《光波导理论与技术 Optical Waveguides Principles and Technologies》课程教学资源（参考文献）Integrated Optics An Introduction

THE BELL SYSTEM TECHNICAL JOURNAL DEVOTED TO THE SCIENTIFIC AND ENGINEERING ASPECTS OF ELECTRICAL COMMUNICATION Volume 48 September 1969 Number 7 Copyright 1969,American Telephone and Telegraph Company Integrated Optics:An Introduction By STEWART E.MILLER (Manuscript received January 29,1969) This paper oullines a proposal for a miniature form of laser beam circuitry.Index of refraction changes of the order of 10-or 10-in a substrate such as glass allow guided laser beams of width near 10 microns. Photolithographic technigues may permit simultaneous construction of complex circuit patterns.This paper also indicates possible miniature forms for a laser,modulator,and hybrids.If realized,this new art would facilitate isolating the laser circuit assembly from thermal,mechanical,and acoustic ambient changes through small overall size;economy should ultimately result. I.INTRODUCTION Laboratory work and experimental repeater work at laser wave- lengths (0.4 to 10 +um)has been carried out by interconnecting the oscillators,modulators,detectors,and so on,using a form of extremely short-range radio.A freely propagating beam has been reflected around corners,occasionally refocused with lenses to avoid energy loss resulting from beam spreading,and often sheltered by tubular enclosures from refractive distortions resulting from ther- mal gradients in the ambient air.Typical separations between com- ponents range from a few centimeters to a foot;aggregations of ap- paratus in a single-channel experimental laser repeater are measured 2059

T H E BELL SYSTE M TECHNICA L JOURNA L DEVOTED TO THE SCIENTIFIC AND ENGINEERING ASPECTS OF ELECTRICAL COMMUNICATION Volume 48 Septembe r 1969 Numbe r 7 Copyright ® 1969, Amtrican Telephone and Telegraph Company Integrated Optics: An Introduction By STEWART E. MILLER (Manuecript received January 29, 1969) This paper outlines a proposal jor a mintcUure form of laser beam circuitry. Index of refraction changes of the order of 10" ' or 10"* in a substrate such as glass allow guided laser beam^ of width near 10 miarons. Photolitíwgraphic techniques may permit simultaneous construction of complex circuit patterns. This paper also indicates possible miniature forms for a laser, modulator, and hybrids. If realized, this new art vmdd facuitóte isolating the laser circuit assembly from thermal, mechanical, and acoustic ambient changes through small overall size; economy should ultimately result. I. INTRODUCTION Laboratory work and experimental repeater work at laser wave￾lengths (0.4 to 10 + μχη) has been carried out by interconnecting the oscillators, modulators, detectors, and so on, using a form of extremely short-range radio. A freely propagating beam has been reflected around comers, occasionally refocused with lenses to avoid energy loss resulting from beam spreading, and often sheltered by tubular enclosures from refractive distortions resulting from ther￾mal gradiente in the ambient air. Typical separations between com￾ponents range from a few centimeters to a foot; aggregations of ap ­ paratus in a single-channel experimental laser repeater are measured 2069

2080 THE BELL SYSTEM TECHNICAL JOURNAL,SEPTEMBER 1969 in square feet.The resulting apparatus is sensitive to ambient temper- ature gradients,to absolute temperature changes,to airborne acousti- cal effects,and to mechanical vibrations of the separately mounted parts.All of these effects are understood and are susceptible to ap- propriate engineering design;but one naturally looks for alternatives. Looking ahead,one sees the possibility of guiding laser beams on miniature transmission lines,analogous to the hollow rectangular waveguide or coaxial cable used extensively in lower frequency re- peaters.Accompanying papers report contributions leading toward the new form of laser circuitry.1-s This paper gives a general view of the proposal and indicates specific component possibilities. II.LASER BEAM GUIDANCE We visualize a dielectric waveguide wherein a region having an index of refraction na is surrounded by a region of index n,as in Fig.1a. Then a two-dimensional analysis shows that the energy in the lowest- order guided wave is confined almost entirely to the n2 region if 1=n(1-△)， (1) where (2) A=free space wavelength a half-width of na region,(A/ana)<1. Table I,calculated from equations (1)and (2)for A 0.6328 um, shows that only a very small change in index Ana is needed to provide the desired guidance.Some higher order modes are above cutoff using these parameters;more exact theory can be used to calculate the smaller guide width which restricts the guidance to a single mode at (a) (b) Fig.1-Waveguide cross sections:(a)rectangular shape,index na n,(b) round shape

2060 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER Ιθβθ (2) λ = free space wavelength a = half-width of n , region, (λ/αη^) « 1. Table I, calculated from equations (1) and (2) for λ = 0.6328 μχα, shows tha t only a very small change in index Δη^ is needed to provide the desired guidance. Some higher order modes are above cutoff using these parameters; more exact theory can be used to calculate the smaller guide width which restricts the guidance to a single mode a t Fig. 1 —Waveguid e cross sections: (a) rectangular shape, index m > ni , (b) round shape . in square feet. The resulting apparatus is sensitive to ambient temper￾ature gradients, to absolute temperature changes, to airborne acousti￾cal effects, and to mechanical vibrations of the separately mounted parts. All of these effects are understood and are susceptible to ap￾propriate engineering design; but one naturally looks for alternatives. Looking ahead, one sees the possibility of guiding laser beams on miniature transmission lines, analogous to the hollow rectangular waveguide or coaxial cable used extensively in lower frequency re￾peaters. Accompanying papers report contributions leading toward the new form of laser circuitryThi s paper gives a general view of the proposal and indicates specific component possibilities. Π. LASER BEAM GUIDANCE We visualize a dielectric waveguide wherein a region having an index of refraction is surrounded by a region of index τ^, as in Fig. la . Then a two-dimensional analysis shows tha t the energy in the lowest￾order guided wave is confined almost entirely to the region if n, = n,(l - Δ), (1) where

INTEGRATED OPTICS 2061 TABLE I-VALUES OF A FOR VARIOUS OPTICAL BEAM WIDTHS Optical Beam Width 2a A 1 mm 104 0.1mm 10 0.01mm 104 the expense of having a larger field component at the nz to n interface where dimensional irregularities may occur.Values of A larger than tabulated for a particular guide width 2a do not appreciably change the field distribution for the lowest order mode in the n region but would allow more propagating modes. It is not important that there be a sharp step in index as in the na to n transition of Fig.1a.Alternatively,the index can taper smoothly from a maximum at the waveguide's center to a lower value at radius r according to* n nall -c(r/a)"] (3) with c=0.16 a 2a laser beam width,provided a >A. (4) The exponent p can have any even positive value;the lowest order mode field always has an approximately cosinusoidal shape in the region 0<r<a with about 1/10 peak value at ra and with approximately exponentially decaying magnitude for r a. The square law index variation,given by p =2 in equation (3), has the well-known property that phase constant differences for the various propagating modes are independent of frequency..The square law medium is free of delay distortion resulting from mode conversion and is unique in that property.s. We can anticipate guiding beams around relatively sharp bends as summarized in Table II.The A's associated with these beam widths may be obtained from equation(2)or Table I.By using a guide which confines the beam to a 5 to 10m width (implies aA of 0.04 to 0.01) the bend radius can be in the 1.8 to 14.5 mm (70 to 570 mils)region, which could facilitate very small circuitry. *A somewhat more accurate expression is given as equation (59)in Ref.5. This permita a series of terms in(r/a)'to represent the index variation

INTEGRATED OPTICS 2061 Optical Beam Width 2a Δ I m m 10-· 0 . 1 m m lOr* 0.0 1 m m 10-« the expense of having a larger field component a t the to Πι interface where dimensional irregularities may occur.*'* Values of Δ larger than tabulated for a particular guide width 2a do not appreciably change the field distribution for the lowest order mode in the n-i region but would allow more propagating modes. It is not important tha t there be a sharp step in index as in the to Πι transition of Fig. la . Alternatively, the index can taper smoothly from a maximum a t the waveguide's center to a lower value a t radius r according to* η = n,[l - c(r/a)n (3) with c = o.ief-V 2a = laser beam width, provided o » λ. (4) The exponent ρ can have any even positive value; the lowest order mode field always has an approximately cosinusoidal shape in the region 0 < r < o with about 1/10 peak value a t r ^ o and with approximately exponentially decaying magnitude for r > a. The square law index variation, given by ρ = 2 in equation (3), has the well-known property tha t phase constant differences for the various propagating modes are independent of frequency.*-' The square law medium is free of delay distortion resulting from mode conversion and is unique in tha t property."-* We can anticipate guiding beams around relatively sharp bends as summarized in Table II. The Δ's associated with these beam widths may be obtained from equation (2) or Table I. By using a guide which confines the beam to a 5 to lO^m width (implies a Δ of 0.04 to 0.01) the bend radius can be in the 1.8 to 14.5 mm (70 to 570 mils) region, which could facilitate very small circuitry. * A somewhat more accurate expression is given as equation (50) in Ref. 5. This permits a series of terms in (r/a)' to represent the index variation. TABLE I—VALUES OF Δ FOR VARIOUS OPTICAL BEAM WIDTHS

2062 THE BELL SYSTEM TECHNICAL JOURNAL,BEPTEMBER 1969 TABLE II-ESTIMATED BENDING RADIUS Laser Beam Eatimated Acoeptable Width Bending Radius in m◆ 2a in mm a0.6334m) 14,500 0.1 14.5 0.01 0.0145 0.005 0.0018 .This estimate is obtained using equation(33)of Ref.9,and includes an allowance of 025 dB maximum loss resulting from a bend of any angle. III.FABRICATION OF SMALL WAVEGUIDES Tiny laser guides can be fabricated in the form of glass fibers. Previous work on fiber-optics for image transmission or incoherent light sensing has provided a considerable body of experience on which to build,not all of which is applicable.So-called "clad"fibers have two discrete regions of index as in Fig.1a.The n region (which car- ries little light)must be as thin as possible in image-transmitting fibers to minimize the"dead"region in the output image.For modulated laser beam transmission the cladding must be much thicker and the "core" (na of Fig.1a)much smaller to yield well-isolated single mode trans- mission. Whereas glass fibers may be used to connect repeater components and certainly are convenient as fexible connections,we can use an- other form of dielectric waveguide for miniature laser circuitry.Fig.2 n Fig.2-Planar waveguide formed using photolithographic techniques

2062 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1969 TABLE II—ESTIMATED BENDING RADIUS Loser Beam EsUmatsd Acceptabla Width Bending Radiiu in m* 2a in mm (λ - 0.633 μιη) 1 14,500 0 . 1 14. 5 0.0 1 0.014 5 0.00 5 0.001 8 * This estimat e is obtained using equation (33) of Ref. 9, and includes an allowance of 02 5 dB maximu m loss resulting from a bend of any angle. ΠΙ. FABRICATION OF SMALL WAVBGTnDBS Tiny laser guides can be fabricated in the form of glass fibers. Previous work on fiber-optics for image transmission or incoherent light sensing has provided a considerable body of experience on which to build, not all of which is applicable. So-called "clad" fibers have two discrete regions of index as in Fig. la . The region (which car￾ries little light) must be as thin as possible in image-transmitting fibers to minimize the "dead" region in the output image. For modulated laser beam transmission the cladding must be much thicker and the "core" (na of Fig. la ) much smaller to yield well-isolated single mode trans￾mission. Whereas glass fibers ma y be used to connect repeater components and certainly are convenient as flexible connections, we can use an￾other form of dielectric waveguide for miniature laser circuitry. Fig. 2 Fig. 2 — Planar waveguide formed using photolithographic techniques

INTEGRATED OPTICS 2063 shows a channel of index na surrounded by a region of index m,which would serve as a dielectric waveguide of the type discussed in con- nection with Fig.1.This might be created in glass using a series of steps as follows.A mask could be used to expose selectively a light- sensitive photo-resist previously placed on a sheet of glass,followed by washing and selective deposition (if needed)of a more durable material for masking purposes.Then a diffusion,bombardment,or ionic replacement process could be used to change the index of refrac- tion of the glass,thereby creating the na channel imbedded in the n substrate.Finally the top layer of n material could be sputtered on the entire top surface. Using photolithographic techniques which are currently evolving for low frequency integrated circuit applications,channel widths in the 2 to 5 um range may be achievable and dimensions on the order of 10 um are readily held.Complicated masking patterns may in time be made,leading to the possibility of simultaneously making complicated laser circuits using combinations of elements such as those described in the following paragraphs." This description is intended to be a broad indication of possible feasibility rather than a blueprint.However,relevant contributions are appearing.G.M.C.Fisher and A.D.Pearson have reported processes which reduce or increase the index of refraction of glass by as much as 0.7 per cent.10 F.K.Reinhart,D.F.Nelson,and J.McKenna have reported the existence of an index increase in gallium phosphide junctions which is effective as a light guide at zero bias.11-18 Optical waveguides formed by proton irradiation have been reported.Further contributions may be anticipated. Some relevant work on two-dimensional light guides has been re- ported.10-20 In this work one transverse dimension of the guided wave was in the 10 to 100 gm region;but the other transverse dimension was orders of magnitude larger.We seek waveguides tightly guided in both transverse dimensions in order to make possible the compo- nents proposed in Section IV. IV.INTEGRATED-CIRCUIT LASER The transmission line of Fig.2 becomes a resonator when mirrors are placed at the ends,or when a series of partially refecting trans- Complicated masking patterns are feasible now where the area involved is small;depth-of-focus problems may require advances in masking to produce the large area patterns we need

INTEGRATED OPTICS 2063 * Complicated masking patterns are feasible now where the area involved is small; depth-of-focus problems ma y require advance s in masking t o produce the large area patterns we need. shows a channel of index surrounded by a region of index iht which would serve as a dielectric waveguide of the type discussed in con￾nection with Fig. 1. This might be created in glass using a series of steps as follows. A mask could be used to expose selectively a light￾sensitive photo-resist previously placed on a sheet of glass, followed by washing and selective deposition (if needed) of a more durable material for masking purposes. Then a diffusion, bombardment, or ionic replacement process could be used to change the index of refrac￾tion of the glass, thereby creating the channel imbedded in the rh substrate. Finally the top layer of τΐχ material could be sputtered on the entire top surface. Using photolithographic techniques which are currently evolving for low frequency integrated circuit applications, channel widths in the 2 to 5 /tm range may be achievable and dimensions on the order of 10 μΐη are readily held. Complicated masking patterns may in time be made, leading to the possibility of simultaneously making complicated laser circuits using combinations of elements such as those described in the following paragraphs.* This description is intended to be a broad indication of possible feasibility rather than a blueprint. However, relevant contributions are appearing. G. M. C. Fisher and A. D . Pearson have reported processes which reduce or increase the index of refraction of glass by as much as 0.7 per cent.*" F . K. Reinhart, D . F . Nelson, and J. McKenna have reported the existence of an index increase in gallium phosphide junctions which is effective as a light guide at zero bias.**'*' Optical waveguides formed by proton irradiation have been reported.** Furthe r contributions ma y be anticipated.*' Some relevant work on two-dimensional light guides has been re￾ported.*"-'"' In this work one transverse dimension of the guided wave was in the 10 to 100 μχη region; but the other transverse dimension was orders of magnitude larger. We seek waveguides tightly guided in both transverse dimensions in order to make possible the compo￾nents proposed in Section IV. IV. INTBGRATED-CIBCUIT LASER The transmission line of Fig. 2 becomes a resonator when mirrors are placed a t the ends, or when a series of partially reflecting trans-