1932 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES. VOL. 42. NO. 10, OCTOBER 1994

Infrared Surface Waves in Circular Hollow Waveguides With Small Core Diameters

F. E. Vermeulen, Member, IEEE, A. M . Robinson, Member, IEEE, C . R. James, and J. N. McMullin, Member, IEEE

Abstract- An asymptotic form of the characteristic equation that describes wave propagation at near-infrared wavelengths in small core hollow circular waveguides is developed. Analytic solutions for the transverse and axial propagation constants are obtained. These demonstrate the transition of the TEI I and TMOI modes to surface waves as the guide radius is increased to values much greater than at cutoff. Relative power density distributions illustrating these mode transitions are shown.

I. INTRODUCTION

N a recent paper, [ l ] investigated modes and attenuation I constants for infrared laser light at 10.6 pm in cylindrical hollow nickel waveguides with small core radii for industrial and medical applications. The changes that occur in the transverse and axial propagation constants as the guide radius is increased from approximately 5 to 500 times the free space wavelength of 10.6 pm have been described. The attendant mode transitions have been depicted in sequences of figures that show successive configurations of lines of force of the electric field intensity. In particular, [I] investigated the hybrid TEll and the TMol modes numerically, and note that for very small guide radii the transverse propagation constants of these modes are approximately equal to those for TEll and TMol modes in cylindrical guides with perfectly conducting walls. As the guide radius is increased, however, both the real and imaginary parts of the transverse propagation constants grow without limit. Also, the TEll mode becomes increasingly transverse magnetic. For large guide radii, therefore, these modes no longer resemble the well-known TEll and TMol modes. Kat0 and Miyagi describe the behavior of these modes in the transverse plane and tentatively designate them in large diameter guides as TM; and TMb, respectively. They describe the attenuation constants of many other modes in their paper, but not those of the TEIl-TM’, and TMol-TMb modes. We will show that these attenuation constants provide the key to complete characterization and understanding of these modes.

In our investigation of the propagation characteristics of micron-sized cylindrical gold-coated waveguides at wave- lengths of 1 to 10 pm [2] for possible applications in sensors and optoelectronic components, we have observed at all of these wavelengths mode transitions for the hybrid TEll mode and for the TMol mode that are similar to the transitions described by Kat0 and Miyagi. We have numerically computed the attenuation constants of these modes and found that they exhibit unusual behavior as the guide radius is increased. As

Manuscript received February 22, 1993; revised November 17, 1993. The authors are with the Department of Electrical Engineering, University

IEEE Log Number 9404164. of Alberta, Edmonton, Alberta, Canada, T6G 2G7.

the guide radius increases from that value where approximate cutoff’ occurs, and a becomes much larger than Xo, the distances that these modes propagate until their fields are attenuated to l / e of their initial values, the propagation distances, at first increase to a maximum. With further in- crease in guide radius, the propagation distances decrease and then become approximately constant. This suggests that gradual transitions to surface-wave-like mode configurations are occurring, whose attenuation constants are independent of guide radius. Indeed, our numerically calculated propagation distances, and our numerically calculated decreases in field intensity with distance from the guide wall, for both TM; and TMb modes, adopting the designation proposed by Kat0 and Miyagi for such modes, agree closely with the corresponding quantities for a surface wave at a planar gold-air interface.

The purpose of this paper is to provide further insight and understanding of mode transitions by extending the work of 111, [2], both of which relied on numerical solution of the characteristic equation, and also related work in 131. We solve the characteristic equation analytically, using asymptotic forms for the functions that occur in this equation. We are able to show that the TMol and TEll modes at infrared frequencies in small radius guides of high refractive index metals, includ- ing gold and nickel, undergo mode transitions as the guide diameter increases to large values, and acquire transverse and axial propagation constants whose respective analytical forms are the same for both modes. Furthermore, they are identical to those of a surface wave at a planar interface. Also, an analytical expression is derived for the ratio P , a measure of the axial magnetic field intensity to axial electric field intensity in a hybrid mode. It is shown analytically that P tends to zero as the guide radius increases, and hence that the TEll mode becomes in the limit a transverse magnetic mode. Time- average relative power density distributions in the transverse plane are shown for the TE1l-TM’, and TMol-TM& modes, which clearly illustrate the shift of power density from the interior region of the guide toward the guide walls as the guide radius increases and the transition to surface waves takes place.

A potential application for surface waves in metal-lined waveguides is in optical interconnections between chips in optoelectronic integrated circuits. Rectangular hollow waveg- uides have been suggested for this purpose [4] and recently semicircular channel waveguides have been fabricated in sili- con using microwave etching 151. Although these waveguides

’ The concept of cutoff frequency loses some of its meaning when applied to propagation in a lossy guiding system because total cutoff does not take place.

001 8-9480/94$04.00 0 I994 IEEE

VERMEULEN er al.: INFRARED SURFACE WAVES IN CIRCULAR HOLLOW WAVEGUIDES WITH SMALL CORE DIAMETERS 1933

Fig. 1. is perpendicular to the plane of the figure.

were filled with a dielectric, they could instead be lined with a metal. The difficulty of fabricating a lid for these devices is eliminated if guiding is achieved using a surface mode. All that is required is a metal with a suitable complex refractive index which allows propagation over a distance of millimetres for near-infrared wavelengths.

Cross section of cylindrical waveguide. The direction of propagation

11. ANALYTIC SOLUTION OF THE ASYMPTOTIC FORM OF THE CHARACTERISTIC EQUATION

A. An Asymptotic Solution for the Transverse and Axial Propagation Constants

Consider a guiding structure consisting of a cylindrical loss- free region of dielectric constant ~d and radius a, surrounded by a region of lossy metal of complex dielectric constant E,,

as shown in Fig. 1. Assume that wave solutions exist with the propagation factor ejwt--?‘, where the axial propagation con- stant is given by y = Q + j p , and Q and U are the attenuation and phase constants, respectively. The wave equation leads to solutions for the axial electric and magnetic field intensities which are, respectively, for radius r 5 a in the dielectric

and w is the radian frequency. The transverse field components are readily determined from (1)-(4) [6]. Matching of the tangential components of the electric and magnetic field inten- sities at the boundary T = a leads to the exact characteristic equation

Po J:, (&a) Po HF)’ ( K m a ) - - ~ - K d J , ( K d a ) KT?7. HL2) ( & L a )

(7)

For the cylindrically symmetric TMol mode, the RHS of (7) vanishes and the characteristic equation for this mode is obtained by setting the second expression on the LHS equal to zero.

Also, in a lossy medium, the complex refractive index N=n- j k and the complex permittivity E = E’ - j ~ ’ ’ are related by

.=E (8)

where n = index of refraction, k = extinction coefficient and E’ and E’’ are the real and imaginary parts of the complex permittivity.

We now consider (7) for the case where the interior of the guide is free space, so that E d =EO. The walls of the guide are nickel (Ni), for which n-jk = 7.39 - j39.3, at 10.6 pm [7]. Although we consider Ni, the work that follows is valid for any guide wall material whose complex refractive index is large enough to satisfy the approximations that will be made. We seek a solution for Kda when the guide radius a is much larger than the free space wavelength Xo. Specifically, we seek the transverse propagation constant for the TM; mode, under the condition

U - >> 1. (9) A0

We make two assumptions about the solution to be obtained. These assumptions are justified on the basis of results produced by numerical solutions of (7). Firstly, to permit us to replace the Bessel and Hankel functions and their derivatives in (7) by their asymptotic forms, we assume that

Irn(Kda) >> 1. (10)

Secondly, to assign an order-of-magnitude value to IKd I / I K , 1 , required to make certain approximations when solving (7), we assume that

Equation (1 1 ) is generally true in an empty waveguide operated far above its cutoff frequency. While we know a priori these two assumptions are correct, such prior knowledge is not necessary. It is only required that the analytic solution that is obtained is consistent with these initial assumptions. Using the derivative formulas for 51 ( z ) and H;’’(z) [6], and the asymptotic forms [6], for IzI + oc

J , ( Z ) + 4; cos ( z - - - - rr 4 2

it is readily shown, by use of (lo), that

Ji ( K i n ) 1 J1(&a) + -j - ~ Kda

and

(12)

(13)

1934 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES. VOL. 42, NO. IO, OCTOBER 1994

Furthermore, consideration of (8) and (1 1) and the numerical value of the complex refractive index of nickel shows that I E , / E o I >> 1 and

Kd2 W p o E 0 s n N -

~ 711 - - N

K& W2/L"E(] (-1 + 2) i" where /SI << 1. Therefore

Further

where E m

E m r = - EO

so that 2iT K , E -(ri - j k ) . A0

Equation (7) now becomes

or

where use of (5) has been made. Using ( I O ) and (14), certain terms may be deleted, rendering the expression in the first braces on the LHS of the equation to unity, and reducing the complexity of the RHS, so that

Thus,

which, by use of (15) and (8), then yields the transverse propagation constant for the TM; mode

Using (16) in ( 5 ) , the axial propagation constant is given by

We note that for sufficiently large values of the asymptotic solution (16) is consistent with the initial assumption (10). Also, solution (17) is consistent with the initial assumption (1 1). From (17) it follows that the attenuation constant is

and the phase constant

Proceeding in a fashion similar to the above, it can be shown that the expressions for 7, Kda, a and p for the TMb mode are identical to the corresponding expressions above for the TM', mode.

B. An Asymptotic Solution ,for P

and (2), conveniently expressed as Except for the &variation, the ratio H2d/Ezd is, from ( I )

Sufficiently above the cutoff frequency, lj-y/u/~l nearly equals the inverse of the intrinsic impedance of free space.

Hence for (PI near 1 , the ratio (Hzdl/(Ezdl is approximately equal to the ratio of the transverse magnetic field to the transverse electric field of a plane wave propagating in free space. For lPI much larger than I , lHzdI dominates lEzdI, and vice versa. The derivation of a general expression for P is similar to that of (7) and is given by

&

1 1

1 J : , (Kdu) 1 HIIL) ' (K, , ,a)

__--

(21) ( l i d a)' (IC,,, u)' P = 'ri

Kda J n ( K d a ) K m a H J : ) ( K n , a ) '

For the TM/, mode we may use ( 1 2) and (1 3) to simplify (21) to its asymptotic form

Use of ( I O ) and (14) reduces this to

(22) J P E P

Kd (1

or, by use of (16) 1

Km Kmu P E j o ( n - jk). (23)

2iTu Invoking once more (10) and (14), as well as (9), we obtain

Kd 1 E,,,,. __ Knl

It may be noted that as 5 grows, P approaches zero, and hence TM', becomes totally transverse magnetic.

VERMEULEN er a/ . : INFRARED SURFACE WAVES I N CIRCULAR HOLLOW WAVEGUIDES WITH SMALL CORE DIAMETERS

TABLE I COMPARISON OF ASYMPTOTIC ANALYTICAL APPROXIMATIONS WITH

EXACT NUMERICAL RESULTS FOR &, FOR Ni AT 10.6 /Iln

K-(dal o + j j ( i i t - ' ) P N Asymptotic 2.904 67.32 0.06255 1401.3 Approximation +J15.44 +5.9293 x 10; +jO.OI I76 for T l I i and See I ) See 2) T.1IA Exact Numerical 2.9 I9 65.22 0.06662 1446.6 Value for T J I ; +j14.89 +5.9291 x 10' +J0.01348 Exact Numerical 2.912 65.21 1446.8 Value for TJfA +j14.92 +5.9291 x 10' 1) The limiting value of j in unbounded free space at 10.6 { tm is j = = 5.9275 x 10' m p l . 2) Using the numerically-obtained value for li,r(c in the asymptotic formula (22) yields the more accurate value for P F 0.OG4G9 + ~ 0 . 0 1 2 6 9 .

C. Compurison of Analytical and Numericul Results f o r Ni at 10.6 pm

Results for = 100 for the asymptotic solutions, (16), (18), (19), (22) and (23), are compared in Table I with exact numerical results obtained by solving the characteristic equation (7) , along with ( 5 ) and (6 ) , by use of Muller's method 181. Also shown is N = &, the number of free space wavelengths in one propagation distance.

The variables of Table I are shown in graphical form in Figs. 2 to 4 for a wide range of e, with the smallest values of 5 corresponding to guide radii just above the values at which approximate cutoff occurs. In Fig. 2(a) and (b) it may be noted that for these smallest values of guide radii the numerically-calculated values of Kdu are almost entirely real and nearly equal to those in a guide with perfectly conducting walls [6] , indicating that the mode structures are virtually the same. For the TEII-TM', mode at 5 = 0.3, Re(Kdu) = 1.807, while dl = 1.841 for the TEll mode in a guide with perfectly conducting walls. For the TMol-TM:, mode at = 0.5, the value is 2.372 versus pol = 2.405 for the TMol mode. At e between 15 to 20 a distinct transition occurs towards the asymptote, and for larger than these values, the asymptotic solutions for K,~u yield increasingly accurate results.

Fig. 3 compares the two asymptotic solutions of IPI for the TEll-TMi mode to the exact numerical solution. Asymptotic solution #1 was obtained by using the asymptotic expression (16) in (22), i.e. (23). Asymptotic solution #2 uses the exact values of Kda in (22), obtained by numerical solution of (7). While this solution is grossly in error for values of below approximately 12, for larger it is virtually coincident on the logarithmic plot of Fig. 3 with the exact numerical values for IPI. Fig. 4 compares the asymptotic solution for N to the exact numerical solution. Initially N increases as

increases. Subsequently, N decreases and approaches a limiting value that is independent of e. This strongly suggests that a transition to a surface wave is occurring. This transition is also implied by the large values of lm( Kdu), indicating that the Bessel functions of ( 1 ) and (2) that describe the radial field variation tend towards modified Bessel functions that exhibit an exponential-like growth with increasing radial distance T ,

rather than an oscillatory behavior.

1935

0 25 50 75 100

a - A"

(a)

100

10

1

Im(K,a)

1

01

,001 1 10 100

a - 1 0

(b)

Fig. 2. Comparison of the asymptotic solution for (a) Re(li,rn) and (b) Im(Ii</o) for TE1, - 7-11: and T.1lol - T.11; to the exact numerical solutions for Ni at 10.6 I'm.

1000

100

10

lPI

1

1

ni ..I.

0 25 50 75 100 125 150

a - 4

Fig. 3 . Comparison of two asymptotic solutions for IPI for the 7 E l 1 - T.11; mode to the exact numerical solution, for Ni at 10.6 pm, Asymptotic solution #2 employs the exact numerical value of Iic/u.

1936 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 42, NO. 10, OCTOBER 1994

N

2000

1500

1000

500

'0 25 50 75 100 125 150

a - 4

Fig. 4. Comparison of the asymptotic solution for N , the number of free space wavelengths the fields travel to l/e attenuation, to the exact numerical value of N , for Ni at 10.6 bm.

111. ANALYTIC DERIVATION OF THE SURFACE WAVE NATURE OF THE AND TMb MODES

We will derive the amplitude and phase variations of the fields of the TMb and TM', modes as a function of the distance z measured from the guide wall (see Fig. 1) when u >> A0,

and show that the field amplitudes diminish exponentially with 2. We will also compare the TMb mode to a TM surface wave at a planar interface.

The asymptotic form of the radial variation of Ezd for large Kdr is [6]

J, ,(Kdr) i /& cos (Kdr - - y ) . For small changes in r , when r has a value close to the guide radius a , the above may be written

Expressing the cosine function in exponential form, taking into account that Im(Kdr) >> 1, and retaining only the r-dependent part of the answer, yields for both the TM; and TMb modes a radial variation for Ezd of e-JKdT when r is near u. Making a change in variable from T to x through the relation r + :I; = a, and retaining only the x-dependent part, yields the variation of E,d for both modes as a function of distance u: measured from the guidewall as

or

Ezd e+Je&Gx. (24)

It follows that the field amplitudes diminish to 1/e of their values at the guide wall in a distance

A0 n2 + k2 27r k

For a Ni guide at A0 = 10.6 pm this distance corresponds to 6.48 Xo. This decrease is independent of guide radius, and

x. ____

hence both the TM; and TMb modes can properly be classified as surface waves.

The TMb mode is readily compared to a TM surface wave propagating along the planar interface between free space and a lossy medium of complex dielectric constant E, and refractive index n-jk. We choose for the latter a propagation factor eJ"t--j'z, and a variation of E, with x of in the free space region, where z is the distance measured from the interface. The variation of E, with z in the lossy medium is chosen as e + J K m x . Matching the tangential fields E, and Hy at the interface leads to the characteristic equation

By replacing E d , Kd and K , in (5) and (6) by E O , K d and I?, respectively, so that these equations are applicable to the present problem, then they and (25) yield

9 2 = - ( 2 ) * ( I+- 1 1 ) and

For I(n - jk)*\ >> 1 these relations reduce to

and ~ 27r 1 Kd E --

X o n - j k

These equations for + and K d for the planar TM surface wave are identical to (17) and (16) for y and Kd for the cylindrical structure. It follows that the TMb mode and the TM surface wave at a planar interface have the same axial propagation constant, and the same variation of amplitude and phase with distance x. Their configurations are therefore identical.

Interestingly, the TM', mode also shares the axial prop- agation constant and the variation in amplitude and phase with distance 5 of the TM surface wave. But the TM; mode differs from the latter since it varies with 4 and has a (small) axial magnetic field. These differences, however, diminish in importance as the guide radius u becomes very large. In that case the fields of the TM; mode vary only slowly with distance measured around the guide circumference, and, as already shown, its axial magnetic field approaches zero.

IV. RELATIVE POWER DENSITY DISTRIBUTIONS IN THE TRANSVERSE PLANE

To illustrate the shift in power density from the interior region of the guide towards the guide wall as the transitions to surface waves occur, we have prepared diagrams of relative power density distributions at 10.6 pm in circular Ni guides.

The time average power density in the transverse plane is computed from E,, E+,,, H , and Hq, which may be obtained

VERMEULEN et al.: INFRARED SURFACE WAVES IN CIRCULAR HOLLOW WAVEGUIDES WITH SMALL CORE DIAMETERS 1937

10 ~

- 9

- 8

- 7

- 6

- 5

- 4

- 3

- 2

- 1

- 0 Fig. 5. wavelength, e, has the values (a) 0.5, (b) 8, (c) 16, (d) 32. The color scale represents the range of field amplitudes from zero (purple) to maximum (red).

Relative power density distribution for the T.\fool - Tllf& mode at 10.6 p m in a circular Ni waveguide. The ratio of guide radius to free space

- 10

- 9

- 8

- 7

- 6

- 5

- 4

- 3

- 2

Fig. 6. wavelength, 5, has the values (a) 0.3, (b) 8, ( c ) 16, (d) 32. The color scale represents the range of field amplitudes from zero (purple) to maximum (red).

Relative power density distribution for the TEI1 - T.'bzl; mode at 10.6 p m in a circular Ni waveguide. The ratio of guide radius to free space

from (1) and (2) [6]. Exact values of Kd and P for the TEIl-TM/, and the TMol-TMb modes are required for various values of e and have been obtained by numerically solving the characteristic equation (7).

Fig. 5 shows the relative power density distribution for the TMol-TMb mode. Fig. 5(a) for which 5 = 0.5, i.e. the guide radius a is just larger than at the approximate cutoff, depicts a power density distribution that can be shown to be virtually identical to that for the TMol mode in a guide with perfectly conducting walls. Here the maximum power density occurs at

a radial distance T somewhat larger than half the radius a of the guide. Fig. 5(b)-(d), for which = 8,16 and 32, respectively, show that the maximum power density shifts sharply towards the guide wall as increases. Fig. 5(d) illustrates the rapid decrease in field amplitude, from a maximum at the guidewall, to a relatively small value a short distance from the wall.

Fig. 6 shows the relative power density distribution for the TE11-TMi mode. Fig. 6(a), for which 5 = 0.3, so that the guide radius is just larger than at the approximate cutoff, shows a power density distribution that can be shown to be virtually

1938 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES. VOL. 42. NO I O . OCTOBER 1994

the same as that of a TEll mode in a guide with perfectly conducting walls. As e is increased, the region of maximum power density elongates horizontally. As e is increased further, the power density in the center of the guide diminishes and two maxima now occur at diametrically opposite locations

171 E. D. Palik, Ed., Handbook of Optical Consrunts o f Solids. Orlando. FL: Academic, 1985.

[XI B. Carnahan, H. A. Luther and J. 0. Wilkes, Applird Numerical Method.\. New York: Wiley, 1969.

[ 9 ] T. Wegmann, private communication.

at the guide wall, as shown in Fig. 6(b) for = 8. A further increase in guide radius, through = 16 and e = 32 shifts the fields yet further towards the guide walls. The radial variation of the relative power density distribution shown in Fig. 6(d) is virtually identical to that in Fig. 5(d), being the same for both guides. Fig. 6(d) has, however, the variation with 4 inherent for the TE11-TMi mode.

V. CONCLUSION

We have derived an asymptotic form for the characteristic equation in a hollow cylindrical guide whose wall has a large complex refractive index. Analytical solutions are obtained which show that for large guide radii, the axial and transverse propagation constants of the TElI-TM’, mode are equal to those of the TMol-TMb mode, and that both modes have un- dergone transitions to surface waves. The axial and transverse propagation constants of these waves are shown to be identical to those of a TM surface wave at a planar interface. Time- average relative power density distributions are shown for both TEll-TM’, and TMol-TMb modes. These show that for small guide radii the power density distributions are virtually identical to those of the TEll and TMol modes in a guide with perfectly conducting walls, while for large guide radii, power flow shifts to a narrow region adjacent to the guide wall.

The authors are presently evaluating the potential of surface wave propgatation in coated microstructural open waveguides for use in sensors and optoelectronic components (21, (41. and for analysis of biological materials in immuno-sensing appli- cations [9]. The wavelengths of interest include wavelengths much less than 10.6 pm, where complex refractive indices are smaller, and the transitions to surface waves described here occur at much smaller waveguide dimensions.

ACKNOWLEDGMENT

The authors wish to thank the Natural Sciences and Engi- neering Research Council of Canada for financial support of this work.

REFERENCES

[ I ] Y. Kato and M. Miyagi, “Modes and attenuation constants in circular hollow waveeuides with small core diameters for the infrared.’’ IEEE Trans. Microwave Theo? Tech., vol. 40, pp. 679-685, 1992. F. E. Vermeulen, T. Wang, C. R. James, and A. M. Robinson, “On the propagation of infrared radiation in hollow microstructural cylindrical waveguides,” .I. Lighrwave Tech., vol. 1 I , pp. 1956-1964, Jan., 1994. D. Pasquet, J. L. Gautier and P. Pouvil, “Mode transformations in very oversized circular waveguides,” Int. J Infrared Milliitzefer Waves, vol. 8, pp. 1129-1 141, 1987. F. E. Vermeulen, C. R. James, and A. M. Robinson, “Hollow microstruc- tural waveguides for propagation of infrared radiation,” J. Lightwave Tech., vol. 9, pp. 1053-1060, 1991. C. Boulas, S. Valette, E. Parrens and A. Fournier. “Low loss multimode waveguides on silicon substrate,” Elecrron. Letr., vol. 28, pp. 1648-1649, 1992. S. Ramo, J . R. Whinnery, and T. Van Duzer, Field., rind Wtrves in Communication Electronics. New York: Wiley, 1984.

Fred E. Vermeulen (S’59-M’62) was born in Stuttgart, Germany. He received the B.Sc. and Ph.D. degrees from the University of Alberta, the M.A.Sc. degree from the University of British Columbia, all in electrical engineering.

From 1966 to 1967, he was a National Research Council Postdoctoral Fellow at the European Organization for Nuclear Research, Geneva, Switzerland, where he was engaged in the study of space charge problems as related to the transport of ion beams. In 1967, he assumed an academic

position at the University of Alberta, where he is currently Professor of Electrical Engineering. His research is in applied electromagnetics, a particular interest being the physical and numerical modeling of wave propagation and electromagnetic heating in lossy materials.

A. M. Robinson (M’84) wd\ born in Vancou ver, Canadd, in 1938 He obtained the B A Sc , M Sc , and Ph D degree\ in engineering physic< and plasma phyxics from the University of British Columbid, in 1961, 1963, and 1966, respectively

From 1966 to I97 1 he was with the Defence Re- sedrch Board. Valcartier, Quebec, Canddd, working on the development of atmospheric presure COz lasers In 1971, he joined the Electrical Engineering Department at the University of Alberta, Edmonton, becoming Professor in 1976 From 1984 to 1990, he

wa\ Director of the Computer Engineering Program His research has involved C 0 2 lasers, molecular spectrojcopy, solar energy, photovoltaic systems, and more recently micromachining and microsensors

Dr Robinson is a member of OSA, Canadidn Association of Physic~sts, Solar Energy Society of Canada and the International Solar Energy Society

C. R. James was born in Vancouver, Canada in 1935 He received the B A Sc , M Sc , and Ph D degrees in electricdl engineering from the University of British Columbid, in 1960, 1961, and 1965. respectively

He was a NATO/NRC Port Doctoral Fellow at Oxford in Theoretical Physics trom 1964 to 1965, and then assumed an dppointment as an Assimnt Professor of Electrical Engineering at the University of Alberta in Edmonton In 1971, he became Pro- fessor and wds Chairinan of Electrical Engineering

trom 1974 to 1987, at which time he becdme Vice President of Research at the University of Alberta until 1993 Hi\ research has been in the fields of laser-plasma interdetions, electromagnetic theory, and microstructural device,

Dr James I \ a member of the American Physical Society, the Canadian As- sociation of Physicist\, and the Cdnadim Society of Electricdl and Computer Engineering

wave devices on silicon Engineering at the Univ Telecommunications Rest

James N. McMullin (M’84) was born in Mon- treal, Canada, in 1947. He received the B.Sc. in physics from McGill University and the Ph.D. de- gree in physics and astronomy from the University of Rochester, Rochester, NY, in 1968 and 1975, respectively.

From 1975 to 1983, he worked in the area of fusion plasma simulation specializing in electro- magnetic wave propagation. Since 1983, he has worked in fibre and integrated optics specializing in simulation and the design and fabrication of guided wafers. Presently, he is a Professor of Electrical

ersity of Alberta and an Affiliate Professor at the -arch Laboratories (TRLabs) in Edmonton, Canada.