782
3
1
Abstract— The design and performance of a LiNbO
3
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 LiNbO
3 optical waveguide has been made.
Index Terms—superconducting microwave device, LiNbO
3 optical modulator, high-Tc superconducting transmission line
I.
INTRODUCTION
E xtensive studies have been made of applications of high- T c 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 LiNbO
3
(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.
II.
D ESIGN OF S UPERCONDUCTING C IRCUITS FOR LiNbO
3
O PTICAL M ODULATOR AND S WITCH
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: yoshida@ed.kyushu-u.ac.jp).
Y. Kanda and M. Ishitobi are Department of Electronics, Fukuoka Institute of Technology, Fukuoka, 811-0295, Japan.
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 = V
2
/ I
2
is the input impedance of the coupling section, and 2 V i
is the signal voltage.
In this circuit model the expression for the output voltage V
2
in terms of F matrix is calculated as
V
2
V i

2

DZ
Z in

0

Z in
B

, (1) where Z in
= V
1
/ I
1
=( AZ + B )/( CZ + D )is the input impedance at the circuits.
(a)
(b)
Optical input
  
Optical waveguide
Optical input
  
Coupling section l
Modulation signal
Coupling section l
LiNbO
3
 
Optical output
LiNbO
3
Booster circuit with CPW transmission Line
Optical output
~
Switching signal
Superconducting electrode
Fig.1. Schematic of superconducting circuits on the Mach-Zehnder type
LiNbO 3 optical waveguides, (a) optical modulator, (b) optical switch
2 V i
Z
Z
0 in
I
V
1
1


A
C
B
D


I
V
2
2
Z
Fig.2. General equivalent circuit model for optical modulator and switch

782 2
(a)
(b)
Fig.3. Spatial profiles of the complex amplitudes of voltage V ( z ) and current
I ( z ) , (a) single resonator , (b) twin resonator
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 = V
2
/ I
2
, are shown in Table I, where

=

+ j
  is the propagation constant,  is the attenuation constant,   
LC is the phase constant,

is the angular frequency, L and C are the inductance and capacitance of the CPW transmission line per 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]
V ( z )
Z

V
2
/ I
2
M (

)


A
C
B
D


  

V

1
2





F (

) V i
(

) e j
 t d

, (2) with
F (

)

( V
2
/ V i
) M (

) , (3)
M (

)
 l
1  l
0
V ( z ) e j

0 z dz
V
2
, (4) where F is referred to as the normalized modulation depth,
V i
  is the Fourier transform of the incident voltage waveform v i
( t ) , i.e.,
V i
 


 v i
( t ) e
 j
 t dt , (5) where V  is the half-wavelength voltage,

0

 n e
/ c
 
, n e
is the refractive index of light wave, c is the light velocity and
M
 
is the term representing the magnitude of the coupling between signal and the optical fields ． The expressions for M for various circuits are shown in Table I.
(a)
2 V i
Z in
Z
0
I
1
V
1
J
0 , 1 jB
1
J
1 , 2 jB
2
J
 n

1 , n jB n
J
 n , n

1
V
2
I
2
Z
Z
0
I
1
I
2 open end
(b)
2 V i
Z in
V
1
Z
0
,

Z
0
V
2
Z
0
,
 l z
D l
D l
Fig.4. Equivalent circuits for (a) n -pole booster circuit for optical modulator,
(b) transmission line for optical switch
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:
Z
0
I
2
/ V i


Z
0
/ Z

V
2
/ V i


A for passband and
TABLE I
P ARAMETERS OF V ARIOUS S UPERCONDUCTING C IRCUITS
V
2
T WIN R ESONATOR sinh


 l / 2

 l z
 sinh
  l / 2
 
S INGLE R ESONATOR
V
2 sinh

 sinh
 
 


Z
0
/ 2
 tanh
 

 l /  2

 e
 l j

/
0 l
2
/ 2
2
 cosh
 
0 l

 l
/
/
2

2
2


 cosh


0 l / 2
  sinh

 l / 2



 

0 jJ
0 , 1
 jJ
0 , 1

1
0






1 jB
1
0
1




 

0 jJ
1 , 2
Z
0 tanh
 
 l
 cosh 
 l
 
2

 e j


0 l
0 l

2

 j

0 l sinh sinh
 
 
 jJ
1 , 2

1
0



 


1 jB n
0
1




 

0 j J
 n , n

1
 j J
 n , n

1

1
0



V
2
Switch cosh

 cosh
 
 

Z
0 coth
 
 l sinh
 

(
 l )
2


( j


0
0 l l )
 cosh
 
2
 cosh


  e j

0 l

 
1 / cosh
Z
0



 sinh

D


 l
D
 
 l
 

Z
0 sinh cosh






D
D

 l
 l

 



782 3
Z
0
I
2
/ V i

0 for offband, where A is the parameter representing the current gain [5].
In order to realize the parallel resonance circuits B i
and inverters J i,i+1 shown in Fig. 4 (a)
， we use half-wavelength resonators and gaps in CPW transmission lines[10].
III.
S IMULATED P ERFORMANCE OF THE O PTICAL M ODULATOR
AND S WITCH
We can calculate the temporal waveforms of the output optical phase difference
 
 
against the input signal voltage v i
( t ) using (1)-(5). In Figs. 5(a) we show an example of the input voltage waveform v i
( t ) with ASK (Amplitude Shift
Keying) modulation signal, and calculated output phase difference
 
 
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)
1.2
0.6
0
-0.6
-1.2
40
20
0 1 2 3
Time (10-
6 sec)
4 5
(b) 0
-20
-40
0 1 2 3
Time (10
-6 sec)
4 5
Fig.5. Time domain characteristics of the optical modulator, (a) input voltage waveform v i
( 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 v i
( 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.
(a)
1
0.8
0.6
0.4
0.2
0
-0.2
0.2
0.4
0.6
0.8
1
Time (10 -9 sec)
(b)
1
0.8
0.6
R
R
= 0 (
= 1 (


/mm)
/mm)
R = 10 (

/mm)
0.4
0.2
0
-0.2
0.2
0.4
0.6
0.8
1
Time (10 -9 sec)
Fig.6. Time domain characteristics of optical switch, (a) incident wave v i
( t ),
(b) optical phase difference
 
( t )
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 S
11
.
IV.
EXPERIMENTS
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 LiNbO
3 substrate, and was cooled down by a refrigerator [4] . In Fig.9 we show the comparison of the observed group delay of S
11
of the device and the simulation results. The observed data are in reasonable agreements with those expected from theory.

782 4
(b)
(a)
4
3.5
3
2.5
2
1.5
1
0.5
0
0
1st
3rd substrate size
10mm × 10mm
1
4th:twin resonator
2
Distance (mm)
2nd
3
4th
3rd
2nd
1st
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
G =197
 m
L =430
 m
1mm
G =110
 m
G =31
 m
Fig.8. Layout of the fabricated booster circuit, where insets show the layouts of J inverters.
4
3
2
1
0
-6 -3 0
Experimental result
Simulation by EM simulator
Simulation by transmission line model
Relative Frequency (%)
3 6
Fig.9 Comparison of the frequency dependence of group delay between theory and experiment
V.
C ONCLUSIONS
The design and performance of a LiNbO
3
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.
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