《光波导理论与技术 Optical Waveguides Principles and Technologies》课程教学资源（参考文献）Dielectric-fibre surface waveguides for optical frequencies

Dielectric-fibre surface waveguides for optical 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 dielectric waveguide which represents a possible medium for the guided transmission of energy at optical frequencies.The particular type of dielectric-fibre waveguide discussed is one with a circular cross-section.The choice of the mode of propagation for a fibre waveguide used for communication purposes is governed by consideration of loss characteristics and information capacity.Dielectric loss,bending loss and radiation loss are discussed,and mode 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 wavelengths are included. List of principle symbols 2 Dielectric-fibre waveguide nth-order Bessel function of the first kind The dielectric fibre with a circular cross-section can =nth-order modified Bessel function of the second support a family of Hom and Eom modes and a family of kind 2 hybrid HEm modes.Solving the Maxwell equations under phase cofficient of the waveguide 2元 the boundary conditions imposed by the physical struc- ture,the characteristic equations are as follows: J first derivative of J for HEm modes Ki=first derivative of Kn n2B2/1,12 hi radial wavenumber or decay coefficient 61 L()62 K(u2 relative permittivity lu J(u)u2 K(u2) Ko free-space propagation coefficient LJu+⊥K2 a radius of the fibre (1) longitudinal propagation coefficient lu1 J(u)u2 K (u2) Boltzman's constant for Eom modes 入 =absolute temperature,K isothermal compressibility E1 Jo(u1)82 Ko(u2) (2) wavelength ui Jo(u) uz Ko(u2) n refractive index Hi)=uth-order Hankel function of the ith type for Hom modes H derivation of H. 1J6(u1)_1Ko(u2) =azimuthal propagation coefficient =vi-jv2 u Jou) u2 Ko(u2) (3) modulation period Subscript n is an integer and subscript m refers to the mth The auxiliary equations defining the relationship between root of J =0 u and u,are ui+uz=(ko a)2(e1-E2) h好=y2+k好e1 1 Introduction -h好=y2+k6e2 A dielectric fibre with a refractive index higher than its surrounding region is a form of dielectric waveguide which ui=hia,i=1 and 2 represents a possible medium for the guided transmission where subscripts 1 and 2 refer to the fibre and the outer of energy at optical frequencies.This form of structure region,respectively. guides the electromagnetic waves along the definable boundary between the regions of different refractive All the modes exhibit cutoffs except the HE mode, which is the lowest-order hybrid mode.It can assume two indexes.The associated electromagnetic field is carried orthogonal polarisations,and it propagates with an partially inside the fibre and partially outside it.The exter- increasing percentage of energy outside the fibre as the nal field is evanescent in the direction normal to the direc- dimensions of the structure decrease.Thus,when operating tion of propagation,and it decays approximately exponentially to zero at infinity.Such structures are often the waveguide in the HE mode,it is possible to achieve a single-mode operation by reducing the diameter of the referred to as open waveguides,and the propagation is fibre sufficiently.Under this condition,a significant pro- known as the surface-wave mode.The particular type of portion of the energy is carried outside the fibre.If the dielectric-fibre waveguide to be discussed is one with a cir- outside medium is of a lower loss than the inside dielectric cular cross-section. medium,the attenuation of the waveguide is reduced.With these properties,HE1 mode operation is of particular interest. Paper 5033E was originally published in the Proceedings IEE,July 1966.It was first The physical and electromagnetic aspects of the received 24th November 1965 and in revised form 15th February 1966. The authors were formerly with Standard Telecommunication Laboratories Ltd dielectric-fibre waveguide carrying the HE mode for use Harlow,Essex.Prof.Kao is now with ITT and Dr.Hockham is with Plessey Com- at optical frequencies will now be studied in detail.Con- pany Ltd.,241 Station Road,Addlestone,Surrey,United Kingdom clusions are drawn as to the feasibility and the expected IEE PROCEEDINGS,Vol.133,Pt.J,No.3,JUNE 1986 191

Dielectric-fibre surface waveguides for optical 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 dielectric waveguide which represents a possible medium for the guided transmission of energy at optical frequencies. The particular type of dielectric-fibre waveguide discussed is one with a circular cross-section. The choice of the mode of propagation for a fibre waveguide used for communication purposes is governed by consideration of loss characteristics and information capacity. Dielectric loss, bending loss and radiation loss are discussed, and mode 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 wavelengths are included. List of principle symbols Jn = nth-order Bessel function of the first kind Kn = nth-order modified Bessel function of the second kind 271 271 B — —, phase coefficient of the waveguide Xg }'n = first derivative of Jn K^, = first derivative of Kn hi = radial wavenumber or decay coefficient €,- = relative permittivity k0 = free-space propagation coefficient a = radius of the fibre y = longitudinal propagation coefficient k = Boltzman's constant T = absolute temperature, K j 5c = isothermal compressibility X = wavelength n = refractive index Hj,0 = uth-order Hankel function of the ith type H'v = derivation of Hu v = azimuthal propagation coefficient = i^ — jv2 L = modulation period Subscript n is an integer and subscript m refers to the mth root of L = 0 1 Introduction A dielectric fibre with a refractive index higher than its surrounding region is a form of dielectric waveguide which represents a possible medium for the guided transmission of energy at optical frequencies. This form of structure guides the electromagnetic waves along the definable boundary between the regions of different refractive indexes. The associated electromagnetic field is carried partially 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 approximately exponentially to zero at infinity. Such structures are often referred to as open waveguides, and the propagation is known as the surface-wave mode. The particular type of dielectric-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 first received 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 can support a family of HOm and EOm modes and a family of hybrid HEnm modes. Solving the Maxwell equations under the boundary conditions imposed by the physical struc￾ture, the characteristic equations are as follows: for HEnm modes n2 /32 — + 1 ) =< — for EOm modes for HOm modes u2 K0 (u2 ) 1 K'p(u2) u2 K0(w2) (1) (2) (3) The auxiliary equations defining the relationship between u1 and u2 are ui + ul= (k0 a)2 (ei - e2) -h\ = y2 + k2 0s2 u( = h(a,i=\ and 2 where subscripts 1 and 2 refer to the fibre and the outer region, respectively. All the modes exhibit cutoffs except the HE M mode, which is the lowest-order hybrid mode. It can assume two orthogonal polarisations, and it propagates with an increasing percentage of energy outside the fibre as the dimensions of the structure decrease. Thus, when operating the waveguide in the HEX1 mode, it is possible to achieve a single-mode operation by reducing the diameter of the fibre sufficiently. Under this condition, a significant pro￾portion of the energy is carried outside the fibre. If the outside medium is of a lower loss than the inside dielectric medium, the attenuation of the waveguide is reduced. With these properties, HE n mode operation is of particular interest. The physical and electromagnetic aspects of the dielectric-fibre waveguide carrying the HE n mode for use at 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

performance of such a waveguide for long-distance- i.e.loss is proportional to4.It is estimated that the loss communication application. is of the order of a few decibels per kilometre at 1 um wavelength. 3 Material aspects 3.1.2 Absorption:Absorption bands in solids are usually The losses of the dielectric-fibre waveguide are governed broad,owing to the close packing of the molecules.They by the bulk losses of the materials which constitute the arise from the natural-vibration frequencies of the molecu- fibre and the surrounding medium.The relative contribu- lar and electronic systems.Near such frequencies,the tion to the total loss is determined by the proportion of energy of the external electromagnetic field couples energy energy within and outside the fibre and the relative losses into the vibration of the molecules and electrons.In the of the two media.In general,it is desirable to have low wavelength region between 100 and 1 um,many longitudi- bulk losses for both media,in order to achieve a satisfac- nal and rotational resonances of molecules are present in tory fibre waveguide with low attenuation almost all substances,especially the long-chain polymers. Strong absorption takes place throughout most of the 3.1 Material-loss characteristics region.In the 0.3-0.1 um region,electronic-resonance The bulk loss in dielectrics is caused by absorption and absorption bands are present.In the intermediate region scattering phenomena.The particular mechanism involved (i.e.1-0.3 um),resonance-absorption phenomena are rela- differs for each material and depends on the operating tively absent.This represents a region for the material to wavelength.The material-loss property is to be examined have low loss. between wavelengths of 100 and 0.1 um,where the physi- In inorganic glasses,it is known that absorption can cal size and the information capabilities of the dielectric- occur owing to the presence of impurity ions.It is known fibre waveguide are convenient. that,in high-quality optical glasses,the main contribution to absorption loss in the 1-3 um region is due to the Fe++ 3.1.1 Scattering:Scattering arises as a result of and Fe+++ions.The ferrous ion has an absorption band (a)lack of order of the structure of the material centred at about 1 um,while the ferric ion has one at (b)structural defects about 0.4 um.At band centre,the absorption due to 1 part (c)particle inclusion per million of Fe+2 in certain glass systems3 is estimated (d)random fluctuation. to result in an absorption coefficient of less than For crystalline materials,the first two mechanisms are pre- 20 dB/km. dominant.Polycrystalline materials and materials which 3.1.3 Present state of low-loss material:The present are partly amorphous and partly crystalline show lack of known low-loss materials in the frequency range of interest order of the structure;this results in high scattering loss. are mainly in the visible part of the spectrum.This is Single-crystal materials are ordered but may have structur- because transparent materials in this frequency range have al defects;if these are few and of small size compared with been in high demand.The best transparent materials the wavelength,the scatter loss may not be very high known in the visible spectrum are high-quality optical However,such materials are usually difficult to obtain in glasses,fused quartz,polymethyl methachrylate and poly- styrene.The best absorption coefficient for glass is long lengths. For amorphous materials,such as organic polymers reported as 0.05%per cm,which is equivalent to and inorganic glasses,mechanisms (c)and (d)are more tan 6=1 x 10-8 at 1 um,giving a bulk loss of about important.Organic polymers often contain all-chemical 200 dB/km.The published data on polymethyl meth- dust particles much larger than 1 um in diameter,caused achrylate give 0.2%per cm,equivalent to a bulk loss of by the uncontrolled environment in which they are manu- about 600 dB/km at 0.7 um wavelength.This is for a factured.This undesirable feature is likely to be eliminated commercial-grade material which is known to suffer from high particle-scattering losses. by the use of a dustfree environment and freshly redistilled Typical absorption/wavelength curves can be seen in monomers and catalysts during manufacture.For inorga- Figs.1,2 and 3,showing the measurements made on glass, nic glasses,the temperatures involved are high enough to cause chemical decomposition of most particle inclusion, 12 resulting in such particles appearing as impurity centres. The glassy state is a result of the supercooling of a 3 liquid;thus the glassy-state solid retains some of the fun- damental behaviour of the liquid state.Therefore localised material-density fluctuation can take place.The scattering due to this can be described by the following expression 9-2 8 [2]: 5 3x1decibels per metre 14 07 0-8 0 For inorganic glass with a fictive temperature of 1000C, Fig.1 Attenuation in SW6 glass the scattering loss is of the order of 1 dB/km.Fictive tem- perature is the temperature at which glass viscosity has quartz and polymethyl methachrylate samples,respec- increased to a value where the glass is regarded as a solid. tively.Work is in progress towards obtaining lower- Crystallite formation is a structural defect for glassy- absorption glasses.Currently this is being given an state materials.The sizes of the crystallites in a glassy additional boost,owing to laser-glass requirements.It is material can be controlled by the rate of cooling.For a foreseeable that glasses with a bulk loss of about fibre,the rate of cooling is high;this results in fewer and 20 dB/km at around 0.6 um will be obtained,as the iron- smaller crystallites.The scattering due to crystallites in impurity concentration may be reduced to 1 part per rapidly cooled glasses obeys the Rayleigh scattering law;million. 192 IEE PROCEEDINGS,Vol.133,Pt.J,No.3,JUNE 1986

performance of such a waveguide for long-distance￾communication application. 3 Material aspects The losses of the dielectric-fibre waveguide are governed by the bulk losses of the materials which constitute the fibre and the surrounding medium. The relative contribu￾tion to the total loss is determined by the proportion of energy within and outside the fibre and the relative losses of the two media. In general, it is desirable to have low bulk losses for both media, in order to achieve a satisfac￾tory fibre waveguide with low attenuation. 3.1 Material-loss characteristics The bulk loss in dielectrics is caused by absorption and scattering phenomena. The particular mechanism involved differs for each material and depends on the operating wavelength. The material-loss property is to be examined between 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 which are partly amorphous and partly crystalline show lack of order 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 with the wavelength, the scatter loss may not be very high. However, such materials are usually difficult to obtain in long lengths. For amorphous materials, such as organic polymers and inorganic glasses, mechanisms (c) and (d) are more important. Organic polymers often contain all-chemical dust particles much larger than 1 fim in diameter, caused by the uncontrolled environment in which they are manu￾factured. This undesirable feature is likely to be eliminated by the use of a dustfree environment and freshly redistilled monomers and catalysts during manufacture. For inorga￾nic glasses, the temperatures involved are high enough to cause chemical decomposition of most particle inclusion, resulting in such particles appearing as impurity centres. The glassy state is a result of the supercooling of a liquid; thus the glassy-state solid retains some of the fun￾damental behaviour of the liquid state. Therefore localised material-density fluctuation can take place. The scattering due to this can be described by the following expression [2]: in — I)2 36 x 103 -—-i 1 - kTpc decibels per metre A 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 has increased 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 glassy material can be controlled by the rate of cooling. For a fibre, the rate of cooling is high; this results in fewer and smaller crystallites. The scattering due to crystallites in rapidly cooled glasses obeys the Rayleigh scattering law; i.e. loss is proportional to X 4. It is estimated that the loss is of the order of a few decibels per kilometre at 1 /an wavelength. 3.1.2 Absorption: Absorption bands in solids are usually broad, owing to the close packing of the molecules. They arise from the natural-vibration frequencies of the molecu￾lar and electronic systems. Near such frequencies, the energy of the external electromagnetic field couples energy into the vibration of the molecules and electrons. In the wavelength region between 100 and 1 /an, many longitudi￾nal and rotational resonances of molecules are present in almost all substances, especially the long-chain polymers. Strong absorption takes place throughout most of the region. In the 0.3-0.1 /mi region, electronic-resonance absorption 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 to have low loss. In inorganic glasses, it is known that absorption can occur owing to the presence of impurity ions. It is known that, in high-quality optical glasses, the main contribution to absorption loss in the 1-3 /an region is due to the Fe+ + and Fe+ + + ions. The ferrous ion has an absorption band centred at about 1 /mi, while the ferric ion has one at about 0.4 /an. At band centre, the absorption due to 1 part per million of Fe + 2 in certain glass systems3 is estimated to result in an absorption coefficient of less than 20 dB/km. 3.1.3 Present state of low-loss material: The present known low-loss materials in the frequency range of interest are mainly in the visible part of the spectrum. This is because transparent materials in this frequency range have been in high demand. The best transparent materials known in the visible spectrum are high-quality optical glasses, fused quartz, polymethyl methachrylate and poly￾styrene. The best absorption coefficient for glass is reported as 0.05% per cm, which is equivalent to tan (5 = 1 x 10~8 at 1 /mi, giving a bulk loss of about 200 dB/km. The published data on polymethyl meth￾achrylate give 0.2% per cm, equivalent to a bulk loss of about 600 dB/km at 0.7 /an wavelength. This is for a commercial-grade material which is known to suffer from high particle-scattering losses. Typical absorption/wavelength curves can be seen in Figs. 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 an additional boost, owing to laser-glass requirements. It is foreseeable that glasses with a bulk loss of about 20 dB/km at around 0.6 /an will be obtained, as the iron￾impurity concentration may be reduced to 1 part per million. 192 IEE PROCEEDINGS, Vol. 133, Pt. J, No. 3, JUNE 1986

Electromagnetic aspects This improvement in loss characteristics has already been explored at microwave frequencies [4],the Eo mode The choice of the mode of propagation for the fibre wave- guide used for communication purposes is governed by the 61228 2*1 06 0- 08 09 10 11 wavelength,um Fig.2 Attenuation in fused quartz 828 Koa 736 Fig.5 HEmode characteristics 6445 61228 552 E2=1 tan 61=3x109 ton62:0 46-0 Eo Ho 16 36-8 27-6 g 8 184 5109 92 8的0ao7o80g100 wavelength,um Fig.3 Attenuation in polymethyl methacrylate consideration of loss characteristics and information 20 30 40 50 capacity. Koa Fig.6 Ho and Eo attenuation 4.1 Dielectric loss For a fibre-dielectric waveguide with free space as its €1-228 lossfree outside medium,it is an advantage to choose the radius,the dielectric constants and the mode of propaga- tan 620 tion so that the ratio of the energy in free space to the energy in the dielectric fibre is large.Examining the char- acteristic eqn.1 of this system,it can be shown that the radial-decay coefficient in the outside medium decreases when a particular mode is near cutoff,corresponding to the proportion of energy in the outside region increasing. The characteristics of the Eo,Ho and HE modes are shown in Figs.4 and 5;the effective losses in decibels are shown in Figs.6 and 7. 名0 5 61.228 e2"1 u2h 61020304050 Fig.7 HE mode attenuation -1h has been used.In the microwave region,the waveguide is a few millimetres in radius.Supporting structures much smaller in size than the operating wavelength may be designed for minimum reflection and radiation losses.The e头ol radial-decay coefficient is usually designed to give the lowest effective attenuation coefficient while allowing the 弘ale) waveguide to negotiate bends without appreciable radi- ation.This aspect will be discussed later. At the visible wavelengths,the operation of a dielectric waveguide with free space as its outer medium is difficult. 5 Koa The physical size,which is now in the submicron range, Fig.4 Ho and Eo mode characteristics becomes a serious snag for exploring the advantage of loss IEE PROCEEDINGS,Vol.133,Pt.J,No.3,JUNE 1986 193

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 0-9 wavelength, >jm Fig. 2 Attenuation infused quartz 1-1 r-20 16 J 05 0-6 07 0-8 0-9 10 1-1 wavelength, pm Fig. 3 Attenuation in polymethyl methacrylate consideration of loss characteristics and information capacity. 4.1 Dielectric loss For a fibre-dielectric waveguide with free space as its lossfree outside medium, it is an advantage to choose the radius, the dielectric constants and the mode of propaga￾tion so that the ratio of the energy in free space to the energy in the dielectric fibre is large. Examining the char￾acteristic eqn. 1 of this system, it can be shown that the radial-decay coefficient in the outside medium decreases when a particular mode is near cutoff, corresponding to the proportion of energy in the outside region increasing. The characteristics of the Eo , Ho and HE U modes are shown in Figs. 4 and 5; the effective losses in decibels are shown in Figs. 6 and 7. €1 .2-28 €2 .1 / / / 7/ 7 7/ ^ko(h) %o(e) / U 1e - U 1h 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 already been explored at microwave frequencies [4], the Eo mode 84 § 8 H •5 2 €^2-28 ~7/ / _ • - - — 1 2 3 4 Koo Fig. 5 HEn mode characteristics SiO10 10"r €, =2-28 ton 8, = 3x10"9 toi A \ \ „ • . - To RT 2O 30 40 5O Koa Fig. 6 HQ and Eo attenuation 10" < 10 10' €, = 2-28 € 2=' ton 01 «3x10 tan 89 » 0 / 10 20 3 0 40 Koo 5 0 Fig. 7 HEll mode attenuation has been used. In the microwave region, the waveguide is a few millimetres in radius. Supporting structures much smaller in size than the operating wavelength may be designed for minimum reflection and radiation losses. The radial-decay coefficient is usually designed to give the lowest effective attenuation coefficient while allowing the waveguide to negotiate bends without appreciable radi￾ation. This aspect will be discussed later. At the visible wavelengths, the operation of a dielectric waveguide 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- energy extends a long way from the surface of the strip. ably less than the wavelength-usually about one tenth. The energy is loosely coupled to or trapped in the wave- This will cause the waveguide to be invisible,even with the guide.Under this condition,a small curvature will cause aid of optical instruments.Supports,of smaller than the large radiation loss;i.e.the critical radius is large. wavelength dimensions,no longer exist.Furthermore this The decay coefficient of a fibre-dielectric waveguide,for size may present problems in power handling and mech- equal ratio of energy outside to the inside,is larger than anical strength.Thus,for optical frequencies,a cladded that of the infinite-strip case.It suggests that the bending structure is necessary,in which the dielectric fibre is loss of the fibre is likely to be smaller than that of the covered with a concentric layer of a second dielectric of equivalent film.The critical radius of curvature with an lower permittivity.With the cladding thickness made equal energy ratio of 100:1 is around 1000 This,at visible to many wavelengths.usually taken to be about 100,the wavelength,is a very sharp physical bend. field at the external boundary may be made arbitrarily small.The waveguide may then be easily supported.For 4.3 Other losses due to radiation the cladded fibre,the choice of the mode of propagation is Physical discontinuities of the dielectric waveguide cause on an information basis. guided-energy loss by radiation.The step discontinuity for the fibre waveguide has been solved [7]for the cases of the 4.2 Bending loss symmetrical Eo modes and the hybrid HE1 mode.The When a surface waveguide follows a curved path,radiation discontinuity was represented by a change in the surface of the guided energy occurs.Exact analysis of this effect for reactance of the structure;a Wiener-Hopf method was a fibre-dielectric waveguide is difficult,as the partial differ- employed.The result can be summarised as follows. ential equation of the system is variable inseparable.Radi- The radiation occurs within a range of angles with the ation from a curved infinite strip of constant radius of peak at some particular value.For the same ratio of reac- curvature has been solved [5,61.It is shown that the char- tances,the angle of elevation for peak radiation is larger acteristic equation describing the system is for the case of higher trapping.The radiation is almost entirely confined to the forward direction.The radiated 1 HOY(kB)HY(kA)-(HY(kB)H(DY(kA) energy is around 7%for a reactance change of 10 times; E H(kB)(H((kA)-H(kB)(HOY(kA) for a 3-times reactance change,the energy radiated is 1% (H(ko B) The transmitted power for these cases is 93 and 99%, respectively,showing that little reflected power is present. H(2)(ko B) Cyclic dimensional changes occur frequently in a fibre where k=ko√e waveguide.The case of the sinusoidal surface-reactance change can be analysed rigorously.Solutions for the sym- A inner radius metrical Eo mode and the hybrid HE mode can be B=outer radius obtained by a transform method [8].The results show that the electro-magnetic radiation supported by the structure A is the radius along the centre of the dielectric where can be expressed in a spectrum of space-harmonic waves of symmetry on either side is still assumed to hold.This is the modulating period.Most of the component waves are valid for 2t/A1,where t is the film thickness.This has trapped,some are forward-propagating and some are been solved approximately previously;the results showed backward-propagating;some,however,are radiative.The that the radiation loss as a function of bending radius is a power contained in the space-harmonic components fast varying function.The results quoted from Reference 5 decreases with the order of the harmonic,except at certain are in Table 1.They show that bending loss is negligible conditions which are described in detail in Reference 8. until a certain critical radius of curvature is reached,when The main contribution is due to the first three com- the bending loss becomes very large.The critical radius is ponents;for the case of the Eo mode it is as shown in Fig. dependent on the transverse-decay coefficient.It is conve- 8.The radiation is dependent on the modulation depth;to nient to define the critical radius as the radius of curvature Ir-amplitude of rth space harmonic at which the loss is X dB/rad.X may be fixed arbitrarily surface reactance~540 depth of modulation O-80 at,say,0.01.With a small transverse-decay coefficient,the 07 Table 1:Characteristic of curved surface waveguide[5] K。A BoA YA 60 63 64+0.91 66 66.1+0.31 0 75 75 +10-4 90 90 +10-14 2 工o 120 126 126.4+0.8j 132 132 +0.03i 150 150 +10-11 1020 3040506070809000 180 180 +1011j KL 480 504 504 +0.002 Fig.8 Space-harmonic amplitude distribution 528 528 +10-0 600 600 +10-16 a first approximation,it is proportional to the square of 720 720 +10-132 the modulation depth. 960 1008 1008 +2×10-7i 1056 1056 +10-22j For more complicated waveforms,the main contribu- 12001200 +10-94 tion is likely to be from the period with the largest modu- 1440 1440 +10-268 lation depth.For waveforms of two or more Bo=propagation coefficient at infinite radius of curvature equal-magnitude sinusoids,the superposition is difficult to y=(Bo+AB+ja)=propagation coefficient of curved waveguide predict,owing to the existence of mutual couplings.An A=radius of curvature analysis with random discontinuity has been reported [9], 194 IEE PROCEEDINGS,Vol.133,Pt.J,No.3,JUNE 1986

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 the aid of optical instruments. Supports, of smaller than the wavelength dimensions, no longer exist. Furthermore this size may present problems in power handling and mech￾anical strength. Thus, for optical frequencies, a cladded structure is necessary, in which the dielectric fibre is covered with a concentric layer of a second dielectric of lower permittivity. With the cladding thickness made equal to many wavelengths, usually taken to be about 100, the field at the external boundary may be made arbitrarily small. The waveguide may then be easily supported. For the cladded fibre, the choice of the mode of propagation is on an information basis. 4.2 Bending loss When a surface waveguide follows a curved path, radiation of the guided energy occurs. Exact analysis of this effect for a 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 of curvature 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 where symmetry on either side is still assumed to hold. This is valid for 2t/A ^ 1, where t is the film thickness. This has been solved approximately previously; the results showed that the radiation loss as a function of bending radius is a fast varying function. The results quoted from Reference 5 are in Table 1. They show that bending loss is negligible until a certain critical radius of curvature is reached, when the bending loss becomes very large. The critical radius is dependent on the transverse-decay coefficient. It is conve￾nient to define the critical radius as the radius of curvature at which the loss is X dB/rad. X may be fixed arbitrarily at, say, 0.01. With a small transverse-decay coefficient, the Table 1: Characteristic of curved surface waveguide [5] K0A 0OA yA 60 63 66 75 90 126 132 150 180 504 528 600 720 960 1008 1056 1200 1440 120 480 64 + 0.9y 66.1 +0.3/ 75 +10-4 / 90 +10-14/ 126.4 + 0.8/ 132 + 0.03/ 150 +10-11y 180 +1011y 504 + 0.002/ 528 +10-10/ 600 +10"16y 720 +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 cause large radiation loss; i.e. the critical radius is large. The decay coefficient of a fibre-dielectric waveguide, for equal ratio of energy outside to the inside, is larger than that of the infinite-strip case. It suggests that the bending loss of the fibre is likely to be smaller than that of the equivalent film. The critical radius of curvature with an energy ratio of 100: 1 is around 1000 X. This, at visible wavelength, is a very sharp physical bend. 4.3 Other losses due to radiation Physical discontinuities of the dielectric waveguide cause guided-energy loss by radiation. The step discontinuity for the fibre waveguide has been solved [7] for the cases of the symmetrical Eo modes and the hybrid HE U mode. The discontinuity was represented by a change in the surface reactance of the structure; a Wiener-Hopf method was employed. The result can be summarised as follows. The radiation occurs within a range of angles with the peak at some particular value. For the same ratio of reac￾tances, the angle of elevation for peak radiation is larger for the case of higher trapping. The radiation is almost entirely confined to the forward direction. The radiated energy 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 fibre waveguide. The case of the sinusoidal surface-reactance change can be analysed rigorously. Solutions for the sym￾metrical Eo mode and the hybrid HEX1 mode can be obtained by a transform method [8]. The results show that the electro-magnetic radiation supported by the structure can be expressed in a spectrum of space-harmonic waves of the modulating period. Most of the component waves are trapped, some are forward-propagating and some are backward-propagating; some, however, are radiative. The power contained in the space-harmonic components decreases with the order of the harmonic, except at certain conditions 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 lo- i O Ir-amplitude of rth surface reactances- depth of modulation - - — <— space \ 540 080 / ' larmonic II / 4; \t Po = propagation coefficient at infinite radius of curvature V= (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 of the 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 more equal-magnitude sinusoids, the superposition is difficult to predict, owing to the existence of mutual couplings. An analysis with random discontinuity has been reported [9], 194 IEE PROCEEDINGS, Vol. 133, Pt. J, No. 3, JUNE 1986

but the results have not been confirmed.The extension of high power density.For a particular wavelength operation, this method to the periodic case did not yield results in the single-mode-waveguide size needs to be smaller than agreement with those obtained by the rigorous solution. the cutoff dimension.If the maximum power density is The loss due to random discontinuity is intuitively antici- 50 MW/cm2,the maximum permissible power input for pated to be low.This,of course,needs further theoretical single-mode (HE)operation must be less than and experimental verification. 5x(0.3384o)2 x 102.For o=0.74 um,the power must be less than 100 mW.Considering the case when the signal/ 4.4 Information capacity noise ratio is to be not less than 20 dB and loss between Three factors affect the information capacity of a wave- repeaters is 50 dB,this will mean that the signal/noise guide structure-mode stability,dispersion and power ratio at input is to be 70 dB above noise. handling. The noise at optical frequencies is mainly quantum 4.4.1 Mode stability:The mode stability of a waveguide noise,and it is given approximately by hvB,where h is Planck's constant,v is the frequency and B is the band- is dependent on the physical and material perfection of the width.For B=1 kHz,this is approximately equal to waveguide.Any imperfection appears as a form of discon- 100 dB,below 1 mW.Hence the bandwidth for a 100 mW tinuity which causes mode conversion.In the case of a input power is 100 MHz.By increasing the permittivity of single-mode waveguide the process of mode conversion gives rise to localised fields,resulting in mainly radiation. the outer medium to approach that of the inner,the power-handling capacity can be made to increase.For a When a single mode can exist in more than one polarisa- waveguide with index matching of 1%,the power handling tion,a discontinuity may couple some power from one to is increased by about ten times;this will enable the infor- the other polarisation configuration.In the case of an mation capacity to increase to 1 GHz. overmoded waveguide,the mode conversion may result in radiation as well as the excitation of propagating modes other than the incident mode.This gives rise to a multi- 5 Physical aspects mode phenomenon. At some later discontinuity,mode reconversion can take The material-loss characteristic is an important physical place.As the modes propagate at different velocities,infor- aspect which has already been discussed.There are further mation distortion takes place.In the single-mode wave- requirements on the material properties for fibre- guide,reconversion between different polarisation can take waveguide application.These are the fabrication and place.However,as the modes are travelling with the same mechanical strength. group velocity,distortion does not take place,owing to incorrect phasal addition.Nevertheless,if the detector is 5.1 Fabrication polarisation-sensitive,amplitude distortion results.Thus, The fabrication of dielectric-fibre waveguides is a process for high information capacity,a single-mode waveguide is of pulling or extrusion.For inorganic glasses,the molten desirable.It is sometimes preferable to have a mode which glass is allowed to flow through an orifice,often at the end has only one polarisation.For the dielectric-fibre wave- of a cone structure.The end is attached to a pulling device and the material is drawn in the plastic state;it is then guide,this favours Eo,Ho or HE1 modes,although the HE mode has two possible polarisations. allowed to cool rapidly.Owing to the high surface-tension energy involved in the plastic state,the resulting fibre has 4.4.2 Dispersion:The dispersion characteristics of very good cylindrical symmetry.The rapid cooling causes dielectric-fibre waveguides have two regions of interest. the high-temperature liquid-state properties to be retained. One region corresponds to operating the waveguide far The surface of the fibre is particularly good when freshly removed from cutoff.Thus,for a highly overmoded wave- made;a tensile strength of 106 Ibf/in2 is possible.Surface guide,extremely flat phase characteristics can be obtained, deterioration due to atmospheric attacks and external giving good dispersion characteristics.This,however,is mechanical influences cause a rapid decrease in the mecha- not desirable,on account of mode instability.The other nical strength.For organic dielectric fibres,similar pro- region occurs when the waveguide is operating very near cesses take place,although the surface forces are now to cutoff.The waveguide wavelength is then nearly equal smaller.The surface perfection still gives very high tensile to the free-space wavelength.The phase characteristics for strength the modes becomes flatter as the order of the mode In the case of cladded fibre,the interface between the decreases.This condition offers single-mode operations for outer and inner materials is protected.Although the the Eo,Ho and HEu modes.The HE mode dispersion strength is dependent mainly on the perfection of the outer characteristic is the best.The group-delay distortion for a surface,the inner surface contributes to the overall 10 km route,using the HE mode under the operating strength.In any case,the cladded structure usually has an condition when the ko a =0.6,can be estimated as follows. outer/inner-dimension ratio of 100:1,and hence derives From the slope of the c/B plot,the slope change over its strength from the relatively large bulk of material 1 Gc/s is taken to be approximately 10-.Assuming that present. the refractive-index change with frequency is negligible,the The physical tolerance of the single fibre is dependent group delay is given approximately by on the variation of the rate of pulling.With a constant speed of pulling and a constant rate of flow,the practical distance x velocityx slope change tolerance achievable at present is claimed to be about 5% with more refinement this may be improved.For cladded =10×10°×3x104×10-6= 3×10-10s fibre,the overall tolerances and the ratio of the outer to inner diameters may again be made to meet a 5%toler- This represents a 24 phase shift for 1 GHz bandwidth. ance limit.In the cladded fibre,the boundary between the inner and the outer materials is not likely to be an abrupt 4.4.3 Power handling:Assuming single-mode operation, transition.A diffusion process necessarily takes place when the power-handling capacity is determined by the break- the two streams are flowing in the liquid state.This causes down condition of the fibre waveguide when subjected to a graded junction to be formed.Thus the important IEE PROCEEDINGS,Vol.133,Pt.J,No.3,JUNE 1986 195

but the results have not been confirmed. The extension of this method to the periodic case did not yield results in agreement 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 theoretical and experimental verification. 4.4 Information capacity Three factors affect the information capacity of a wave￾guide structure — mode stability, dispersion and power handling. 4.4.1 Mode stability: The mode stability of a waveguide is dependent on the physical and material perfection of the waveguide. Any imperfection appears as a form of discon￾tinuity which causes mode conversion. In the case of a single-mode waveguide the process of mode conversion gives 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 to the other polarisation configuration. In the case of an overmoded waveguide, the mode conversion may result in radiation as well as the excitation of propagating modes other than the incident mode. This gives rise to a multi￾mode phenomenon. At some later discontinuity, mode reconversion can take place. As the modes propagate at different velocities, infor￾mation distortion takes place. In the single-mode wave￾guide, reconversion between different polarisation can take place. However, as the modes are travelling with the same group velocity, distortion does not take place, owing to incorrect phasal addition. Nevertheless, if the detector is polarisation-sensitive, amplitude distortion results. Thus, for high information capacity, a single-mode waveguide is desirable. It is sometimes preferable to have a mode which has only one polarisation. For the dielectric-fibre wave￾guide, this favours Eo , Ho or HE n modes, although the H E n mode has two possible polarisations. 4.4.2 Dispersion: The dispersion characteristics of dielectric-fibre waveguides have two regions of interest. One region corresponds to operating the waveguide far removed from cutoff. Thus, for a highly overmoded wave￾guide, extremely fiat phase characteristics can be obtained, giving good dispersion characteristics. This, however, is not desirable, on account of mode instability. The other region occurs when the waveguide is operating very near to cutoff. The waveguide wavelength is then nearly equal to the free-space wavelength. The phase characteristics for the modes becomes flatter as the order of the mode decreases. This condition offers single-mode operations for the Eo , Ho and HE U modes. The HE n mode dispersion characteristic is the best. The group-delay distortion for a 10 km route, using the HE n mode under the operating condition when the koa = 0.6, can be estimated as follows. From the slope of the ca/(i plot, the slope change over 1 Gc/s is taken to be approximately 10~6 . Assuming that the refractive-index change with frequency is negligible, the group delay is given approximately by distance x velocity"1 x slope change = 10 x 109 x 1 3 x 1014 x 10" 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 than the cutoff dimension. If the maximum power density is 50 MW/cm2 , the maximum permissible power input for single-mode (HEn ) operation must be less than 57i(0.338/i.o) 2 x 102 . For i 0 = 0.74 ^m, the power must be less than 100 mW. Considering the case when the signal/ noise ratio is to be not less than 20 dB and loss between repeaters is 50 dB, this will mean that the signal/noise ratio at input is to be 70 dB above noise. The noise at optical frequencies is mainly quantum noise, and it is given approximately by hvB, where h is Planck's constant, v is the frequency and B is the band￾width. For B = 1 kHz, this is approximately equal to 100 dB, below 1 mW. Hence the bandwidth for a 100 mW input power is 100 MHz. By increasing the permittivity of the outer medium to approach that of the inner, the power-handling capacity can be made to increase. For a waveguide with index matching of 1%, the power handling is 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 physical aspect which has already been discussed. There are further requirements on the material properties for fibre￾waveguide application. These are the fabrication and mechanical strength. 5.1 Fabrication The fabrication of dielectric-fibre waveguides is a process of pulling or extrusion. For inorganic glasses, the molten glass is allowed to flow through an orifice, often at the end of a cone structure. The end is attached to a pulling device and the material is drawn in the plastic state; it is then allowed to cool rapidly. Owing to the high surface-tension energy involved in the plastic state, the resulting fibre has very good cylindrical symmetry. The rapid cooling causes the high-temperature liquid-state properties to be retained. The surface of the fibre is particularly good when freshly made; a tensile strength of 106 lbf/in2 is possible. Surface deterioration due to atmospheric attacks and external mechanical influences cause a rapid decrease in the mecha￾nical strength. For organic dielectric fibres, similar pro￾cesses take place, although the surface forces are now smaller. The surface perfection still gives very high tensile strength. In the case of cladded fibre, the interface between the outer and inner materials is protected. Although the strength is dependent mainly on the perfection of the outer surface, the inner surface contributes to the overall strength. In any case, the cladded structure usually has an outer/inner-dimension ratio of 100 : 1, and hence derives its strength from the relatively large bulk of material present. The physical tolerance of the single fibre is dependent on the variation of the rate of pulling. With a constant speed of pulling and a constant rate of flow, the practical tolerance achievable at present is claimed to be about 5%; with more refinement this may be improved. For cladded fibre, the overall tolerances and the ratio of the outer to inner diameters may again be made to meet a 5% toler￾ance limit. In the cladded fibre, the boundary between the inner and the outer materials is not likely to be an abrupt transition. A diffusion process necessarily takes place when the two streams are flowing in the liquid state. This causes a 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- surface-reactance variations;the effect of bending was also tected but also graded.This gives rise to even less stringent examined.Both Eo and HE modes were investigated. tolerance requirements;however,the formation of a scat- tering centre in this region may exist. 6.1.1 Sinusoidal surface-reactance variation:A parallel- The dependence of tolerance requirements on the varia- plate surface-wave resonator was used to determine the tion of surface reactance can be calculated 87.Numerical relative losses of various rods with sinusoidally modulated calculations for three separate radii are as follows: surface reactances,as shown in Figs.9 and 10,for the Eo a=a1,a=0.00018 and HE modes,respectively.The independent variables are the pitch and the depth of modulation.The apparatus a2=1.1a1,g=0.003 is shown schematically in Fig.11,and the results are a3=1.2a1,g=0.096 shown in Figs.12 and 13 for the Eo and HE modes, respectively.Both theoretical and experimental results are a,is chosen to be equivalent to a normalised surface reac- included. tance of 0.038 for a constant modulating depth of 0.8.This shows that dimensional tolerances become less critical 6.1.2 Bending loss:The bending loss of the corrugated- with the decrease in fibre inner diameter. metal-rod waveguides were measured for the rod carrying the Eo mode.The result shows that no significant loss can 6 Experimental investigations be measured until the bending radius is below a certain figure(Fig.14).The radius for measurable loss corresponds In electromagnetic investigations,the experiments were to less than 100 4o. carried out at some convenient microwave frequencies The system measurements were carried out at visible and 6.2 Optical experiments near-infrared wavelengths. The experiments at optical frequencies were aimed at developing the technique and instrumentation for quanti- 6.1 Microwave scaled measurements tative assessment of the waveguide performance.The The corrugated metallic rods [10,11],with corrugated initial experiments were on the launching of waveguide pitch much smaller than the operating wavelength,are modes.The optical system was as shown in Fig.15.The used to simulate the dielectric-fibre waveguide.To a first light source used was a helium-neon single-transverse- approximation,the surface reactance of such a waveguide mode laser and a gallium arsenide semiconductor laser. is derived by considering only the fundamental space har- The optical waveguides used were cladded fibres with monic.The choice of this type of waveguide,as opposed to signal-yellow glass as inner core.The refractive-index dielectric rods,is the ease of accurately machining such a matching gives single-mode operation at 6328 A wave- modulated-surface reactance rod.The required tolerance length when the inner-core diameter is 4 um.The range of about 0.0005 in (0.013 mm)is difficult,if not impossible, of fibre sizes used was 3-13 um.The fibres were mounted to achieve on a dielectric structure.Measurements were in capillary tubes and set in epoxy resin;this enabled the carried out at X band frequencies (i.e.approximately ends to be optically polished.Some of the observed single- 10 GHz)to assess the radiation loss due to sinusoidal mode and multimode field-intensity distributions are Aamttttt www Fig.9 Corrugated waveguides supporting Eo modes 111111111133300130 ir177777177777777770 CCEELLUUELULLELLLLL +。4,,d。。a。g4g,ad4 cauaawue■d。44d tdikcan LLL】11 710 Fig.10 Corrugated waveguides supporting HE mode 196 IEE PROCEEDINGS,Vol.133,Pt.J,No.3,JUNE 1986

guiding boundary of the cladded structure is not only pro￾tected but also graded. This gives rise to even less stringent tolerance 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]. Numerical calculations for three separate radii are as follows: a = a1 , a = 0.00018 a2 = l.lfli, a = 0.003 a3 = !, a = 0.096 fli is chosen to be equivalent to a normalised surface reac- tance of 0.038 for a constant modulating depth of 0.8. This shows that dimensional tolerances become less critical with the decrease in fibre inner diameter. 6 Experimental investigations In electromagnetic investigations, the experiments were carried out at some convenient microwave frequencies. The system measurements were carried out at visible and near-infrared wavelengths. 6.1 Micro wa ve scaled measuremen ts The corrugated metallic rods [10, 11], with corrugated pitch much smaller than the operating wavelength, are used to simulate the dielectric-fibre waveguide. To a first approximation, the surface reactance of such a waveguide is derived by considering only the fundamental space har- monic. The choice of this type of waveguide, as opposed to dielectric rods, is the ease of accurately machining such a modulated-surface reactance rod. The required tolerance of about 0.0005 in (0.013 mm) is difficult, if not impossible, to achieve on a dielectric structure. Measurements were carried out at X band frequencies (i.e. approximately 10 GHz) to assess the radiation loss due to sinusoidal surface-reactance variations; the effect of bending was also examined. Both Eo and HEn modes were investigated. 6.1.1 Sinusoidal surface-reactance variation: A parallel￾plate surface-wave resonator was used to determine the relative losses of various rods with sinusoidally modulated surface reactances, as shown in Figs. 9 and 10, for the Eo and HE^ modes, respectively. The independent variables are the pitch and the depth of modulation. The apparatus is shown schematically in Fig. 11, and the results are shown in Figs. 12 and 13 for the Eo and HEU modes, respectively. Both theoretical and experimental results are included. 6.1.2 Bending loss: The bending loss of the corrugated- metal-rod waveguides were measured for the rod carrying the Eo mode. The result shows that no significant loss can be measured until the bending radius is below a certain figure (Fig. 14). The radius for measurable loss corresponds to less than 100 k0. 6.2 Optical experiments The experiments at optical frequencies were aimed at developing the technique and instrumentation for quanti- tative assessment of the waveguide performance. The initial experiments were on the launching of waveguide modes. The optical system was as shown in Fig. 15. The light source used was a helium-neon single-transverse- mode laser and a gallium arsenide semiconductor laser. The optical waveguides used were cladded fibres with signal-yellow glass as inner core. The refractive-index matching gives single-mode operation at 6328 A wave- length when the inner-core diameter is < 4 jum. The range of fibre sizes used was 3-13 fim. The fibres were mounted in capillary tubes and set in epoxy resin; this enabled the ends 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 196 IEE PROCEEDINGS, Vol. 133, Pt. J, No. 3, JUNE 1986

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 wavemeter theoretical M:0-695 X0▣090 isolator level-setting attenuato 8 surface-wave resonator 05 amplifier 10 15 2-0 mode c.r.o. mode loss transducer transducer as function of无 Fig.11 Microwave measuring equipment Fig.13 Radiation loss as a function of L/(HE mode) -llmit of experimental accuracy experimental points 20 fo -9Gc/s X=0-04 B :1013 Ko 1-0 “4 theoretical 8 radius,ft 0.6 Fig.14 Experimental bending loss of a fibre carrying the Eo mode at a frequency of9 GHz 06 Table 2:Details of modes photographed 04 Photo- Mode Fibre Corrected Corrected Approximate graph in core wavelength input spot Fig.16 diameter diameter 0+2 m um um 1.80 0.590 1.15 b EHt 4.50 0.560 3.00 TMo2 or TE02 8.45 0.553 3.00 20 40 60 80 d 0 3.05 0.550 3.00 KoL TEo1+HE21 HE12+EH11 H 8,45 0.580 3.00 12 TE02+HE22 or H 8.45 0.545 3.00 Fig.12 Radiation loss as a function of koL(Eo mode) TMo2+HE22 9 EH+HE H 8.45 0.630 3.00 achieved by the positioning of the light spot and the rota- tion of the light polarisation.The cutoff of some of the higher-order modes may be observed by using a white- A preliminary experiment on the butt jointing of two light source through a monochromator.The use of a fibres has been carried out.It was observed that,when the gallium arsenide laser was aimed at discovering methods fibres were placed with a gap of less than 1 mm,the energy of aligning a near infrared system when visual observation transfer was not less than 10%if a matching fluid was cannot be made.With the aid of an image convertor and a placed in the gap.The first fibre acted as the light source monochromotor x 95 oil-immersion objectives fibre onolyser He-Ne or en pin hole Fig.15 Schematic diagram of the experimental optical apparatus IEE PROCEEDINGS,Vol.133,Pt.J,No.3,JUNE 1986 197

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 mods transducer mode transducer Fig. 11 Microwave measuring equipment 5 10 1-5 2 0 radiation loss as function of -L Xo Fig. 13 Radiation loss as afunction of L/Xo {HEl{ mode) T.— limit of experimental accuracy jexperimental points O.Ci attenuation, dt 6 \ \ \ \ \ TO =9oC/5" i =,0,3 \ 3 4 5 radius, ft Fig. 14 Experimental bending loss of a fibre carrying the Eo mode at a frequency of 9 GHz Table 2: Details of modes photographed KOL 12 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 the higher-order modes may be observed by using a white￾light source through a monochromator. The use of a gallium arsenide laser was aimed at discovering methods of aligning a near infrared system when visual observation cannot be made. With the aid of an image convertor and a Photo- Mode graph in Fig. 16 Fibre Corrected Corrected Approximate core wavelength input spot diameter diameter a b c d e f 9 HE,, EH,, TM0 2 or TE02 TE0 ,+HE2 1 HE,2 + EH,, TE02 + HE22 or TMO2 + HE22 EH + HE E C H D H H H fjm 1.80 4.50 8.45 3.05 8.45 8.45 8.45 //m 0.590 0.560 0.553 0.550 0.580 0.545 0.630 /i/m 1.15 3.00 3.00 3.00 3.00 3.00 3.00 A preliminary experiment on the butt jointing of two fibres has been carried out. It was observed that, when the fibres were placed with a gap of less than 1 mm, the energy transfer was not less than 10% if a matching fluid was placed in the gap. The first fibre acted as the light source monochromator x 95 oil-immersion objectives fibre laser He-Ne or GaAs lens Pin hol 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,different the core needs to be about 1%higher than that of the mode patterns from the one carried by the first fibre could cladding.This form of waveguide operates in a single HE11,Eo or Ho mode and has an information capacity in excess of 1 GHz.It is completely flexible and calls for a mechanical tolerance of around 10%,which can be readily met in practice.Thus,compared with existing coaxial- cable and radio systems,this form of waveguide has a larger information capacity and possible advantages in basic material cost.The realisation of a successful fibre waveguide depends,at present,on the availability of suit- able low-loss dielectric material.The crucial material problem appears to be one which is difficult but not impossible.Certainly,the required loss figure of around 20 dB/km is much higher than the lower limit of loss figure imposed by fundamental mechanisms. 8 Acknowledgment The authors wish to acknowledge the contribution of Mr. R.W.Lomax in carrying out the fibre-mode experiment and dielectric-loss measurements,and to thank Standard Telecommunication Laboratories Ltd.for permission to publish the paper. 9 References 1 COLLIN,R.E.:Field theory of guided waves'(McGraw-Hill,1960) 2 MAURER,R.D.:'Light scattering by glasses',J.Chem.Phys.,1956, 25.D.1206 3 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. Fig.16 Photographs of light patterns produced by modes Appl.Phys,1955,26,p.368 6 POTTER,S.V.:'Propagation in the azimuth direction of a cylindrical surface wave',Ph.D.Thesis,University College London,1963 be observed,if the second fibre was not a single-mode 7 BREITHAUPT,R.W.:The diffraction of a cylindrical surface wave structure. by surface discontinuities',Ph.D.Thesis,University College London, 1965 8 HOCKHAM,G.:'Surface wave propagation on varying reactive 7 Conclusions cylindrical structures',Ph.D.Thesis,1969,University of London 9 JONES,A.L.:'Coupling of optical fibres and scattering in fibres',J. Theoretical and experimental studies indicate that a fibre 0pt.Soc.Amer,1965,55,p.261 of glassy material constructed in a cladded structure with a 10 SAVARD,J.Y.:'An investigation of higher order surface waves on core diameter of about 100 o represents a possible practi- cylindrical structures',Ph.D.Thesis,University College,London,1961 11 BARLOW,H.E.M.,and KARBOWIAK,A.E.:'An experimental cal optical waveguide with important potential as a new investigation of the properties of corrugated cylindrical surface wave- form of communication medium.The refractive index of guides',Proc.IEE,1954,101,Pt.III,p.182 198 IEE PROCEEDINGS,Vol.133,Pt.J,No.3,JUNE 1986

for the second fibre; by offsetting the second fibre, different mode 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-mode structure. 7 Conclusions Theoretical and experimental studies indicate that a fibre of glassy material constructed in a cladded structure with a core diameter of about 100 XQ represents a possible practi- cal optical waveguide with important potential as a new form of communication medium. The refractive index of the core needs to be about 1% higher than that of the cladding. This form of waveguide operates in a single HE^ , Eo or Ho mode and has an information capacity in excess of 1 GHz. It is completely flexible and calls for a mechanical tolerance of around 10%, which can be readily met in practice. Thus, compared with existing coaxial￾cable and radio systems, this form of waveguide has a larger information capacity and possible advantages in basic material cost. The realisation of a successful fibre waveguide depends, at present, on the availability of suit￾able low-loss dielectric material. The crucial material problem appears to be one which is difficult but not impossible. Certainly, the required loss figure of around 20 dB/km is much higher than the lower limit of loss figure imposed by fundamental mechanisms. 8 Acknowledgment The authors wish to acknowledge the contribution of Mr. R.W. Lomax in carrying out the fibre-mode experiment and dielectric-loss measurements, and to thank Standard Telecommunication Laboratories Ltd. for permission to publish the paper. 9 References 1 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. 1206 3 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 cylindrical surface wave', Ph.D. Thesis, University College London, 1963 7 BREITHAUPT, R.W.: 'The diffraction of a cylindrical surface wave by surface discontinuities', Ph.D. Thesis, University College London, 1965 8 HOCKHAM, G.: 'Surface wave propagation on varying reactive cylindrical 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 on cylindrical structures', Ph.D. Thesis, University College, London, 1961 11 BARLOW, H.E.M., and KARBOWIAK, A.E.: 'An experimental investigation of the properties of corrugated cylindrical surface wave￾guides', Proc. IEE, 1954, 101, Pt. Ill, p. 182 198 IEE PROCEEDINGS, Vol. 133, Pt. J, No. 3, JUNE 1986