Optical frequency multiplication technique using cascaded modulator to achieve RF power advantage

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Optical frequency multiplication technique using
cascaded modulator to achieve RF power advantage
Gazi Mahamud Hasan
1*
, Mehedi Hasan
1
, Karin Hinzer
1
, Trevor Hall
1
1
Photonic Technology Laboratory, Centre for Research in Photonics,
University of Ottawa
Ottawa, Canada
*
ghasa102@uottawa.ca
Abstract— An optical millimeter-wave generation scheme
consisting of four Mach-Zehnder modulator in series, each
biased at its maximum transmission point is analysed by an
optical path tracing method. Simulation using Virtual Photonic
Inc. software package is presented as a proof of concept. The
simulation results show that the proposed architecture can
perform frequency octupling function with a significant RF
advantage. The suppression of carrier and other unwanted
harmonics by design, lower RF input power, wide operating
range in terms of modulation index with satisfactory
performance, and a simple filterless architecture make this
circuit an attractive choice to be integrated in any material
platform that offers electro-optic modulators.
I. I
NTRODUCTION
The demand of high capacity wireless communication
networks to deliver multi-Gb/s services and to support ever
growing data traffic can be met by the usage of a suitable
broadband frequency spectrum. Congested lower frequency
bands and complicated electronic millimeter-wave (mm-
wave) generation suggests frequency multiplication
techniques based on external modulation in optical domain
to be an attractive choice to access mm-wave band. Various
multiplication factors have been achieved employing Mach-
Zehnder modulator (MZM) [1-2], polarization modulator
[3], Sagnac loop [4] etc. In [2], the generation of V-band 60
GHz and W-band 80 GHz mm-wave signals utilizing
frequency octupling is experimentally demonstrated. A
generalized architecture is proposed for any multiplication
factor which shows greater RF power efficiency over
functionally equivalent parallel structure [5-6].
In this report, a cascaded configuration consisting of 4
MZMs, each biased at its minimum transmission point
(MITP) is proposed as a superior optical millimeter-wave
generation scheme. The functionality of frequency octupling
is analyzed by an optical path tracing method. An optical
path can be expressed as a phasor if the optical components
are optically linear. The time variant nature of active
elements can be handled by a focus on pure RF carriers and
the Jacobi-Anger expansion. Satisfactory performance in
terms of spectral purity, tunability and RF power efficiency
is observed by simulation. Its simple architecture has the
feasibility to be integrated in any material platform that
offers electro-optic modulators.
II. O
PERATION
P
RINCIPLE
The proposed frequency octupling circuit utilizing
cascaded MZM configuration is shown in Fig. 1(a). The
series architecture can be modelled by its equivalent parallel
architecture. There are 2
N
paths through the structure
corresponding to all choices of the upper and lower arms in
each stage. An abstract graph can be considered in which
the vertices describe splitters (defined by their transmission
matrices) and edges describe optical components in the arms
such as active phase shifters driven by RF signals and or
delays and pre-set phase biases. Selecting one port at a
vertex as input and one port at a different vertex as output
every possible path can be traced and summed. The total
transmission can be represented as,
where N is the no. of MZM stages, m=(πV
RF
)/V
π
is the
modulation index, ΔØ
p
= (pπ)/N (p=0, 1, 2, 3) is the phase
shift of the p
th
RF drive introduced to the p
th
MZM and ω
RF
is
the RF angular frequency. The RF and optical phase
differences between two arms of each differentially driven
MZM are expressed by σ
p
and α
p
respectively. For the
proposed system, α
p
= σ
p
=1 for the upper arm and α
p
= σ
p
=  1
for the lower arm are defined for each MZM biased at
MITP. Equation (1) can be characterized by employing
where r
σ
and θ
σ
define the phasor relationship of each path.
Utilizing Fig. 1(b), Fig. 1(c) and the Jacobi-Anger
expansion, the output can be expressed as
E
out
= E
in
[{J
4
(r
+
m)+J
4
(r
-
m)}sin(4ω
RF
t)  {J
12
(r
+
m)
+J
12
(r
-
m)}sin(12ω
RF
t) + {J
20
(r
+
m)+J
20
(r
-
m)}sin(20ω
RF
t)….]
(3)
Fig. 1. (a) Schematic diagram of the proposed frequency octupling
architecture. LD: laser diode; PD: photo-diode; LO: local oscillator,
(b) Argand diagram showing 16 paths of the parallel equivalent
architecture where each segment represents the individual arm’s RF
phase and the phase information of it being differentially driven. Red
defines σ
p
= 1 and blue defines σ
p
= -1, (c) The summation of the
phasors lies on the same path forms a constellation of 16 points. For
MITP bias, red defines ρ
α
= 1, blue defines ρ
α
= -1.
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where J
n
is the Bessel function of the first kind of order n,
r
+
=(2.828)cos(π/8)
and r

=(2.828)sin(π/8). Equation (3)
suggests the suppression of all the sidebands alongside the
optical carrier by design except the odd multiples of the 4
th
harmonic. The effects of the unsuppressed higher-order
harmonics can be neglected for m<π. Biasing all MZMs at
MATP can be employed to perform frequency 16-tupling
[7] but then the operating range in terms of modulation
index becomes narrow because of the emergence of carrier
breakthrough, which can be deduced from Fig. 1(c). All
paths are added with same optical phase so nullification of
J
0
(mr
±
) cannot be obtained by design.
III. S
IMULATION
AND
R
ESULTS
The proposed system is simulated using the Virtual
Photonics Inc. (VPI) software package. A continuous wave
distributed feedback (DFB) laser at a wavelength of 1550
nm with average power of 100 mW is used as the optical
input. A 5 GHz sinusoidal RF drive signal is applied with
appropriate RF phase. A PIN diode with a responsivity of
0.8 A/W is used for detecting the output signal.
The optical and electrical spectra at the output of the
configuration are shown in fig. 2. As shown in fig. 2(a), the
power of the two 4
th
order harmonics is 70 dB higher than
that of the other pronounced unwanted harmonics. The
optical carrier and all the sidebands except the odd multiple
of 4
th
order are effectively suppressed. After beating at the
photodetector, a pristine frequency component at 40 GHz is
obtained as shown in fig. 2(b).
A comparison is made among the proposed architecture
and two other frequency 8-tupling configurations to evaluate
the RF power efficiency. From fig. 3, it can be obtained that
the proposed cascaded architecture biased at MITP can
perform more efficiently at low RF input. The architecture
utilizing 2 cascaded MZMs, each biased at MATP shows
narrow operating range as a specific RF input is needed to
suppress the carrier [8]. A wider operating range in term of
modulation index can be achieved by the parallel
architecture at the expense of high RF drive [9]. Besides, the
outer MZI should be biased at MITP to suppress carrier,
Fig. 3. Comparison between the proposed cascaded architecture and two
other architectures in terms of (a) RF input-output power and (b) ESHSR.
Fig. 4. Effects on ESHSR due to the variation of (a) extinction ratio of
MZMs and (b) RF phase angle
which needs employment of optical delay line or directional
coupler, triggering additional excess optical loss relative to
the proposed cascaded architecture.
The effects of unbalanced splitting ratio intrinsic to the
MZM is checked. As shown in fig. 4(a), a flat response in
terms of ESHSR can be observed when all the MZMs are
having same finite extinction ratio. The situation changes
when the extinction ratio is different for each MZM. ESHSR
greater than 40 dB can be achieved when the extinction ratio
of MZM
1
is 25 dB and for others, it is kept at 30 dB. Strong
dependence on precise RF drive phase is observed in fig.
4(b). Operation with ESHSR greater than 20 dB can be
achieved with ±1 drift in RF drive phase.
IV. C
ONCLUSION
In summary, an optical millimeter wave generation
architecture is proposed as an energy efficient method with
~7 dB RF advantage compared to functionally equivalent
circuit. Moreover, the circuit requires no optical or electrical
filtering and careful adjustment of RF drive level for
sideband suppression. The proposed architecture can be
integrated in any material platform that offers linear electro-
optic modulators.
R
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Fig. 1. (a) Optical spectrum and (b) electrical spectrum of the
frequency 8-tupling signal
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