K.C. Kao and G.A. Hockham - spectrum.ieee.org · Dielectric-fibre surface waveguides for optical frequencies K.C. Kao and G.A. Hockham Indexing terms: Optical fibres, Waveguides Abstract:

Dielectric-fibre surface waveguides foroptical frequencies

K.C. Kao and G.A. Hockham

Indexing terms: Optical fibres, Waveguides

Abstract: A dielectric fibre with a refractive index higher than its surrounding region is a form of dielectricwaveguide which represents a possible medium for the guided transmission of energy at optical frequencies. Theparticular type of dielectric-fibre waveguide discussed is one with a circular cross-section. The choice of themode of propagation for a fibre waveguide used for communication purposes is governed by consideration ofloss characteristics and information capacity. Dielectric loss, bending loss and radiation loss are discussed, andmode stability, dispersion and power handling are examined with respect to information capacity. Physical-realisation aspects are also discussed. Experimental investigations at both optical and microwave wavelengthsare included.

List of principle symbols

Jn = nth-order Bessel function of the first kindKn = nth-order modified Bessel function of the second

kind 271271

B — —, phase coefficient of the waveguideXg

}'n = first derivative of JnK ,̂ = first derivative of Knhi = radial wavenumber or decay coefficient€,- = relative permittivityk0 = free-space propagation coefficienta = radius of the fibrey = longitudinal propagation coefficientk = Boltzman's constantT = absolute temperature, Kj5 c = isothermal compressibilityX = wavelengthn = refractive indexHj,0 = uth-order Hankel function of the ith typeH'v = derivation of Huv = azimuthal propagation coefficient = i^ — jv2L = modulation periodSubscript n is an integer and subscript m refers to the mthroot of L = 0

1 IntroductionA dielectric fibre with a refractive index higher than itssurrounding region is a form of dielectric waveguide whichrepresents a possible medium for the guided transmissionof energy at optical frequencies. This form of structureguides the electromagnetic waves along the definableboundary between the regions of different refractiveindexes. The associated electromagnetic field is carriedpartially inside the fibre and partially outside it. The exter-nal field is evanescent in the direction normal to the direc-tion of propagation, and it decays approximatelyexponentially to zero at infinity. Such structures are oftenreferred to as open waveguides, and the propagation isknown as the surface-wave mode. The particular type ofdielectric-fibre waveguide to be discussed is one with a cir-cular cross-section.

Paper 5O33E was originally published in the Proceedings IEE, July 1966. It was firstreceived 24th November 1965 and in revised form 15th February 1966.The authors were formerly with Standard Telecommunication Laboratories Ltd.,Harlow, Essex. Prof. Kao is now with ITT and Dr. Hockham is with Plessey Com-pany Ltd., 241 Station Road, Addlestone, Surrey, United Kingdom

2 Dielectric-fibre waveguide

The dielectric fibre with a circular cross-section cansupport a family of HOm and EOm modes and a family ofhybrid HEnm modes. Solving the Maxwell equations underthe boundary conditions imposed by the physical struc-ture, the characteristic equations are as follows:for HEnm modes

n2/32

— + 1 ) =< —

for EOm modes

for HO m modesu2 K0(u2)

1 K'p(u2)u2 K0(w2)

(1)

(2)

(3)

The auxiliary equations defining the relationship betweenu1 and u2 are

ui + ul= (k0 a)2(ei - e2)

-h\ = y2 + k20s2

u( = h(a,i=\ and 2

where subscripts 1 and 2 refer to the fibre and the outerregion, respectively.

All the modes exhibit cutoffs except the H E M mode,which is the lowest-order hybrid mode. It can assume twoorthogonal polarisations, and it propagates with anincreasing percentage of energy outside the fibre as thedimensions of the structure decrease. Thus, when operatingthe waveguide in the HEX1 mode, it is possible to achieve asingle-mode operation by reducing the diameter of thefibre sufficiently. Under this condition, a significant pro-portion of the energy is carried outside the fibre. If theoutside medium is of a lower loss than the inside dielectricmedium, the attenuation of the waveguide is reduced. Withthese properties, H E n mode operation is of particularinterest.

The physical and electromagnetic aspects of thedielectric-fibre waveguide carrying the H E n mode for useat optical frequencies will now be studied in detail. Con-clusions are drawn as to the feasibility and the expected

IEE PROCEEDINGS, Vol. 133, Pt. J, No. 3, JUNE 1986 191

Authorized licensed use limited to: IEEE Publications Staff. Downloaded on October 6, 2009 at 14:33 from IEEE Xplore. Restrictions apply.

performance of such a waveguide for long-distance-communication application.

3 Material aspects

The losses of the dielectric-fibre waveguide are governedby the bulk losses of the materials which constitute thefibre and the surrounding medium. The relative contribu-tion to the total loss is determined by the proportion ofenergy within and outside the fibre and the relative lossesof the two media. In general, it is desirable to have lowbulk losses for both media, in order to achieve a satisfac-tory fibre waveguide with low attenuation.

3.1 Material-loss characteristicsThe bulk loss in dielectrics is caused by absorption andscattering phenomena. The particular mechanism involveddiffers for each material and depends on the operatingwavelength. The material-loss property is to be examinedbetween wavelengths of 100 and 0.1 /an, where the physi-cal size and the information capabilities of the dielectric-fibre waveguide are convenient.

3.1.1 Scattering: Scattering arises as a result of(a) lack of order of the structure of the material(b) structural defects(c) particle inclusion(d) random fluctuation.

For crystalline materials, the first two mechanisms are pre-dominant. Polycrystalline materials and materials whichare partly amorphous and partly crystalline show lack oforder of the structure; this results in high scattering loss.Single-crystal materials are ordered but may have structur-al defects; if these are few and of small size compared withthe wavelength, the scatter loss may not be very high.However, such materials are usually difficult to obtain inlong lengths.

For amorphous materials, such as organic polymersand inorganic glasses, mechanisms (c) and (d) are moreimportant. Organic polymers often contain all-chemicaldust particles much larger than 1 fim in diameter, causedby the uncontrolled environment in which they are manu-factured. This undesirable feature is likely to be eliminatedby the use of a dustfree environment and freshly redistilledmonomers and catalysts during manufacture. For inorga-nic glasses, the temperatures involved are high enough tocause chemical decomposition of most particle inclusion,resulting in such particles appearing as impurity centres.

The glassy state is a result of the supercooling of aliquid; thus the glassy-state solid retains some of the fun-damental behaviour of the liquid state. Therefore localisedmaterial-density fluctuation can take place. The scatteringdue to this can be described by the following expression[2]:

in — I)2

36 x 103 -— - i 1 - kTpc decibels per metreA

For inorganic glass with a fictive temperature of 1000°C,the scattering loss is of the order of 1 dB/km. Fictive tem-perature is the temperature at which glass viscosity hasincreased to a value where the glass is regarded as a solid.

Crystallite formation is a structural defect for glassy-state materials. The sizes of the crystallites in a glassymaterial can be controlled by the rate of cooling. For afibre, the rate of cooling is high; this results in fewer andsmaller crystallites. The scattering due to crystallites inrapidly cooled glasses obeys the Rayleigh scattering law;

i.e. loss is proportional to X 4. It is estimated that the lossis of the order of a few decibels per kilometre at 1 /anwavelength.

3.1.2 Absorption: Absorption bands in solids are usuallybroad, owing to the close packing of the molecules. Theyarise from the natural-vibration frequencies of the molecu-lar and electronic systems. Near such frequencies, theenergy of the external electromagnetic field couples energyinto the vibration of the molecules and electrons. In thewavelength region between 100 and 1 /an, many longitudi-nal and rotational resonances of molecules are present inalmost all substances, especially the long-chain polymers.Strong absorption takes place throughout most of theregion. In the 0.3-0.1 /mi region, electronic-resonanceabsorption bands are present. In the intermediate region(i.e. 1-0.3 /an), resonance-absorption phenomena are rela-tively absent. This represents a region for the material tohave low loss.

In inorganic glasses, it is known that absorption canoccur owing to the presence of impurity ions. It is knownthat, in high-quality optical glasses, the main contributionto absorption loss in the 1-3 /an region is due to the Fe+ +

and Fe+ + + ions. The ferrous ion has an absorption bandcentred at about 1 /mi, while the ferric ion has one atabout 0.4 /an. At band centre, the absorption due to 1 partper million of Fe + 2 in certain glass systems3 is estimatedto result in an absorption coefficient of less than20 dB/km.3.1.3 Present state of low-loss material: The presentknown low-loss materials in the frequency range of interestare mainly in the visible part of the spectrum. This isbecause transparent materials in this frequency range havebeen in high demand. The best transparent materialsknown in the visible spectrum are high-quality opticalglasses, fused quartz, polymethyl methachrylate and poly-styrene. The best absorption coefficient for glass isreported as 0.05% per cm, which is equivalent totan (5 = 1 x 10~8 at 1 /mi, giving a bulk loss of about200 dB/km. The published data on polymethyl meth-achrylate give 0.2% per cm, equivalent to a bulk loss ofabout 600 dB/km at 0.7 /an wavelength. This is for acommercial-grade material which is known to suffer fromhigh particle-scattering losses.

Typical absorption/wavelength curves can be seen inFigs. 1, 2 and 3, showing the measurements made on glass,

Fig. 1 Attenuation in SW6 glass

quartz and polymethyl methachrylate samples, respec-tively. Work is in progress towards obtaining lower-absorption glasses. Currently this is being given anadditional boost, owing to laser-glass requirements. It isforeseeable that glasses with a bulk loss of about20 dB/km at around 0.6 /an will be obtained, as the iron-impurity concentration may be reduced to 1 part permillion.

192 IEE PROCEEDINGS, Vol. 133, Pt. J, No. 3, JUNE 1986


4 Electromagnetic aspects

The choice of the mode of propagation for the fibre wave-guide used for communication purposes is governed by the

0-6 " 07 0-8 0-9wavelength, >jm

Fig. 2 Attenuation infused quartz

1-1

r-20

16

J05 0-6 07 0-8 0-9 10 1-1

wavelength, pm

Fig. 3 Attenuation in polymethyl methacrylate

consideration of loss characteristics and informationcapacity.

4.1 Dielectric lossFor a fibre-dielectric waveguide with free space as itslossfree outside medium, it is an advantage to choose theradius, the dielectric constants and the mode of propaga-tion so that the ratio of the energy in free space to theenergy in the dielectric fibre is large. Examining the char-acteristic eqn. 1 of this system, it can be shown that theradial-decay coefficient in the outside medium decreaseswhen a particular mode is near cutoff, corresponding tothe proportion of energy in the outside region increasing.The characteristics of the Eo , Ho and H E U modes areshown in Figs. 4 and 5; the effective losses in decibels areshown in Figs. 6 and 7.

€1 .2-28€2 .1

/ /

/

7/7

7/

^ko(h)%o(e)

/

U1e- U 1 h

2 3 4 5 KOO

Fig. 4 Ho and Eo mode characteristics

IEE PROCEEDINGS, Vol. 133, Pt. J, No. 3, JUNE 1986

This improvement in loss characteristics has alreadybeen explored at microwave frequencies [4], the Eo mode

84§8

H•5 2

€̂ 2-28

~7/

/_ • - - —

1 2 3 4Koo

Fig. 5 HEn mode characteristics

SiO10

10"r

€, =2-28

ton 8, = 3x10"9 toi

A\\

„ •

.

-ToRT

2O 30 40 5OKoa

Fig. 6 HQ and Eo attenuation

10"

<10

10'

€, = 2-28€2='ton 01 «3x10tan 89 » 0

/

10 20 3 0 40Koo

5 0

Fig. 7 HEll mode attenuation

has been used. In the microwave region, the waveguide is afew millimetres in radius. Supporting structures muchsmaller in size than the operating wavelength may bedesigned for minimum reflection and radiation losses. Theradial-decay coefficient is usually designed to give thelowest effective attenuation coefficient while allowing thewaveguide to negotiate bends without appreciable radi-ation. This aspect will be discussed later.

At the visible wavelengths, the operation of a dielectricwaveguide with free space as its outer medium is difficult.The physical size, which is now in the submicron range,becomes a serious snag for exploring the advantage of loss

193


reduction. The radius for low-loss operation is consider-ably less than the wavelength — usually about one tenth.This will cause the waveguide to be invisible, even with theaid of optical instruments. Supports, of smaller than thewavelength dimensions, no longer exist. Furthermore thissize may present problems in power handling and mech-anical strength. Thus, for optical frequencies, a claddedstructure is necessary, in which the dielectric fibre iscovered with a concentric layer of a second dielectric oflower permittivity. With the cladding thickness made equalto many wavelengths, usually taken to be about 100, thefield at the external boundary may be made arbitrarilysmall. The waveguide may then be easily supported. Forthe cladded fibre, the choice of the mode of propagation ison an information basis.

4.2 Bending lossWhen a surface waveguide follows a curved path, radiationof the guided energy occurs. Exact analysis of this effect fora fibre-dielectric waveguide is difficult, as the partial differ-ential equation of the system is variable inseparable. Radi-ation from a curved infinite strip of constant radius ofcurvature has been solved [5, 6]. It is shown that the char-acteristic equation describing the system is

•(4)

where k = /cON/£,-

A = inner radius

B = outer radius

A is the radius along the centre of the dielectric wheresymmetry on either side is still assumed to hold. This isvalid for 2t/A ^ 1, where t is the film thickness. This hasbeen solved approximately previously; the results showedthat the radiation loss as a function of bending radius is afast varying function. The results quoted from Reference 5are in Table 1. They show that bending loss is negligibleuntil a certain critical radius of curvature is reached, whenthe bending loss becomes very large. The critical radius isdependent on the transverse-decay coefficient. It is conve-nient to define the critical radius as the radius of curvatureat which the loss is X dB/rad. X may be fixed arbitrarilyat, say, 0.01. With a small transverse-decay coefficient, the

Table 1: Characteristic of curved surface waveguide [5]K0A 0OA yA

60 63667590126132150180504528600720

960 1008105612001440

120

480

64 + 0.9y66.1 +0.3/75 +10-4/90 +10-14/

126.4 + 0.8/132 + 0.03/150 +10-11y180 +1011y504 + 0.002/528 +10-10/600 +10"16y720 +10-132/

1008 +2 * 10-7/1056 +10-22/1200 +10-94/1440 +10-268/

energy extends a long way from the surface of the strip.The energy is loosely coupled to or trapped in the wave-guide. Under this condition, a small curvature will causelarge radiation loss; i.e. the critical radius is large.

The decay coefficient of a fibre-dielectric waveguide, forequal ratio of energy outside to the inside, is larger thanthat of the infinite-strip case. It suggests that the bendingloss of the fibre is likely to be smaller than that of theequivalent film. The critical radius of curvature with anenergy ratio of 100: 1 is around 1000 X. This, at visiblewavelength, is a very sharp physical bend.

4.3 Other losses due to radiationPhysical discontinuities of the dielectric waveguide causeguided-energy loss by radiation. The step discontinuity forthe fibre waveguide has been solved [7] for the cases of thesymmetrical Eo modes and the hybrid H E U mode. Thediscontinuity was represented by a change in the surfacereactance of the structure; a Wiener-Hopf method wasemployed. The result can be summarised as follows.

The radiation occurs within a range of angles with thepeak at some particular value. For the same ratio of reac-tances, the angle of elevation for peak radiation is largerfor the case of higher trapping. The radiation is almostentirely confined to the forward direction. The radiatedenergy is around 7% for a reactance change of 10 times;for a 3-times reactance change, the energy radiated is 1%.The transmitted power for these cases is 93 and 99%,respectively, showing that little reflected power is present.

Cyclic dimensional changes occur frequently in a fibrewaveguide. The case of the sinusoidal surface-reactancechange can be analysed rigorously. Solutions for the sym-metrical Eo mode and the hybrid HEX1 mode can beobtained by a transform method [8]. The results show thatthe electro-magnetic radiation supported by the structurecan be expressed in a spectrum of space-harmonic waves ofthe modulating period. Most of the component waves aretrapped, some are forward-propagating and some arebackward-propagating; some, however, are radiative. Thepower contained in the space-harmonic componentsdecreases with the order of the harmonic, except at certainconditions which are described in detail in Reference 8.The main contribution is due to the first three com-ponents; for the case of the Eo mode it is as shown in Fig.8. The radiation is dependent on the modulation depth; to

4)0-5•0- 3 0 ,o.§0-3

% O-2

l o - iO

Ir-amplitude of rthsurface reactances-depth of modulation

- - — <—

space \540080

/

'

larmonic

II

/

4;\t

Po = propagation coefficient at infinite radius of curvatureV= (Po + A/? +jct) = propagation coefficient of curved waveguide

A = radius of curvature

10 20 30 40 50 60 70 80 90 100

Fig. 8 Space-harmonic amplitude distribution

a first approximation, it is proportional to the square ofthe modulation depth.

For more complicated waveforms, the main contribu-tion is likely to be from the period with the largest modu-lation depth. For waveforms of two or moreequal-magnitude sinusoids, the superposition is difficult topredict, owing to the existence of mutual couplings. Ananalysis with random discontinuity has been reported [9],



but the results have not been confirmed. The extension ofthis method to the periodic case did not yield results inagreement with those obtained by the rigorous solution.The loss due to random discontinuity is intuitively antici-pated to be low. This, of course, needs further theoreticaland experimental verification.

4.4 Information capacityThree factors affect the information capacity of a wave-guide structure — mode stability, dispersion and powerhandling.

4.4.1 Mode stability: The mode stability of a waveguideis dependent on the physical and material perfection of thewaveguide. Any imperfection appears as a form of discon-tinuity which causes mode conversion. In the case of asingle-mode waveguide the process of mode conversiongives rise to localised fields, resulting in mainly radiation.When a single mode can exist in more than one polarisa-tion, a discontinuity may couple some power from one tothe other polarisation configuration. In the case of anovermoded waveguide, the mode conversion may result inradiation as well as the excitation of propagating modesother than the incident mode. This gives rise to a multi-mode phenomenon.

At some later discontinuity, mode reconversion can takeplace. As the modes propagate at different velocities, infor-mation distortion takes place. In the single-mode wave-guide, reconversion between different polarisation can takeplace. However, as the modes are travelling with the samegroup velocity, distortion does not take place, owing toincorrect phasal addition. Nevertheless, if the detector ispolarisation-sensitive, amplitude distortion results. Thus,for high information capacity, a single-mode waveguide isdesirable. It is sometimes preferable to have a mode whichhas only one polarisation. For the dielectric-fibre wave-guide, this favours Eo , Ho or H E n modes, although theH E n mode has two possible polarisations.

4.4.2 Dispersion: The dispersion characteristics ofdielectric-fibre waveguides have two regions of interest.One region corresponds to operating the waveguide farremoved from cutoff. Thus, for a highly overmoded wave-guide, extremely fiat phase characteristics can be obtained,giving good dispersion characteristics. This, however, isnot desirable, on account of mode instability. The otherregion occurs when the waveguide is operating very nearto cutoff. The waveguide wavelength is then nearly equalto the free-space wavelength. The phase characteristics forthe modes becomes flatter as the order of the modedecreases. This condition offers single-mode operations forthe Eo , Ho and H E U modes. The H E n mode dispersioncharacteristic is the best. The group-delay distortion for a10 km route, using the H E n mode under the operatingcondition when the koa = 0.6, can be estimated as follows.

From the slope of the ca/(i plot, the slope change over1 Gc/s is taken to be approximately 10~6. Assuming thatthe refractive-index change with frequency is negligible, thegroup delay is given approximately by

distance x velocity"1 x slope change

= 10 x 109 x 13 x 1014 x 1 0 " 6 = - x 10 - 1 0

This represents a 24° phase shift for 1 GHz bandwidth.

4.4.3 Power handling: Assuming single-mode operation,the power-handling capacity is determined by the break-down condition of the fibre waveguide when subjected to

high power density. For a particular wavelength operation,the single-mode-waveguide size needs to be smaller thanthe cutoff dimension. If the maximum power density is50 MW/cm2, the maximum permissible power input forsingle-mode (HE n ) operation must be less than57i(0.338/i.o)2 x 102. For i 0 = 0.74 ^m, the power must beless than 100 mW. Considering the case when the signal/noise ratio is to be not less than 20 dB and loss betweenrepeaters is 50 dB, this will mean that the signal/noiseratio at input is to be 70 dB above noise.

The noise at optical frequencies is mainly quantumnoise, and it is given approximately by hvB, where h isPlanck's constant, v is the frequency and B is the band-width. For B = 1 kHz, this is approximately equal to100 dB, below 1 mW. Hence the bandwidth for a 100 mWinput power is 100 MHz. By increasing the permittivity ofthe outer medium to approach that of the inner, thepower-handling capacity can be made to increase. For awaveguide with index matching of 1%, the power handlingis increased by about ten times; this will enable the infor-mation capacity to increase to 1 GHz.

5 Physical aspects

The material-loss characteristic is an important physicalaspect which has already been discussed. There are furtherrequirements on the material properties for fibre-waveguide application. These are the fabrication andmechanical strength.

5.1 FabricationThe fabrication of dielectric-fibre waveguides is a processof pulling or extrusion. For inorganic glasses, the moltenglass is allowed to flow through an orifice, often at the endof a cone structure. The end is attached to a pulling deviceand the material is drawn in the plastic state; it is thenallowed to cool rapidly. Owing to the high surface-tensionenergy involved in the plastic state, the resulting fibre hasvery good cylindrical symmetry. The rapid cooling causesthe high-temperature liquid-state properties to be retained.The surface of the fibre is particularly good when freshlymade; a tensile strength of 106 lbf/in2 is possible. Surfacedeterioration due to atmospheric attacks and externalmechanical influences cause a rapid decrease in the mecha-nical strength. For organic dielectric fibres, similar pro-cesses take place, although the surface forces are nowsmaller. The surface perfection still gives very high tensilestrength.

In the case of cladded fibre, the interface between theouter and inner materials is protected. Although thestrength is dependent mainly on the perfection of the outersurface, the inner surface contributes to the overallstrength. In any case, the cladded structure usually has anouter/inner-dimension ratio of 100 : 1, and hence derivesits strength from the relatively large bulk of materialpresent.

The physical tolerance of the single fibre is dependenton the variation of the rate of pulling. With a constantspeed of pulling and a constant rate of flow, the practicaltolerance achievable at present is claimed to be about 5%;with more refinement this may be improved. For claddedfibre, the overall tolerances and the ratio of the outer toinner diameters may again be made to meet a 5% toler-ance limit. In the cladded fibre, the boundary between theinner and the outer materials is not likely to be an abrupttransition. A diffusion process necessarily takes place whenthe two streams are flowing in the liquid state. This causesa graded junction to be formed. Thus the important

1EE PROCEEDINGS, Vol. 133, Pt. J,No. 3, JUNE 1986 195


guiding boundary of the cladded structure is not only pro-tected but also graded. This gives rise to even less stringenttolerance requirements; however, the formation of a scat-tering centre in this region may exist.

The dependence of tolerance requirements on the varia-tion of surface reactance can be calculated [8]. Numericalcalculations for three separate radii are as follows:

a = a1 , a = 0.00018a2 = l.lfli, a = 0.003

a3 = !, a = 0.096fli is chosen to be equivalent to a normalised surface reac-tance of 0.038 for a constant modulating depth of 0.8. Thisshows that dimensional tolerances become less criticalwith the decrease in fibre inner diameter.

6 Experimental investigations

In electromagnetic investigations, the experiments werecarried out at some convenient microwave frequencies.The system measurements were carried out at visible andnear-infrared wavelengths.

6.1 Micro wa ve scaled measuremen tsThe corrugated metallic rods [10, 11], with corrugatedpitch much smaller than the operating wavelength, areused to simulate the dielectric-fibre waveguide. To a firstapproximation, the surface reactance of such a waveguideis derived by considering only the fundamental space har-monic. The choice of this type of waveguide, as opposed todielectric rods, is the ease of accurately machining such amodulated-surface reactance rod. The required toleranceof about 0.0005 in (0.013 mm) is difficult, if not impossible,to achieve on a dielectric structure. Measurements werecarried out at X band frequencies (i.e. approximately10 GHz) to assess the radiation loss due to sinusoidal

surface-reactance variations; the effect of bending was alsoexamined. Both Eo and H E n modes were investigated.

6.1.1 Sinusoidal surface-reactance variation: A parallel-plate surface-wave resonator was used to determine therelative losses of various rods with sinusoidally modulatedsurface reactances, as shown in Figs. 9 and 10, for the Eoand HE^ modes, respectively. The independent variablesare the pitch and the depth of modulation. The apparatusis shown schematically in Fig. 11, and the results areshown in Figs. 12 and 13 for the Eo and HEU modes,respectively. Both theoretical and experimental results areincluded.

6.1.2 Bending loss: The bending loss of the corrugated-metal-rod waveguides were measured for the rod carryingthe Eo mode. The result shows that no significant loss canbe measured until the bending radius is below a certainfigure (Fig. 14). The radius for measurable loss correspondsto less than 100 k0.

6.2 Optical experimentsThe experiments at optical frequencies were aimed atdeveloping the technique and instrumentation for quanti-tative assessment of the waveguide performance. Theinitial experiments were on the launching of waveguidemodes. The optical system was as shown in Fig. 15. Thelight source used was a helium-neon single-transverse-mode laser and a gallium arsenide semiconductor laser.The optical waveguides used were cladded fibres withsignal-yellow glass as inner core. The refractive-indexmatching gives single-mode operation at 6328 A wave-length when the inner-core diameter is < 4 jum. The rangeof fibre sizes used was 3-13 fim. The fibres were mountedin capillary tubes and set in epoxy resin; this enabled theends to be optically polished. Some of the observed single-mode and multimode field-intensity distributions are

Fig. 9 Corrugated waveguides supporting Eo modes

Fig. 10 Corrugated waveguides supporting HElt mode



shown in Fig. 16; the modes have been identified, and suitable lens system, alignment was possible. The observa-these are tabulated in Table 2. Preferential excitation is tion of modes has been achieved.

swept frequency source

trigger

isolator

wavemeter

levs)-setting attenuator

surface - wave resonator

c.r.o.

ornplifier

modstransducer

modetransducer

Fig. 11 Microwave measuring equipment

5 10 1-5 2 0radiation loss as function of -L

Xo

Fig. 13 Radiation loss as afunction of L/Xo {HEl{ mode)

T.— limit of experimental accuracyjexperimental points O.Ci

atte

nuat

ion ,

dt

6

\

\

\

\

\

TO =9oC/5"

i =,0,3

\

3 4 5radius, ft

Fig. 14 Experimental bending loss of a fibre carrying the Eo mode at afrequency of 9 GHz

Table 2: Details of modes photographed

KOL12

Fig. 12 Radiation loss as afunction ofko L (Eo mode)

achieved by the positioning of the light spot and the rota-tion of the light polarisation. The cutoff of some of thehigher-order modes may be observed by using a white-light source through a monochromator. The use of agallium arsenide laser was aimed at discovering methodsof aligning a near infrared system when visual observationcannot be made. With the aid of an image convertor and a

Photo- Modegraph inFig. 16

Fibre Corrected Corrected Approximatecore wavelength input spotdiameter diameter

abcde

f

9

HE,,EH,,TM0 2 or TE02TE0,+HE2 1HE,2 + EH,,TE02 + HE22

orTMO2 + HE22

EH + HE

ECHDH

H

H

fjm1.804.508.453.058.45

8.45

8.45

//m0.5900.5600.5530.5500.580

0.545

0.630

/i/m1.153.003.003.003.00

3.00

3.00

A preliminary experiment on the butt jointing of twofibres has been carried out. It was observed that, when thefibres were placed with a gap of less than 1 mm, the energytransfer was not less than 10% if a matching fluid wasplaced in the gap. The first fibre acted as the light source

monochromator x 95 oil-immersionobjectives

fibre

laserHe-Ne orGaAs

lens Pin h o l e

polariser" eyepieces

Fig. 15 Schematic diagram of the experimental optical apparatus

analyser

IEE PROCEEDINGS, Vol. 133, Pt. J, No. 3, JUNE 1986 197


for the second fibre; by offsetting the second fibre, differentmode patterns from the one carried by the first fibre could

Fig. 16 Photographs of light patterns produced by modes

be observed, if the second fibre was not a single-modestructure.

7 Conclusions

Theoretical and experimental studies indicate that a fibreof glassy material constructed in a cladded structure with acore diameter of about 100 XQ represents a possible practi-cal optical waveguide with important potential as a newform of communication medium. The refractive index of

the core needs to be about 1% higher than that of thecladding. This form of waveguide operates in a singleHE^ , Eo or Ho mode and has an information capacity inexcess of 1 GHz. It is completely flexible and calls for amechanical tolerance of around 10%, which can be readilymet in practice. Thus, compared with existing coaxial-cable and radio systems, this form of waveguide has alarger information capacity and possible advantages inbasic material cost. The realisation of a successful fibrewaveguide depends, at present, on the availability of suit-able low-loss dielectric material. The crucial materialproblem appears to be one which is difficult but notimpossible. Certainly, the required loss figure of around20 dB/km is much higher than the lower limit of loss figureimposed by fundamental mechanisms.

8 Acknowledgment

The authors wish to acknowledge the contribution of Mr.R.W. Lomax in carrying out the fibre-mode experimentand dielectric-loss measurements, and to thank StandardTelecommunication Laboratories Ltd. for permission topublish the paper.

9 References1 COLLIN, R.E.: 'Field theory of guided waves' (McGraw-Hill, 1960)2 MAURER, R.D.: 'Light scattering by glasses', J. Chem. Phys., 1956,

25, p. 12063 STEELE, F.N., and DOUGLAS, R.W.: 'Some observations on the

absorption of iron in silicate and borate glasses', Phys. Chem. Glasses,1965, 6, (6), p. 246

4 GOUBAU, G.: 'Single conductor surface wave transmission line',Proc. Inst. Radio Engrs, 1951, 39, p. 619

5 ELLIOTT, R.S.: 'Azimuthal surface waves on circular cylinders', J.Appl. Phys., 1955, 26, p. 368

6 POTTER, S.V.: 'Propagation in the azimuth direction of a cylindricalsurface wave', Ph.D. Thesis, University College London, 1963

7 BREITHAUPT, R.W.: 'The diffraction of a cylindrical surface waveby surface discontinuities', Ph.D. Thesis, University College London,1965

8 HOCKHAM, G.: 'Surface wave propagation on varying reactivecylindrical structures', Ph.D. Thesis, 1969, University of London

9 JONES, A.L.: 'Coupling of optical fibres and scattering in fibres', J.Opt. Soc. Amer., 1965, 55, p. 261

10 SAVARD, J.Y.: 'An investigation of higher order surface waves oncylindrical structures', Ph.D. Thesis, University College, London, 1961

11 BARLOW, H.E.M., and KARBOWIAK, A.E.: 'An experimentalinvestigation of the properties of corrugated cylindrical surface wave-guides', Proc. IEE, 1954, 101, Pt. Ill, p. 182



Documents

K.C. Kao and G.A. Hockham - spectrum.ieee.org · Dielectric-fibre surface waveguides for optical frequencies K.C. Kao and G.A. Hockham Indexing terms: Optical fibres, Waveguides Abstract: