782
1
Design and Performance of Superconducting
Circuits for LiNbO3 Optical Modulator and Switch
K. Yoshida, Y. Kanda, H. Yoshihara, H. Kanaya, S. Shinkai and M. Ishitobi
Abstract— The design and performance of a LiNbO3 optical
modulator and switch, which employ superconducting circuits,
have been studied. Based on a novel design method of the booster
circuit using superconducting coplanar waveguide transmission
lines, we designed a voltage amplifier with center frequency of
10GHz, bandwidth of 5MHz, and the voltage gain of 33dB using
an electromagnetic wave simulator. We also designed a high speed
optical switch combining optical directional coupler and
Mach-Zehnder interferometer. A preliminary experiment with
YBCO electrode on MgO substrate flip-chip-bonded on LiNbO3
optical waveguide has been made.
Index Terms—superconducting microwave device, LiNbO3
optical modulator, high-Tc superconducting transmission line
signal voltage is applied to the Mach-Zehnder type optical
waveguide throughout the coupling section with a length l via
the standing-wave voltage occurring in the CPW resonator
which is short circuited or open ended .
In Fig.2 we show a general equivalent circuit model of an
optical modulator and a switch, where the F matrix (ABCD)
represents both the booster circuits for optical modulator and
the transmission line for the optical switch, Z=V2/I2 is the input
impedance of the coupling section, and 2Vi is the signal voltage.
In this circuit model the expression for the output voltage V2 in
terms of F matrix is calculated as
V2 2DZ in  B 
,

Vi
Z 0  Z in
I. INTRODUCTION
E
xtensive studies have been made of applications of high- Tc
superconducting transmission lines with low loss and low
dispersion to microwave passive devices[1]. We have been
studying the applications of superconducting transmission lines
to
LiNbO3
(LN)
optical
modulators
of
the
traveling-wave-type[2,3] as well as the resonant-type[4,5]. In
our previous paper[5], we proposed a novel design theory for
booster circuit for resonant type LN optical modulators for
sub-carrier optical transmission (radio over fiber) [6], and
experiments using YBCO films have been made[4,7]. Recently,
there are also great demands for high-speed optical routing
switches for Terabit photonic network.
In this paper, we present a general formulation of the design
of booster circuits for LN optical modulators and switches: We
designed two types of booster circuits, a single-resonator-type
and twint-resonator-type made of coplanar waveguide (CPW)
transmission lines short-circuited at the end, and carried out
experiments. We also studied the high-speed optical switch
using LN and superconducting CPW transmission line.
(1)
where Zin=V1/I1=(AZ+B)/(CZ+D)is the input impedance at the
circuits.
Optical
input

Coupling section
l
Optical
output


(a)
LiNbO 3
Booster circuit with CPW
transmission Line
Modulation
signal
Optical waveguide
Coupling section
l
Optical
input
(b)
Optical
output
LiNbO 3
~
Switching
signal
Superconducting
electrode
II. DESIGN OF SUPERCONDUCTING CIRCUITS FOR LiNbO3
OPTICAL MODULATOR AND SWITCH
In Figs. 1(a) and 1(b) we show the schematic figures of the
LN optical modulator with the booster circuits and the optical
switch using superconducting CPW transmission lines. The
Manuscript received Aug.5, 2002.
K. Yoshida, H. Yoshihara, H. Kanaya and S. Shinkai are with Department
of Electronics, Graduate School of Information Science and Electrical
Engineering, Kyushu University, Fukuoka, 812-8581, Japan
( e-mail:
[email protected]).
Y. Kanda and M. Ishitobi are Department of Electronics, Fukuoka Institute
of Technology, Fukuoka, 811-0295, Japan.
Fig.1. Schematic of superconducting circuits on the Mach-Zehnder type
LiNbO3 optical waveguides, (a) optical modulator, (b) optical switch
2Vi
Z0
I1
Zin
V1
I2
A
C

B
D 
V2
Z
Fig.2. General equivalent circuit model for optical modulator and switch
782
2
 t  
 1
V 2

 F ( )Vi ( )e
jt
d ,
(2)
with
F ( )  (V2 / Vi )M ( ) ,
(3)
1 l V ( z ) j 0 z
(4)
e dz ,
l 0 V2
where F is referred to as the normalized modulation depth,
of the incident voltage
Vi   is the Fourier transform
M ( ) 
(a)
waveform vi (t ) , i.e.,
Vi     vi (t )e jt dt ,

(5)

where V is the half-wavelength voltage,  0  ne / c  , ne is
the refractive index of light wave, c is the light velocity and
M   is the term representing the magnitude of the coupling
(b)
between signal and the optical fields．The expressions for M for
various circuits are shown in Table I.
Z0 I 1
(a)
Fig.3. Spatial profiles of the complex amplitudes of voltage V(z) and current
I(z) , (a) single resonator , (b) twin resonator
2Vi
Zin
V1 J 0,1
Z0
In Figs.3(a) and 3(b), we show the spatial profiles of the
complex amplitudes of voltage V(z) in the coupling section
( 0  z  l ) for the cases of a single resonator and twin
resonators, respectively. If we take the coordinate system as
shown in Figs.3(a), 3(b) and 4(b), assuming the shorted or open
ends at z=l, the expressions for V(z) and the input impedance at
z=0, Z=V2/I2, are shown in Table I, where = +jis the
2Vi
jB1
Zin
jB2
J n 1,n
J1, 2
I1
V1
J n ,n1 V2
I2
Z0,
I2
jBn
Z
V2
open end
Z0,
(b)
0
z
l
D-l
l
D
propagation constant,  is the attenuation constant,    LC
Fig.4. Equivalent circuits for (a) n-pole booster circuit for optical modulator,
(b) transmission line for optical switch
is the phase constant,  is the angular frequency, L and C are the
inductance and capacitance of the CPW transmission line per
In order to realize a broadband booster circuit for exciting a
large standing-wave voltage in the short circuited CPW as
shown in Figs.3(a) and 3(b), we followed the procedures
described in the design theory [5,9]. It is noted that in this
design values the output current is given as:
for
passband
and
Z 0 I 2 / Vi  Z 0 / Z V2 / Vi   A
unit length, respectively, and Z 0  L / C is the characteristic
impedance.
In the presence of the standing-wave voltage, the induced
total optical phase difference (t) at the output end of the
push-pull type optical modulator can be calculated as [5,8]
TABLE I
PARAMETERS OF VARIOUS SUPERCONDUCTING CIRCUITS
TWIN RESONATOR
V(z)
V2

sinh  l / 2  z  l / 2
sinhl / 2
SINGLE RESONATOR

l / 2e j l / 2 coshl / 2  cosh 0l / 2
l / 22  0l / 22 sinhl / 2
l coshl   e j l  j 0l sinhl 
l 2   0l 2 sinhl 
A B


C D
 0

 jJ 0,1
1
 jJ 0,1   1 0  0


0   jB1 1  jJ1, 2

1
 jJ1, 2   1
  
0   jBn

Switch
sinh l  z 
sinhl 
Z 0 tanhl 
0
M()
V2
Z0 / 2tanhl / 2
Z  V2 / I 2
Z
0

cosh l  z 
coshl 
Z0 cothl 

0  0

1  jJ n ,n1
V2
1
 jJ n ,n1 

0


l sinhl   j 0l coshl   e j l
(l ) 2  (  0l ) 2 coshl 


0

Z 0 sinh D  l 
 cosh D  l 






1
/
Z
sinh


D

l

cosh D  l  
0

782
3
Z 0 I 2 / Vi  0 for offband, where A is the parameter
1
(a)
Voltage (arb.unit)
representing the current gain [5].
In order to realize the parallel resonance circuits Bi and
inverters Ji,i+1 shown in Fig. 4 (a)，we use half-wavelength
resonators and gaps in CPW transmission lines[10].
III. SIMULATED PERFORMANCE OF THE OPTICAL MODULATOR
AND SWITCH
0.8
0.6
0.4
0.2
0
-0.2
We can calculate the temporal waveforms of the output
optical phase difference  t  against the input signal voltage
0.2
0.4
0.6
Time (10-9sec)
0.8
1
input voltage waveform vi (t ) with ASK (Amplitude Shift
Keying) modulation signal, and calculated output phase
difference  t  for the case of A=45 (voltage gain of 33dB) is
shown in Fig. 5(b). It is shown that designed voltage gains are
confirmed, indicating that a low driving-voltage optical
modulator is possible by designing a large current gain A.
(a)
Voltage (arb.unit)
1.2
(b)
Optical phase difference
vi (t ) using (1)-(5). In Figs. 5(a) we show an example of the
1
0.6
0.4
0.2
0
-0.2
0.6
R= 0 (/mm)
R= 1 (/mm)
R= 10 (/mm)
0.8
0.2
0.4
0.6
Time (10-9sec)
0.8
1
Fig.6. Time domain characteristics of optical switch, (a) incident wave vi(t),
(b) optical phase difference (t)
0
-0.6
In Fig. 7(a), we show the configuration of the booster circuit
made of meander CPW transmission lines. The length of the
half-wavelength resonator and the geometry of inverters are
decided in the same manner as described in [10].
In Figs. 7(a) and 7(b) we show the spatial distribution of the
amplitude of the standing wave voltage calculated by the EM
simulator and the transmission-line model, respectively. A
reasonable agreement is obtained for the spatial distribution of
the standing wave voltage for both cases. In Fig.9, we show
calculated frequency dependences of group delay of the
scattering parameter S11.
-1.2
(b)
Optical Phase difference (t)
0
1
2
3
Time (10- 6sec)
4
5
40
20
0
-20
-40
0
1
2
3
Time (10-6sec)
4
5
IV. EXPERIMENTS
Fig.5. Time domain characteristics of the optical modulator, (a) input voltage
waveform vi(t) of ASK signal, (b) output optical phase difference in the case of
A=45
In Figs. 6(a) and 6(b), we present the simulation results for
the optical switch calculated from (1)-(5). In this case the input
voltage waveform vi(t) is the RZ (Return to Zero) signal, and
output phase difference (t) is shown for various electrode
resistances. In the simulation we used l=2mm, D=10mm and R
represents the resistance of the transmission line per unit length.
It is shown that waveforms is distorted in the presence of
electrode losses, and that ideal switching is possible when
electrode resistance is very low.
In order to confirm the proposed design theory we carried out
the experiment. In Fig.8 we show the pattern of the booster
circuit with the meanderline 3-pole Chebyshev filter fabricated
by a YBCO thin film on a MgO substrate with the dimension of
10[mm]x10[mm]. The YBCO electrode on MgO substrate was
flip-chip bonded onto an optical waveguide in a LiNbO3
substrate, and was cooled down by a refrigerator [4] . In Fig.9
we show the comparison of the observed group delay of S11 of
the device and the simulation results. The observed data are in
reasonable agreements with those expected from theory.
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4
Experimental result
Simulation by EM simulator
4
Group Delay (ns)
4th:twin resonator
3rd
(a)
2nd
Simulation by transmission line model
3
2
1
1st
0
-6
(b)
Voltage (arb.unit)
substrate size
10mm×10mm
4th
3rd
2nd
1st
1
2
Distance (mm)
3
V. CONCLUSIONS
The design and performance of a LiNbO3 optical modulator
and switch, which employ superconducting circuits, have been
studied. Based on the new design theory for the high gain LN
optical modulator, we designed the practical device with the
voltage gain of 33 [dB] by EM simulator, and demonstrated the
expected performance. A preliminary experiment of the
designed optical modulator using the flip-chip bonding of the
YBCO thin film on MgO substrate was also made.
Fig.7. Booster circuits designed by the electromagnetic wave simulator, (a)
configuration of the booster circuit made of meander CPW transmission line
(b) spatial distribution of the standing-wave-voltage expected from the
transmission line model
REFERENCES
R. R. Mansour, “Microwave Superconductivity,” IEEE Trans.
Microwave Theory Tech., vol 50, No. 3, pp. 750-759, 2002.
[2] K. Yoshida, T. Uchida, S. Nishioka, Y. Kanda and S. Kojiro, “Design and
performance of a velocity matched broadband optical modulator with
superconducting electrodes,” IEEE Trans. Appl. Supercond., vol 9, pp.
3905-3908, 1999.
[3] K. Yoshida, Y. Kanda, and S. Kohjiro, “A traveling-wave-type LiNbO3
optical modulator with superconducting electrodes,” IEEE Trans.
Microwave Theory Tech., vol 47, pp. 1201-1205, 1999.
[4] K. Yoshida, H. Morita, Y. Kanda, T. Uchiyama, H. Shimakage, and Z.
Wang, “Optical modulator with superconducting resonant electrodes for
sub-carrier optical transmission,” Inst. Phys. Conf. Ser. No. 167, pp.
375-378, 2000
[5] K. Yoshida, H. Takeuchi, H. Kanaya, Y. Kanda, T. Uchiyama, and
Z.Wang, “Broadband and low driving-voltage LiNbO3 optical modulator
with high Tc superconducting transmission line,” IEEE Trans. Appl.
Supercond., vol 11 No.1, pp. 442-445, 2001.
[6] N. Dagli, “Wide-bandwidth lasers and modulators for RF photonics,”
IEEE Trans. Microwave Theory Tech., vol 47, pp. 1151-1171, 1999.
[7] E. Rozan, C. Collado, A. Garcia, J. M. O’Callaghan, and R. Pous,
“Design and fabrication of coplanar YBCO structure on Lithium
Niobate,” IEEE Trans. Appl. Supercond., vol 9, pp. 2866-2869, 1999.
[8] M. Izutsu, H. Murakami and T. Sueta, “Guided wave light modulator
using a resonant coplanar electrode,” IEICE Trans. Electron., vol. J71C,
pp. 653-658, 1988.
[9] G. Matthaei, L. Young, and E. Jones, Microwave Filters,
Impedance-Matching Networks, and Coupling Structures. New York:
McGraw-Hill, 1964.
[10] H. Kanaya, T. Shinto, K. Yoshida, T. Uchiyama, and Z.Wang,
“Miniaturized HTS coplanar waveguide bandpass filters with highly
packed meanderlines,” IEEE Trans. Appl. Supercond., vol 11 No.1, pp.
481-484, 2001.
[1]
L=430m
G=197m
1mm
6
Fig.9 Comparison of the frequency dependence of group delay between theory
and experiment
4
3.5
3
2.5
2
1.5
1
0.5
0
0
-3
0
3
Relative Frequency (%)
G=110m
G=31m
Fig.8. Layout of the fabricated booster circuit, where insets show the layouts
of J inverters.