printed dipole array using evolutionary programming, Proc IEEE AP-SInt Symp, Atlanta, GA, 1998, pp 42–45.

8. A. Hoorfar, Mutation-based evolutionary algorithms and their appli-cations to optimization of antennas in layered media, IEEE AP-S IntSymp, Orlando, FL, 1999, pp 2876–2879.

9. A. Hoorfar and Y. Liu, A study of Cauchy and Gaussian mutationoperators in the evolutionary programming optimization of antennastructures, Proc 16th Ann Rev Appl Computat Electromagn, Monterey,CA, 2000, pp 63–69.

10. S. Chakrawarty and R. Mittra, Design of microwave filters using abinary coded genetic algorithm, IEEE AP-S Int Symp, Salt Lake City,UT, 2000, pp 144–147.

11. H.A. Macleod, Thin-film optical filters, Adam Hilger Ltd., London,1969.

© 2003 Wiley Periodicals, Inc.

OPTICALLY CONTROLLED MICROSTRIPLOAD AND STUB ON SILICONSUBSTRATE

Avanish Bhadauria,1 Nasimuddin,1 A. K. Verma,1

Enakshi Khular Sharma,1 and B. R. Singh2

1 Department of Electronic ScienceUniversity of Delhi South CampusNew Delhi–110021, India2 CEERI, Pilani–333031, India

Received 31 April 2003

ABSTRACT: In this paper we report the modeling and experimentalmeasurements for optical control of a microstrip load and �g/4 stub fab-ricated on high-resistivity silicon substrate. We present the basic circuitmodel of a photoinduced or optical load created by a laser spot at theend of an open microstrip line. The modeled optical load has been usedto simulate reflections at open microstrip line terminated by the opticalload. The results obtained by both simulation and measurement showthat an optical load created at the open termination of a microstrip linecan control the reflection parameter of the line. A similar optical loadcreated at the end of an open �g/4 stub on a microstrip line has beenshown to control the transmitted power at the design frequency. Themeasurement results compare well with those predicted by both a simplecircuit simulation and a simulation carried out on the Ansoft Maxwellsimulator using a termination obtained by an equivalent circuit model ofthe optical load. © 2003 Wiley Periodicals, Inc. Microwave OptTechnol Lett 39: 271–276, 2003; Published online in Wiley Inter-Science (www.interscience.wiley.com). DOI 10.1002/mop.11188

Key words: optical load; optically controlled stub

1. INTRODUCTION

The direct optical control of microwave devices has been an areaof interest over the last few years [1–7]. This technique offers highisolation between the controlling optical source and controlledmicrowave device, ultrafast response, and high-power handlingcapacity. The optical control of passive microwave devices onsemiconducting substrate is based on the fact that when energyphotons greater than the band gap are incident on the surface,electron-hole pairs are created by light absorption and spread intothe substrate, due to carrier diffusion, to give an inhomogeneouscarrier distribution in the illuminated substrate. The electron hole-plasma gives rise to a complex dielectric constant [4] or finiteconductivity [5] in the semiconducting substrate. The absorptionand penetration depth of the plasma depend on the optical wave-length and substrate parameters. Such an electron-hole plasma,

created at the end of the open microstrip line due to illumination bylaser spot, changes the dielectric constant within the illuminatedregion in the semiconducting substrate. The optically illuminatedregion can be considered as a cylinder filled with a complexdielectric constant, whose value varies with substrate depth, andcan be modeled as a capacitor with complex capacitance. Thisleads to an equivalent circuit model of a capacitance in parallel toa resistance. The resistance decreases from several kilo-ohms inthe dark state to a few ohms with an increase in optical intensity.

In this paper we report the modeling and experimental mea-surements on optical control of a microstrip load and �g/4 stub ona microstrip line fabricated on high resistivity silicon substrate.The typical structure of the optically controlled microstrip load and�g/4 stub are shown in Figure 1(a) and 1(b). An optical load iscreated by illumination of the open end of the microstrip line by afocussed laser beam from a laser diode. Our measurement andmodeled results show that optical power levels of 20–30 mWcreate an almost resistive load termination, which can be used tocontrol the reflection parameter �S11� of line. The line, hence, actsas a variable optically controlled load with a narrowband matchingwith return loss better than 30 dB for a frequency defined bydesign. Haider et al. [1] also reported investigations on a similarmicrostrip line using an extremely high-power (600 mW) Argonion laser. More recently, a dc bias was also applied for increasedcontrol [2–3] and the authors used the Microwave Design System(MDS) and Atlas software to arrive at an equivalent circuit model.At such large power levels, at the Argon-ion wavelength theoptical load created shows a significant capacitive component andmatching frequency varies with optical intensity. A similar opticalload created at the end of an open �g/4 stub, as shown in Figure1(b), can be used to control the transmitted power �S21�. Simulatedand actual measurements show that the transmission coefficient�S21� increases from � �33 dB with no illumination to almost 0dB with relatively low optical power levels at the design frequency(5.0 GHz). Thus, the device can be used as an optically controlledattenuator. Both structures were also analyzed on the Ansoft Max-well simulator with a “black box” load termination obtained byusing circuit modeling at the open end of the microstrip line. Themeasured results agreed with those predicted by the simulation.

2. OPTICALLY ILLUMINATED SEMICONDUCTINGSUBSTRATE

2.1 Optically Generated Carrier ProfileWhen a high-resistivity semiconducting substrate is illuminatedwith radiation above bandgap (�0 � 1.0 �m for silicon), anelectron-hole plasma is created due to optically generated carriers.The distribution of optically generated carriers in the semiconduc-tor under optical illumination is strongly influenced by carrierdiffusion and the surface recombination process. Assuming 1Ddiffusion, the optically generated carrier profile satisfies the fol-lowing differential equation [6]:

Figure 1 Typical structure of an optically controlled (a) microstrip loadand (b) �g/4 stub on a microstrip line

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 39, No. 4, November 20 2003 271

La2

d2nop

d y2 � nop � ��G�y�, (1)

where La is the ambipolar diffusion length, defined as

La � � 2�n�p�kBT

e��n � �p�� 1/ 2

, (2)

where � is the excess carrier lifetime, �n and �p are the respectiveelectron and hole mobilities, kB is Boltzmann’s constant, T is theabsolute temperature, and e is the electronic charge.

The position dependent optical carrier pump or generation rateG( y) is

G� y� ���

h

P

A�1 � R�exp���y�, (3)

where � is the wavelength-dependent radiation absorption coeffi-cient, R is surface reflectivity, P/A is the incident intensity, h isPlanck’s constant, c is the velocity of light in free space, and � isthe wavelength-dependent internal quantum efficiency of material.The appropriate boundary conditions are nop( y) 3 0 as y 3 �and at the surface y � 0 (when surface recombination is taken intoaccount):

dnop

d y�

s

Dnop�0�, (4)

where s and D � La2/� are the surface recombination velocity and

the diffusion coefficient, respectively. With these boundary con-ditions, the solution of Eq. (1) for the optically generated carrierprofile within the illuminated region is obtained as

nop� y� � � 1

hc� �1 � R��S�p�

1 � �2La2

� �exp���y� ��La

2 � s�

La � s�exp��y

La�� P

A, (5)

where S(�) is relative spectral response of the semiconductingmaterial exhibiting the peak response at optical wavelength �p(�850 nm for silicon). It is seen from the above equation that thecarrier profile is proportional to the absorption term exp(��y) anda surface recombination velocity controlled diffusion term propor-tional to exp(�y/La). The resultant carrier profile is characterizedby the typical loss of carrier concentration due to surface recom-bination within the surface region and by a relatively large plasmadepth which can exceed an optical penetration depth of 1/�. Thetypical values of the various parameters for silicon are: La � 47�m, � (650 nm) � 3600 cm�1, � (850 nm) � 700 cm�1, �p �850 nm, s � 102 cm/s, S (850 nm) � 1.0, S (650 nm) � 0.7, andR � 0.3, � can vary from 2 to 200 �s [2].

2.2 Complex Dielectric Constant and Conductivity ProfileThe plasma created due to photoexcited electron hole pairs in theoptically illuminated semiconducting substrate changes both thereal as well as imaginary parts of the complex dielectric constant.In terms of optically generated carriers, the complex dielectricconstant can be written as [4]:

* � � � j, (6)

where

� � L �

e2�p2� pl

m*pl�

ph

m*ph�

0�1 � �2�p2�

�nee

2�e2

m*e0�1 � �2�e2�

, (7)

�

e2�p� pl

m*pl�

ph

m*ph�

0��1 � �2�p2�

�nee

2�e

m*e0��1 � �2�e2�

, (8)

with L the dielectric constant of unilluminated semiconductor. ne

and np are the density of photo-induced electron and holes and weassume nop � ne � np with �pl ph, where pl and ph denotethe densities of light and heavy holes, respectively. The collisiontime times �e and �p (assumed to be equal for light and heavyholes) are given by

�e ��em*e

e, �p �

�pm*pe

(9)

and the corresponding conductivity can be written as

� � �0. (10)

The typical values of the various parameters for silicon are:L � 11.8, pl � 0.14np, ph � 0.86np, m*e � 0.259m0, m*p �0.38m0, �e � 2.2 � 10�13 s, �p � 1.3 � 10�13 s.

For the frequencies in the range of few GHz, the terms �2�p2

1 and �2�e2 1, the conductivity profile due to optical illumina-

tion can approximately expressed as (assuming all holes to besimilar):

�op� y� � e��n � �p�� 1

hc� �1 � R��S�p�

1 � �2La2

� �exp���y� ��La

2 � s�

La � s�exp��y

La�� P

A. (11)

The carrier concentration nop( y), real part of dielectric constant�( y), and conductivity �( y) have been plotted in Figure 2(a)–(c)at different incident intensity levels. �( y) and �( y) are almostfrequency independent, while ( y) is inversely proportional tofrequency.

3. OPTICAL LOAD AT THE END OF AN OPENMICROSTRIP LINE

3.1 Equivalent Circuit Model of the Optical LoadThe optical load created by a focused laser spot on the semicon-ductor substrate can be considered as a parallel plate capacitor ofa circular cross section filled with an inhomogeneous complexdielectric constant, as shown in Figure 3(a). The complex capac-itance C* of the capacitor can be expressed as

C* � C� � jC �0A

�0

d d y

*� y�

�0A

�i�1

n1

*i� y�

, (12)

where d � n� and yi � i�. In the complex capacitance C*, C�corresponds to a capacitance while C corresponds to an equiva-lent resistance. Hence, the equivalent load can be considered as aparallel combination of a resistance and a capacitance, as shown in

272 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 39, No. 4, November 20 2003

Figure 4(a) and (b) with the resistance and capacitance in theequivalent circuit, shown in Fig. 3(b), given by

C � C� and R �1

G�

1

�C

and the total admittance is

Y � j�C* � j�C � G.

For illumination with a 650-nm laser diode focused to a spot �250�m in diameter, the variation of resistance and capacitance withfrequency at different power levels is shown in Figure 4(a) and (b).The resistance generated by optical illumination is almost inde-pendent of frequency. The capacitance shows frequency depen-dence at relatively low power levels, while at higher power levelsit also becomes independent of frequency. When the plasma depthis comparable to substrate thickness, the created load is almostresistive with resistance, given by

R �1

A �0

d d y

�� y�. (15)

Substituting �( y) from Eq. (11) in the above expression, theresistance can be written as

R ��1 � �2La

2�hc

�1 � R�e��n � �p��S�p�P

� �0

d d y

�exp���y� ��La

2 � s�

La � s�exp��y

La�� . (16)

It is clear from the above expression that the optically generatedresistance created depends on the power levels and not on the areaof the spot. The capacitance, however, depends strongly on thearea of the spot.

For the silicon substrate within a wavelength range 500–900nm, where �La � 1 and �La � s� /La, the above expressionreduces to

R ��1 � s� /La�hcLa

2

�1 � R�e��n � �p�S�p�P�ed/La � 1�. (17)

Figure 2 Variation of (a) optically generated carriers, (b) real part ofdielectric constant, and (c) conductivity with substrate depth in a siliconsubstrate illuminated by a laser spot of diameter 250 �m at different powerlevels

Figure 3 (a) Equivalent capacitor formed by illumination of a semicon-ductor substrate by a semiconductor substrate by a laser spot and (b) thecorresponding equivalent circuit model

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 39, No. 4, November 20 2003 273

3.2 Reflection Coefficient �S11� of the Open Microstrip Line Ter-minated by the Optical LoadFinally, an open microstrip terminated with the optical load can beconsidered as the terminated by a load with impedance given by

Zopt �1

j�C*. (18)

Such a load created at the end of microstrip line of characteristicimpedance Z0 will result in a reflection coefficient (or S11), givenby

S11 �Zin � 50

Zin � 50, (19)

where Zin is the impedance due to Zopt seen at the input port

Zin � Z0

Zoptcos �l � jZ0sin �l

Z0cos �l � jZoptsin �l. (20)

The propagation constant � on the microstrip line is given by

� �2�

�g�

2�f

c�eff, (21)

where eff is the effective dielectric constant of the microstrip lineand l is the length of the line. To study the behavior experimen-tally, a microstrip line resonator was fabricated on a high resistiv-ity (� 3000 cm) silicon substrate. The microstrip resonating linefabricated was of the length �7.2 mm and characteristic imped-ance Z0 � 30 . On a silicon substrate of thickness 300 �m withr � 11.8, this corresponds to a line width w � 604 �m andeff � 8.559. Such a line will give a sharp resonance whenterminated with 50 at a frequency for which l � �g/ 2 or

f �c

2l�eff

� 6.97 GHz. (22)

For the above line, we first carried out calculations for reflectionparameter �S11� obtained by Eqs. (19) and (20). The variation ofthe reflection parameter �S11� with frequency at different incidentpower levels in mW is plotted in Figure 5(a). A simulation wasalso carried on the Ansoft Maxwell Simulator in which the mi-crostrip line of w � 604 �m on a silicon substrate was terminatedin a “black box” with its S11 (magnitude and angle) defined byEqs. (18), (19) with a 50 excitation port. The results obtained bysimulation at different power levels are shown in Figure 5(b).Figure 5(a) and (b) shows a similar behavior. As the optical powerlevel increases, the value of �S11� at the resonance frequency �7.0GHz decreases, reaching a minimum at �29 mW that correspondsto a termination of �50 , and a further increase in the powerlevels leads to an increase in �S11� at the resonance dip. For allthese calculations, � in Eq. (5) was used as 18 �s.

4. EXPERIMENTAL MEASUREMENTS ON AN OPTICALLYCONTROLLED LOAD

As mentioned in section 3, for actual measurements a 7.2-mmopen-ended 30 microstrip line was fabricated on high-resistivitysilicon substrate and mounted on a jig. The jig was mounted on anx-y-z translation stage for appropriate positioning with respect tothe focused spot and fed directly by a 50 SMA connector. Foroptical illumination, two laser diodes with maximum power of�20 mW, each emitting at wavelength 650 nm with focussingoptics, were used. The 8757 HP scalar network analyzer with adirectional bridge was used to measure the reflection parameter�S11� of the 30 line terminated in the optically load. The opticalpower level was estimated by a Newport power meter (1815-C) byplacing the detector head at the focussed laser spot position. Themeasured �S11� versus frequency curves at different optical powerlevels are plotted in Figure 5(c). The results show the resonant dipat 7.0 GHz; with an increase in optical illumination levels, the dipmoves downward to a minimum value of �S11� � �40.00 dB at�29 mW. The resonance frequency is in agreement with Eq. (22)and the large dip at 29 mW confirms the earlier prediction that apower level of �29 mW creates a resistive optical load of �50 .With a further increase in optical illumination, the minimum value�S11� increases and the resonance dip moves upward. At the opticallevel power in use, a change in the optical power level onlychanges the value of �S11� at the resonant dip, however, theresonant frequency remains unchanged. This implies that for theload created at these power levels, capacitive effects are notsignificant. This is also in agreement with the simulated results.Hence, the optical termination can be used to control the reflectionand provide narrowband matching.

5. THE OPTICALLY CONTROLLED STUB

5.1 Simulation of Stub Terminated by an Optical LoadWith the results obtained by the modeling and measurements on anoptically induced load at the end of an open microstrip, the

Figure 4 Variation of (a) equivalent resistance and (b) equivalent ca-pacitance with frequency at different power levels

274 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 39, No. 4, November 20 2003

following conclusions can be drawn: (i) the modeling of the loadas a complex capacitance is satisfactory, and (ii) at the used opticalpower levels the experimental results agree with the theoreticalprediction.

A similar optical load can be created at the end of an open �g/4stub on a microstrip line fabricated on a high-resistivity substrate,and can be used to control the transmitted power �S21� at the designfrequency. Hence, the modeled and experimentally verified opticalload was used to study the behavior of an open �g/4 microstripstub fabricated on a 50 microstrip line (w � 234 �m and eff �7.87) and terminated by the optical load, as shown in Figure 1(b).Both reflection parameter �S11� and transmission parameter �S21�are obtained by a simple circuit analysis as

S21 �2Zin

2Zin � Z0, (23)

S11 ��Z0

2Zin � Z0, (24)

where Zin is the transformed optical load at the stub terminationgiven by

Zin � Z0

Zoptcos �l � jZ0sin �l

Z0cos �l � jZoptsin �l. (25)

The length l for the design frequency of 5 GHz is given by l ��g/4 � 5.34 mm.

First, we carried out calculations for reflection parameter �S11�and transmission parameter �S21� obtained by Eqs. (23)–(25). Thevariation of the transmission parameter �S21� with frequency atdifferent incident power levels in mW is plotted in Figure 6(a).

A simulation was also carried out on an Ansoft MaxwellEnsemble simulator to study the transmission through the 50 microstrip line with �g/4 stub using “black box” termination at theopen end of the stub. The results are shown in Figure 6(b). Figure6(a) and (b) shows that in the open condition (with no illuminationspot) the transmission parameter �S21� is as small as � �33 dB atthe design frequency of 5.0 GHz, thus implying a band rejectionbehavior, as expected for the stub with an open termination (Zop

3 �). As the optical power increases, the transmission parameter�S21� increases and the response becomes flat at relatively highoptical power (greater than 25 mW).

5.2 Experimental Measurement on the Optically Controlled StubTo carry out the actual measurements, the open ended �g/4 stubwas fabricated on a microstrip line of Z0 � 50 and mounted ona jig with an SMA connector at both ends. The laser spot was thenfocused at the open end of the stub and measurement of both �S11�and �S21� was carried out at different power levels. The experi-mental results shown in Figure 6(c) show a behavior similar to thesimulation results with increasing optical power levels. In theabsence of illumination, the transmission parameter �S21� has aminimum value at 5.13 GHz. As the incident optical power in-creases, the response becomes flat and the frequency selectivebehavior vanishes at �24 mW, which corresponds to terminationof �53 . Hence, the optically controlled stub can be used as anoptically controlled attenuator in the 5.0-GHz band with a maxi-mum attenuation of �33 dB.

6. CONCLUSION

In conclusion, we have modeled the optical load created by illu-minating a high-resistivity silicon substrate by a focused laserbeam. Such an optical load created at the end of a microstrip linehas been shown to control the reflection parameter of the resonantline and provide an optically controlled narrowband matching. Asimilar optical load created at the end of open end of �g/4 stub on

Figure 5 Simulated results for variation in reflection coefficient �S11�with frequency obtained by (a) simple circuit analysis, (b) Ansoft Maxwellensemble simulator, and (c) experimental measurements at different powerlevels

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 39, No. 4, November 20 2003 275

a microstrip line has been shown to control the transmissionparameter and, hence, form an optically controlled attenuator. Inboth cases, the simulation results and actual measurements are ingood agreement.

ACKNOWLEDGMENTS

Financial support from CSIR (India) and Department of Informa-tion Technology (formerly DOE, India) is acknowledged.

REFERENCES

1. J. Haider, A. Vilcot, M. Bauthinon, and E. Pic, Optically controlledpassive microwave structure, Proc Sino-French workshop on fiber andintegrated optics, Shanghai, China, 1995, p. 14.

2. B. Boyer, J. Haider, A. Vilcot, and M. Bouthinon, Tunable microwaveload based on biased photoinduced plasma in silicon, IEEE TransMicrowave Theory Tech 45 (1997), 1362.

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4. C.H. Lee, P.S. Mak, and A.P. DeFonzo, Optical control of millimeter-wave propagation in dielectric waveguide, IEEE J Quantum Electron16 (1980), 277.

5. W. Platte and B. Sauerer, Optically CW-induced losses in semicon-ductor coplanar waveguide, IEEE Trans Microwave Theory Tech 37(1989), 139.

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7. A.K. Verma, Enakshi K. Sharma, Nasimuddin Avanish Bhadauria, andB.R. Singh, Optically controlled microstrip load, National symposiumon advances in microwave and light waves, 2000, p. 250.

8. Yasushi Horri and Makato Tsutsumi, Scattering parameters of semi-conductor microstripline under laser spot illumination, MTT-S Digest96 (1996), 1675.

9. S.M. Sze, Physics of semiconductor devices, John Wiley & Sons, NewYork, (second edition), pp. 51–57.

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© 2003 Wiley Periodicals, Inc.

THREE-DIMENSIONALRECONSTRUCTION OF A SHALLOWLYBURIED MINE USING TIME-DOMAINDATA

Hui Zhou, Takashi Takenaka, and Toshiyuki TanakaDepartment of Electrical and Electronic EngineeringNagasaki University1-14 Bunkyo-machi, Nagasaki 852-8521, Japan

Received 16 April 2003

ABSTRACT: A two-dimensional (2D) time-domain inverse scatteringtechnique for reconstructing lossy media is extended to three-dimen-sional (3D) cases. Forward and inversion algorithms of this approachare carried out by the finite-difference time-domain (FDTD) method.The reconstruction of a mine buried in soil illustrates that this method isone of useful techniques to detect buried mines. © 2003 Wiley Periodi-cals, Inc. Microwave Opt Technol Lett 39: 276–280, 2003; Publishedonline in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.11189

Key words: inverse scattering problem; time domain; mine detection;three-dimensional object; finite-difference time domain

Figure 6 Simulated results for variation in transmission coefficient �S21�with frequency obtained by (a) simple circuit analysis, (b) Ansoft Maxwellensemble simulator, and (c) experimental measurements at different powerlevels

276 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 39, No. 4, November 20 2003