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Analysis of a high-speed laser-controlled microstrip directional coupler
Electronics Vol. 30, No. I, pp. 133-137, 1987 Printed in Great Britain. All rights reserved Solid-State
Copyright
0
0038-I lOI/ 1987 Pergamon
$3.00 I- 0.00 Journals Ltd
ANALYSIS OF A HIGH-SPEED LASER-CONTROLLED MICROSTRIP DIRECTIONAL COUPLER 1. ANDERSSON and Chalmers
University
S. T. ENG
of Technology, Department of Electrical S-412 96 Gothenburg, Sweden
Measurements,
(Received 22 January 1986; in revised form 21 May 1986) Abstract-A new type of high-speed optoelectronic microwave device is proposed and analyzed. The device is a laser-controlled microstrip directional coupler that utilizes the photoconductivity produced by laser illumination, The analysis, which is based on the even and odd mode approach, shows that several important advantages over conventional microstrip directional couplers are obtained. The device is capable of controlling the coupling parameters with a controlling range which varies at different ports but is at least 3 dB. Moreover, a comparison with conventional microstrip directional couplers shows that when illuminated, an improved bandwidth of more than 50% is achieved.
1. JNTRODUCTJON
Laser-controlled solid-state or optoelectronic devices utilizing laser-induced photoconductivity have gained much attention for high-speed applications because of picosecond precision, high power handling, and simplicity of operation. Moreover, since the controlling signal is optical and the controlled signal is electrical, an inherently high isolation is obtained. Such devices have successfully been used for high-speed switching and gating[l-71, generation of ultra-short kilovolt pulses[8], high frequency generation[9-121, and picosecond high isolation sampling[ 13-l 51. In this paper, we present an analysis of a new laser-controlled microstrip directional coupler, which minimizes some of the problems that arise when using these laser-controlled devices. One of the major problems has been the electrical reflections introduced by the illumination and/or the gap structure used which must be minimized since they degrade the performance of the device. Although, like previous devices[l-5,7-151, this new optoelectronic device is based on a gap structure, there will be no electrical reflections caused by the device structure used. The analysis shows that the electrical reflections caused by the illumination are minimized if the illumination is appropriate. It is also shown that the bandwidth can be improved by the illumination. Furthermore, this device can be used for laser-controlled switching of high-frequency electrical signals without introducing additional reflections and without suffer from the capacitive leakage problem caused by the gap capacitance, which would degrade the switching performance at high frequencies[2,4].
of a conventional microstrip quarter-wave directional coupler with four identical and symmetrical ports deposited on a semi-insulating semiconductor substrate. Power losses and dispersion effects are neglected and low-resistance ohmic contacts are assumed. Let the gap be illuminated by two identical and symmetrically spaced laser beams. Assuming that the illumination will cause a semiconductor skin depth that is much larger than the optical absorption depth (6, + I/U), and that the photoexcited regions are much smaller than the microstrip wavelength (1, $ W, ~/LX),then the photoexcited regions can be represented as lumped conductances[3]. Thus, the effect of the illumination can be described by two identical shunt conductances as shown in Fig. 2. The steady-state conductance is given by:
G=+‘-W(r.+&‘,
where q is the quantum efficiency, e is the electronic charge, hv is the photon energy, R is the surface reflectivity, p, and pp are the effective drift mobilities of electrons and holes, t is the effective carrier
Figure
XRT
PORT 4
PORT 1
2. ANALYSIS
controlled
(1)
t Seml-~nsulatlng
3
PORT 2
Substrate
1 is a schematic presentation of a lasermicrostrip directional coupler. It consists
Fig. 1. Schematic
133
presentation of a laser-controlled strip directional coupler.
micro-
134
I. ?XT I
PORT 4 -
ANDERSSON
on a computer. The expressions for an impedance matched device are presented in Appendix. Generally, the illumination will change the impedance of the device and reflections will be introduced. However, with appropriate illumination it is possible to change the coupling characteristics and minimize the reflections. Conditions for this optimum performance can easily be derived (see Appendix). The illuminating beams must be placed at each end of the coupling region (0, = 0). By introducing the conventional coupling factor k,
3
PORT 2
PORT 1
Fig. 2. Equivalent lumped-element device.
representation
and S. T. ENG
of the k=p
z, - Z” z, + z,’
lifetime, POis the uniformly distributed optical power, and s is the strip separation. The transient conductance corresponding to ultra-short optical pulses is given by[2]:
(2) where E is the energy in the uniformly distributed optical pulse. Because of the symmetrical and reciprocal structure of the device, the even and odd mode approach can be used for analysis[l6]. This method reduces the four-port problem to that of a two-arm network for both the even and odd mode cases. The cascade of the resulting two-terminal pair networks may be analyzed by the use of the ABCD (voltage-current) matrix. The even and odd mode ABCD matrices for the laser-controlled device (see Fig. 2) are easily obtained and are given by:
conductance
required
can
be ex-
k G=---. l-k
(6)
The effect of this optimum illumination can be seen by comparing the characteristics for non-illuminated and illuminated states. Table 1 which summarizes these characteristics for several frequencies, shows that at the center frequency the illumination will only affect the transmission to ports 2 and 3. The illumination will decrease the transmission to port 2 but increase the transmission to port 3. Thus, the transmission to port 3 can be switched on and off by the illumination. The transmission to port 2 will always be higher than the transmission to port 3. At even harmonics all four parameters will be affected by the illumination and reflections will be introduced. The effect of these reflections will be discussed in Section 3.
jZ, sin e
M men=
(3)
COST 1 jZ,sine, ~0~8,
c0s(e - 28,)
L
I[
x jY, sin(e - 28,) X [ 2G 1
the normalized pressed as:
01
jY,sinO, case,
I[ 1 1
0
2G
1
jZ, sin(e - 28,) c0s(e - 28,)
1
jZ,case, sin 8, ’
1 (4)
where Z,, Z,, Y,, and Y, are the normalized even and odd mode impedances and admittances, respectively, G is the normalized conductance, and 8, 8, are the phase angles corresponding to the coupling length and the illumination points, respectively. The impedances and admittances are all normalized with respect to that of a matched generator and load (Z,.). The characteristics of the four-port device are obtained by superposition of the even and odd mode reflection and transmission coefficients[ 161. After extensive but straightforward arithmetics the expressions describing the reflection and the transmission coefficients are obtained. To study the performance of the device the expressions have been implemented
3. RESULTS
AND DISCUSSIONS
Figure 3 shows the coupling characteristics of a matched non-illuminated microstrip directional coupler with a design coupling factor of - 6.0 dB at 3.0 GHz (center frequency). The transmission to port 2 (dashdotted line) and port 4 (solid line) is - 1.2 and - 6.0 dB at the center frequency, as indicated by Table 1. The transmission to port 4 depends strongly on the frequency and limits the bandwidth of the Table
I.
Couplmg characteristics of a matched directional at the harmonics of the center freauencv No illumination f =
0
r,t
IT,1
Optimum
(1+ 2nj.1, f=W
Ji-k’
0
0
0
0
IT,l
k
0
illumination
f = 2n/; I
k +k I
I
IT31
Where n=O,l,2..
/=(1+2nM
coupler
I+k
k l+k
k
k I+k
Analysis of a high-speed laser-controlled
microstrip directional coupler
135
________.____.___ ;
-6
i-l
/
/-
/
/ 0
1
2
3
4
5
Frequency
Fig.
6
7
6
9
-30
0. 1
0.0
0. 2
0. 4
0. 3
0.5
CGHzl
3. Coupling characteristics of a matched illuminated microstrip directional coupler.
non-
directional coupler to 3.3 GHz. Figure 4 shows the coupling characteristics of the same directional coupler when using the optimum illumination. There is no reflection (dashed line) at the center frequency and the transmission to port 4 (solid line) is -6.0 dB as for the non-illuminated state. The transmission to port 2 (dash-dotted line) and port 3 (dotted) have changed to -4.8 dB and - 10.8 dB, respectively. Thus, the illumination has reduced the transmission to port 2 by 3.6 dB and increased the transmission to port 3 from zero to - 10.8 dB. Moreover, the bandwidth of the device has increased to 4.9 GHz, i.e. by 50%. This bandwidth improvement has been obtained at the expense of increased reflection at port 1, and if this increased reflection is critical, the useful bandwidth has to be reduced. The increase in the reflection will, however, be less pronounced at low coupling factors. The maximum bandwidth will be further increased if the coupling factor is reduced. From Table 1 it can be calculated that the bandwidth of port 4 is infinite if the coupling factor is less than -7.6 dB. Consequently, the useful bandwidth of the directional coupler for both the non-illuminated and illuminated state is limited by either the accepted reflection or the non-illuminated transmission to port 4. Figures 5 and 6 show the reflection at port 1 (dashed line) and the transmission to ports 2
Fig. 5. The reflection at port 1 (dashed line) and the transmission to ports 2 (dashdotted line), 3 (dotted line), and 4 (solid line) at the center frequency versus the excitation
position.
(dashclotted line), 3 (dotted line), and 4 (solid line) at the center frequency when the illumination deviates from the optimum conditions (no reflection). As can be seen in Fig. 5, the position of the excitation points is not critical when the conductance is optimized [Equation (6)]. A deviation of 20% (t&j@ = 0.1) from the optimum excitation points (Q, = 0) will cause a reflection of less than -24 dB while the
I.
-30
/
/-
,l.\,...,
0. 1
/
,,,,,, 10
1
Normalized
Conductance
Fig. 6. The reflection at port 1 (dashed line) and the transmission to ports 2 (dasheddotted line), 3 (dotted line), and 4 (solid line) at the center frequency versus the normalized conductance.
0 ---_
---__--
-
-30
1
I
0
1
2
\,I
,
3
4
Frequency
--
II 5
6
7
9
9
CGHzl
Fig. 4. Coupling characteristics of a matched illuminated microstrip directional coupler.
-6
-9
Coup1
ing
-12
-15
Factor
CdBl
-19
Fig. 7. Optical power vs coupling factor for a coupler on a 400 pm thick InP:Fe substrate (hv = 1.5 eV, 7 = 100%, R = 28%, p. + pp = 2000 cm’/Vs, r = I ns).
136
I. ANDERSSON and S. T. ENG
transmissions will change less than 0.4dB. Figure 6 shows the performance when the conductance varies and the position of the excitation is optimized (0, = 0). The reflection is low for conductance values up to the optimum values (G = 1.0, k = -6 dB). The transmission to port 3 will increase monotonically when increasing the conductance. Thus, by varying the conductance, the transmission to port 3 can be tuned. The changes in the transmissions to ports 2 and 4 are of the order of 3.6 dB or less, for conductances up to the optimum value. From equation (6) it is obvious that the conductance required for optimum conditions will decrease at low coupling factors. However, as the coupling factor is reduced, the strip separation has to be increased very rapidly. As a result, the optical power or energy needed will be higher at low coupling factors. Figure 7 shows calculated optical power vs coupling factor for a coupler in a 50 Q-system, using some typical numbers for 1nP:Fe (t, = 12.55). A substrate thickness of 400 pm and a - 6 dB coupling correspond to a strip separation of approx. 10 pm while a coupling of - 18 dB requires a strip separation of 450 pm. The strip separations required for specific coupling factors have been calculated from the equations for coupled microstrip lines described by Gupta et a1.[17]. Figure 7 clearly shows, that the power levels at high coupling factors can be obtained with commercially available high-power semiconductor lasers (25 mW at -6 dB). At lower coupling factors the power levels are about 1 W, and semiconductor lasers with very high output power have to be used. Two factors limit the speed of the device: the transit time and the effective carrier lifetime. The transit time is the time required for the microwave signal to travel from one illumination point to the other. Consequently, the laser pulses must be at least as long as the transit time. The transit time is 1 ns or less for GHz-frequencies. The effective carrier life time, which limits the speed at which the conductance can be changed, depends on the substrate material. By choosing a high-speed material such as GaAs:Cr or InP:Fe, the effective carrier lifetime may be less than 1 ns[5,14]. Thus, the speed of the device is about 1 ns or faster. The main disadvantage of this device compared with a conventional coupler is the excess power loss caused by the illumination. The magnitude of the excess loss can be calculated from Table 1 and will be approximately 30% for a -6 dB coupler. This loss will be less for devices with low coupling factors. Finally, some comments on the lumped element approach used in this paper. This mode1 is a good approximation of the device, for illumination spot sizes (strip separations) that are less than 5% of the microstrip wavelength (the corresponding error is approx. 3%). For devices on 400pm thick InP:Fe substrates, this limit corresponds to a strip separation of approx. 1.8 mm (k = - 30 dB) at 3 GHz while at 20GHz the strip separation limit is approx. 270pm
(k = - 15 dB). If larger illumination spots (strip separations) are used, the device must be analyzed by distributed elements and the model used in this paper is not applicable.
4.CONCLUSIONS
A new optoelectronic device, a laser-controlled microstrip directional coupler, has been proposed and analyzed. The results obtained show that the center-frequency characteristics can be modified by the illumination without introducing additional reflections. The transmission to port 3 can be tuned and controlled by the illumination with a corresponding reduction in the transmission to port 2. The transmission to port 4 will under optimum conditions be unaffected in terms of the coupling factor. The transmission-controlling range (or dynamic range) is different at each port and varies from a minimum of 3 dB at port 4 to a large value at port 3. Moreover, if reflection is not critical, the directional coupler can be used with infinite bandwidth in the illuminated state, a significant improvement compared to a conventional coupler which has quite a limited bandwidth. The conductance values required for this optimum performance can be obtained with commercially available high-power semiconductor lasers. The speed is in the subnanosecond range, and the device is capable of high-speed operation. Power losses and dispersion effects will change the performance of the directional coupler but can be neglected, at least as a first-order approximation. Acknowledgements-The authors wish to thank Dr T. Andersson for stimulating discussions and reading the manuscript. This work was supported by the National Swedish Board for Technical Development (STU).
REFERENCES 1. D. H. Auston, Appl. Phys. Letf. 26, 101 (1975). 2. A. M. Johnson and D. H. Auston, IEEE .I. Quantum Electron. QE-11, 283 (1975). 3. W. Platte and Appelhaus, Electron. Lett. 12, 270 (1976). 4. W. Platte, Electron. Lett. 12, 437 (1976). 5. C. H. Lee, Appl. Phys. Lett. 30, 84 (1977). 6. W. Platte, IEEE Trans. Microwave Theory Techn. MTT-29, 1010 (1981). 7. V. Bruckner and F. Kerstan, Electron. Lett. 20, 738 (1984). 8. P. Lefur and D. H. Auston, Appl. Phys. Len. 28, 21 (1976). 9. J. M. Proud Jr and S. Norman, IEEE Trans. Microwave Theory Techn. MTT-26, 137 (1978). 10. G. Mourou, C. V. Stancampiano and D. Blumenthal, Appl. Phys. Lett 38, 470 (1981). 11. G. Mourou, C. V. Stancampiano, A. Antonetti and A. Orszag, Appl. Phys. Left. 39, 295 (1981). 12. R. Heidemann, T. Pfeiffer and D. Jager, Electron. Lett. 18, 783 (1982). 13. A. .I. Low and J. E. Carroll, Solid-State Electron Dev. 2, 185 (1978). and P. F. Moulton, Appl. Phys. Letf. 14. F. J. Leonberger 35, 712 (1979).
Analysis
of a high-speed
laser-controlled
15. D. H. Auston, A. M. Johnson, P. R. Smith and J. C. Bean, Appl. Phys. Left. 37, 371 (1980). 16. J. Reed and G. J. Wheeler, IRE Trans. Microwave Theory Techn. MTT-4, 246 (1956). 17. K. C. Gupta, R. Garg and I. J. Bahl, Microstrip Lines and Slotlines, 1st edn, p. 337. Artech House Inc., Dedham, MA (1979).
microstrip
directional
137
coupler
B2 = - G*Za cos e[(l + Z@ sin4 0, + 2(1 - z:) x sin2 S,] + 2sin O{Zc + Z,, + 2GZ, + G2Z, x [(l + z:) ~0~22 8, + (I-Z:) A, = 2G cos B[(l + Z@ + 2Gz;
~0~2 e,]} sin22 8, + (1 - z:)
x cos2 f3,] + 2G sin e[(l - 2:) sin2 0, - GZ: sin4 0,] B3 = - G*Z, cos 8[(1 + Z:) sin4 8, + 2(1 -z:) x sin2 e,i + 2GZ, sin e{2 + G[( 1 + 2;) ~0~~2 8, + (I - z:) c~~2 e,]} A, = 2G COS2e[i - z: + (1 + Z:) COS2 e,]
APPENDIX It is well-known that coupler (G = 0) is matched
a non-illuminated if:
directional
.Z; = 1 = Z,Z” = Y,Y”,
=
’
A, +j4
64.3
P+jQ’
=A,+_&
T
2
(A3)
P+jQ’
3
(A4)
P+jQ’
2G2[(1 -Zd)
x {2[1 + Za + G(l + Zd)] sin2 0, + G(1 - Z”,) sin4 0,) Ed = - G*Z, cos2 e[(l - 2;) sin4 0, + 2(1 + Z:) x sin2 O,] + G sir? 8[2Z,(l - GZ,(l
x (1 + Z@ + GZ,(l P = 4cosz0[l
+ 2:) sin2 0,
- Z,!j)sin4 ($1 + sin2 0[Z, - Z,
+ GZ,(l - 2:) + 2G*Z,(l-
Z@ + [GZ,
+ Z;)] cos2 e,]
+ GZ(l + z:) + 2G*Z: sin22 8,
+ G(l - Z;) cos2 e,] - sin2 e{(Z, + Z,)*
+ 4G(l + Z@ + 2G*(l + Z2,)[(1 + Z;) cos*2 0, + (1 -z@
=A,+&
T
-Zi)+
x ~0~~2 8, + (1 + z:) ~0~2 e,]) + G sin e cos e (Al)
where Z, is the normalized characteristic impedance of the input/output port tranmission lines (see Fig. 2), Z,, Z,, Y, and Y, are the normalized even and odd mode impedances and admittances, respectively. Now consider the case where the non-illuminated device is impedance matched and port 1 is excited with an electrical signal. The reflection and transmission coefficients for the illuminated device are then given by: r
-sinZB{Z~--Zi+2G(l
~0~2 e,]) + G(1 - z:) sin e cos e
x {[(4 + 2G(l + Za)] sin2 0, + G(l - 2:) sin4 0,) Q = - 2GZ; COS’0[( 1 + z;) sin4 0, + 2( 1 - 2;)
(A5) where r, is the reflection coefficient at port 1 and T,, T,, T4, are the transmission coefficients to port 2, 3 and 4, respectively, and: A, = - 2G {cos2 t?[l - Z: + (1 + Z~)cos2 0,] + sinI 8 x [l - Zi - 2GZf cos2 0,] + sin0 cos 0 x [l + Zi + ZGZi]sin 2 8,) B, = GZ,{Gcos*~[(l
-Zi)sin48,
x sin2 e,] - sin2 0[G(l
_ sin2 8[(2 + G[l + Z:])cosZ + G(l - z;)cos4
+2(1
+Z@
- Za)sin4 e, + 4sin2 e,]
x sin2 t?,] + 2G sin’ O[(Z, + Z,) (1 - 23) x sin2 8, - GZ,(l
+ Z;) sin4 e,] + sin2 0
x [2(Z, + Z,) + 4GZ, + 2G*Z,(l + G(1 + Z;)(Z,
+ Z,) + G(l - Z;,(Z,+
where G is the normalized conductance and 0, 8, are the phase angles corresponding to the coupling length and the illumination points, respectively. From equation (A2) can be seen that no reflection (r, = 0) will be introduced at the center frequency (6 = x /2) if:
e,]) G=
A, = 2~0s 0[2 + G(l + z;) + 2G*Z; sin22 B,
x sin2 0, - GZ20 sin4 e,]
Z,
+ 2GZ,) cos2 e,],
8,
+ G(l - Z@ cos2 0,] + 2G sin 0[(1 - Z:)
+ Z:,
These relations mination.
describe
8, = 0,
646)
1-z* 0. 2z:
(A7)
the conditions
for optimum
illu-
Copyright
0
0038-I lOI/ 1987 Pergamon
$3.00 I- 0.00 Journals Ltd
ANALYSIS OF A HIGH-SPEED LASER-CONTROLLED MICROSTRIP DIRECTIONAL COUPLER 1. ANDERSSON and Chalmers
University
S. T. ENG
of Technology, Department of Electrical S-412 96 Gothenburg, Sweden
Measurements,
(Received 22 January 1986; in revised form 21 May 1986) Abstract-A new type of high-speed optoelectronic microwave device is proposed and analyzed. The device is a laser-controlled microstrip directional coupler that utilizes the photoconductivity produced by laser illumination, The analysis, which is based on the even and odd mode approach, shows that several important advantages over conventional microstrip directional couplers are obtained. The device is capable of controlling the coupling parameters with a controlling range which varies at different ports but is at least 3 dB. Moreover, a comparison with conventional microstrip directional couplers shows that when illuminated, an improved bandwidth of more than 50% is achieved.
1. JNTRODUCTJON
Laser-controlled solid-state or optoelectronic devices utilizing laser-induced photoconductivity have gained much attention for high-speed applications because of picosecond precision, high power handling, and simplicity of operation. Moreover, since the controlling signal is optical and the controlled signal is electrical, an inherently high isolation is obtained. Such devices have successfully been used for high-speed switching and gating[l-71, generation of ultra-short kilovolt pulses[8], high frequency generation[9-121, and picosecond high isolation sampling[ 13-l 51. In this paper, we present an analysis of a new laser-controlled microstrip directional coupler, which minimizes some of the problems that arise when using these laser-controlled devices. One of the major problems has been the electrical reflections introduced by the illumination and/or the gap structure used which must be minimized since they degrade the performance of the device. Although, like previous devices[l-5,7-151, this new optoelectronic device is based on a gap structure, there will be no electrical reflections caused by the device structure used. The analysis shows that the electrical reflections caused by the illumination are minimized if the illumination is appropriate. It is also shown that the bandwidth can be improved by the illumination. Furthermore, this device can be used for laser-controlled switching of high-frequency electrical signals without introducing additional reflections and without suffer from the capacitive leakage problem caused by the gap capacitance, which would degrade the switching performance at high frequencies[2,4].
of a conventional microstrip quarter-wave directional coupler with four identical and symmetrical ports deposited on a semi-insulating semiconductor substrate. Power losses and dispersion effects are neglected and low-resistance ohmic contacts are assumed. Let the gap be illuminated by two identical and symmetrically spaced laser beams. Assuming that the illumination will cause a semiconductor skin depth that is much larger than the optical absorption depth (6, + I/U), and that the photoexcited regions are much smaller than the microstrip wavelength (1, $ W, ~/LX),then the photoexcited regions can be represented as lumped conductances[3]. Thus, the effect of the illumination can be described by two identical shunt conductances as shown in Fig. 2. The steady-state conductance is given by:
G=+‘-W(r.+&‘,
where q is the quantum efficiency, e is the electronic charge, hv is the photon energy, R is the surface reflectivity, p, and pp are the effective drift mobilities of electrons and holes, t is the effective carrier
Figure
XRT
PORT 4
PORT 1
2. ANALYSIS
controlled
(1)
t Seml-~nsulatlng
3
PORT 2
Substrate
1 is a schematic presentation of a lasermicrostrip directional coupler. It consists
Fig. 1. Schematic
133
presentation of a laser-controlled strip directional coupler.
micro-
134
I. ?XT I
PORT 4 -
ANDERSSON
on a computer. The expressions for an impedance matched device are presented in Appendix. Generally, the illumination will change the impedance of the device and reflections will be introduced. However, with appropriate illumination it is possible to change the coupling characteristics and minimize the reflections. Conditions for this optimum performance can easily be derived (see Appendix). The illuminating beams must be placed at each end of the coupling region (0, = 0). By introducing the conventional coupling factor k,
3
PORT 2
PORT 1
Fig. 2. Equivalent lumped-element device.
representation
and S. T. ENG
of the k=p
z, - Z” z, + z,’
lifetime, POis the uniformly distributed optical power, and s is the strip separation. The transient conductance corresponding to ultra-short optical pulses is given by[2]:
(2) where E is the energy in the uniformly distributed optical pulse. Because of the symmetrical and reciprocal structure of the device, the even and odd mode approach can be used for analysis[l6]. This method reduces the four-port problem to that of a two-arm network for both the even and odd mode cases. The cascade of the resulting two-terminal pair networks may be analyzed by the use of the ABCD (voltage-current) matrix. The even and odd mode ABCD matrices for the laser-controlled device (see Fig. 2) are easily obtained and are given by:
conductance
required
can
be ex-
k G=---. l-k
(6)
The effect of this optimum illumination can be seen by comparing the characteristics for non-illuminated and illuminated states. Table 1 which summarizes these characteristics for several frequencies, shows that at the center frequency the illumination will only affect the transmission to ports 2 and 3. The illumination will decrease the transmission to port 2 but increase the transmission to port 3. Thus, the transmission to port 3 can be switched on and off by the illumination. The transmission to port 2 will always be higher than the transmission to port 3. At even harmonics all four parameters will be affected by the illumination and reflections will be introduced. The effect of these reflections will be discussed in Section 3.
jZ, sin e
M men=
(3)
COST 1 jZ,sine, ~0~8,
c0s(e - 28,)
L
I[
x jY, sin(e - 28,) X [ 2G 1
the normalized pressed as:
01
jY,sinO, case,
I[ 1 1
0
2G
1
jZ, sin(e - 28,) c0s(e - 28,)
1
jZ,case, sin 8, ’
1 (4)
where Z,, Z,, Y,, and Y, are the normalized even and odd mode impedances and admittances, respectively, G is the normalized conductance, and 8, 8, are the phase angles corresponding to the coupling length and the illumination points, respectively. The impedances and admittances are all normalized with respect to that of a matched generator and load (Z,.). The characteristics of the four-port device are obtained by superposition of the even and odd mode reflection and transmission coefficients[ 161. After extensive but straightforward arithmetics the expressions describing the reflection and the transmission coefficients are obtained. To study the performance of the device the expressions have been implemented
3. RESULTS
AND DISCUSSIONS
Figure 3 shows the coupling characteristics of a matched non-illuminated microstrip directional coupler with a design coupling factor of - 6.0 dB at 3.0 GHz (center frequency). The transmission to port 2 (dashdotted line) and port 4 (solid line) is - 1.2 and - 6.0 dB at the center frequency, as indicated by Table 1. The transmission to port 4 depends strongly on the frequency and limits the bandwidth of the Table
I.
Couplmg characteristics of a matched directional at the harmonics of the center freauencv No illumination f =
0
r,t
IT,1
Optimum
(1+ 2nj.1, f=W
Ji-k’
0
0
0
0
IT,l
k
0
illumination
f = 2n/; I
k +k I
I
IT31
Where n=O,l,2..
/=(1+2nM
coupler
I+k
k l+k
k
k I+k
Analysis of a high-speed laser-controlled
microstrip directional coupler
135
________.____.___ ;
-6
i-l
/
/-
/
/ 0
1
2
3
4
5
Frequency
Fig.
6
7
6
9
-30
0. 1
0.0
0. 2
0. 4
0. 3
0.5
CGHzl
3. Coupling characteristics of a matched illuminated microstrip directional coupler.
non-
directional coupler to 3.3 GHz. Figure 4 shows the coupling characteristics of the same directional coupler when using the optimum illumination. There is no reflection (dashed line) at the center frequency and the transmission to port 4 (solid line) is -6.0 dB as for the non-illuminated state. The transmission to port 2 (dash-dotted line) and port 3 (dotted) have changed to -4.8 dB and - 10.8 dB, respectively. Thus, the illumination has reduced the transmission to port 2 by 3.6 dB and increased the transmission to port 3 from zero to - 10.8 dB. Moreover, the bandwidth of the device has increased to 4.9 GHz, i.e. by 50%. This bandwidth improvement has been obtained at the expense of increased reflection at port 1, and if this increased reflection is critical, the useful bandwidth has to be reduced. The increase in the reflection will, however, be less pronounced at low coupling factors. The maximum bandwidth will be further increased if the coupling factor is reduced. From Table 1 it can be calculated that the bandwidth of port 4 is infinite if the coupling factor is less than -7.6 dB. Consequently, the useful bandwidth of the directional coupler for both the non-illuminated and illuminated state is limited by either the accepted reflection or the non-illuminated transmission to port 4. Figures 5 and 6 show the reflection at port 1 (dashed line) and the transmission to ports 2
Fig. 5. The reflection at port 1 (dashed line) and the transmission to ports 2 (dashdotted line), 3 (dotted line), and 4 (solid line) at the center frequency versus the excitation
position.
(dashclotted line), 3 (dotted line), and 4 (solid line) at the center frequency when the illumination deviates from the optimum conditions (no reflection). As can be seen in Fig. 5, the position of the excitation points is not critical when the conductance is optimized [Equation (6)]. A deviation of 20% (t&j@ = 0.1) from the optimum excitation points (Q, = 0) will cause a reflection of less than -24 dB while the
I.
-30
/
/-
,l.\,...,
0. 1
/
,,,,,, 10
1
Normalized
Conductance
Fig. 6. The reflection at port 1 (dashed line) and the transmission to ports 2 (dasheddotted line), 3 (dotted line), and 4 (solid line) at the center frequency versus the normalized conductance.
0 ---_
---__--
-
-30
1
I
0
1
2
\,I
,
3
4
Frequency
--
II 5
6
7
9
9
CGHzl
Fig. 4. Coupling characteristics of a matched illuminated microstrip directional coupler.
-6
-9
Coup1
ing
-12
-15
Factor
CdBl
-19
Fig. 7. Optical power vs coupling factor for a coupler on a 400 pm thick InP:Fe substrate (hv = 1.5 eV, 7 = 100%, R = 28%, p. + pp = 2000 cm’/Vs, r = I ns).
136
I. ANDERSSON and S. T. ENG
transmissions will change less than 0.4dB. Figure 6 shows the performance when the conductance varies and the position of the excitation is optimized (0, = 0). The reflection is low for conductance values up to the optimum values (G = 1.0, k = -6 dB). The transmission to port 3 will increase monotonically when increasing the conductance. Thus, by varying the conductance, the transmission to port 3 can be tuned. The changes in the transmissions to ports 2 and 4 are of the order of 3.6 dB or less, for conductances up to the optimum value. From equation (6) it is obvious that the conductance required for optimum conditions will decrease at low coupling factors. However, as the coupling factor is reduced, the strip separation has to be increased very rapidly. As a result, the optical power or energy needed will be higher at low coupling factors. Figure 7 shows calculated optical power vs coupling factor for a coupler in a 50 Q-system, using some typical numbers for 1nP:Fe (t, = 12.55). A substrate thickness of 400 pm and a - 6 dB coupling correspond to a strip separation of approx. 10 pm while a coupling of - 18 dB requires a strip separation of 450 pm. The strip separations required for specific coupling factors have been calculated from the equations for coupled microstrip lines described by Gupta et a1.[17]. Figure 7 clearly shows, that the power levels at high coupling factors can be obtained with commercially available high-power semiconductor lasers (25 mW at -6 dB). At lower coupling factors the power levels are about 1 W, and semiconductor lasers with very high output power have to be used. Two factors limit the speed of the device: the transit time and the effective carrier lifetime. The transit time is the time required for the microwave signal to travel from one illumination point to the other. Consequently, the laser pulses must be at least as long as the transit time. The transit time is 1 ns or less for GHz-frequencies. The effective carrier life time, which limits the speed at which the conductance can be changed, depends on the substrate material. By choosing a high-speed material such as GaAs:Cr or InP:Fe, the effective carrier lifetime may be less than 1 ns[5,14]. Thus, the speed of the device is about 1 ns or faster. The main disadvantage of this device compared with a conventional coupler is the excess power loss caused by the illumination. The magnitude of the excess loss can be calculated from Table 1 and will be approximately 30% for a -6 dB coupler. This loss will be less for devices with low coupling factors. Finally, some comments on the lumped element approach used in this paper. This mode1 is a good approximation of the device, for illumination spot sizes (strip separations) that are less than 5% of the microstrip wavelength (the corresponding error is approx. 3%). For devices on 400pm thick InP:Fe substrates, this limit corresponds to a strip separation of approx. 1.8 mm (k = - 30 dB) at 3 GHz while at 20GHz the strip separation limit is approx. 270pm
(k = - 15 dB). If larger illumination spots (strip separations) are used, the device must be analyzed by distributed elements and the model used in this paper is not applicable.
4.CONCLUSIONS
A new optoelectronic device, a laser-controlled microstrip directional coupler, has been proposed and analyzed. The results obtained show that the center-frequency characteristics can be modified by the illumination without introducing additional reflections. The transmission to port 3 can be tuned and controlled by the illumination with a corresponding reduction in the transmission to port 2. The transmission to port 4 will under optimum conditions be unaffected in terms of the coupling factor. The transmission-controlling range (or dynamic range) is different at each port and varies from a minimum of 3 dB at port 4 to a large value at port 3. Moreover, if reflection is not critical, the directional coupler can be used with infinite bandwidth in the illuminated state, a significant improvement compared to a conventional coupler which has quite a limited bandwidth. The conductance values required for this optimum performance can be obtained with commercially available high-power semiconductor lasers. The speed is in the subnanosecond range, and the device is capable of high-speed operation. Power losses and dispersion effects will change the performance of the directional coupler but can be neglected, at least as a first-order approximation. Acknowledgements-The authors wish to thank Dr T. Andersson for stimulating discussions and reading the manuscript. This work was supported by the National Swedish Board for Technical Development (STU).
REFERENCES 1. D. H. Auston, Appl. Phys. Letf. 26, 101 (1975). 2. A. M. Johnson and D. H. Auston, IEEE .I. Quantum Electron. QE-11, 283 (1975). 3. W. Platte and Appelhaus, Electron. Lett. 12, 270 (1976). 4. W. Platte, Electron. Lett. 12, 437 (1976). 5. C. H. Lee, Appl. Phys. Lett. 30, 84 (1977). 6. W. Platte, IEEE Trans. Microwave Theory Techn. MTT-29, 1010 (1981). 7. V. Bruckner and F. Kerstan, Electron. Lett. 20, 738 (1984). 8. P. Lefur and D. H. Auston, Appl. Phys. Len. 28, 21 (1976). 9. J. M. Proud Jr and S. Norman, IEEE Trans. Microwave Theory Techn. MTT-26, 137 (1978). 10. G. Mourou, C. V. Stancampiano and D. Blumenthal, Appl. Phys. Lett 38, 470 (1981). 11. G. Mourou, C. V. Stancampiano, A. Antonetti and A. Orszag, Appl. Phys. Left. 39, 295 (1981). 12. R. Heidemann, T. Pfeiffer and D. Jager, Electron. Lett. 18, 783 (1982). 13. A. .I. Low and J. E. Carroll, Solid-State Electron Dev. 2, 185 (1978). and P. F. Moulton, Appl. Phys. Letf. 14. F. J. Leonberger 35, 712 (1979).
Analysis
of a high-speed
laser-controlled
15. D. H. Auston, A. M. Johnson, P. R. Smith and J. C. Bean, Appl. Phys. Left. 37, 371 (1980). 16. J. Reed and G. J. Wheeler, IRE Trans. Microwave Theory Techn. MTT-4, 246 (1956). 17. K. C. Gupta, R. Garg and I. J. Bahl, Microstrip Lines and Slotlines, 1st edn, p. 337. Artech House Inc., Dedham, MA (1979).
microstrip
directional
137
coupler
B2 = - G*Za cos e[(l + Z@ sin4 0, + 2(1 - z:) x sin2 S,] + 2sin O{Zc + Z,, + 2GZ, + G2Z, x [(l + z:) ~0~22 8, + (I-Z:) A, = 2G cos B[(l + Z@ + 2Gz;
~0~2 e,]} sin22 8, + (1 - z:)
x cos2 f3,] + 2G sin e[(l - 2:) sin2 0, - GZ: sin4 0,] B3 = - G*Z, cos 8[(1 + Z:) sin4 8, + 2(1 -z:) x sin2 e,i + 2GZ, sin e{2 + G[( 1 + 2;) ~0~~2 8, + (I - z:) c~~2 e,]} A, = 2G COS2e[i - z: + (1 + Z:) COS2 e,]
APPENDIX It is well-known that coupler (G = 0) is matched
a non-illuminated if:
directional
.Z; = 1 = Z,Z” = Y,Y”,
=
’
A, +j4
64.3
P+jQ’
=A,+_&
T
2
(A3)
P+jQ’
3
(A4)
P+jQ’
2G2[(1 -Zd)
x {2[1 + Za + G(l + Zd)] sin2 0, + G(1 - Z”,) sin4 0,) Ed = - G*Z, cos2 e[(l - 2;) sin4 0, + 2(1 + Z:) x sin2 O,] + G sir? 8[2Z,(l - GZ,(l
x (1 + Z@ + GZ,(l P = 4cosz0[l
+ 2:) sin2 0,
- Z,!j)sin4 ($1 + sin2 0[Z, - Z,
+ GZ,(l - 2:) + 2G*Z,(l-
Z@ + [GZ,
+ Z;)] cos2 e,]
+ GZ(l + z:) + 2G*Z: sin22 8,
+ G(l - Z;) cos2 e,] - sin2 e{(Z, + Z,)*
+ 4G(l + Z@ + 2G*(l + Z2,)[(1 + Z;) cos*2 0, + (1 -z@
=A,+&
T
-Zi)+
x ~0~~2 8, + (1 + z:) ~0~2 e,]) + G sin e cos e (Al)
where Z, is the normalized characteristic impedance of the input/output port tranmission lines (see Fig. 2), Z,, Z,, Y, and Y, are the normalized even and odd mode impedances and admittances, respectively. Now consider the case where the non-illuminated device is impedance matched and port 1 is excited with an electrical signal. The reflection and transmission coefficients for the illuminated device are then given by: r
-sinZB{Z~--Zi+2G(l
~0~2 e,]) + G(1 - z:) sin e cos e
x {[(4 + 2G(l + Za)] sin2 0, + G(l - 2:) sin4 0,) Q = - 2GZ; COS’0[( 1 + z;) sin4 0, + 2( 1 - 2;)
(A5) where r, is the reflection coefficient at port 1 and T,, T,, T4, are the transmission coefficients to port 2, 3 and 4, respectively, and: A, = - 2G {cos2 t?[l - Z: + (1 + Z~)cos2 0,] + sinI 8 x [l - Zi - 2GZf cos2 0,] + sin0 cos 0 x [l + Zi + ZGZi]sin 2 8,) B, = GZ,{Gcos*~[(l
-Zi)sin48,
x sin2 e,] - sin2 0[G(l
_ sin2 8[(2 + G[l + Z:])cosZ + G(l - z;)cos4
+2(1
+Z@
- Za)sin4 e, + 4sin2 e,]
x sin2 t?,] + 2G sin’ O[(Z, + Z,) (1 - 23) x sin2 8, - GZ,(l
+ Z;) sin4 e,] + sin2 0
x [2(Z, + Z,) + 4GZ, + 2G*Z,(l + G(1 + Z;)(Z,
+ Z,) + G(l - Z;,(Z,+
where G is the normalized conductance and 0, 8, are the phase angles corresponding to the coupling length and the illumination points, respectively. From equation (A2) can be seen that no reflection (r, = 0) will be introduced at the center frequency (6 = x /2) if:
e,]) G=
A, = 2~0s 0[2 + G(l + z;) + 2G*Z; sin22 B,
x sin2 0, - GZ20 sin4 e,]
Z,
+ 2GZ,) cos2 e,],
8,
+ G(l - Z@ cos2 0,] + 2G sin 0[(1 - Z:)
+ Z:,
These relations mination.
describe
8, = 0,
646)
1-z* 0. 2z:
(A7)
the conditions
for optimum
illu-