principle ... 101
6.2.2 Simulation for Frequency 12-tupling microwave generation ... 104
Chapter 7 New schemes for frequency 10-tupling microwave generation ... 106
7.1 Frequency 10-tupling microwave generation scheme based on one DP-MZM. ... 106
7.1.1 Basic principle ... 106
7.1.2 Simulation for Frequency 10-tupling microwave generation ... 108
7.2 Frequency 10-tupling microwave generation scheme based on two parallel DP-MZMs. ... 113
7.2.1 Basic principle ... 113
7.2.2 Simulation for Frequency 10-tupling microwave generation ... 116
7.3 Conclusion ... 118
Chapter 8 Experiment ... 118
8.1 Validating modulation index ... 118
8.1.1 Principle ... 119
8.1.2 Simulations and experimental results ... 120
8.1.3 Conclusion ... 122

8.2 Generation of frequency-quadrupled microwave signals based on one DPMZM ... 122
8.2.1 Principle ... 123
8.2.2 Simulation structure ... 124
8.2.3 Experimental results ... 125
8.2.4 Conclusion ... 127
Chapter 9 Conclusion and future work ... 128
9.1 Conclusion ... 128
9.2 Future work ... 129
Chapter 10 References ... 130

1
Chapter 1 Introduction
1.1 Microwave photonics
1.1.1 Background
Since the 1970s, with the rapid development of semiconductor lasers, high-speed
photodetectors, erbium-doped fiber amplifiers, optical wavelength division multiplexing,
integrated optics, optical fibers and other optical technologies, optical fiber communication
has been developed rapidly and attracted more and more people's attention and interest.
Optical fiber communication has many advantages such as small volume, light weight, low
loss, high bandwidth, no electromagnetic interference and ease to reuse (wavelength,
polarization, space) and so on. At the same time, microwave technology has also developed
swiftly. Microwave communication can be transmitted in any direction in space and be easily
constructed and reconstructed to realize the interconnection of mobile devices.
However, with people's demand for increasing information capacity and greater instantaneous
bandwidth of a signal, more and more spectrum resources are occupied, which causes
traditional wireless spectrum resources to fail to meet people's daily needs. Now microwave
technology is being developed to a higher frequency band (30 GHz-70 GHz) or even 100GHz.
But, traditional microwave transmission media have a great loss in long-distance transmission.
Traditional electronic microwave signal generators have many disadvantages such as a
complex structure, large volume and high cost. In addition, there are many difficulties in
generating a high-frequency signal. Under this background, microwave photonics [1-4] appear
and become an interdisciplinary technology which combines microwave and photonics
technologies.
1.1.2 Microwave photonic link
The basic concept of a microwave photonic link [5] is given in figure 1, which includes a light
source, an electrophonic detector and a transmission medium.

2
Figure 1 The basic concept of a microwave photonic link
The input electrical signal is modulated to the optical signal through the electro-optical
conversion, and then the RF signal with contains information is transmitted through an optical
fiber. Finally, the output electrical signal is generated by the photoelectric converter. Compared
with conventional electrical transmission links such as coaxial cable or waveguide, microwave
photonic links have many advantages, such as small size, wide bandwidth, high capacity, low
cost, low dispersion and anti-electromagnetic interference [6].
1.2 Advantages
Due to the optical fiber, the transmission loss is small, which makes sure that the fiber can
transmit the signal to long-distance base stations, and this can avoid using expensive
microwave sources and reducing the cost of the system. On the other hand, it is difficult for
microwave signals, especially for high-frequency signals, to do digital processing in the
electric field. Nevertheless, the optical technology not only can achieve the processing of
microwave signals in the optical domain but also can be applied to the microwave signal delay
[7], filter (microwave photonic filter) [8] and frequency conversion. Microwave photonics
technologies make full use of advantages of the photon technique, such as low cost, large
bandwidth and anti-electromagnetic interference, and it can also effectively solve the
microwave communication to high frequency and large capacity development of problems.
1.3 Research fields and applications
The research content of microwave photonics involves various fields related to microwave
technology and optical fiber technology, but it mainly includes two aspects:
using the
photonics technology to generate, convert, control and process millimeter/micro wave signals,

3
which are difficult to achieve in a traditional microwave system;
using the photonics
technology to improve the performance of wireless communication networks. At present, [9]
the speed of wireless communication transmission has achieved to Gb/s.
The main application field of microwave photonics is Radio over Fiber (ROF). The ROF
system can realize long-distance high-capacity communications. In the ROF system, the RF
signal is loaded on the optical wave by the transmitter, which ensures that the signal can be
transmitted through optical fibers. And then, the RF signal is recovered through the
photoelectric detector at the receiving end. The complex microwave processing units are
arranged in the central station. The base station only keeps the optical-electrical conversion
units and microwave transmit antenna [10]. In this way, we can realize signal distribution and
transmission of signals between the central station and the base station. It greatly reduces the
cost of base station construction and improves frequency reuse and increase cell density. In the
military field, microwave photonics is applied to phased array radars, radar antennas [11] and
optical fiber remote systems [12]. Optically controlled wideband phased array radars have
many advantages such as strong anti-interference ability, high resolution, fast scanning, small
volume and light weight. So, it is very suitable for airborne and shipborne radar systems.
1.4 Conclusion
Microwave photonics makes full use of the advantages of photonic technologies that are low
cost, wide bandwidth, anti-electromagnetic interference and effectively develops microwave
communications to have higher frequency and larger capacity. Its research field includes
optoelectronic devices, optical controlled microwave systems, microwave signal generation
and processing, wireless communication systems and many other fields. This thesis mainly
introduces and studies how to produce high-frequency high-quality microwave signals by the
optical methods.

4
Chapter 2 Optical generation of micro/millimeter wave technology
2.1 Background
High-frequency and high-quality millimeter/micro wave generation technology plays an
important role in radio-over-fiber communication technology, radar systems, millimeter wave
imaging systems and spectrum sensing systems. In the traditional microwave signal generation
technology, the low-frequency microwave signal is multiplied to the high-frequency band
through multiple frequency multipliers in the electrical field. While with an increase in
millimeter wave frequencies, its performance of frequency stability and phase noise will be
greatly reduced. In addition, we also need extra auxiliary devices, such as a phase-locked loop,
that cause structure complexity and the cost of the device is also rapidly improved.
However, with the development of microwave photonic technology, it is possible to replace
traditional methods by using microwave photonics to produce high-frequency high-stability
millimeter/micro wave photonics. The millimeter/micro wave signals are generated by the
microwave photonic technology and it has the following advantages:
The system structure is relatively simple. The devices usually only contain an optical
source, a modulator, a filter and a photoelectric detector. After a reasonable setting, the
millimeter-wave generation can be realized by beating required optical harmonic sidebands at
the photoelectric detector.
Breaking through the bottleneck of the frequency response of electronic devices. Using the
photonic frequency multiplication to generate microwave signal, which can greatly reduce the
frequency responses of modulators and microwave devices.
Long-distance coverage capability. The adoption of transmission feeding network based on
an optical fiber makes it possible to achieve long-distance coverage.
The basic principle of optical generation of millimeter/micro wave signals is to produce two
coherent harmonic frequency components by using the optical method, and the generated

5
microwave signals can be obtained by a photodetector and its frequency is the frequency
difference of the two-frequency components.
The generation of microwave signals usually has the following ways: direct modulation,
optical heterodyne, Optoelectronic Oscillate and external modulation.
2.2 Optical Heterodyne
In the optical domain, a high-frequency and wide-band frequency-tunable millimeter/micro
wave signal can be generated by optical heterodyning. Two-beam optical waves with different
wavelengths are beaten at a photodetector. Its frequency is equal to the frequency difference of
two-beam optical waves [13]. The basic structure is shown in the following figure.
Figure 1 Diagram of the basic principle of heterodyne method [13]
Compared to other optical generation schemes of microwave signals, the generation of
microwave signals in this way cannot be easily influenced by the fiber-optic dispersion effects
and the frequency range of generated microwave signals can be flexibly adjusted and the
frequency can reach the THZ band in theory. The system is only limited by the bandwidth of
the photodetector and the generated microwave signals have a high signal-to-noise ratio
(SNR).
However, if the light from the two free-running lasers beats directly, it will make the generated
millimeter/micro wave signals have great phase noise and high frequency jitter. So, additional
measures are required to lock two light waves in phase. But, to a certain extent, it increases cost
and complexity of the system. Nowadays we often use optical lock-on techniques to achieve
phase correlation. Those techniques include Optical Injection Locking (OIL), Optical Phase

6
Locke Loop (OPLL) and Optical Injection Phase--Locked Loop (OIPLL). Next, the
advantages and disadvantages of these schemes and their realization principles will be
introduced.
2.2.1 Optical Injection Locking
The basic principle of Optical Injection Locking is that the master laser diode (LD) is
modulated by the radio frequency signal and the nonlinear effect in semiconductor lasers is
utilized to generate ±n order sidebands. After that, the generated ±n order sidebands are
injected into the slave LD to lock two slave lasers respectively. Figure 2 shows an Optical
Injection Locking [14] structure, which consists of one master laser diode, two slave laser
diodes and one radio frequency signal source.
Figure 2 Schematic for optical injection locking [13]
From figure 2, we can know that the master LD is modulated by the RF signal and from the
frequency spectrum we can see an optical carrier and first- and second-order sidebands are
generated at the output port of the master LD. These sidebands are injected into the slave-1 and
slave-2 lasers respectively through an isolator and a coupler. Adjusting the running frequencies
of two slave LDs makes sure the output optical signal from the slave-1 and slave-2 lasers can
be locked at 2 order sidebands respectively. So, the wavelength of the master and slave LDs
have a good phase correlation. The output of sidebands from the slave-1 and slave-2 lasers are
coupled by a coupler and then two coupled optical waves are beaten at a photoelectric detector
(PD) to generate a frequency-quadrupled millimeter/micro wave signal with low phase noise.

7
However, because the locking range of optical injection locking is small, it is not unsuitable for
commercial lasers with large linewidths. Dalma Novak utilized optical injection locking
technology to generate a millimeter/micro wave signal at 34.64GHz [15].
2.2.2 Optical Phase Lock Loop
Two optical waves with phase correlation can also be obtained by optical phase lock loops
(OPLL) method [16] and figure 3 demonstrates its system structure. From the figure, we can
know that an OPLL consists of a master laser, a slave laser, a photoelectric detector, an RF
signal amplifier, a phase detector, a loop filter and an RF signal reference source. In order to get
effective phase locking, two narrow linewidth lasers are used to ensure that phase instability
only occurs in the low frequency band, which can reduce the length of the feedback loop.
Figure 3 An Optical Phase Lock Loop
Two optical waves from LD1 and LD2 are beaten in the PD to generate a microwave signal and
its frequency is the frequency difference of output optical wave between LD1 and LD2. The
generated microwave signal is injected into the phase detector to compare with the RF signal
and get a voltage signal at the loop filter which is proportional to the phase difference between
two signals. The voltage signal is fed into LD1 to change laser phase by controlling laser
injection current. In this way, it decreases the phase difference between LD1 and LD2 and
realizes phase locking of two optical waves.
In the OPLL system, LD 1 and LD 2 are operating at different frequencies. The OPLL
technology can greatly decrease the phase noise. It also has a very wide range of locking.
Although generated signal via OPLL has a relatively wide linewidth, the OPLL technology

8
needs the laser with a complicated structure and a narrow linewidth, which increase cost and
operational difficulty. According to a report, in an OPPL system a continuous microwave
signal with a <1mHZ linewidth can be realized by utilizing two ND: YAG lasers and its tuning
range is 6-34HZ [17].
2.2.3 Optical injection phase Locking Loop
In order to further improve the quality of the generated signal, a scheme of optical injection
locking is proposed. Optical phase lock loops can be combined into an optical locking system
[18]. As shown in figure 4, the OIPLL system mainly includes a master laser, a slave laser, a
photoelectric detector, a modulator, a phase detector, a loop filter and an RF signal reference
source.
Figure 4 Optical Injection Phase-Lock Loop diagram [18]
Figure 4, explains that the optical signal from the master laser is split into two parts by a
coupler. One part is modulated by a modulator to generate a series of optical sidebands, which
is then injected into the slave laser. Through adjusting the running frequency of the slave laser,
the optical signal output from the slave laser can be locked to the sidebands of the modulated
signal. Another part of the optical signal from a master laser is coupled with the optical signal
from the slave laser by a coupler and then they are beaten at photodetector to generate a
microwave signal. Its frequency is the frequency difference between the master laser and the
slave laser. The generated microwave signal is injected into the phase detector to compare with

9
the RF signal and get a voltage to control the laser phase. Phase locking can be obtained when
the frequency difference between two lasers is the same as the RF signal frequency.
The OIPLL technology combines the advantages of OIL and OPLL and has such advantages as
low phase noise and a wide locking range and deficiencies as a too complex structure and
difficulty to achieve.
Although these three methods can achieve phase lock, all of them are not suitable for
large-scale promotion. Because these phase-locked measures always entail a complex structure,
which increases the system cost and complexity.
2.3 Opto-electronic Oscillator
An opto-electronic oscillator (OEO) [19] is a new kind of microwave signal generation
technology, which can produce a large range, low phase noise and high-quality microwave
signal.
An OEC schemes mainly includes a laser, an electro-optic modulator, an energy storage
medium, a photoelectric detector and an electric filter, which form a self-feedback structure.
The specific structure is shown in figure 5. When this feedback system has more loop gains
than losses, it will result in self-sustained oscillation and the system can generate a stable
microwave and optical signal.

10
Figure 5 The block diagram of single-loop optoelectronic oscillator [19]
From the figure, we can know that the output optical signal from LD is modulated by a
modulator to generate a series of harmonic components. And then the generated harmonic
components pass through the optical storage element and are converted to an electrical signal
from an optical signal at the photodetector. The electric filter is used for selecting frequencies.
The electrical signal is amplified by the electrical amplifier and then fed back to the
electro-optic modulator to form a feedback loop. An electrical amplifier provides a link gain
for link oscillation, and the electrical signal in the loop can set up stable self-oscillation after
several cycles. In addition, the oscillation frequency of the system is mainly determined by the
energy storage time of the energy storage medium, the bias voltage of the electro-optic
modulator and the filter characteristic of the filter.
But this structure also has some disadvantages: the optoelectronic circuit, photoelectric
detector and electric filter introduce noise that reduces signal quality. Due to the loop structure,
the system can only generate specific frequency microwave signals, so frequency tunability is
limited.

11
2.4 External modulation method
The above several kinds of structures are based on the heterodyne method whose main flaw is
that optical signals with two different frequencies should maintain stable phase coherence to
ensure the relatively small phase noise is obtained, which undoubtedly increases system
complexity. While the method of generating millimeter/micro wave based on external
modulation can effectively avoid this problem. Not only that, when the generated signal
frequency exceeds 30 GHz, the cost of radio frequency devices needed by the heterodyne
method rises abruptly. While the structure based on external modulation [20] can easily
produce a high-quality and high-frequency signal with the aid of low-frequency devices.
Commonly an external modulator is comprised of an intensity modulator and a phase
modulator.
The main principle of microwave generation based on external modulation is that a plurality of
optical sidebands is generated by using external modulators, and two specific optical sidebands
are selected by adjusting the parameters of modulators and setting filter. Finally, by beating
selected optical sidebands at the PD, the frequency multiplication microwave signal is
obtained. The external modulation technology has the following advantages:
a. The optical frequency component is derived from the same carrier wave, so it has a good
phase correlation and the generated millimeter/micro wave signal has small phase noise.
b. Noise of the optical source has little influence on the generated millimeter/micro wave
signal.
c. The structure is simple and the reliability is high
d. Stability and phase noise performance of generated microwave signals depend on the
microwave driving signals and the performance of external modulators, so it reduces the
performance requirements of the device. The more important advantage is that we can achieve
frequency tunability by changing the frequency of the microwave driving signals.
Figure 6 shows the scheme for generating a frequency-doubling microwave signal based on a
Mach-Zehnder modulator (MZM).

12
Figure 6 Photonic generation of microwave by external modulation
Due to the flexibility and simplicity of the system structure, by changing the number and
structure of external modulators we can get different schemes for generating microwave
signals. Moreover, by adjusting DC bias voltage and phase difference of microwave driving
signals we can get 2-, 4-, 8-, 12-times frequency multiplication signals.
It is worth noting that, due to the development of high-frequency electronic devices, currently
60 GHz commercial microwave source modules have been introduced to the market. So, the
method of generating microwave signals in the optical domain should be developed to a higher
frequency to magnify its own advantages. In this thesis, a new scheme will be proposed to
generate high-quality and high-frequency microwave signals based on the external modulation
technology. In the next chapter, the theory and simulation of the external optical modulator will
be presented.

13
Chapter 3 Optical external modulator
3.1 Electro-optic effect
The function of an external optical modulator is to modulate the phase or intensity of the
optical signal with an electric signal to realize electro-optical conversion of the signal. The
different functions of the optical modulator can be produced by utilizing the linear
electro-optic effect of the electro-optic crystal [21].
The electro-optic effect refers to when the electric field is applied to the electro-optic crystal,
the refractive index of the electro-optic crystal will change. And then due to the change of the
refractive index, the propagation state of the optical signal in the crystal will be changed.
Therefore, the electro-optic effect can be used to control the amplitude, phase, propagation
direction and polarization state of the optical wave signal.
The modulation principle of the external optical modulator is to utilize the electro-optic effect
of the electro-optic crystal to change phase of the optical signal output. The phase difference
between the input optical signal and the output optical signal is expressed as:
0
/
2
n
L
=
; (1)
Where
2
3
E
n
n
-
=
n
is the variation of refractive index; E is the applied electric field; n is
refractive index;
is the electro optical coefficient; L is transmission distance of optical signal;
0
is optical wavelength in vacuum.
3.2 Mach-Zehender Modulator
Now Mach-Zehender Modulators (MZMs) are the most widely used external optical
modulators in microwave photonics. A MZM has a simple structure and it is easy to be coupled
with lasers and optical fibers, so it is widely used in microwave photonic links. Lithium
Niobate (LiNbO3) is its main constituent material. As LiNbO3 has many advantages such as
low loss and high electro-optical efficiency, it has become the first choice to produce

14
high-speed optical modulators. The modulation principle of MZMs is based on the
electro-optic effect of LiNbO3.
In general, the single channel LiNbO3 crystal can be regarded as a phase modulator. But most
common modulators are intensity modulators that consist of two parallel LiNbO3 crystals.
Common MZMs have three kinds of structures that include single-drive MZMs, dual-drive
MZMs, and dual-parallel MZMs. Figure 1 is a typical Mach-Zehender Modulator model.
Figure 1 Basic structural schematics for MZM
A MZM includes two interference arms which are parallel. Usually, the upper and lower arms
are arranged in an equilibrium state, suggesting that the optical path difference is zero. The
incident light is divided into two paths after entering the MZM. The driving electrodes in both
arms can load alternating current (AC) voltage and direct current (DC) bias voltage. Through
controlling AC voltage and DC voltage we can introduce phase difference to two parallel arms.
It means a phase modulation is carried out on each arm. After phase modulation, two optical
waves generate emergent light via interference.
Single-drive MZMs only have one driving electrode, so it can merely use bias voltage to
control the phase difference between two arms. Dual-drive MZMs have two driving electrodes.
The two sub-MZMs are integrated into the main MZM arms to make up a double parallel
MZM (DPMZM) and DPMZM has three driving electrodes. If there is no special note, a
dual-drive MZM is the default in this paper.

15
The next section will focus on the simulation research and establishment of a mathematical
model of dual-drive MZMs.
3.3 Dual Drive MZM
The mathematical model of MZM modulated light wave is shown below.
Assume that input optical signal is a single-frequency carrier and its electric field expression is
expressed as:
)
exp(
0
0
t
jw
E
E
in
=
; (2)
Where E
0
is the amplitude of optical signal; W
0
is angular frequency of optical signal; Assume
that initial phase of the RF signal is 0; The voltages on the two interference arms are
respectively set as:
)
sin(
)
(
1
1
1
1
t
w
V
V
t
V
m
m
dc
+
=
; (3)
)
sin(
)
(
2
2
2
2
t
w
V
V
t
V
m
m
dc
+
=
; (4)
Where
1
dc
V and
2
dc
V respectively show DC bias voltage 1 and DC bias voltage 2 which are
loaded on the upper arm and lower arm;
1
m
V and
2
m
V are amplitude of two RF signal;
1
m
w and
2
m
w are frequency of the RF signals;
The phase changes on the two arms are respectively expressed as:
1
1
1
1
1
1
1
1
)
sin(
)
(
V
t
w
V
V
V
V
t
V
t
m
m
dc
+
=
=
; (5)
2
2
2
2
2
2
2
2
)
sin(
)
(
V
t
w
V
V
V
V
t
V
t
m
m
dc
+
=
=
; (6)
Where
1
V
and
2
V are the half-wave voltage of the two interference arms. In general, the
half-wave voltages of the upper and lower arms are the same, implying that
2
1
V
V
V
=
=
.

16
Assume that the upper and lower arms are modulated by one RF signal, so
2
1
m
m
m
w
w
w
=
=
and
2
1
m
m
m
V
V
V
=
=
.
The electric field at the output of the MZM can be expressed as:
[
]
[
]
))
(
exp(
2
2
))
(
exp(
2
2
2
0
0
1
0
0
+
+
+
=
t
w
j
E
t
w
j
E
E
out
; (7)
The formula is simplified and expressed as:
)
cos(
)
2
exp(
2
1
2
1
-
+
=
j
E
E
in
out
; (8)
Given the phase difference
2
1
-
=
, the
can be changed by adjusting the DC bias
voltage of the two arms.
Because the output optical signal from the MZM is beaten at the photoelectric detector to
generate electrical signals, the mathematical expression of the output current from PD is
expressed as:
=
=
=
2
cos
)
(
2
cos
)
(
)
(
)
(
2
2
2
t
RI
t
E
R
t
E
t
RE
I
in
in
out
out
out
; (9)
Where
)
(t
E
out
presents the conjugated form of
)
(t
E
out
;
R is the responsivity of the photo detector.
When
0
=
,
)
(
)
(
t
I
t
I
in
out
=
the output light intensity is the strongest.
When
2
=
,
2
)
(
)
(
t
I
t
I
in
out
=
the output light intensity is half of the maximum light intensity.
When
=
,
0
)
(
=
t
I
out
the output light intensity is the weakest.
The transmission response of the MZM is expressed as:

17
))
cos(
1
(
2
1
)
2
(
cos
2
+
=
=
=
in
out
I
I
T
; (10)
Figure 2 shows the transfer function curve of the MZM.
Figure 2 Transfer function curve of the MZM
From the figure, we can know that the DC bias voltage determines the modulation region of the
MZM. The top of the transfer function is the maximum transmission point (MATP); when the
modulator is biased at this point, odd-order sidebands will be suppressed. The bottom of the
transfer function is the minimum transmission point (MITP); when the modulator is biased at
this point, even-order sidebands will be suppressed. At the center of the transfer function is the
quadrature transmission point (QTP); when the modulator is biased at this point, linear
modulation of RF signals can be realized. Both even- and odd-order sidebands will be
obtained.
It is obvious that different modulation modes and wave transmission characteristics can be
realized at different transmission points.
3.4 Modulation theory
Intensity modulation is the most widely used modulation method for dual-drive MZMs that
include double-sideband (DSB) modulation, single-sideband (SSB) modulation and optical
carrier suppressed double-sideband (OCS-DSB) modulation. These analog modulation

18
methods can be obtained by setting the amplitude and initial phase of the RF signal and DC
bias voltage.
In practical applications, in order to avoid causing modulation chirps, two RF signals are
loaded on the upper and lower arms respectively. Two RF signals usually have fixed phase
differences and their amplitudes are opposite. In other words, the MZM works in a push-pull
mode (
2
1
m
m
m
V
V
V
-
=
=
). According to the Bessel Functions of the First Kind, we can know
that
-
=
+
=
+
n
n
jn
jnwt
m
J
wt
jm
)]
exp(
)
(
[
)]
sin(
exp[
; (11)
-
=
+
=
+
-
n
n
n
jn
jnwt
m
J
wt
jm
)]
exp(
)
(
1
-
[
)]
sin(
exp[
; (12)
)
(
)
1
(
)
(
m
J
m
J
n
n
n
-
=
-
;
The electric field at the output of MZM can be expressed as:
))]
sin(
(
exp[
2
))]
sin(
(
exp[
2
2
1
t
w
V
V
V
j
E
t
w
V
V
V
j
E
E
m
m
dc
in
m
m
dc
in
out
+
·
-
+
+
+
·
=
;
))]
sin(
exp[
2
]
)
sin(
exp[
2
2
1
t
w
jm
j
E
j
t
w
jm
E
m
in
m
in
-
-
+
+
+
=
;
))]
exp(
)
1
(
)
)(exp(
(
[
]
exp[
2
1
-
-
+
·
+
+
=
-
=
j
jn
m
J
j
t
nw
t
jw
E
n
n
n
m
c
o
; (13)
Where
1
and
2
are the phase shifts introduced by the DC bias voltage.
V
V
dc1
1
=
and
V
V
dc2
2
=
;
is the phase difference between upper and lower arms with the loaded RF
signals;
2
1
+
=
is the phase shift of the modulator. The value of
is determined by the bias
voltage difference
2
1
dc
dc
V
V
-
;

19
The value of
)
(m
J
n
is determined by n and m, where m is the modulation index and its
expression is
V
V
m
m
=
. The value of m is determined by the RF voltage and the half wave
voltage. Figure 3 shows the first kind of Bessel function curve from order 0 to order 5.
Figure 3 The first kind of Bessel function curve.
From expression 3, through setting the initial phase difference and the voltage of RF signal and
relative DC bias we can get three different modulation modes, namely DSB, SSB and
OCS-DSB modulation.
3.4.1 Double-sideband (DSB) modulation
When
k
2
=
and
2
=
,
n
n
j
j
jn
)
1
(
1
)
exp(
)
1
(
)
exp(
-
·
-
=
-
-
+
. When m <<
1 the MZM works in small-signal modulation. As per the first kind of Bessel function curve,
we can know that the high-order Bessel function value is smaller than the low-order one. So
only the first-order optical sidebands and carrier wave are considered in small-signal
modulation. The electric field at the output of the MZM at DSB modulation can be expressed
as:
)]
1
)(
(
)
exp(
)
1
)(
(
)
exp(
)
1
)(
(
)[
exp(
2
)
(
1
1
0
1
j
m
J
t
jw
j
m
J
t
jw
j
m
J
j
t
jw
E
t
E
m
m
c
o
out
+
-
-
+
+
-
+
=
; (14)

20
The output light signal is composed of three spectral components, which are an optical carrier
and two first-order optical sidebands. We often regard such a spectrum of a signal as the DSB
signal.
OptiSystem is simulation software of optical fiber communications systems. It is widely used
in the design of microwave photonic links. We have simulated DSB modulation by OptiSystem
14.1. The block diagram of its modulation principle is shown below.
Figure 4 Simulation diagram of DSB modulation
In the simulation, the wavelength of the optical carrier emitted from a CW laser is 1550 nm.
The input RF signal is a 20 GHz sinusoidal wave. The extinction ratio is set at 100 dB. The
parameters setting for operating LiNbO3 Mach-Zehnder Modulator are shown below.

21
Figure 5 Parameters setting for operating LiNb Mach-Zehnder Modulator
From the expression
+
+
+
+
+
+
=
)
)
sin(
cos(
)
)
sin(
cos(
2
)
(
2
2
1
2
0
2
1
1
1
0
0
V
t
w
V
V
V
t
w
V
t
w
V
V
V
t
w
E
t
E
m
m
dc
m
m
dc
out
; (15)
We can see that the parameters setting for MZM and Expression (15) have the following
correspondence:
Switching bias voltage V
1
4V
Switching RF voltage V
2
4V
Bias voltage 1
V
dc1
2V
Bias voltage 2
V
dc2
0
Modulation voltage 1
V
pp
=2V
m1
0.1V
Modulation voltage 2
V
pp
=2V
m2
-0.1V
In the Optisystem software, the modulation voltage is the peak-to-peak voltage of the RF
signal.
Because
1
2
1
)
(
2
V
V
V
dc
dc
-
=
=
, we set
2
1
=
dc
V
V and
0
1
=
dc
V
.
V
V
m
m
=
<<1, so we set
1
.
0
1
=
m
V
V and
1
.
0
2
-
=
m
V
V. Figure 6 shows the simulation spectrum of DSB modulation.

22
Wavelength(nm) Frequency(Hz)
Figure 6 Optical spectrum and electric spectrum of the generated microwave at DSB modulation
From the above simulation results, we can know that the output optical spectrum includes a
carrier wave and two first-order optical sidebands. The optical carrier wave beats with two
first-order sidebands respectively in the PD to generate a microwave signal and its frequency is
still 20 GHz. DSB modulation has the following advantages: The system configuration is
simple and easy to implement and it can work in high-frequency systems. But due to the effect
of fiber dispersion, different frequencies sidebands have different phase shifts, which will lead
to generated two same frequency signals have different phase. The amplitude of electrical
signal will produce periodic fading after superposition and the system has low receiving
sensitivity after the optical fiber transmission, which will affect system performance.
3.4.2 Single-sideband (SSB) modulation
When
2
= and
2
±
=
,
n
n
j
jn
j
jn
)
1
(
)
2
exp(
)
exp(
)
1
(
)
exp(
-
·
=
-
-
+
. We assume
2
=
,
the electric field at the output of the MZM at SSB modulation can be expressed as:
)]
(
)
exp(
2
)
1
)(
(
)[
exp(
2
)
(
1
0
1
m
J
t
jw
j
j
m
J
j
t
jw
E
t
E
m
c
o
out
+
-
+
=
; (16)

23
From Expression (16) we can find that the output light signal is composed of two spectral
components, which are the optical carrier and one first-order optical sidebands. We often
consider such a signal spectrum as the SSB signal.
The block diagram of its modulation principle is shown below.
Figure 7 Simulation diagram of SSB modulation
Because of
2
= , an electrical phase shifter is used to introduce a 90-degree phase difference
between two RF signals.
The parameters setting for the MZM and expression at SSB modulation is the same as at DSB
modulation.
Figure 8 shows the simulation spectrum of SSB modulation.

24
Figure 8 Optical spectrum and electric spectrum of generated microwave at SSB modulation
The simulation results in the above can know the output optical spectrum includes a carrier
wave and one first-order optical sidebands. Optical carrier wave beat with one first-order
sideband at PD to generate a microwave signal and its frequency is 20 GHz. Compare to the
DSB modulation, SSB modulation does not appear the periodic fading effect in the optical
fiber transmission, so the transmission performance is better than DSB modulation. It also can
work at a high frequency communication system.
3.4.3 Optical carrier suppressed double-sideband (OCS-DSB) modulation
When
k
2
=
and
=
,
n
n
j
jn
)
1
(
1
)
exp(
)
1
(
)
exp(
-
-
=
-
-
+
.
The electric field at the output of the MZM at OCS-DSB modulation can be expressed as:
)]
-j
exp(
)
(
2
)
exp(
)
(
2
)[
exp(
2
)
(
1
1
1
t
w
m
J
t
jw
m
J
j
t
jw
E
t
E
m
m
c
o
out
-
+
=
; (16)
From expression (16) we can find that the output light signal is composed of two spectral
components, which are two first-order optical sidebands. We often say that such a signal's
spectrum as the OCS-DSB signal.
The block diagram of its modulation principle is shown below.
Excerpt out of 136 pages

Details

Title
Microwave photonic frequency multiplier with 10 times frequency multiplication
College
Charles Darwin University  (School of Engineering and Information Technology)
Course
Electrical and Electronics Engineering
Grade
82
Author
Year
2017
Pages
136
Catalog Number
V432864
ISBN (eBook)
9783668749344
ISBN (Book)
9783668749351
File size
6096 KB
Language
English
Tags
microwave
Quote paper
Chongjia Huang (Author), 2017, Microwave photonic frequency multiplier with 10 times frequency multiplication, Munich, GRIN Verlag, https://www.grin.com/document/432864

Comments

  • No comments yet.
Read the ebook
Title: Microwave photonic frequency multiplier with 10 times frequency multiplication



Upload papers

Your term paper / thesis:

- Publication as eBook and book
- High royalties for the sales
- Completely free - with ISBN
- It only takes five minutes
- Every paper finds readers

Publish now - it's free