acteristics are obtained when the bias voltage of the diodes variesin the 0.7–0.8-V range. The maximum �S21� value is about 7.5 dB.When tuning the phase shift in the 38.5–41.5-GHz band, �S21�maximum variation is about 0.6 dB. Figure 13 presents the mea-sured phase shift of the global device. Measured phase variation is47° according to the frequency, when the bias voltage of the diodesvaries in the [0.7–0.8 V] range.

Figures 14 and 15 presents the measured magnitude of the �S11�and �S22� reflection coefficients. When tuning the phase shift, �S11�is kept lower than �12 dB over the 38.5–39.5-GHz band. �S22�shows a output good matching over the 38.5–44.5-GHz frequencyband and is also kept lower than �12 dB over the 39–41-GHzband. Power consumption is 160 mW.

4. CONCLUSION

In this paper, we have described a technique to improve theperformances of a phase shifter based upon a classical amplifier.The role of the amplifier is to reduce the sensitivity of the trans-mission level while maintaining the phase-shift properties andperformances. The approach has been applied to the design of anactive module at around 41.5 GHz for optical-transmission appli-cation at 40 Gb/s.

Measured results of the circuit, fully integrated in GaAs tech-nology, have shown a 6.0-dB gain over the 38.5–44.5-GHz rangeand a phase shift of 45°. The �S21� magnitude variation has beenreduced to 0.6 dB when tuning the phase shift, thus validating ourtechnique.

REFERENCES

1. O. Leclerc et al., Dense WDM (0.27 b/s/Hz) 4 � 40 Gb/s dispersion-managed transmission over 10000 km with in-line optical regenerationby channel pairs, Electron Lett 36 (2000), 337–338.

2. A. Cenac, L. Nenert, L. Billonnet, B. Jarry, and P. Guillon, Broadbandmonolithic analog phase shifter and gain circuit for frequency tunablemicrowave active filters, IMS’98, IEEE MTT-S Int Microwave SympDig, Baltimore, MD, 1998.

3. D01PH process, OMMIC, 2001.4. Advanced Design System, ADS, Agilent technologies, 2001.

© 2004 Wiley Periodicals, Inc.

IMPROVEMENT OF MMW IRRADIATIONUNIFORMITY IN CULTURE DISHESFOR EXPERIMENTS ON MMWBIOLOGICAL EFFECTS

Jianxun ZhaoDepartment of Biomedical EngineeringSchool of Electronic EngineeringXidian UniversityXi’an 710071, P. R. China

Received 15 July 2003

ABSTRACT: Methods to improve the uniformity of the millimeter-wave(MMW) dose distribution on the cell monolayer in culture dishes aretested via experiments on MMW biological effects at the cellular level.Calculated using the finite-difference time-domain (FDTD) numericaltechnique, the MMW dose distribution, represented by the distribution ofthe MMW power density (PD) irradiated into cells and that of theMMW power absorption density (PAD) of cells, is analyzed for threeculture dishes of different configurations. Results indicate that enlargingthe culture dish diameter and reducing its bottom thickness are two ef-fective methods to improve the MMW irradiation uniformity. © 2004Wiley Periodicals, Inc. Microwave Opt Technol Lett 40: 258–261,2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.11346

Key words: millimeter wave; irradiation uniformity; power density;power absorption density; finite-difference time-domain numerical tech-nique

1. INTRODUCTION

In experiments on millimeter-wave (MMW) biological effects atthe cellular level, using culture dishes serving as cell containers, auniformly distributed MMW irradiation in the culture dish isexpected so that cells cultured on the upper surface of the dishbottom, that is, the cell monolayer, can receive the same amount ofirradiation dose [1]. However, this expectation has always beendifficult to realize. Since MMW has a very short wavelengthcomparable to the geometries of the culture dish, the influence ofthe culture dish configuration as well as other factors upon theMMW electromagnetic field (EMF) is significantly strong; hence,a highly irregular MMW irradiation pattern is usually unavoidable[2]. As a matter of fact, previous studies have found that, inside thesame culture dish, the maximal value of the MMW power density(PD) that actually irradiated into one point in the cell monolayermay be eight times as much as the minimal PD value existing inanother point in the cell monolayer, only a few millimeters awayfrom the former point [3, 4]. Experiments on MMW biologicaleffects in the cellular level are undermined by the irregularity ofMMW irradiation and the outcomes are usually far from thoseanticipated. We hope that the improvement in MMW irradiationuniformity will promote a variety of these experiments and there-fore speed up the deployment of studies in this frontier of scientificresearch. Methods for improving MMW irradiation uniformityneed to be studied seriously and systematically for these experi-ments, which will be a main task in related experimental dosimetrystudies, once the problem has fully emerged and its importance hasbeen recognized.

Two methods are tested as a first step toward the goal of MMWirradiation uniformity improvement in culture dishes. Because theMMW EMF in the cell monolayer inside the culture dish isdifficult to measure directly with instruments, data on the MMWdose distribution are obtained with a numerical method for EMFevaluation during the testing process.

Figure 15 Measured �S22�dB parameter of the phase shifter

258 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 40, No. 3, February 5 2004

2. MMW EMF EVALUATION AND MMW DOSEDESCRIPTION

The numerical method applied here for MMW EMF evaluation isthe finite-difference time-domain (FDTD) numerical technique,which is based on the central finite-difference discretization of thetime-dependent Maxwell’s curl equations, given by

� � E � ���H�t

, (1)

� � H � �E � ��E�t

, (2)

where E and H are the electric-field and magnetic-field intensities,respectively; and �, �, and � are the permeability, conductivity andpermittivity, respectively, of the involved media [5]. Upon thediscretization of the domain involved in calculation into a mesh ofcells and the discretization of time, the finite-difference approxi-mation of Eqs. (1) and (2) yields six numerical equations forcalculating E and H components [6]. On condition that dimensionsof the cells are given by the side length of � and the time incrementis �t, that the mesh coordinates (i, j, k) represent the spacecoordinates (i�, j�, k�), and that the time is provided as n�t, thecomponents of E and H in the x direction, for example, are derivedfrom the following two of the six numerical equations:

Exn�1�i � 1/ 2, j, k� � CAx�i � 1/ 2, j, k� Ex

n�i � 1/ 2, j, k�

� CBx�i � 1/ 2, j, k��Hzn�1/ 2�i � 1/ 2, j � 1/ 2, k�

Hzn�1/ 2�i � 1/ 2, j 1/ 2, k� � Hy

n�1/ 2�i � 1/ 2, j, k 1/ 2�

Hyn�1/ 2�i � 1/ 2, j, k � 1/ 2��, (3)

Hxn�1/ 2�i, j � 1/ 2, k � 1/ 2� � Hx

n�1/ 2�i, j � 1/ 2, k � 1/ 2�

� ��t/������Ezn�i, j, k � 1/ 2� Ez

n�i, j � 1, k � 1/ 2�

� Eyn�i, j � 1/ 2, k � 1� Ey

n�i, j � 1/ 2, k��, (4)

where

CAx�i � 1/ 2, j, k� �2�x�i � 1/ 2, j, k� �x�i � 1/ 2, j, k��t

2�x�i � 1/ 2, j, k� � �x�i � 1/ 2, j, k��t,

(5)

CBx�i � 1/ 2, j, k� �2�t/�

2�x�i � 1/ 2, j, k� � �x�i � 1/ 2, j, k��t.

(6)

The rest four components of E and H in the y and z directions canbe derived from the other four similar equations. For the calculat-ing process to securely converge, � and �t must satisfy Courant’scondition:

�t �/�c0�3�, (7)

where c0 is the velocity of light in vacuo.The second-order absorbing boundary conditions (ABCs) are

used in the study to calculate the electric field on six boundaries ofthe mesh representing the domain of calculation to ensure theaccuracy and precision of the FDTD method [7].

The results of the MMW EMF evaluation are provided astime-dependent periodical fluctuations of E and H at each point inthe mesh.

Represented by �, the dimensions of the cells composing themesh are usually quite small. In this study, they are nearly 1/10 ofthe minimal MMW wavelength in the mesh. That is why E and Hcomponents are considered to be uniform in each single cell. At thesame time, the time increment �t in this study is selected to be only1/64 of the MMW period; thus, the difference between the Hcomponent value at time (n � 1/ 2)�t and its value at time n�t canbe reasonably neglected. Supported by above considerations, com-ponents of E and H at points (i�, j�, k�) in the domain and at timen�t are derived from the results of the FDTD method as

Exn�i, j, k� � Ex

n�i � 1/ 2, j, k�, (8)

TABLE 1 Permittivities and Conductivities of Materials

Material Permittivity � (F/m) Conductivity � (S/m)

Air 8.85419E�12 0Culture dish glass 6.30418E�11 6.53682E�02Culture solution 8.85419E�11 6.95406E�01

Culture solution is represented by water for its permittivity and conduc-tivity.

Figure 1 Geometries of the original culture dish with culture solution,cell monolayer, and adjacent space in the volume for FDTD calculation(unit: mm)

Figure 2 PD and PAD distributions over the horizontal cross sectionthrough the cell monolayer in the original culture dish (unit: dB)

Figure 3 Geometries of the culture dish enlarged in diameter withculture solution, cell monolayer, and adjacent space in the volume forFDTD calculation (unit: mm)

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 40, No. 3, February 5 2004 259

Eyn�i, j, k� � Ey

n�i, j � 1/ 2, k�, (9)

Ezn�i, j, k� � Ez

n�i, j, k � 1/ 2�, (10)

Hxn�i, j, k� � Hx

n�1/ 2�i, j � 1/ 2, k � 1/ 2�, (11)

Hyn�i, j, k� � Hy

n�1/ 2�i � 1/ 2, j, k � 1/ 2�, (12)

Hzn�i, j, k� � Hz

n�1/ 2�i � 1/ 2, j � 1/ 2, k�. (13)

The experimental MMW dose is described in two ways: thepower density (PD) of the MMW irradiated into cells and theMMW power absorption density (PAD) of cells. PD and PAD atpoints (i�, j�, k�) and time n�t are derived according to thefollowing equations respectively

PDn�i, j, k� � �Eyn�i, j, k� Hz

n�i, j, k� Ezn�i, j, k� Hy

n�i, j, k��2

� �Ezn�i, j, k� Hx

n�i, j, k� Exn�i, j, k� Hz

n�i, j, k��2

� �Exn�i, j, k� Hy

n�i, j, k� Eyn�i, j, k� Hx

n�i, j, k��21/ 2, (14)

PADn�i, j, k� � ��i, j, k��Exn�i, j, k��2

� �Eyn�i, j, k��2 � �Ez

n�i, j, k��2. (15)

3. MMW DOSE DISTRIBUTION AND UNIFORMITYIMPROVEMENT

Since the cell monolayer is cultured on the upper surface of theculture dish, that is, the bottom of the culture solution, MMWdevices used in experiments are usually designed to provide anupward irradiating direction in order to avoid the possibility thatthe MMW energy might be totally absorbed by the highly con-ductive culture solution before reaching the cells. This design isaccepted in many experiments and therefore is analyzed in thisstudy. The incident MMW is a 6-mm (50-GHz) sinusoidal uniformplane wave with a PD of 1.0 mW/cm2.

The domain targeted in calculation is a 64 mm � 64 mm � 24mm cubic volume containing the culture dish, the cell monolayerand the culture solution, which is divided into 320 � 320 � 120 �12,288,000 cells side length of � � 0.2 mm that is nearly 1/10 ofthe smallest wavelength existing in the culture solution. The timeincrement is fixed at �t � 3.125 � 10�13 s, that is, 1/64 of theMMW period.

Four kinds of material are enclosed in the domain, namely, air,the culture dish glass, the cell monolayer, and the culture solution.With a high water content, the cell monolayer can be considered aspart of the culture solution. Thus the PD and PAD at the bottom ofthe culture solution are those for the cells cultured there. Permit-tivities and conductivities of relevant materials are listed in Table1 as their approximated values.

3.1. MMW Dose Distribution in the Original Culture DishThe MMW dose distribution in the original culture dish is calcu-lated first. The culture dish has an outer diameter of 25 mm, aninner diameter of 21 mm, and a height of 10 mm. The thickness ofthe culture dish, including that of the dish bottom, is 2 mm. Theculture solution inside the culture dish is 5 mm in depth. Finally,the cell monolayer is assumed to shape into a circle whose diam-eter is 15.75 mm, that is, 3/4 of the inner diameter of the culturedish. Geometries of objects related to the original culture dish areshown in Figure 1 as the top view and the front view.

Results regarding the MMW dose distribution in the culture dish,that is, the distribution of the MMW PD irradiated into the cells andthe distribution of the MMW PAD of the cells, are plotted in Figure2(a) and (b) as their time-averaged values. Units of PD and PAD aremW/cm2 and 10�2 mW/cm3. Plotted data on PD and PAD have beentransformed to 10 times the denary logarithm of their original valuesbeforehand so as to enhance the image clarity in the area where theoriginal value is very small. It is clearly found in the plots that PD andPAD distributions in the original culture dish are rather irregular. Themean value of the PD distributed on the cell monolayer is 0.152mW/cm2. The standard deviation (SD) of PD distribution is 0.0241mW/cm2 and the relative standard deviation (RSD) is 0.0241/0.152 �15.9%. The mean value of the PAD distributed on the cell monolayeris 14.8 mW/cm3. The SD of PAD distribution is 2.40 mW/cm3 andthe RSD is 2.40/14.8 � 16.2%.

3.2. MMW Dose Distribution in the Culture Dish with EnlargedDiameterThe first method aimed at improving the MMW irradiation uni-formity is to enlarge the culture dish diameter. The new culturedish has an outer diameter of 50 mm, which is twice that of theoriginal culture dish, and the inner diameter of the culture dish isincreased to 46 mm accordingly. The other parameters’ dimen-sions remain unchanged. Plots of the top and front views of objectsrelated to the culture dish with an enlarged diameter are depictedin Figure 3.

Figure 4 PD and PAD distributions over the horizontal cross sectionthrough the cell monolayer in the culture dish enlarged in diameter (unit:dB)

Figure 5 Geometries of the culture dish enlarged in diameter and re-duced in bottom thickness with culture solution, cell monolayer, andadjacent space in the volume for FDTD calculation (unit: mm)

Figure 6 PD and PAD distributions over the horizontal cross sectionthrough the cell monolayer in the culture dish enlarged in diameter andreduced in bottom thickness (unit: dB)

260 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 40, No. 3, February 5 2004

Resultant data on the time-averaged values of the MMW PDirradiated into the cell monolayer and the MMW PAD of the cellmonolayer are shown in Figure 4(a) and (b) as representatives ofthe MMW dose distribution in the new culture dish. Units of PDand PAD are mW/cm2 and 10�2 mW/cm3. 10-time denary loga-rithm of PD and PAD are plotted to provide clear views throughoutthe entire data region. These two plots indicate that, in the culturedish enlarged in diameter, the MMW dose distribution, includingthe PD distribution and the PAD distribution, is improved in theuniformity property. The mean value of the PD distributed on thecell monolayer is 0.148 mW/cm2. The SD of PD distribution is0.0171 mW/cm2 and the RSD is 0.0171/0.148 � 11.6%, smallerthan that of the original culture dish. The mean value of the PADdistributed on the cell monolayer is 14.4 mW/cm3. The SD of PADdistribution is 1.74 mW/cm3 and the RSD is 1.74/14.4 � 12.1%,also smaller than that of the original culture dish.

3.3. MMW Dose Distribution in the Culture Dish with EnlargedDiameter and Reduced Bottom ThicknessThe second method aimed at improving the MMW irradiationuniformity is to reduce the culture dish bottom thickness. Thistime, the newly designed culture dish has the same geometries asthe abovementioned culture dish (enlarged in diameter), exceptthat its bottom thickness is reduced to 0.4 mm from the original 2mm. Figure 5(a) and (b) illustrates the top and front views ofobjects related to the culture dish with an enlarged diameter and areduced bottom thickness.

Time-averaged values of the MMW dose distribution, includ-ing the MMW PD irradiated into the cells and the MMW PAD ofthe cells in the third culture dish, are shown in Figure 6(a) and (b).Based on the original PD data unit of mW/cm2 and PAD data unitof 10�2 mW/cm3, both plots clearly reveal the 10-time denarylogarithm of the PD and the PAD values over their distributionarea with the indication that considerable improvement can beachieved in the MMW irradiation uniformity with the culture dishenlarged in diameter and reduced in bottom thickness at the sametime. The mean value of the PD distributed on the cell monolayeris 0.365 mW/cm2. The SD of PD distribution is 0.0108 mW/cm2

and the RSD is 0.0108/0.365 � 2.96%, smaller than that of theculture dish with an enlarged diameter and much smaller than thatof the original culture dish. The mean value of the PAD distributedon the cell monolayer is 36.2 mW/cm3. The SD of PAD distribu-tion is 1.07 mW/cm3 and the RSD is 1.07/36.2 � 2.96%, alsosmaller than that of the culture dish with an enlarged diameter andmuch smaller than that of the original culture dish.

4. CONCLUSION

With the help of the FDTD numerical technique, analysis of theMMW EMF in culture dishes of different configurations has

proved that both methods, namely, enlarging the diameter andreducing the bottom thickness of the culture dish, are considerablyeffective in improving the uniformity of the MMW PD irradiatedinto the cell monolayer and that of the MMW PAD of these cells.As a matter of fact, based on these selected geometrical descrip-tions of the culture dish, the culture solution, the cell monolayer,and so forth, as well as other parameters on the material electro-magnetic properties, the results have revealed that, with the appli-cation of both methods, the RSD of the PD distribution over thecell monolayer is reduced from 15.9% to 2.96% and, meanwhile,the RSD of the PAD distribution over the cell monolayer decreasesfrom 16.2% to 2.96%. These data are obtained on the premise thatthe diameter of the cell monolayer is fixed at 15.75 mm, that is, 3/4of the inner diameter of the original culture dish. In other words,it can be said that these data are applicable when cells targeted inexperiments are those located less than 3/4 of the inner radius ofthe original culture dish away from the bottom center of all threeculture dishes. If the targeted cells are selected cautiously within amuch smaller scope, for example, at a diameter of 10.5 mm or even5.25 mm (within 1/2 or even 1/4 of the inner radius of the originalculture dish away from the bottom center of these dishes, similarconclusions are reached with reference to Tables 2 and 3, in whichstatistics about the MMW PD and PAD distributions on cellmonolayers of these smaller diameters are listed.

REFERENCES

1. A.G. Pakhomov, Y. Akyel, O.N. Pakhomova et al., Current state andimplications of research on biological effects of millimeter waves: Areview of the literature, Bioelectromagn 19 (1998), 393–413.

2. J.X. Zhao, Analysis of millimeter wave power density received by cellmonolayers inside culture dishes, Int J Infrared Millimeter Waves 22(2001), 1577–1586.

3. J.X. Zhao, Dosimetry of MMW power density and power absorptiondensity for cells in culture dishes in experiments on MMW biologicaleffects (part one), 3rd Int EMF Seminar China: Electromagn Fields BioEffects, 2003.

4. J.X. Zhao, Dosimetry of MMW power density and power absorptiondensity for cells in culture dishes in experiments on MMW biologicaleffects (part two), 3rd Int EMF Seminar China: Electromagn Fields BioEffects, 2003.

5. A. Taflove, Computational electrodynamics: the finite-difference time-domain method, Artech House, Boston, MA, 1995.

6. H.Y. Chen and H.H. Wang, Current and SAR induced in a human headmodel by the electromagnetic fields irradiated from a cellular phone,IEEE Trans Microwave Theory Tech 42 (1994), 2249–2254.

7. G. Mur, Absorbing boundary conditions for the finite-difference ap-proximation of the time-domain electromagnetic-field equations, IEEETrans Electromagn Compat 23 (1981), 377–382.

© 2004 Wiley Periodicals, Inc.

TABLE 2 Statistics Regarding the MMW PD and PADDistributions on the Cell Monolayer Diameter of 10.5 mm

Culture Dish First Dish Second Dish Third Dish

PDmean (mW/cm2) 0.150 0.148 0.362PDSD (mW/cm2) 0.0283 0.0192 0.0106PDRSD (%) 18.8 13.0 2.92PADmean (mW/cm3) 14.6 14.5 35.9PADSD (mW/cm3) 2.82 1.97 1.05PADRSD (%) 19.3 13.6 2.94

The first culture dish is the original one, the second dish is enlarged indiameter, and the third dish is reduced in bottom thickness at the sametime.

TABLE 3 Statistics Regarding the MMW PD and PADDistributions on the Cell Monolayer Diameter of 5.25 mm

Culture Dish First Dish Second Dish Third Dish

PDmean (mW/cm2) 0.153 0.156 0.362PDSD (mW/cm2) 0.0239 0.0259 0.0119PDRSD (%) 15.7 16.7 3.29PADmean (mW/cm3) 14.8 15.2 35.9PADSD (mW/cm3) 2.50 2.70 1.18PADRSD (%) 16.9 17.8 3.28

The first culture dish is the original one, the second dish is enlarged indiameter, and the third dish is reduced in bottom thickness at the sametime.

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 40, No. 3, February 5 2004 261