# Detection of an Optical Signal Using Difference Frequency Generation in a Periodically PoledLiTaO3 Microwave Waveguide

Authors: Hiroshi Murata; Yasuyuki Okamura
Journal: Advances in OptoElectronics
 (2008)

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## Abstract

The detection of an optical signal modulated at 15 GHz was demonstrated experimentally by using difference frequency generation based on a second-order nonlinear optical effect in a periodically poledLiTaO3 microwave rectangular waveguide.  The measured frequency dependence of the generated microwave signal was in good agreement with the theoretically expected result.  An interesting application of the proposed device is the detection of high-speed optical clock detection.


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## Body

## 1. Introduction

The detection of a high-speed optical signal is indispensable in many optoelectronic
systems. The operational principle of standard
photodetectors is based on the generation of photocarriers by the injection of
an optical signal into a semiconductor/metal, where detected signals are
obtained as a photocurrent according to the envelope of the injected optical
signal to the detectors. Therefore, amplitude/intensity-modulated
optical signals can be detected directly. However phase/frequency-modulated optical
signals cannot. The speed of standard
photodetectors is limited by the transit time of the photocarriers through the
device or an RC time constant. Therefore, detection efficiency decreases as optical signal frequency increases,
and signal detection modulated at high frequency ranges over millimeter-waves
is rather difficult except for specifically tailored ultra-fast detectors like
the unitraveling-carrier photodiode (UTC-PD) [1].Difference
frequency generation (DFG) based on a second-order nonlinear optical effect is
another candidate for the detection of a high-speed optical signal [2–4]. Using DFG, it is possible to shift the spectrum of a modulated optical signal
from lightwave frequency ranges to micro-/millimeter-wave frequency ranges
directly. Therefore, not only amplitude/intensity-modulated optical signals,
but also phase/frequency-modulated signals are applicable. In next generation optical fiber
communication networks, several types of advanced vector modulation signals
(frequency shift keying (FSK)/phase shift keying (PSK)/amplitude and phase shift
keying (APSK)) are important for extremely high-bit-rate data transfer. The DFG technique is applicable to the conversion
of optical FSK/PSK/APSK signals, which are hard to detect directly using
conventional photocurrent based devices. The conversion of optical orthogonal frequency-division multiplexing (OFDM)
signals to a microwave frequency range is also possible by using the DFG technique.Several
studies on signal generation/conversion based on DFG from a second-order
nonlinear optical effect have been reported [2–4]. However, the conversion efficiency is low due to the difficulty of phase
matching which comes from the differences in the velocities between the lightwaves
and the micro-/millimeter waves. Furthermore, the Manley-Rowe relationship, which expresses the
difference in the photon energy between lightwaves and micro-/millimeter waves
[5], causes even lower output power.In this
paper, we present the detection of an optical signal modulated at a microwave
frequency using DFG in periodically-poled LiTaO3 with a microwave
resonator structure composed of a straight microwave waveguide. In order to obtain high conversion
efficiency, a periodically poled structure of ferroelectric optical crystal is
adopted for quasi-phase-matching (QPM) between the lightwave and the microwave. The microwave Fabry-Perot resonator is also
utilized for the enhancement of the output signal by the resonance effect. This device has the following advantages: it
has a simple structure, only the optical signal at the target frequency is converted,
the other optical signals including an optical carrier can pass through the
device without disturbance, peak detection frequency can be tailored by tuning
the polarization reversal period and the resonance condition, and the signal
conversion efficiency becomes greater at higher frequencies unlike conventional
photodetectors.In the following
sections, the device structure, analysis, design, and experimental results of
the proposed device are presented.


## 2. Device Structure

Figure1 shows the structure of the DFG-based optical signal detection device we have
proposed. LiTaO3 is adopted as
a nonlinear optical material for DFG. LiNbO3 or other ferroelectric optical crystals with second-order
optical nonlinearity are also applicable. The surfaces of the four sidewalls of the long rectangular LiTaO3 crystal are covered with a thin metal film in order to construct a microwave rectangular
waveguide. Both ends of the rectangular LiTaO3 crystal are uncovered for light beam coupling and microwave output.  A channel optical waveguide structure is also
applicable for confining and guiding lightwaves along the crystal. The LiTaO3 crystal is periodically
poled for QPM between the lightwave and the microwave. By DFG in the LiTaO3 crystal, a
microwave signal is generated when the  modulation frequency of the input optical signal
coincides with the designed frequency determined by the poling period and the microwave
resonance condition.Basic structure of the optical signal
detection device with periodically poled structure and microwave rectangular
waveguide. The whole structure is (a), and its cross sectional view is (b).
(a)(b)Periodic
poling structure is designed for QPM between the modulated lightwave and the
generated microwave. In DFG for optical
signal detection, the frequency difference between the two lightwaves, which
corresponds to the frequency of the generated microwave, is rather small
compared with their individual frequencies. Therefore, the quasi-velocity-matching (QVM) scheme between the light
group velocity and the microwave phase velocity [6] is useful for the design of
the poling period for the QPM.The
structure of the microwave resonator is just a Fabry-Perot cavity. Since the refractive index value of LiTaO3 in the microwave frequency range is rather large (~6.5) compared with air,
about half of the microwave signal generated through DFG in the LiTaO3 crystal is reflected at both ends of the microwave rectangular waveguide and propagates
backwards and forwards in it. As a
result, the Fabry-Perot cavity can be constructed without specific
mirrors/reflectors in the microwave frequency ranges.


## 3. Analysis and Design

In the DFG shown in Figure1, the coupling between the two lightwave modes, with angular
frequencies ω1 and ω2, and
the microwave mode of ω3 propagating to the +y direction is
described by using coupled-mode equations assuming the slowly varying amplitude
approximation [5](1)jdA1dy=κ1ΓA2A3exp[−j(β2+β3−β1)y],jdA2dy=κ2ΓA1A3*exp[−j(β1−β3−β2)y],jdA3dy=κ3ΓA1A2*exp[−j(β1−β2−β3)y], where A1, A2,
and A3 are the complex amplitudes
of the electric field of each mode, κ1, κ2, and κ3 are
the coupling constants determined by the nonlinear coefficient of the crystal
and the polarization of the three modes, Γ is the parameter defined by the overlap of the
field distribution of the three modes, and β1, β2, and β3 are
the phase constants of the three modes.The key
point of the device design is to utilize a single guided-mode structure for the
output microwave signal at the designed frequency. If there are several microwave guided modes
or radiation modes in the device at the designed frequency range, the nonlinear
polarization induced by the second order nonlinear optical effect might be simultaneously
coupled to several modes propagating with different phase constants.  Then, the generated signal by DFG might be
spread out over these modes, and it is difficult to obtain high conversion
efficiency.Here,
we setA3 as the mode in
the microwave frequency range and introduce a microwave waveguide with a
rectangular structure. Adopting the periodically
poled structure, the sign of the three coupling constants (κ1, κ2, and κ3) is modulated along the propagation direction. Therefore, the phase-mismatching among the
three modes can be compensated for and high-efficiency coupling can be obtained. The length, L, of each polarization-reversed/nonreversed region to realize
efficient DFG for the microwave at angular frequency ω3=ω1−ω2=2πfm
is expressed by the following equation:(2)L=π|β1−β2−β3|≈π|(∂β/∂ω)(ω1−ω2)−β3|=π|(ng/c)ω3−(nm/c)ω3|=c2fm(nm−ng), where ng
is the group index of the lightwaves which is expressed by ng=c(∂β/∂ω), nm is the effective index of the microwave mode in the rectangular waveguide, and c is the lightwave velocity in
vacuum.  This final transformed equation
is equivalent with the QVM condition in traveling-wave electro-optic modulators
[6].It is clear
from (2) that there is an optimum detection frequency for the poling period. Therefore, the proposed detection device is a
band-operating device. The frequency
response of the signal detection determined by the QPM can be calculated using
the coupled-mode equation (1) taking into account the reversal of the sign of
the coupling coefficient by polarization reversal. The calculated example is shown in Figure 2,
where the total device length, Lt, was set as Lt=9L. The QPM bandwidth is
inversely proportional to the total device length Lt. The frequency
response of the proposed device
is also dependent on the resonance condition of the Fabry-Perot cavity
structure. Therefore, the final
frequency response is determined by the multiplication of the response by the
QPM shown in Figure 2 and the response by the Fabry-Perot resonator.Figure 2
Calculated frequency dependence by the QPM.In order to utilize the largest nonlinear coefficient of the LiTaO3 crystal, d33, a z-cut LiTaO3 crystal
substrate was adopted and the z-axis
of the crystal was set parallel to the shorter side in the cross-section. Under this configuration, the polarization
directions of the two lightwave modes that we set were the same and parallel to
the z-axis. Therefore, the generated microwave by the DFG
with the d33 nonlinear
coefficient was polarized along the z-axis. This means that the TE guided mode in the microwave rectangular
waveguide can be obtained. The
calculated dispersion relationship of the TE10 mode is shown in Figure 3. By setting the length of the shorter side
of the crystal to an appropriate value, the microwave rectangular waveguide
only supports a TE10 mode in the designed frequency range and a
high-efficiency DFG signal generation can be expected.Calculated dispersion characteristics
of the guided modes in the LiTaO3 microwave rectangular waveguide
with a=2 mm and b=0.4 mm.
(a)(b)


## 4. Experiments

The prototype device was fabricated using az-cut LiTaO3 substrate. First, a periodically poled structure was
fabricated in a 0.4 mm thick crystal substrate by use of the pulse voltage
applying method. The period of the
poling, 2L, was set to 10.2 mm, where
the designed lightwave wavelength was 1550 nm (the group index of the
extraordinary light is ng=2.17)
and the peak detection frequency was 15 GHz using a microwave rectangular
waveguide, with a cross-section of 2.0×0.4 mm (the effective index of
the TE10 mode is nm=4.13 at 15 GHz). Next, the periodically poled
crystal was cut with a diamond saw to 45.9 mm along the propagation direction
and 2.0×0.4 mm in cross-section,
which was designed for the cutoff frequency of the microwave rectangular waveguide
at 11.6 GHz and for a single-mode structure with a frequency range from 11.6 GHz
to 23.1 GHz. After cutting, both ends of
the crystal were polished. Finally, a 2 μm thick Al film was deposited
on the four sidewalls of the crystal by use of electron-beam vapor deposition.The microwave resonance characteristics of the fabricated device were measured by
use of a pair of microwave probe antennas and a network analyzer. The measured microwave transfer
characteristic through the fabricated device is shown in Figure4. The resonance peaks in a Fabry-Perot cavity
were clearly observed. The measured
separation of the adjoining resonance frequency, Δf, was Δf~1 GHz
around 15 GHz, which was in good agreement with the calculated value from the
following equation:(3)Δf=c2Ltnm, where c is the lightwave
velocity in vacuum, Lt
is the total length of the device, and nm is the effective index of the microwave TE10 mode propagating in the rectangular waveguide, which was calculated as ~4 in
the designed frequency range. Therefore,
a single-mode microwave propagation characteristic in the designed frequency
range was confirmed experimentally. The
measured unloaded Q-factor around each resonance frequency was ~50. In Figure 4, the transmission signal is
rather small below 14 GHz, which was due to the cutoff characteristics of the
microwave probe antennas used in the measurement.Figure 4
Measured microwave resonance characteristics of the fabricated device.The experimental setup for optical signal detection is shown in Figure5. The light source was a 1550 nm CW DFB laser
diode. The CW lightwave from the laser
diode was deeply modulated by use of a high-speed optical intensity modulator
with a driving modulation frequency from 13 GHz to 18 GHz and amplified by use of
an Erbium-doped optical fiber amplifier. The intensity modulated lightwave with a power of 20 mW was focused on
the end surface of the fabricated device using a lens of a 50 mm in focal
length. The output microwave signal,
which was emitted from the end of the DFG device, was measured using a
microwave horn antenna and a microwave spectrum analyzer. An example of the detected signal spectrum is
shown in Figure 6. A clear signal was
observed at 15.1 GHz. The measured
frequency response of the detected signal is shown in Figure 7. The peak detection frequency was 15.1 GHz,
which was in good agreement with the expected characteristics calculated from
the frequency response by the QPM (Figure 2) and the measured microwave
resonance characteristics of the fabricated device (Figure 4). The detected signal power level (~0.1 pW) was comparable
with the estimated value using the d33 nonlinear coefficient
of LiTaO3, the microwave frequency, the light wavelength, the device
length and cross-section, the unloaded Q-factor of the Fabry-Perot resonator,
and the coupling efficiency between the device and the horn antenna used in the
measurement.Figure 5
Experimental setup for the detection of an optical signal modulated at ~15 GHz.Figure 6
Measured spectrum of the detected signal. The modulation frequency was 15.1 GHz
and the input lightwave power was 20 mW.Figure 7
Measured frequency dependence of the detected signal with the input lightwave power of 20 mW.


## 5. Discussion and Conclusion

In the experiment, the coupling between the DFG device and the microwave
horn antenna was small (<−10 dB), since the radiated microwave
from the device rapidly spread out from the end of the rectangular waveguide
with a small cross-section of 2.0×0.4 mm, which is rather small compared with the wavelength of
the emitted microwave in air of 20 mm. By
using an appropriate microwave circuit for increasing the coupling efficiency
such as a microwave lens or a large aperture array of antennas, we expect to
enhance the output power by ~10 dB. The
application of an optical waveguide structure is also attractive for increasing
the conversion efficiency with diffraction-less light propagation over a long
interaction length. It should be noted
that the output power level of the detected signal is proportional to the
square of the signal frequency. Therefore, as the signal frequency becomes higher, the larger conversion
efficiency is obtainable. By increasing
the output power with these techniques, it is expected that the detection of
optical clock signals at a high-repetition frequency without disturbance from
other data signals would be obtainable. This would be useful for the next generation optical communication
networks.An optical heterodyne scheme injecting another phase-locked laser beam to
the DFG device is also applicable for converting the signal to other frequency
ranges, which is useful for extracting subcarrier multiplexed signals in orthogonal
frequency-division multiplexing (OFDM) schemes or radio-on-fiber (ROF) systems.



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*Source: 587091-2008-11-23.xml*