WAVEGUIDE STAR COUPLER USING MULTIMODE INTERFERENCE

Abstract: A radiation coupling device (10) incorporates a rectangular multimode beamsplitter waveguide (20) connected at one end to a set of input waveguides (18). The input waveguides (18) have inserted within them respective fibre optic waveguides (22). The input waveguides (18) are connected at periodic positions across the beamsplitter waveguide's transverse cross section. The beamsplitter waveguide (20) is also connected at its other end to retroreflecting mirror (24). Radiation propagating in fundamental mode in any one of the input waveguides (18) passes along the beamsplitter waveguide (20) and is retroreflected at the mirror (24). On return, it becomes divided between the input waveguides (18) by virtue of modal dispersion (multimode interference) in the beamsplitter waveguide (20). The device (10) therefore acts as a star coupler.

Description: WAVEGUIDE STAR COUPLER USING MULTIMODE INTERFERENCE This invention relates to a radiation coupling device for coupling a single input to a plurality of outputs. The present invention provides a radiation coupling device incorporating a lrtulti ode waveguide, and wherein: (1 ) a plurality of subsidiary waveguides arranged for fundamental mode operation are connected to the multimode waveguide, (2) reflecting means are arranged to return to the subsidiary waveguides radiation received by the multimode waveguide therefrom, and (3) the relative dimensions and positioning of the subsidiary and multimode waveguides and the reflecting means are arranged to provide for input radiation propagating as a fundamental mode of any one of the subsidiary waveguides to undergo modal dispersion within the multimode waveguide and thereafter to excite the fundamental mode of each of the subsidiary waveguides after return from the reflecting means. The invention provides the advantage that it lends itself to construction in compact form with relatively efficient radiation intensity coupling. It may be implemented in differing waveguide media, such as hollow waveguides suitable for coupling to fibre optics and solid waveguides suitable for optical micro-circuitry. In a preferred embodiment of the invention, the subsidiary waveguides are of square cross-section, the multimode waveguide is of rectangular cross- section, the reflecting means is retroreflecting, the subsidiary waveguides are ported centrally to respective like subdivisions of the multimode waveguide's transverse cross-section, and the path length of radiation within the multimode waveguide is 8b^/λK, where K is the number of subsidiary waveguides, b is half the transverse width of the multimode waveguide and λ is the radiation wavelength within the multimode waveguide. The subsidiary waveguides may be arranged for connection to respective fibre optic waveguides. The subsidiary and multimode waveguides may be hollow cored with alumina ceramic waveguide walls. The subsidiary and multimode waveguides may alternatively be ridge waveguides of semiconductor material. In order that the invention might be more fully understood, embodiments thereof will now be described, by way of example only, with reference to the accompanying drawings, in which:- Figure 1 is a schematic sectional plan view of a coupling device of the invention; Figures 2 and 3 are sectional side views on lines II-II and III-III respectively in Figure 1 ; Figure 4 illustrates transverse electric field intensity distributions at a number of longitudinal positions in a multimode rectangular waveguide; Figure 5 illustrates the variation of radiation power coupling to waveguide modes as a function of the aspect ratio of a multimode rectangular waveguide; Figure 6 provides perspective views of waveguide modes; Figure 7 illustrates the variation in modal amplitudes in a multimode rectangular waveguide as a function of input waveguide displacement from a coaxial location; and Figures 8, 9 and 10 are schematic sectional views of a further device of the invention. Referring to Figure 1, there is. shown in a plan a central horizontal section of a radiation coupling device of the invention indicated generally by 10. Vertical sections on lines II-II and III-III in Figure 1 are shown in Figures 2 and 3 respectively. The coupling device 10 is formed from three parallel-surfaced sheets of alumina ceramic material, these being a base sheet 12, a central sheet 14 and a cover sheet 16 indicated between chain lines in Figures 2 and 3. The central sheet 14 is slotted by milling through its thickness, which defines four input waveguides 18a to 18d and a beamsplitter waveguide 20. The input waveguides will be referred to collectively as 18. The waveguides 18 and 20 have side walls (not shown) defined by flat surfaces formed in the milling of the central sheet 1 . They have upper and lower walls (not shown) provided respectively by a lower surface 16' of the cover sheet 16 and an upper surface 12' of the base sheet 12. The beamsplitter waveguide 20 is of rectangular cross-section, being of length , width 2b and height 2a as indicated by scales 30. Here L, a and b are parameters which may vary between different embodiments of the invention. In the device 10, b = 8a. The input waveguides 18 are of square section with side 2a. The length L of the beamsplitter waveguide 20 is given by:- L = 2nb 2 /λ Q . (1 ) where λ 0 is a free-space operating wavelength of the device 10 and n is the refractive index of the medium within the beamsplitter waveguide 20. Since the waveguide 20 is hollow and air filled, n = 1. The input waveguides 18a to 18d have inserted within them respective fibre optic waveguides 22a to 22d referred to collectively as 22. The beamspliιr._r waveguide 20 is connected to a retroreflecting mirror 24. The beamsplitter waveguide 20 has a central longitudinal axis indicated by a dotted line 26. The input waveguides 18a to 18d have respective, central longitudinal axes 28a to 28d parallel to and coplanar with the beamsplitter waveguide axis 26. The axes 28a to 28d are referred to collectively as 28. They are located centrally of respective quarters of the transverse cross-section of the beamsplitter waveguide 20, as indicated by an uppermost scale 30 in Figure 1. The uppermost scale 30 is calibrated for the width (2b) of the beamsplitter waveguide 20. It has a zero position on the beamsplitter waveguide axis 26. Scale positions -3b/4, -b/4, +b/4 and +3b/4 locate the input waveguide axes 28a to 28d respectively. These positions are located centrally of beamsplitter waveguide quarters; these quarters are defined by scale intervals -b to -b/2, -b/2 to 0, 0 to +b/2 and +b/2 to +b respectively of which -b/2 and +b/2 are not shown. The axes 28 are therefore located periodically (in the spatial sense) across the transverse cross-section of the beamsplitter waveguide 20. The input waveguides 18a to 18d have respective entrance and exit apertures (not referenced) located in planes orthogonal to the axis 26. For the purposes of analysis of the operation of the device 10, y and z Cartesian co-ordinate axes are shown at 32. The z axis is the device's longitudinal axis 26. The x and y axes are transverse vertical and transverse horizontal respectively; of these, the x axis is not shown at 32 as it is perpendicular to the plane of the drawing. The scale 32 indicates the horizontal yz plane of the Figure 1 section; x = 0 and y = 0 are on the z axis; z = 0 is a transverse vertical plane perpendicular to the plane of Figure 1 indicated by a chain line 34 located where the input waveguides 18 merge with the beamsplitter waveguide 20. Figure 4 provides graphs of transverse electric field intensity distributions calculated for a reference waveguide (not shown) . This waveguide is 8L in length, eight times that of the beamsplitter waveguide 20, but it has the same transverse cross-section as the latter. Each intensity distribution shows intensity I as a function of transverse horizontal position y across the reference waveguide, and x = 0. This is indicated by axes 70. Each distribution s plotted at a respective z value; The latter are spaced at intervals of 2 along the reference waveguide. At z = 0, as shown on a longitudinal scale 72, an intensity distribution curve 74 indicates initial conditions at one end of the reference waveguide. The curve 74 has a maximum 74a centred at y = -3b/4 as shown on a transverse scale 76. The maximum 74a is equivalent to radiation propagating as a fundamental mode (a half-cycle of a sine wave) of one of the input waveguides 18, and is located at a position corresponding to that of the input waveguide 18a. Other than in the region of maximum 74a, the curve 74 is zero. The maximum 74a is of constant optical phase. It is treated as an input excitation of the reference waveguide. The former produces multimode excitation of the latter. As will be described later in more detail, the reference waveguide modes which are excited have different propagation constants in the longitudinal z direction. In consequence, their phase relationships with respect to one another vary with z. The in-phase input maximum 74a is decomposed into a linear combination of the modes of the reference waveguide at z=0, and these modes produce varying intensity distributions as z increases indicating changes in their mutual interference. The in-phase input maximum 74a at z=0 changes at x=2L to a distribution 78. The latter has four maxima 78a and 78d not all of like phase, and which are centered on positions corresponding the input waveguide axes 28a to 28d respectively; ie their centres are at y= -3b/4, -b/4, +b/4 and +3b/4 respectively. Between adjacent pairs of maxima, such as 78a and 78b, the curve 78 goes to zero. The phases of maxima 78a to 78d are ~n /A , re, 0, "π /4 respectively. At z = 4L, the transverse intensity distribution is shown by a curve 80 having two maxima 80a and 80b centered at y value -3b/4 and +3b/4. The maxima 80a and 80b are not of like phase. At z = 6 , the distribution is shown by a curve 82 having four maxima 82a to 82d. Between adjacent maxima on the curve 82, the intensity is zero. The maxima 82a to 82d are located in the y dimension exactly as maxima 78a to 78d respectively. The radiation phase variations along the curves 78 and 82 differ however. In consequence, the intensity distribution represented by the curve 82 gives rise to a single maximum intensity distribution represented by the curve 84 at z = 8L. This compares with the change from four to two maxima between curves 78 and 80 over a like change in z, and is due to differing phase conditions. The single maximum 84a of the curve 84 is centred at y = +3b/4 as shown on a scale 86. Elsewhere the curve 84 is zero. - It is equivalent to a reflection of the curve 74 in the xz plane at y=0 It can also be shown that an individual intensity maximum (not shown) at any one of the other input waveguide axis positions y = +3b/4, +b/4 and -b/4 gives rise to four intensity maxima 78a to 78d at a distance 2L along a reference waveguide as described earlier. Referring now also to Figure 1 once more, radiation is input from a coherent source (not shown) along one of the fibre optic waveguides 22a to 22d, from which the radiation passes to a respective one of the input waveguides 18a to 18d associated therewith. The radiation is arranged to excite the fundamental mode of the chosen input waveguide. The input waveguides 18 may be designed to support only the fundamental mode of radiation propagation. Alternatively, the input waveguides 18 may be capable of supporting higher order modes of radiation propagation, in which case the input radiation is arranged to excite only the fundamental mode. Radiation propagates along the chosen input waveguide (eg 18a) until it reaches the beamsplitter waveguide 20. This gives rise to a constant phase, half-cycle sine wave intensity maximum in the plane 34 at one end of the beamsplitter waveguide 20. This maximum is centered on one of the axes 28. Radiation propagates from the plane 34 along the beamsplitter waveguide 20 to the mirror 24, and is retroreflected. The radiation therefore returns to the input waveguides 18 having executed a double transit (2L) of the beamsplitter waveguide 20. This radiation consequently becomes divided into four maxima by the optical path of twice the length of the beamsplitter waveguide 20, as described with reference to Figure 3. The beamsplitter waveguide 20 and mirror 24 consequently image the radiation fundamental mode at the aperture of any one of the input waveguides on to the apertures of all four input waveguides. Here the apertures referred to are in the plane 34 where the input and beamsplitter waveguides 18 and 20 merge together, ie where the input waveguides 18 are connected or ported to the beamsplitter waveguide 20. All four input waveguides 18 therefore receive retroreflected radiation, and couple it to respective fibre optic waveguides 22. In consequence, each of the fibre optic waveguides 22 receives input of radiation corresponding to a respective one of the maxima 78a to 78d. This shows that input radiation to any one of the fibre optic waveguides 22 is returned to all four of these waveguides. The device 10 therefore acts as a star coupler. Because of its alumina construction, the device 10 is suitable for use with C0 2 laser radiation for which λ Q is 10.59 microns. Suitable waveguide size parameters are 2b = 3mm and 2a = 0.375mm (since b = 8a). The device 10 is hollow, and therefore n = 1 in Equation (1). The latter may therefore be written:- L = 2b 2 /λ Q . (2) For 2b = 3 mm and λ Q = 10.59 microns:- = 1.5 x 3/1.059 x 10 -2 mm (3) The length of the beamsplitter waveguide 20 is therefore 425 mm. It should be noted that the lengths of the input and fibre optic waveguides 18 and 22 do not affect the operation.of the device 10 to any appreciable extent (ignoring imperfections). The theoretical propagation characteristics of a rectangular waveguide (such as the beamsplitter waveguide 20) will now be analysed. It is assumed that this waveguide has height 2a, width 2b and is bounded by walls of a homogeneous dielectric material with complex dielectric constant ε. It is also assumed that these walls are highly reflecting, and do not attenuate propagating waveguide modes significantly. The waveguide has height, width and length dimensions which are parallel to the x, y and z axes respectively. It has normalized linearly polarised modes of the kind EH^. The electric field contribution E^ (x, y, z) of the mnth mode EH^ at the point (x, y, z) has been calculated by Laakmann et al in Appl. Opt. Vol. 15, No 5, pages 1334-1340, May 1976 as follows: where m is the mode number relating to the field dependency along the x axis, n is the mode number relating to the field dependency along the y axis, z is the distance along the z axis, Yum = (β mn + iO jj in) ' tne Propagation constant of the mn th mode, 3-^ and α^. being the mn*-" mode's phase and attenuation coefficients, and "cos" above "sin" indicates the former applies to odd mode numbers (m or n as appropriate) and the latter to even mode numbers. The phase coefficient β mn is given by If the negative term in parenthesis in equation (6.1) is small compared with unity, (paraxial radiation approximation), which is satisfied in practice, then the binomial theorem may be used to rewrite Equation (6.1) as:- 2rt 1 1/ λm \2 J mn X 1 - 1 Ul ( ) 2 }] (6.2) where a, b, m and n are as previously defined, and λ is the wavelength of the radiation propagating in the waveguide. Equation (5) sets out the electric field contributions obtainable from all linearly polarised modes of a rectangular waveguide. It is calculated on the basis that the electric field contribution of each mode is zero at the side walls of the waveguide, ie at y = +b and -b (y = 0 being on the axis 26). This is satisfied for a beamsplitter waveguide 20 with reflecting walls. Not all rectangular waveguide modes are necessarily excited by a given input. In the case of the device 10, the heights of the waveguides 18 and 20 are matched and equal to 2a. Any input square section waveguide 18 which is selected to provide input supplies an excitation in the form of its fundamental or lowest order mode EHi1 . This is coupled to the various EHmn modes of the rectangular section beamsplitter waveguide 20. The input EH-|f mode consequently becomes decomposed into a linear combination of the EHmn modes with respective complex multiplicative coefficients Aπm- This is expressed by:- EH11 =∑A,mn .EHmn (7) Essentially the A mn amplitude coupling coefficients are the coefficients of a Fourier series which represents the electric field at an input aperture where the relevant input waveguide 18 merges into the beamsplitter waveguide 20. The EHmT , modes are mutually orthogonal, and in consequence the coefficients A mn can be calculated from overlap integrals of the form: +b +a Amn = f J EHn . EH mn . dy.dx (8) From Equations (5) to (8) it is possible to calculate how the amplitude + coefficients of the excited rectangular waveguide modes vary as a function of b/a. The ratio b/a is that of the widths of the central and input waveguides. Figure 5 illustrates the variation of lAmnl 2 with b/a. This shows the effect on power coupling of varying the beamsplitter waveguide width to height ratio. For convenience, Figure 5 illustrates modal power coupling to the beamsplitter waveguide 20 which would occur from an input waveguide located coaxially about the device axis 26. Figure 5 indicates that A n = 0 except when m = 1 and n is odd. This is because of the axially symmetric nature of the excitation conditions. Consequently, the modes excited are only the symmetric modes EH11, EH13, EH15 etc. Because of waveguide height matching, under these excitation conditions modes for which m>1 are not excited. The forms of some of the lower order EH^ waveguide modes are shown as electric field amplitude distributions in Figure 6. These were obtained by computation, and are shown as graphs A to F in quasi-two dimensional form. For convenience, the co-ordinate axes shown at G are rotated with respect to the axes 32 in Figure 1. The axes x and y correspond to transverse vertical and transverse horizontal directions in the beamsplitter waveguide 20 as before. The graphs A to F correspond to modes as follows:- A : EHτι ; B : EH 2 1 ; C : EH 31 ; D : EH 12 ; E : EH 13 ; F : EH 22 . Of these, A, C and E are symmetric modes and B, D and F are antisymmetric modes. To clarify this, let E(x) and E(-x) be respectively the electrical field amplitude distributions on positive and negative parts respectively of the x axis in Figure 1; E(x=0) is on the z axis .26. Let E(y) and E(-y) be the equivalents for the y axis. For a symmetric mode:- E(x) = E(-x) and E(y) = E(-y) (9.1) For an antisymmetric mode, either one of or both of (9.2) and 9.3) below apply:- E(x) = -E(-x) (9.2) E(y) = -E(-y) (9.3) As illustrated in Figure 5, with coaxial excitation of the beamsplitter waveguide 20, and when b/a = 3, only the modes EH-j 1 , EH13, EH15 and EH17 are excited. These modes have approximate relative powers 0.52, 0.33, 0.13 and 0.2 respectively. When b/a = 6, the modes EH^ to EH1 13 are excited with respective relative powers from 0.27 to 0.02. The fact that the axes 28 of the input waveguides 18 are displaced from the z axis 26 produces mode excitation effects shown in Figure 7. This drawing provides the relative amplitudes A^ of the waveguide modes EH^ for m = 1 and n - 1, 2, 3 and 4. At zero offset, ie for coincident input and beamsplitter waveguide axes, the antisymmetric modes EHι and EH1 have zero amplitude. In contrast, at zero offset, the symmetric modes EH^ and EH- | 3 have amplitudes greater than 0.5. As the offset increases, H^ and EH^ 3 reduce in amplitude and EH 1 and EH14 increase. There is a maximum in EH^ 2 at an offset of b/2. There are positive and negative maxima in EH14 at offsets of b/4 and 3b/4. This demonstrates that relative modal amplitudes vary with degree of offset of an input waveguide axis from the beamsplitter waveguide axis 26. However, as outlined earlier, it can be shown that an input waveguide 18 connected at a periodic position with respect to the beamsplitter waveguide's transverse (y) dimension produces a number of periodically located maxima after some propagation distance. In Figure 1, the waveguides 18 have axes 28 located centrally of respective quarters of the beamsplitter waveguide 20. Each input waveguide is capable of producing four maxima 78a to 78d. More generally for a beamsplitter waveguide notionally divided longitudinally into N equal subdivisions, an input waveguide coaxial with the centre of such a subdivision and offset from the axis 38 would produce N periodically spaced maxima distant 8L/N along a reference waveguide as described in relation to Figure 3. In consequence, the device 10 may be adapted for any number of inputs. Where they merge into the beamsplitter waveguide, these inputs must have waveguide axes or centres at spatially periodic locations offset from the beamsplitter waveguide axis. The location periodicity or corresponding notional number of subdivisions N sets the required length of the beamsplitter waveguide, which is 4L/N. The invention offers the advantage that for coupling devices requiring a relatively low degree of splitting, ie a low value of N, the number of modes that the beamsplitter waveguide 20 must support is small. For instance the electric field distribution illustrated in Figure 4 may be substantially fully described using the seven lowest order modes, that is EHiι to EH17. Therefore a device, such as the device 10, with N=4 and a waveguide width to height ratio, a -~ 8, need only support the seven lowest order modes. In general the modes required are in the region of the 2N lowest order modes. Whereas the invention has been described in terms of hollow waveguides, solid semiconductor material waveguides may also be employed. For example, Nd-YAG laser radiation is suitable for use with ridge waveguides of the ternary semiconductor material system Al χ Gaι_ χ As. Metal microwave waveguides may also be used. Referring now to Figures 8, 9 and 10, there is shown a further embodiment of the invention in the form of a radiation coupling device indicated generally by 100. Figure 9 is a horizontal section of the device 100, and Figures 8 and 10 are vertical sections on lines VIII-VIII and X-X respectively. The device 100 is equivalent to that described earlier, except that it is implemented as a ridge waveguide structure suitable for construction by semiconductor lithography techniques. Description of the device 100 will be restricted to aspects where it differs from the device 10. The device 100 comprises a GaAs substrate 112 surmounted by a multilayer waveguide structure 114 shown as a single layer for convenience. The structure 114 incorporates a plurality of semiconductor layers (not shown) of the Al χ Ga^_ χ As system. It is configured to form four input waveguides 118a to 118d and a beamsplitter waveguide 120. The input waveguides are of square cross-section with side 2a, and the beamsplitter waveguide is of length L, width 2b and height 2a. The length L obeys Equation (1), in which the refractive index n is equal to the value in an Al χ Gaι_ χ As waveguide core layer of appropriate value of x. The free space wavelength λ Q of operation may be that of an Nd-YAG laser, ie 1.06μm. The device 100 incorporates a retroreflecting end mirror 124 connected to the beamsplitter waveguide 120. The device 100 operates as described earlier, except that the input waveguides 118a to 118d do not communicate with fibre optic waveguides. Instead it is envisaged that they would extend directly to other parts of an integrated optic circuit (not shown) . The foregoing description with reference to Figures 1 to 10 demonstrates that radiation coupling is achievable to locations in the width dimension of a rectangular waveguide. For example, in Figure 4 the maxima 74a and 84a are laterally displaced relative to one another parallel to the y axis across the waveguide width. If a beamsplitter waveguide is constructed with height sufficiently greater than 2a, then it will have a multimode structure in the x dimension in addition to that in the y dimension previously described. In particular, a square cross-section beamsplitter waveguide of height and width 2b = 4a and length L will convert an input waveguide fundamental EH-JI mode at y equal to -3b/4 into sixteen fundamental mode maxima after reflection back to the input. These maxima will be arranged in a four by four square array. In this instance, two dimensional waveguide modes EH^ (m, n = 1, 3, 5...) are excited instead of only the one dimensional equivalents (m = 1, n = 1, 3, 5...) of Figures 1 to 10. Consideration of two versions of Figure 4 at right angles to one another indicates that more complex coupling is possible in two dimensions with appropriate beamsplitter waveguide geometry and location of inputs. The foregoing remarks regarding square waveguides may be extended to rectangular waveguides. Beam division into K intensity maxima in a reference waveguide with appropriately located off-centre input and width dimension of width 2b occurs at a distance L κ given by:- L κ = 16b 2 /λK (10) where λ is the radiation wavelength within the reference waveguide. For a reference waveguide with an orthogonal width dimension of width 2a, division into J intensity maxima occurs at a length j given by:- L j = 16a 2 /λJ (11) If simultaneous division into J and K intensity maxima is required in mutually orthogonal transverse dimensions of the same length of waveguide, the waveguide cross-section dimensions b/a will be given by equating L j and L κ and taking the square root as follows: b/a = - (K/J) (12) In consequence beam division into a nine by four array of intensity maxima will occur in a rectangular reference waveguide with b equal to 3a/2 at a distance of 4a /λ. To construct a two-dimensional star coupling device of the invention incorporating a retroreflecting mirror, the required length of beamsplitter waveguide is one half of the reference wavelength length of L κ or j as defined above.

Claims: CLAIMS 1. A radiation coupling device incorporating a multimode waveguide, and wherei :- (1 ) a plurality of subsidiary waveguides arranged for fundamental mode operation are connected to the multimode waveguide, (2) reflecting means are arranged to return to the subsidiary waveguides radiation received by the multimode waveguide therefrom, and (3) the relative dimensions and positioning of the subsidiary and multimode waveguides and the reflecting means are arranged to provide for input radiation propagating as a fundamental mode of any one of the subsidiary waveguides to undergo modal dispersion within the multimode waveguide and thereafter to excite the fundamental mode of each of the subsidiary waveguides after return from the reflecting means. 2. A device according to Claim 1 wherein the subsidiary waveguides are of square cross-section, the multimode waveguide is of rectangular cross- section, the reflecting means is retroreflecting, the subsidiary waveguides are ported centrally to respective like subdivisions of the multimode waveguide's transverse cross-section, and the path length of radiation within the multimode waveguide is 8b /λK, where K is the number of subsidiary waveguides, b is half the transverse width of the multimode waveguide and λ is the radiation wavelength within the multimode waveguide. 3. A device according to Claim 1 or 2 arranged for connection of the subsidiary waveguides to respective fibre optic waveguides. 4. A device according to Claim 1, 2, or 3 wherein the subsidiary and multimode waveguides are hollow cored. 5. A device according to Claim 4 having alumina ceramic waveguide walls. ' 6. A device according to Claim 1 or 2 wherein the subsidiary and multimode waveguides are ridge waveguides of semiconductor material.

Inventors: JENKINS RICHARD MICHAEL, JENKINS, RICHARD, MICHAEL
Applicants: JENKINS RICHARD MICHAEL, SECR DEFENCE BRIT, THE SECRETARY OF STATE FOR DEFENCE IN HER BRITANNI
Application year: 1993
Main classification: G02B6
IPC codes: G02B6