CA2319949A1 - Metal optical waveguide and modulator and switch incorporating same - Google Patents

Abstract

The purely bound electromagnetic modes of propagation supported by asymmetric waveguide structures comprised of a thin lossy metal film of fini te width on a dielectric substrate and covered by a different dielectric superstrate have been characterized at optical wavelengths. The dispersion of the modes with film thickness and width has been assessed and the effects caused by varying the difference between the superstrate and substrate dielectric constants on the characteristics of the modes have been determined. In general, the modes supported by these structures exhibit some characteristic s that are consistent with those observed for the modes supported by similar symmetric structures and asymmetric slab guides. Like symmetric structures, the higher order modes have a cutoff width below which they are no longer propagated, and some of the modes have a cut-off thickness. Unlike symmetric structures, all modes that have a decreasing attenuation with decreasing fil m thickness have a cutoff thickness. Under certain conditions, an asymmetric structure can support a long-ranging mode having a field distribution that i s suitable to excitation using an end-fire technique. Like asymmetric slab waveguides, the attenuation of the long-ranging mode near cutoff decreases very rapidly, much more so than the attenuation related to the long-ranging mode in a similar symmetric structure. The cutoff thickness of a long-rangin g mode in an asymmetric finite-width structure is larger than the cutoff thickness of the s b mode in a similar asymmetric slab waveguide. This implies that th e long-ranging mode supported by an asymmetric finite-width structure is more sensitive to the asymmetry in the structure compared to the s b mode support ed by a similar slab waveguide. This result is interesting and potentially usef ul in that the propagation of such a mode can be affected by a smaller change in t he dielectric constant of the substrate or superstrate compared with similar sl ab structures.

Description

METAL OPTICAL WAVEGUIDE AND MODULATOR AND SWITCH
INCORPORATING SAME
DESCRIPTION
TECHNICAL FIELD:
The invention relates to optical devices and is especially applicable to waveguide structures and integrated optics.
BACKGROUND ART:
This specification refers to several published articles. For convenience, the articles are cited in full in a numbered list at the end of the description and cited by that number in the specification itself. The contents of these articles are incorporated herein by reference and the reader is directed to them for reference.
In the context of this patent specification, the term "optical radiation"
embraces electromagnetic waves having wavelengths in the infrared, far infrared, visible and ultraviolet ranges.
The terms "finite" and "infinite" as used herein are used by persons skilled in this art to distinguish between waveguides having "finite" widths in which the actual width is significant to the performance of the waveguide and the physics governing its operation and so-called "infinite" waveguides where the width is so great that it has no significant effect upon the performance and physics or operation.
Interest in the modes supported by thin metal films has recently intensified due to their useful application in optical communications devices and components. Metal films are commonly employed in optical polarizing devices [1 1 ] while long-range surface plasmon-polaritons can be used for signal transmission [6].
At optical wavelengths, the electromagnetic properties of some metals (gold, silver and copper, for example) closely resemble those of an electron gas, or equivalently of a cold plasma. Numerous experiments as well as classical electron theory yield an equivalent negative dielectric constant for many metals when excited by an electromagnetic wave at or near optical wavelengths (1,2].
It is also well-known that the interface between semi-infinite materials having positive and negative dielectric constants can guide TM (Transverse Magnetic) surface waves. In the case of a metal-dielectric interface at optical wavelengths, these waves are termed plasmon-polariton modes and propagate as electromagnetic fields coupled to surface plasmons (surface plasma oscillations) which are comprised of conduction electrons in the metal [3].

2 Plasmon-polariton waves guided by a metal-dielectric interface are in general quite lossy. Even long-range surface plasmons guided by a metal film can be lossy by comparison with dielectric waveguides. Known devices exploit this high loss associated with surface plasmons for the construction of plasmon-polariton based modulators and switches. Generally, known plasmon-polariton based modulator and switch devices can be classified along two distinct architectures. The first architecture is based on the phenomenon of attenuated total reflection (ATR) and the second architecture is based on mode coupling between a dielectric waveguide and a nearby metal. Both architectures depend on the dissipation of optical power within an interacting metal structure.
ATR based devices depend on the coupling of an optical beam, which is incident upon a dielectric-metal structure placed in optical proximity, to a surface plasmon-polariton mode supported by the metal structure. At a specific angle of incidence, which depends on the materials used and the particular geometry of the device, coupling to a plasmon mode is maximised and a drop in the power reflected from the metal surface is observed. ATR based modulators make use of this attenuated reflection phenomenon along with means for varying electrically or otherwise at least one of the optical parameters of one of the dielectrics bounding the metal structure in order to shift the angle of incidence where maximum coupling to plasmons occurs.
Electrically shifting the angle of maximum coupling results in a modulation of the intensity of the reflected light. Examples of devices that are based on this architecture are disclosed in references (18] to [31].
Mode coupling devices are based on the optical coupling of light propagating in a dielectric waveguide to a nearby metal film placed a certain distance away and in parallel with the dielectric waveguide. The coupling coefficient between the optical mode propagating in the waveguide and the plasmon-polariton mode supported by the nearby metal film is adjusted via the materials selected and the geometrical parameters of the device. Means is provided for varying electrically or otherwise, at least one of the optical parameters of one of the dielectrics bounding the metal. Varying an optical parameter (the index of refraction, say) varies the coupling coefficient between the optical wave propagating in the dielectric waveguide and the lossy plasmon-polariton wave supported by the metal. This results in a modulation in the intensity of the light exiting the dielectric waveguide. References [32] to [35] disclose various device implementations based upon this phenomenon.

3 Reference [36] further discusses the physical phenomenon underlying the operation of these devices.
Reference [37] discusses an application of the ATR phenomenon for realising an optical switch or bistable device.
It is also known that a metal film of a certain thickness bounded by dielectrics above and below can serve as an optical slab waveguiding structure, with the core of the waveguide being the metal film (a slab waveguide is a planar, infinitely wide structure). When the film is thin enough, the plasmon-polariton modes guided by the interfaces become coupled due to field tunnelling through the metal, thus creating supermodes that exhibit dispersion with metal thickness. The modes supported by infinitely wide symmetric and asymmetric metal film structures are well-known; some notable disclosures relating to such modes include references [3] to [9]. Infinitely wide structures, however, are of limited practical interest since they offer one-dimensional field confinement only, with confinement provided along the vertical axis, perpendicular to the direction of wave propagation. This implies that optical fields spread out laterally as they propagate away from a point source used as the excitation.
Metal films of finite thickness and width however offer two-dimensional field confinement in the plane transverse to the direction of propagation.
Such structures may be useful for signal transmission and routing or to construct passive components such as couplers and power splitters if suitable low-loss waveguides can be fabricated. In reference [10], the present applicant reported an investigation into the purely bound mode spectrum supported by symmetric structures comprising a thin metal film of finite width embedded in a homogeneous dielectric and optical devices employing such waveguide structures are the subject of the present applicant's copending Canadian patent application number 2,314,723 and United States Provisional patent application number 60/171,606, which are incorporated herein by reference.
Those patent applications disclose, among other things, the implementation of modulator devices based on the low-loss propagation of plasmon-polariton modes along thin metal waveguides of finite width and surrounded by a homogeneous dielectric. The modulators are based on either a Mach-Zehnder or coupled strip architecture. The Mach-Zehnder devices are based on inducing a relative phase difference between the light waves propagating along each strip in order to create destructive interference between the waves as they are combined. The coupled strip devices are based on inducing a change in the coupling parameters of the strips.

4 DISCLOSURE OF INVENTION:
The present invention is concerned with enhancing certain of the above-described optical devices and to this end provides optical devices based upon the waveguiding characteristics of asymmetric structures which support the purely bound plasmon-polariton mode spectrum.
According to one aspect of the present invention, there is provided an optical device comprising a waveguide structure formed by a thin strip of a material having a relatively high free charge carrier density surrounded by a material having a relatively low free carrier density, the strip having finite width and thickness with dimensions such that optical radiation having a wavelength in a predetermined range couples to the strip and propagates along the length of the strip as a plasmon-polariton wave, characterized in that the material comprises two distinct portions with the strip extending therebetween, at least one of the two distinct portions having at least one variable electromagnetic property, and that the device further comprises means for varying the value of said electromagnetic property of said one of the portions so as to vary the propagation characteristics of the waveguide structure arid the propagation of the plasmon-polariton wave.
In preferred embodiments of the invention, for one said value of the electromagnetic property, propagation of the plasmon-polariton wave is supported and, for another value of said electromagnetic property, propagation of the plasmon-polariton wave is at least inhibited. Such preferred embodiments may comprise modulators or switches.
Different embodiments of the invention may employ different means of varying the electromagnetic property, such as varying the size of at least one of said portions, especially if it comprises a fluid.
The at least one variable electromagnetic property of the material may comprise permittivity, permeability or conductivity. Where the electromagnetic property is permittivity, the varying means may vary the permittivity by inducing a change in one or more of an electrical field in material of said portion, mechanical strain in the material of said portion, and temperature of the material of said portion.
Where the electromagnetic property is permeability, the varying means may vary the permeability by inducing a change in one or more of a magnetic field in material of said portion, mechanical strain in the material of said portion, and temperature in the material of said portion.
The appended claims set out other embodiments of the invention.

Various objects, features, aspects and advantages of the present invention will become apparent from the following detailed description, taken in conjunction with the attached drawings, of preferred embodiments of the invention which are described by way of example only.

5 BRIEF DESCRIPTION OF THE DRAWINGS:
Figures 11a) and 1 (b) are a cross-sectional side view and a plan view, respectively of a waveguide structure formed by a core comprising a lossy metal film of thickness t, width w and permittivity E2. The metal film is supported by a homogeneous semi-infinite substrate of permittivity E, and the cover or superstrate is a homogeneous semi-infinite dielectric of permittivity E3.
Figures 2(a) and 2(b) illustrate dispersion characteristics with thickness of the first seven modes supported by such a metal film waveguide of width w = 1 ,um. The ab and sb modes supported for the case w = oo are shown for comparison. (a) Normalized phase constant. (b) Normalized attenuation constant.
Figures 3(al,(b),(c) and (d) illustrate spatial distribution of the EY field component related to the sse mode supported by such a metal film waveguide of width w = 1 ,um for four film thicknesses. The waveguide cross-section is located in the x-y plane and the metal region is outlined as the rectangular dashed contour. The field distributions are normalized such that max; ~{EY} i =
1.
Figures 4(a),(bl,(c) and (d) illustrate spatial distribution of the EY field component related to two higher order modes supported by a metal film waveguide of width w = 1 ,um for two film thicknesses. In all cases, the waveguide cross-section is located in the x-y plane and the metal region is outlined as the rectangular dashed contour. The field distributions are normalized such that max;~t{EY}; = 1.
Figure 5 illustrates dispersion characteristics with thickness of the first six modes supported by a metal film waveguide of width w = 1 ,um. The ab and sb modes supported for the case w = ~ are shown for comparison. (a) Normalized phase constant. (b) Normalized attenuation constant.
Figures 6(a1,(bl,(c) and (d) illustrate spatial distribution of the EY field component related to modes supported by a metal film waveguide of width w - 1 ,um. In all cases, the waveguide cross-section is located in the x-y plane and the metal region is outlined as the rectangular dashed contour. The field distributions are normalized such that max;~t{Ey}; = 1.

6 Figures 7(a) and 7(b) illustrate dispersion characteristics with thickness of the first six modes supported by a metal film waveguide of width w = 0.5 ,um. The ab and sb modes supported for the case w - ~ are shown for comparison. (a) Normalized phase constant. (b) Normalized attenuation constant.
Figures 8(a) and 8(b) illustrate dispersion characteristics with thickness of the SSb and Sab modes supported by a metal film waveguide of width w - 0.5 ,um for various cases of E3. (a) Normalized phase constant; the inset shows an enlarged view of the region bounded by 0.04 <_ t <_ 0.08 ,um and 2.0 <_ ,Bl,Bo <_ 2.3. (b) Normalized attenuation constant; the inset shows an enlarged view of the region bounded by 0.05 <- t <_ 0.08 ,um and 7.0 x 10-3 <- a/~o _< 2.0 x 10'2.
Figures 9(al,(b),(c) and (d) illustrate spatial distribution of the Ey field component related to the sab' mode supported by a metal film waveguide of width w = 0.5 ,um for four film thicknesses. The waveguide cross-section is located in the x-y plane and the metal region is outlined as the rectangular dashed contour. The field distributions are normalized such that max; ~t{EY} ;
_ 1.
Figures 10(a),(b),(c) and (d) illustrate a contour plot of ~tf Sz} associated with the long-ranging modes supported by metal film waveguides of width w - 0.5 ,um and having different superstrate permittivities E3. In all cases, the outline of the metal film is shown as the rectangular dashed contour.
Figures 1 1 (a) and 11 (b) are a schematic front view and corresponding top plan view of an electro-optic modulator employing the waveguide structure of Figures 1 (a1 and 1 (b1.
Figures 12(a) and 12(b) are a schematic front view and corresponding top view of an alternative electro-optic modulator;
Figure 12(c) illustrates an alternative connection arrangement of the modulator of Figure 12(a);
Figure 13 is a schematic front view of a third embodiment of electro-optic modulator;
Figure 14 is a schematic front view of a magneto-optic modulator;
Figure 15 is a schematic front view of a thermo-optic modulator;
Figure 16 is a schematic perspective view of an electro-optic switch;
Figure 17 is a schematic perspective view of a magneto-optic switch;
and Figure 18 is a schematic perspective view of a thermo-optic switch.

7 BEST MODE(S~ FOR CARRYING OUT THE INVENTION:
The present invention is predicated upon a comprehensive investigation of the purely bound modes of propagation supported by an important class of asymmetric waveguiding structures comprising of a thin lossy metal film of finite width, supported by a semi-infinite homogeneous dielectric substrate and covered by a different semi-infinite homogeneous dielectric superstrate.
Embodiments of the invention also rely upon an investigation of the evolution of modes due to variations in the physical parameters of the waveguides.
In order to facilitate an understanding of the specific optical devices embodying the invention, their theoretical basis will first be explained with reference to Figures 1 to 10(d).
A. Description of the Waveguide Structure Referring to Figure 1, the waveguide structure comprises a metal film 100 of thickness t, width w and equivalent permittivity E2, supported by a semi-infinite homogeneous dielectric substrate 102 of permittivity E, and covered by a semi-infinite homogeneous dielectric superstrate 104 of permittivity e3. The Cartesian coordinate axes x and y used for the analysis are also shown; propagation takes place along the z axis, which is out of the page.
It is assumed that the metal region shown in Figure 1 can be modeled as an electron gas over the wavelengths of interest. According to classical or Drude electron theory, the complex relative permittivity of the metal region is given by the well-known plasma frequency dispersion relation [3]:
z z _ _ WP WP U
Er 2 1 WZ + UZ ] W / WZ + U2, where cu is the excitation frequency, cv P is the electron plasma frequency and v is the effective electron collision frequency, often expressed as v=1 it with r defined as the relaxation time of electrons in the metal. When cv2 + v2 < cv p2 (which is the case for many metals at optical wavelengths) a negative value for the real part of e~,2 is obtained, implying that plasmon-polariton modes can be supported at interfaces with normal dielectrics.
B. Electromagnetic VIlave and Field Equations The modes supported by the structure illustrated in Figure 1 are obtained by solving a suitably defined boundary value problem based on Maxwell's equations written in the frequency domain for a lossy inhomogeneous isotropic medium. Uncoupling Maxwell's equations yields the following time-harmonic vectorial wave equations for the E and H fields:
v x v x E-w2 s (x, y) ~ E = o (2) v x E-' (x, y) vxH-c.~2~,H = o (3) where the permittivity E is a complex function of cross-sectional space, describing the waveguide structure. For the structures analyzed in this specification,,u is homogeneous and taken as the permeability of free space,uo.
The above serve as the physical basis for the analysis of the structures of interest.
The boundary value problem is solved numerically by applying the Method of Lines (MoL). The MoL is a well-known numerical technique and its application to various electromagnetic problems, including optical waveguiding, is well-established [12]. The MoL is rigorous, accurate and flexible. It can handle a wide variety of waveguide geometries, including the structures at hand. The method is not known to generate spurious or non-physical modes.
Except for a 1-D spatial discretization (applied along the x direction in this case), the method is exact. The MoL formulation used in this study is detailed in [13], and its application to the modelling of waveguiding structures such as those of concern in this specification is summarized in [10]; the formulation will therefore not be repeated here.
The MoL generates mode solutions that satisfy Equations (2) and (3).
Since the structures under consideration are invariant along the propagation axis (taken to be in the +z direction), the mode fields vary along this dimension according to e-'~ where y = a+j,8 is the complex propagation constant of the mode, a being its attenuation constant and ,B its phase constant. The spatial distribution of all six field components related to a mode can also be generated by the MoL over the 2-D cross-section of the structure if they are desired.
The physical symmetry of the structure along the center vertical axis is exploited to increase the accuracy of the results and to reduce the numerical effort required to generate the mode solutions. This is achieved by placing either an electric wall (Ete" _ ~) or a magnetic wall (Hta~ _ ~) boundary condition along the y axis shown in Figure 1.The top and bottom boundary conditions are placed at infinity and the remaining lateral boundary condition is either placed far enough from the guide to have a negligible effect on the mode calculation, or a lateral absorbing boundary condition is used to simulate infinite space, depending on the level of confinement observed in the resulting mode.

As discussed in reference [10], the propagation constant of a mode computed using the method of lines converges in a monotonic or smooth manner with a reduction in the discretization interval, which means that it is sensible to apply an extrapolation technique to generate more accurate values for the propagation constant (14]. The convergence of the computed propagation constants has been monitored and extrapolated values obtained using Richardson's extrapolation formula [15], were used to generate most of the graphs in the attached drawings.
C. Modes Supported by Metal Film Slab Waveguides In general, only two purely bound TM surface modes, each having three field components, are guided by an infinitely wide metal film waveguide [5].
In the plane perpendicular to the direction of wave propagation, the electric field of the modes comprises a single component, normal to the interfaces and having either a symmetric or asymmetric spatial distribution across the waveguide. The symmetric mode can have a small attenuation constant and is often termed a long-range surface plasmon-polariton. The fields related to the asymmetric mode penetrate more into the metal than the fields associated with the symmetric mode and are usually much lossier by comparison. In addition to purely bound modes, leaky modes are also known to be supported by these structures.
In the symmetric metal slab structure (similar to Figure 1 but w = ~ and E3 - E,) the spatial distribution of the mode fields is truly symmetric or asymmetric about the horizontal axis passing through the center of the metal film; that is, the fields can be generated by placing an electric wall of symmetry along this axis. In this structure, the loss associated with the asymmetric mode increases with decreasing film thickness as the fields penetrate progressively deeper into the lossy metal. In the case of the symmetric mode, the attenuation decreases with decreasing film thickness, as the mode evolves towards the TEM (Transverse ElectroMagnetic) wave supported by the background. There is no cutoff thickness for either mode in this structure. As the thickness of the film increases, both the symmetric and asymmetric modes become degenerate, their propagation constants converging to that of a plasmon-polariton mode supported by the interface between semi-infinite metallic and dielectric regions, which is given via the following equations[5]:
Er~l~r~2 Er,1 + ~r,2 a a/~3o + _~ Er,l~r~2 (51 ~r,l + Er,2 5 where ,Bo = cv/co with co being the velocity of light in free space, and E~,, and E~,2 are the complex relative permittivities of the materials.
In the asymmetric metal slab structure (like that shown in Figure 1 but w = ~ and E3 ~ E,), the spatial distribution of the mode fields is not truly symmetric or asymmetric about the center horizontal axis. Rather, the 10 distributions are symmetric-like or asymmetric-like; that is the distributions have the general form of those found in the symmetric structure but the fields are localized near one of the interfaces. The modes however are still called symmetric and asymmetric modes. The symmetric mode field distribution has a maximum at the interface with the dielectric of lowest permittivity while the asymmetric mode has a maximum at the interface with the dielectric of highest permittivity. The loss associated with the asymmetric mode increases with decreasing film thickness and this mode does not have a cut-off thickness. The loss associated with the symmetric mode decreases with decreasing film thickness and a cut-off thickness for the mode exists; that is, the mode is not supported for films of thickness less than a cut-off value. It is reasonable that a cut-off thickness for the symmetric mode exists in an asymmetric structure since the mode cannot evolve into a TEM wave supported by the background as t ~ 0. The background comprises the interface between semi-infinite dielectric media and such an interface cannot support a TEM mode. As the thickness of the metal film increases, the modes of the asymmetric structure evolve into uncoupled plasmon-polariton modes supported by the isolated top and bottom interfaces. The propagation constant of the mode localized at the bottom interface converges to the value given by Equations (4) and (5) and the propagation constant of the mode localized at the top interface is given by these same equations by substituting E, with E3.
The widely accepted nomenclature for identifying the modes of infinitely wide structures consists in using the letters a or s for asymmetric or symmetric transverse field distributions, respectively, followed by a subscript b or I
for bound or leaky modes, respectively. This nomenclature is used for the modes of symmetric as well as asymmetric metal slab structures.
D. Modes Supported by Symmetric Structures Constructed From Metal Films of Finite Width.

The purely bound modes supported by a thin lossy metal film of finite width, embedded in an infinite homogeneous dielectric (E3 = E~ in Figure 1 ) have recently been characterized [10] and [38]. Only the features of these modes that are relevant to the current study are summarized here; a complete description and a discussion of the modes can be found in [10] and [38].
The modes supported by a symmetric structure are not TM in nature but if the structure has an aspect ratio wlt > 1, then the Ey field component dominates. The modes can be divided into four families depending on the symmetry of their fields. Four symmetries, corresponding to the four possible combinations of electric and magnetic walls placed along the center horizontal and vertical axes, exist and define the families. A mode nomenclature, based on the one used to identify modes in metal slab waveguides, describes the spatial distribution of the main transverse electric field component, which is the Ey component in most structures of practical interest. A pair of letters a or s identify whether the main transverse electric field component is asymmetric or symmetric with respect to the y and x axes, respectively. A superscript is then used to track the number of extrema observed in the spatial distribution of this field component along the largest dimension (usually along the x axis) between the corners. A second superscript n could be added to track the extrema along the other dimension (the y axis) if modes exhibiting them are found. Finally, a subscript b or / is used to identify whether the mode is bound or leaky. Leaky modes are known to exist in metal film slab structures and it is envisaged that they will exist in metal films of finite width.
The ssb, sab, asb and aab modes are the first modes supported (one for each of the four possible quarter-symmetries) and thus may be considered as the fundamental modes. In addition to the four fundamental modes, higher order modes having additional variations in the spatial distribution of their mode fields are supported.
The dispersion of all modes with film thickness is in general consistent with the behaviour observed for the purely bound modes supported by the metal film slab waveguide. In addition, one of the fundamental modes and some higher order modes have cut-off thicknesses. The higher order modes have a cut-off width, below which they are no longer propagated. The effect on the modes of varying the background permittivity is consistent with the general behaviour observed for the modes supported by a metal film slab waveguide. In addition, the cut-off width of the higher order modes decreases with decreasing background permittivity while all cut-off thicknesses increase.

One of the fundamental modes supported by the symmetric structure, the Ssb mode exhibits very interesting characteristics and is potentially quite useful. This mode evolves with decreasing film thickness towards the TEM
wave supported by the background, (an evolution similar to that exhibited by the sb mode in metal film slab waveguidesl, its losses and phase constant tending asymptotically towards those of the TEM wave. In addition, decreasing the film width reduces the losses below those of the sb mode supported by the corresponding metal film slab waveguide. Reducing the background permittivity further reduces the losses. However, a reduction in losses is always accompanied by a reduction in field confinement to the waveguide core which means that attenuation and confinement must be traded-off one against the other. The mode evolved into its most useful form has a field distribution that renders it excitable using end-fire techniques [16]. In reference [17], the present inventor et al. disclosed that plasmon-polariton waves supported by thin metal films of finite width have recently been observed experimentally at optical communications wavelengths using this method of excitation [17].
III. Mode Characteristics and Evolution With Film Thickness: Small Asymmetry A. Mode Solutions for a Metal Film Slab Waveguide The study begins with the reproduction of results for an infinitely wide asymmetric metal film waveguide (similar to that shown in Figure 1 but with w = ~), taken from the standard work on such structures [51. In order to remain consistent with their results, the optical free-space wavelength of excitation is set to ~lo = 0.633 ,um and their value for the relative permittivity of the silver film at this wavelength is used: E,,2 = -19 - j0.53. The relative permittivity of the bottom and top dielectric regions are set to E,,~ = 4 (n, = 2) and E~,3 = 3.61 (n3 = 1.9); these values create a structure having a small asymmetry with respect to the horizontal dimension.
The dispersion curves of the sb and ab modes supported by the infinitely wide structure were computed using the MoL and the results are shown in Figure 2. From this figure, it is seen that the propagation constant of the ab mode tends towards that of the plasmon-polariton mode supported by the bottom interface, given by Equations (4) and (5), as the thickness of the film increases. It is also noted that this mode does not exhibit a cutoff thickness while it is clear that the sb mode has one near t = 18 nm. The propagation constant of the sb mode is seen to tend towards the value of a plasmon-polariton mode supported by the top interface as the thickness increases.
These results are in perfect agreement with those reported in [5].

B. Modes Supported by a Metal Film of Width w = 7 ,um The study proceeds with the analysis of the structure shown in Figure 1 for the case w = 1 ,um. The material parameters and free-space wavelength that were used in the previous case w - oo were also used here. The dispersion curves for the first seven modes were computed using the MoL and the results are shown in Figure 2.
In this asymmetric structure, true field symmetry exists only with respect to the y axis. With respect to the horizontal dimension, the modes have a symmetric-like or asymmetric-like field distribution with field localization along either the bottom or top metal-dielectric interface. The modes that have a symmetric-like distribution with respect to the horizontal dimension are localized along the metal-dielectric interface with the lowest dielectric constant, while modes that have an asymmetric-like distribution with respect to this axis are localized along the metal-dielectric interface with the highest dielectric constant. This behaviour is consistent with that observed for asymmetric metal slab waveguides.
The mode nomenclature adopted for symmetric structures [10] can be used without ambiguity to describe the modes supported by asymmetric structures as long as the modes are identified when the metal film is fairly thick, before significant coupling begins to occur through the metal film, and while the origin of the mode can be identified unambiguously. As the metal film thickness decreases, the modes (and their fields) can evolve and change considerably more in an asymmetric structure compared to a symmetric one.
The number of extrema in the main transverse electric field component of the mode is counted along the lateral dimension at the interface where the fields are localized. This number is then used in the mode nomenclature.
It was observed in [10) that the modes supported by a metal film of finite width are in fact supermodes created from a coupling of "edge" and "corner" modes supported by each metal-dielectric interface defining the structure. As the thickness and width of the metal decrease, the coupling between these interface modes intensifies leading to dispersion and possibly evolution of the supermode. In asymmetric structures, the bound modes are also supermodes created in a similar manner, except that dissimilar interface modes may couple to each other to create the supermode. For instance, a mode having one field extremum along the top interface (along the top edge bounded by the corners) may couple with a mode having three extrema along the bottom interface. The main selection criterion determining which interface modes will couple to create the supermode is a similarity in the value of their propagation constants. For all modes supported by an asymmetric structure, an apparent symmetry or asymmetry with respect to the horizontal dimension can still be observed in the corner modes.
The sa6, aab, ssb and asb modes are the fundamental modes supported by the structure. The sab and aab modes are comprised of coupled corner modes, resembling the corresponding modes in a symmetric structure [10], except that the fields are localized near the substrate. These two modes do not change in character as the thickness of the film decreases. A narrowing of the metal film would eventually break the degeneracy observed in Figure 2.
For a sufficiently large thickness (about 100 nm for the present structure), the ssb and asb modes are comprised of coupled corner modes much like the corresponding modes in a symmetric structure except that the fields are localized near the superstrate. As the thickness of the metal film decreases, both of these modes begin to evolve, changing completely in character for very thin films. Figures 3(a) to 3(d) show the evolution of the EY
field component related to the ssb mode as the thickness of the film ranges from 100 nm (Figure 3(a) to 40 nm (Figure 3(d1). It is clearly seen that the mode evolves from a symmetric-like mode having fields localized near the superstrate to an asymmetric-like mode having fields localized along the substrate-metal interface. A similar evolution is observed for the asb mode.
This change in character is also apparent in their dispersion curves: they follow the general behaviour of a symmetric-like mode for large thicknesses but then slowly change to follow the behaviour of an asymmetric-like mode as the thickness decreases. Since the substrate dielectric constant is larger than the superstrate dielectric constant, the mode is "pulled" from a symmetric-like mode to an asymmetric-like mode (having field localization at the substrate-metal interface) as the metal film becomes thinner.
Figures 4(a) to 4(d) show the Ey field component related to the ssb and sab modes for two film thicknesses. From this figure it is noted that the top and bottom edge modes comprising a supermode are different from each other. In part (a) for instance, it is seen that the bottom edge mode has three extrema and is of higher order than the top edge mode which has one extremum. A similar observation holds for part (c) where it can be seen that the bottom edge mode has one extremum while the top one has none. In this structure, the substrate has a higher dielectric constant than the superstrate so the phase constant of a particular substrate-metal interface mode will be higher than the phase constant of the same mode at the metal-superstrate interface.
Since a supermode is created from a coupling of edge modes having similar propagation constants, it should be expected that in an asymmetric structure different edge modes may couple to create a supermode. Higher-order modes have in general smaller values of phase constant compared to lower-order modes, so in structures having E3 < E~, all supermodes are comprised of a 5 bottom edge mode of the same order or higher than the top edge mode, as shown in Figure 4. If E3 > E~, then the opposite statement is true.
A careful inspection of the fields associated with the ssb, sab and aab modes reveals that as the thickness of the film decreases, the mode fields may evolve in a smooth manner similar to that 10 shown in Figure 3, but in addition a change or "switch" of the constituent edge modes may also occur. For instance, from Figure 4(c), the sab mode is seen to comprise a substrate-metal interface mode having one extremum for a film thickness of 100 nm, while for a thickness of 60 nm the substrate-metal interface mode has three extrema, as shown in Figure 4(dl. Since higher-order 15 modes have in general lower phase constants than lower-order modes, this change in edge modes causes a reduction in the phase constant of the sab mode in the neighbourhood of 60 nm, as shown in Figure 2 (a).
Another change occurs near 40 nm as the corner modes switch from being symmetric-like (as in Figures 4(c) and 4(d~) to being asymmetric-like with respect to the horizontal dimension. This change is again reflected in the dispersion curve of the sab mode as its phase constant is seen to increase with a further decrease in thickness. In general, the changes in the edge and corner modes are consistent with the directions taken by the dispersion curves as the film thickness decreases, thus explaining the oscillations in the curves seen in Figure 2.
The only potentially long-ranging mode supported by this structure at the wavelength of analysis is the sse mode. As shown in Figure 2, the mode has a cutoff thickness near t = 22 nm and though the attenuation drops quickly near this thickness, it should be remembered that the field confinement does so as well. Furthermore, the spatial distribution of the main transverse field component related to this mode evolves with decreasing thickness in the manner shown in Figure 4(al and 4(b1, such that near cutoff the spatial distribution has strong extrema along the top and bottom edges. These extrema render the mode less excitable using an end-fire technique so coupling losses would be higher compared to the fundamental symmetric mode in symmetric waveguides. Also, the fact that the mode would be operated near its cutoff thickness implies that very tight tolerances are required in the fabrication of structures. Nevertheless, it should be possible to observe propagation of this mode in a suitable structure using an end-fire experiment (16,17].
IV. Mode Characteristics and Evolution With Film Thickness: Large Asymmetry A. Mode Solutions for a Metal Film Slab Waveguide The study proceeds with the analysis of structures having a large difference in the dielectric constants of the substrate and superstrate. With respect to Figure 1, the relative permittivities of the substrate and superstrate are set to E~,, = 4 (n, = 2) and E~,3 = 2.25 (n3 = 1.5), respectively, the width of the metal film is set to w = oo, and the dielectric constant of the metal region and the wavelength of analysis are set to the same values as in Section III. The dispersion curves of the sb and ab modes supported by this structure can be seen in Figure 5. Comparing with Figure 2, it is observed that the sb mode has a larger cutoff thickness in a structure having a large asymmetry than in a structure having similar substrate and superstrate dielectric constants.
The results shown were computed using the MoL and are in perfect agreement with those reported in (5].
B. Modes Supported by a Metal Film of Width w = 1 ,um The structure shown in Figure 1 was analyzed using the MoL for w =
1 ,um and for the same material parameters and free-space wavelength as those given above for w = ~. The dispersion curves of the first six modes supported by the structure are shown in Figure 5.
An inspection of the mode fields related to the sab and aab modes reveals that these modes are again comprised of coupled corner modes with fields localized at the substrate-metal interface. The modes do not change in character as the thickness of the film decreases and a narrowing of the metal film would eventually break the degeneracy observed in Figure 5.
The spatial distribution of the Ey field component related to the, ssb, asb, sab and aab modes is given in Figure 6. It is noted from this figure that in all cases the metal-superstrate interface modes are similar:
they have fields with no extrema along the interface but rather that are localized near the corners and have either a symmetric or asymmetric distribution with respect to the y axis. These corner modes are in fact the lowest order modes supported by the metal-superstrate interface; they have the largest value of phase constant and thus are most likely to couple with edge modes supported by the substrate-metal interface to form a supermode. From Figures 61a) and 6(b) it is observed that the substrate-metal interface modes comprising the Ssb and asb modes are of very high order. This is expected since the substrate dielectric constant is significantly higher than the superstrate dielectric constant and higher order modes have lower values of phase constant. The Ssb and asb modes shown in Figures 61a) and 6(b) indeed have fields that are localized along the metal-superstrate interface, while the Sab and aab modes shown in Figures 6 (c) and 6(d) have fields that are localized along the substrate-metal interface.
One effect caused by increasing the difference between the substrate and superstrate dielectric constants, is that the difference between the orders of the top and bottom edge modes comprising a supermode can increase. This effect can be observed by comparing Figure 3(a) with Figure 6(a). In the former, there is no difference between the orders of the top and bottom edge modes, while in the latter the difference in the orders is 5. Another effect is that the degree of field localization increases near the interface between the metal and the dielectric of higher permittivity, for all modes that are asymmetric-like with respect to the horizontal dimension. This effect can be seen by comparing the fields related to the Sab mode shown in Figures 6(c) and 4(c1. A comparison of the fields related to the Sab and aab modes reveals that this effect is present in these modes as well.
From the dispersion curves shown in Figure 5(a), it is apparent that the normalized phase constant of all modes converge with increasing film thickness to normalized phase constants in the neighbourhood of those supported by plasmon-polariton waves localized along the associated isolated edge. The normalized phase constant of modes having fields localized at the substrate-metal interface, converge with increasing film thickness to normalized phase constants in the neighbourhood of that related to the ab mode, while the normalized phase constant of modes having fields localized along the metal-superstrate interface converge to values near that of the sb mode. This behaviour is present though less apparent in structures where the asymmetry is smaller, such as the one analyzed in Section III.
By comparing Figures 2 and 5, it is noted that the dispersion curves of the modes are much smoother when the difference in the substrate and superstrate dielectric constants is large. This is due to the fact that the edge modes comprising the supermodes are less likely to change or switch as they do in a structure having similar substrate and superstrate dielectric constants.
Thus modes that start out being symmetric-like with respect to the horizontal dimension remain so as the thickness of the film decreases. The cutoff ' CA 02319949 2000-09-20 thickness of the symmetric-like modes also increases as the difference between the substrate and superstrate dielectric constants increases.
It is apparent that introducing a large asymmetry can hamper the ability of the structure to support useful long-ranging modes. Any mode that is long s ranging would likely have fields with numerous extrema along the width of the interface between the metal film and the dielectric of higher permittivity, as shown in Figures 61a) and 6(b1.
V. Mode Dispersion with Film Width: Small Asymmetry An asymmetric structure comprising the same dielectrics as the structures studied in Section III, but having a metal film of width w = 0.5 Nm was analyzed at the same free-space wavelength in order to determine the impact of a narrowing film width on the modes supported. The structure was analyzed using the MoL and Figure 7 gives the dispersion curves obtained for the first few modes supported.
Comparing Figure 7 with Figure 2 reveals that reducing the width of the film does not cause major changes in the behaviour of the fundamental modes, but does have a major impact on the higher order modes. It is noted that reducing the film width increases the cutoff thickness of the Ssb mode. This higher order mode is symmetric-like with respect to the horizontal dimension, and the cutoff thickness of the symmetric-like modes in general increases as the width of the film decreases due to a reduction in field confinement to the metal film. The aab mode was sought but not found for this film width.
It is also noted by comparing Figures 7 and 2 that the Sab mode evolves quite differently depending on the width of the film. For a film width of w =
1 ,um, the mode follows the general behaviour of an asymmetric-like mode whereas for a film width of w = 0.5,um, the mode evolves as a symmetric-like mode, and has a cutoff thickness near t = 27 nm. When the film is wide, it becomes possible for numerous higher order edge modes (having similar values of phase constant) to be supported by the substrate-metal or metal-superstrate interfaces, so edge modes comprising a supermode are likely to change or switch as the thickness of the film is reduced as shown in Figures 4(c) and 4(d). For a narrow metal film, some of the higher order edge modes may be cutoff thus rendering changes in edge modes impossible. In such a case, the supermode may be forced to evolve in a smooth manner with decreasing film thickness. A close inspection of the mode fields related to the Sab mode for a film width of w = 0.5 ,um reveals that there are no changes to the edge modes as the thickness decreases, rather the mode evolves smoothly from its field distribution at a large thickness (similar to that shown in Figure 4 (c)) to having a symmetric-like distribution with only one extremum along the top and bottom edges of the film. A change in behaviour due to a change in the width of the metal film was observed only for the Sab mode in this study, but such changes are in general not limited to this mode.
The Sab and Ssb modes could be made to propagate over useful distances in this structure, if they are excited near their cutoff thicknesses.
However, the difficulties outlined in Section III B regarding the excitation of modes near cutoff also hold here.
VI. Evolution of the Ssb and Sati Modes With Structure Asymmetry The SSb and Sab modes are of practical interest. The Ssb mode is the main long-ranging mode supported by symmetric finite-width metal film structures, and as demonstrated in the previous section, the Sab mode can be the main long-ranging mode supported by asymmetric finite-width structures.
In metal films of the right thickness, they are also the modes that are the most suitable to excitation in an end-fire arrangement.
Structures comprising a substrate dielectric having n, = 2, of a metal film of width w = 0.5 ,um, and of various superstrate dielectrics having n3 =
2, 1.99, 1.95 and 1.9 were analyzed at the same free-space wavelength as in Section III. The equivalent permittivity of the metal film was also set to the same value as in Section III. These analyses were performed in order to investigate the effects on the propagation characteristics of the Ssb and Sab modes caused by a slight decrease in the superstrate permittivity relative to the substrate permittivity. Figure 8 shows the dispersion curves with film thickness, obtained for these modes in the four structures of interest.
As seen in Figure 8(a) and its inset, the dispersion curves of the modes intersect at a certain film thickness only for the symmetric case (n3 = n~).
As soon as some degree of asymmetry exists, the curves no longer intersect, though they may come quite close to each other if the asymmetry is small, as seen in the case of n3 = 1.99. As the degree of asymmetry increases, the separation between the curves increases.
The evolution with film thickness of the Sab mode is shown in Figure 9 for the case n3 = 1.99 and for thicknesses about t = 59 nm (near the maximum in its phase dispersion curve). The evolution of this mode for the cases n3 = 1.95 and 1.9 is similar to that shown. The evolution with film thickness of the SSb mode is similar in these structures to the evolution shown in Figure 3 for the case w = 1 ,um and n3 = 1.9. Comparing Figures 9 and 3, reveals that the modes "swap" character near t = 59 nm. For film thicknesses sufficiently above this value, the modes exhibit their defining character as shown in Figures 3(a) and 9(a), but for film thicknesses below it, each mode 5 exhibits the other's character, as shown in Figures 3(d) and 9(d). This character swap is present for the three cases of asymmetry considered here (n3 =1.99, 1.95 and 1.9) and explains the behaviour of the dispersion curves shown in Figure 8.
From Figure 8, it is noted that a cutoff thickness exists for the long-10 ranging mode as soon as an asymmetry is present in the structure. It is also observed that the cutoff thickness increases with increasing asymmetry. In the case of n3 = 1.99, the cutoff thickness of the mode is near t = 12 nm, while for n3 = 1.9 the cutoff thickness is near t = 27 nm. As the width of the metal film w increases, the cutoff thickness of the Sab mode decreases as long as 15 the mode remains long-ranging (recall that the character of this mode may also change with film width such that its behaviour is similar to the ab mode in the corresponding slab structure, as shown in Figure 2). Also, it is clear from Figure 7 that the cutoff thickness of the Sab mode is greater than the cutoff thickness of the sb mode supported by the corresponding slab structure. These 20 results imply that the long-ranging mode supported by a thin narrow metal film is more sensitive to differences in the superstrate and substrate permittivities than the sb mode supported by the corresponding slab structure. This is reasonable in light of the fact that in finite-width structures the mode fields tunnel through the metal as in slab structures, but in addition the fields also wrap around the metal film.
Figure 8~b) shows that near cutoff, the attenuation of the Sab mode supported by an asymmetric structure drops much more rapidly than the attenuation of the Ssb mode supported by a symmetric structure. Thus a means for range extension, similar to that observed in asymmetric slab structures [6], exists for metal films of finite width, though the difficulties related to the excitation of a mode near its cutoff thickness as described in Section III B also apply here.
Figures 10(a) to 10(d) show contour plots of ~?{SZ} associated with the long-ranging modes for the four cases of superstrate permittivity considered.
SZ is the z-directed component of the Poynting vector and its spatial distribution is computed from the spatial distribution of the mode fields using:
SZ = ( Ely' - E~Ix~ ) / 2 ( 6 ) where Hxy denotes the complex conjugate of Hx,y. Figure 10(a) shows the contour plot associated with the Ssb mode supported by a symmetric structure (n3 = n~ = 2) of thickness t = 20 nm. Figures 10(b),(c) and (d) show contours associated with the Sab mode for the three cases of structure asymmetry considered. The contour plots shown in Figures 10(b),(c) and (d) are computed for film thicknesses slightly above cutoff, representative of the thicknesses that would be used to observe these long-ranging modes experimentally. From this figure, it is noted that the contour plots become increasingly distorted and the fields increasingly localized at the metal-superstrate interface as the degree of asymmetry in the structure increases.
It is also apparent by comparing Figures 10(a) and 10(d) that in an end-fire experiment, less power should be coupled into the Sab mode supported by the asymmetric structure with n3 = 1.9, compared to the Ssb mode supported by the symmetric structure. End-fire coupling losses seem to increase with increasing structure asymmetry.
The high sensitivity of the long-ranging mode supported by thin metal films of finite width, to structure asymmetry is potentially useful. A small induced asymmetry (created via an electro-optic effect present in the dielectrics say) can evidently effect a large change in the propagation characteristics of the long-ranging mode. From Figure 8, it is apparent that a difference between the substrate and superstrate refractive indices as small as n, - n3 = ~n =
0.01 is sufficient to create an asymmetric structure where the long-ranging mode has a cutoff thickness of about t = 12 nm. From Figure 8la), a slightly larger difference of ~n = 0.05 changes the normalized phase constant of the long-ranging mode by 0(,8/,Bo) ~ 0.025 for a metal film thickness of t = 20 nm.
Both of these effects are potentially useful.
VII. Conclusion The long-ranging modes supported by asymmetric structures of finite width have a rapidly diminishing attenuation near their cutoff thickness (like asymmetric slab structures). The rate of decrease of the attenuation with decreasing thickness near cutoff is greater than the rate related to the SSb mode in symmetric structures. However field confinement also diminishes rapidly near cutoff, implying that the structures ought to be fabricated to very tight tolerances and that all metal-dielectric interfaces should be of the highest quality. It has also been found that decreasing the width of the film increases the cutoff thickness of the main long-ranging mode. Below this cutoff thickness no purely bound long-ranging mode exists. The long-ranging mode supported by metal films of finite-width are thus more sensitive to the asymmetry in the structure compared to the sb mode supported by similar slab waveguides. This is a potentially useful result in that a small induced change in substrate or superstrate refractive index can have a greater impact on the long-ranging mode supported by a finite-width structure compared to a similar slab waveguide.
Specific Embodiments of modulation and switching devices Modulation and switching devices will now be described which make use of the fact that an asymmetry induced in optical waveguiding structures having as a guiding element a thin narrow metal film may inhibit propagation of the main long-ranging purely bound plasmon-polariton mode supported.
The asymmetry in the structure can be in the dielectrics surrounding the metal film. In this case the permittivity, permeability or the dimensions of the dielectrics surrounding the strip can be different. A noteworthy case is where the dielectrics above and below the metal strip have different permittivities, in a manner similar to that shown in Figure 1.
A dielectric material exhibiting an electro-optic, magneto-optic, thermo optic, or piezo-optic effect can be used as the surrounding dielectric medium.
The modulation and switching devices make use of an external stimulus to induce or enhance the asymmetry in the dielectrics of the structure.
Figure 1 1 depicts an electro-optic modulator comprising two metal strips 1 10 and 112 surrounded by a dielectric 114 exhibiting an electro-optic effect.
Such a dielectric has a permittivity that varies with the strength of an applied electric field. The effect can be first order in the electric field, in which case it is termed the Pockets effect, or second order in the electric field (Kerr effect), or higher order. Figure 11 (a) shows the structure in cross-sectional view and Figure 11 (b) shows the structure in top view.
The bottom metal strip 110 and the surrounding dielectric 1 14 form the optical waveguide. The bottom metal strip 110 is dimensioned such that a purely bound long-ranging plasmon-polariton wave is guided by the structure at the optical wavelength of interest. Since the guiding strip 1 10 is comprises a metal, it is also used as an electrode and is connected to a voltage source 116 via a minimally invasive electrical contact 118 as shown. The second metal strip 112 is positioned above the first at a distance large enough that optical coupling between the strips is negligible. It is noted that the second strip could also be placed below the waveguiding strip instead of above. The second strip acts as a second electrode.

The intensity of the optical signal output from the waveguide can be varied or modulated by varying the intensity of the voltage V applied by the source 116. When no voltage is applied, the waveguiding structure is symmetric and it supports a plasmon-polariton wave. When a voltage is applied, an asymmetry in the waveguiding structure is induced via the electro-optic effect present in the dielectric 14 and the propagation of the plasmon-polariton wave is inhibited. The degree of asymmetry induced may be large enough to completely cut-off the main purely bound long-ranging mode thus enabling a very high modulation depth to be achieved.
Figures 12(a) and 2(b) show an alternative design for an electro-optic modulator which is similar to that shown in Figure 1 1 (a) but comprising electrodes 112A and 1128 placed above and below, respectively, the metal film 1 10 of the optical waveguide. Figure 121a) shows the structure in cross-sectional view and Figure 12(b) shows the structure in top view. A first voltage source 116A connected to the metal film 110 and the upper electrode 112A
applies a first voltage V, between them. A second voltage source 112B
connected to metal film 110 and lower electrode 112B applies a voltage V2 between them. The voltages V~ and V2, which are variable, produce electric fields E~ and E2 in portions 114A and 1148 of the dielectric material. The dielectric material used exhibits an electro-optic effect. The waveguide structure shown in Figure 12(cl is similar in construction to that shown in Figure 12(a) but only one voltage source 116C is used. The positive terminal ( + ) of the voltage source 116C is shown connected to metal film 110 while its negative terminal (-) is shown connected to both the upper electrode 112A
and the loser electrode 112B. With this configuration, the electric fields E, and E2 produced in the dielectric portions 114A and 114B, respectively, are in opposite directions.
Thus, in the waveguide structure of Figure 12(a), selecting appropriate values for the voltages V~ and V2 induces the desired asymmetry. In the waveguide structure of Figure 12(c), the asymmetry is induced by the relative direction of the electric field above and below the waveguiding strip 110 since the voltage V applies to the electrodes 112A and 112B produces electric fields acting in opposite directions in the portions 114A and 114B of the dielectric material.
The structures shown in Figures 12(a),(b) and (c) can operate to very high frequencies since a microwave transmission line is in effect created by the three metals (stripline).

Figure 13 shows in cross-sectional view yet another design for an electro-optic modulator. In this case, the metal film 110 is embedded in the middle of dielectric slab 114 with first portion 114D above it and second portion 1 14E below it. Electrodes 112D and 112E are placed laterally along the edges of the upper portion 114D of the dielectric 1 14 as shown and connected to voltage source 116E which applies voltage to them to induce the desired asymmetry in the structure. Alternatively, the electrodes 1 12D, 112E could be placed laterally along the bottom portion 114E of the dielectric 114, the distinct portions of the dielectric material still being above and below the strip.
Figure 14 shows an example of a magneto-optic modulator where the waveguiding strip 110 and overlying electrode 112F are used to carry a current / in the opposite directions shown. The dielectric material surrounding the metal waveguide 110 exhibits a magneto-optic effect. The magnetic fields generated by the current / add in the dielectric portion between the electrodes 110 and 112F and essentially cancel in the portions above the top electrode 1 12F and below the waveguide 110. The applied magnetic field thus induces the desired asymmetry in the waveguiding structure.
Figure 15 depicts a thermo-optic modulator wherein the waveguiding strip 1 10 and the overlying electrode 1 12G are maintained at temperatures TZ
and T~ respectively. The dielectric material 114 surrounding the metal waveguide exhibits a thermo-optic effect. The temperature difference creates a thermal gradient in the dielectric portion 1146 between the electrodes. The applied temperatures thus induce the desired asymmetry in the waveguiding structure.
It should be appreciated that the modulator devices described above with references to Figures 11 (a) to 15 may also serve as variable optical attenuators with the attenuation being controlled via the external stimulus, i.e. voltage, current, temperature, which varies the electromagnetic property.
Figures 16, 17 and 18 depict optical switches that operate on the principle of "split and attenuate". In each case the input optical signal is first split into N outputs using a power divider; a one-to-two power split being shown in Figures 16, 17 and 18. The undesired outputs are then "switched off" or highly attenuated by inducing a large asymmetry in the corresponding output waveguides. The asymmetry must be large enough to completely cut-off the main purely bound long-ranging mode supported by the waveguides. The asymmetry is induced by means of overlaying electrodes as in waveguide structures of Figures 11, 14 or 15, respectively. In the switches shown in Figures 16, 17 and 18, the basic waveguide configuration is the same and comprises an input waveguide section 120 coupled to two parallel branch sections 122A and 1228 by a wedge-shaped splitter 124. All four sections 120, 122A, 1228 and 124 are co-planar and embedded in dielectric material 126. The thickness of the metal film is d3. Two rectangular electrodes 128A
5 and 1288, each of thickness d~, are disposed above branch sections 122A and 1228, respectively, and space form them by a thickness d2 of the dielectric material 126. Each of the electrodes 128A and 1288 is wider and shorter than the underlying metal film 122A or 1228, respectively. In the switch shown in Figure 16, the asymmetry is induced electro-optically by means of a first 10 voltage source 130A connected between metal film 122A and electrode 128A
for applying voltage V~, therebetween and a second voltage source 130A
connected between metal film 1228 and electrode 1288 for applying a second voltage V2 therebetween. In the switch shown in Figure 17, the asymmetry is induced magneto-optically by a first current source 132A connected between 15 metal film 122A and electrode 128A, which are connected together by connector 134A to complete the circuit, and a second current source 1328 connected between metal film 1228 and electrode 1288 which are connected together by connector 1348 to complete the circuit.
In the switch shown in Figure 18, the asymmetry is induced thermo 20 optically by maintaining the metal strips 122A and 1228 at temperature To and the electrodes 128A and 1288 at temperatures T, and T2, respectively.
It will be appreciated that, in Figures 16, 17 and 18, the dielectric surrounding the metal waveguide will be electro-optic, magneto-optic or thermo-optic, as appropriate.
25 In general, any of the sources, whether of voltage, current or temperature, may be variable.
Although the switches shown in Figures 16, 17 and 18 are 1 x 2 switches, the invention embraces 1 x N switches which can be created by adding more branch section and associated electrodes, etc.
It should be appreciated that the present invention is not limited to the specific waveguide configurations and combinations described hereinbefore but with suitable adaptation could be applied to selected ones of the configurations disclosed in the afore-mentioned co-pending Canadian and US provisional patent applications [38]. For example, where the dielectric material is magneto-optic, the magnetic field could be produced by a coil formed by metal-plated via holes and surface conductors, or a solenoid having magnetic poles either side of the strip.

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Claims (25)

What is claimed is:

1. An optical device comprising a waveguide structure formed by a thin strip of a material having a relatively high free charge carrier density surrounded by a material having a relatively low free carrier density, the strip having finite width and thickness with dimensions such that optical radiation having a wavelength in a predetermined range couples to the strip and propagates along the length of the strip as a plasmon-polariton wave, characterized in that the material comprises two distinct portions with the strip extending therebetween, at least one of the two distinct portions having at least one variable electromagnetic property, and that the device further comprises means for varying the value of said electromagnetic property of said one of the portions so as to vary the propagation characteristics of the waveguide structure and the propagation of the plasmon-polariton wave.

2. A device according to claim 1, characterized in that for one said value of the electromagnetic property for said one of the portions propagation of the plasmon-polariton wave is supported and for another value of said electromagnetic property of said one of said portions propagation of the plasmon-polariton wave is at least inhibited.

3. A device according to claim 1, characterized in that said means for varying the electromagnetic property changes the size of at least one of said portions.

4. A device according to claim 3, characterized in that one of said portions is a fluid.

5. A device according to claim 1 or 2, characterized in that said electromagnetic property is permittivity and the varying means varies the permittivity by inducing a change in one or more of an electrical field in material of said portion, mechanical strain in material of said portion, and temperature in the material of said portion.

6. A device according to claim 1 or 2, characterized in that said electromagnetic property is permeability and the varying means varies the permeability by inducing a change in one or more of a magnetic field in material of said portion, mechanical strain in the material of said portion, and temperature in the material of said portion.

7. An optical device according to claim 1, wherein said free charge carrier density of the surrounding material is substantially negligible.

8. A device according to claim 1, for optical radiation having a free-space wavelength near 1550 nm, wherein the strip comprises a metal and has thickness less than about 0.1 microns and width of a few microns.

9. A device according to claim 1, wherein the strip is straight, curved, bent, or tapered.

10. A device according to claim 1, characterized in that the material is electro-optic and the varying means comprises an electrode overlying said one of said portions and means for applying a potential difference between the electrode and the strip.

11. A device according to claim 1, characterized in that the material is electro-optic and the varying means comprises first and second electrodes disposed one at each side of the strip, said one of the portions being between the first electrode and the strip and the other of said portions being between the second electrode and the strip, and means for applying a potential difference between the strip and at least one of the first and second electrodes.

12. A device according to claim 11, wherein the applying means comprises a first voltage source for applying a first potential difference between the strip and the first electrode and a second voltage source for applying a second potential difference between the strip and the second electrode.

13. A device according to claim 11, wherein the applying means comprises means for coupling one terminal of a voltage source to the strip and a second terminal of the voltage source in common to the first and second electrodes.

14. A device according to claim 1, wherein the material is electro-optic, the strip is embedded in the material with the said one of the portions adjacent one surface of the strip, and the varying means comprises first and second electrodes disposed laterally of the strip at opposite sides of said one of said portions and means of applying a potential difference between the electrodes, the other of said portions being adjacent an opposite surface of the strip.

15. A device according to claim 1, wherein the material is magneto-optic and the varying means comprises means for establishing a current flowing in at least one of the strip and an adjacent electrode, the said one of the portions being between the electrode and the strip.

16. A device according to claim 1, wherein the material is thermo-optic, at least one electrode is provided adjacent to the strip with said one of the portions therebetween, and the varying means comprises means for establishing a temperature difference between the strip and the electrode.

17. A device according to claim 1, further comprising a plurality of waveguide structures similar in construction to the first-mentioned structure and each comprising one of a plurality of said strips, the plurality of strips having respective proximal ends juxtaposed to one end of the first-mentioned strip to form a combiner/splitter, the arrangement being such that said optical radiation leaving said first-mentioned strip via said one end will be split between said plurality of strips and conversely said optical radiation coupled to said one end by said plurality of strips will be combined to leave said first-mentioned strip by an opposite end, wherein the varying means is coupled to at least one of the plurality of strips.

18. A device according to claim 17, wherein the material is electro-optic and the waveguide structures comprise an input strip for receiving said optical radiation at one end thereof and end-coupled to a splitter at an opposite end thereof, first and second branch strips each having a proximal end coupled to the splitter for receiving a portion of the radiation, the varying means comprising an electrode adjacent a respective one of the branch strips with said one of the portions therebetween and means for applying a potential difference between the electrode and said one of the branch strips.

19. A device according to claim 18, wherein the varying means further comprises a second electrode adjacent the other branch strip with a second one of said portions therebetween and means for applying a second potential difference between the second electrode and the second branch strip.

20. A device according to claim 17, wherein the material is magneto-optic and the waveguide structures comprise an input strip for receiving said optical radiation at one end thereof and end-coupled to a splitter at an opposite end thereof, first and second branch strips each having a proximal end coupled to the splitter for receiving a portion of the radiation, the varying means comprising an electrode adjacent a respective one of the branch strips with said one of the portions therebetween and means for establishing a current flowing in said electrode and said one of the branch strips.

21. A device according to claim 20, wherein the varying means further comprises a second electrode adjacent the other branch strip with a second one of said portions therebetween and means for establishing a second current flowing in the second electrode and the second branch strip.

22. A device according to claim 17, wherein the material is thermo-optic and the waveguide structures comprise an input strip for receiving said optical radiation at one end thereof and end-coupled to a splitter at an opposite end thereof, first and second branch strips each having a proximal end coupled to the splitter for receiving a portion of the radiation, the varying means comprising an electrode adjacent a respective one of the branch strips with said one of the portions therebetween and means for establishing a temperature difference between said electrode and said one of the branch strips.

23. A device according to claim 22, wherein the varying means further comprises a second electrode adjacent the other branch strip with a second one of said portions therebetween and means for establishing a second temperature difference between the second electrode and the second branch strip.

24. A device according to claim 15, wherein the varying means comprises a coil formed by metal-plated via holes and surface conductors.

25. A device according to claim 15, wherein the varying means comprises a solenoid having magnetic poles either side of the strip.