Patent Description:
Optical waveguides including multi-mode dielectric waveguides are designed for the transmission of electromagnetic waves in the optical band. An optical waveguide is basically a light conduit configured, by means of properly selected core and surrounding cladding materials with higher and lower refractive indexes, respectively, to confine and transport light therein without leaking it to the environment.

Optical waveguides can be classified according to their geometry (slab (planar) or strip, cylindrical, etc.), mode structure (single-mode, multi-mode), refractive index distribution (step or gradient index) and e.g. material (glass, polymer, semiconductor, etc.). Refraction of light at the core/cladding interface is generally governed by the Snell's law. When light arrives at the interface between the core and cladding materials above a so-called critical angle it is completely reflected back into the core material based on a phenomenon called `total internal reflection' (TIR).

In terms of wave-optics, a multi-mode waveguide is, as the name alludes, capable of guiding the waves of several modes, i.e. a discrete set of solutions of Max-well's equations with boundary conditions, in addition to the main mode. In practice, the larger the core dimensions of the waveguide the greater the number of modes is. The multi-mode waveguides and related equipment for interfacing the light with the waveguide are typically easier to construct than the single-mode counterparts due to e.g. larger dimensions generally enabling the utilization of coarser, more affordable hardware and manufacturing methods. However, multimode distortion limits the `bandwidth x distance' product of multi-mode waveguides in contrast to single-mode solutions. It also complicates (or prevents) the realization of advanced waveguide circuits that densely integrate a large number of waveguide components (couplers, filters etc.). Therefore, such circuits are typically realized with single-mode waveguides, while multimode waveguides are mainly used in point-to-point links and to realize relatively simple waveguide circuits.

Multimode waveguides can also be locally used as part of single-mode waveguide circuits. They can form components, such as multi-mode interference (MMI) couplers, where multiple modes are temporarily excited, but the light eventually couples back into single-mode waveguides. They can also be used to propagate light only in the fundamental mode, but in this case light must be coupled adiabatically between the single and multimode waveguide sections to avoid the excitation of higher order modes. And finally, multimode waveguides can be placed behind single-mode waveguides when multimode distortion is no longer relevant, for example when coupling light into a large-area photodetector.

By definition, the modes of a multi-mode straight waveguide propagate unperturbed without mutual coupling, unless some perturbation occurs, such as a change in the waveguide shape. In particular, bends can induce significant coupling between the different modes such that in the straight section at the end of the bend, also higher order modes (HOM) will be in general excited, even if only the fundamental mode was excited in a straight section preceding the bend. The higher the curvature <NUM>/R (bend radius R), the higher is the degree of unwanted coupling and, in general, also the higher the number of significantly excited modes.

Indeed, one basic design rule of single-moded photonic integrated circuits dictates that any bent waveguide must be single-moded so that the undesired coupling between the modes and subsequent detrimental mode beating and power radiation in the bend may be avoided. For integration purposes the bend radius is typically to be minimized, which requires the use of HIC waveguides. Further, the higher the index contrast the smaller the waveguide shall be in order to ensure the single-mode condition. Sub-micron waveguides could be utilized for achieving dense integration, but they pose many additional challenges, including polarization dependence and low coupling efficiency to optical fibre modes. Furthermore, for scalable production they require expensive state-of-the-art fabrication tools in order to resolve submicron features and are also very sensitive to nanometer-scale fabrication errors.

As a reference one may introduce a single-moded rib waveguide that can be realized on a silicon-on-insulator (SOI) wafer by dry etching the originally <NUM> thick Si layer down to approximately <NUM> thickness around an unetched <NUM> wide rib that forms the waveguide. Despite its large dimensions and high index contrast this waveguide is single-moded because the higher order modes radiate power away from the rib along the surrounding <NUM> thick Si slab. However, the slab also enables the fundamental mode to radiate power into the slab when the rib waveguide is bent. Therefore the minimum bending radius for such a rib waveguides is approximately <NUM>. To avoid the radiation losses of the fundamental mode in a bend the rib waveguide can be locally converted into a multi-mode strip waveguide or the etch depth can be locally increased around the bend [Reference: <NPL>)]. However, in practice this has led to the inevitable excitation of HOMs if the bending radius has been reduced by a factor of <NUM> or more with respect to the corresponding low-loss rib waveguide bend.

In the article <NPL>, a study on waveguide curvatures and the corresponding losses is presented. Various curvatures are measured and their losses reported. Single mode and multi-mode waveguides are found to be quite different in terms of losses vs. effective radius, without any particular correlation with regard to behavior of light in single mode and multimode waveguides.

The article by <NPL>, discusses about an ideal trajectory for ultracompact low-loss waveguide bends. The aim of the article is to present a novel design for <NUM> bent multimode waveguides for single mode operation, wherein radiation losses are minimized. In the <NUM> thick channel discussed in the article, the radiation is already remarkably high when the radius of curvature is a few micrometres. Therefore, the article focuses on reducing radiation loss.

The goal of shrinking the bend radius of multimode HIC waveguides could be sought by a matched arc approach, which relies on matching the length of a circular bend to an integer multiple of beating lengths between the fundamental mode and the first higher order mode (HOM) of the bent waveguide to ensure that, at the end of the bend, only the fundamental mode will be excited despite the fact that HOMs have been excited during propagation in the bent section. Nevertheless, the obtained bending radii are still relatively large, in practice e.g. two orders of magnitude larger than the waveguide width, and in particular, manufacturing thereof is challenging due to very stringent tolerance requirements.

The objective is to at least alleviate one or more aforesaid problems and to provide an optical multi-mode HIC waveguide with improved, tight bend(s).

The utility of the suggested solution arises from multiple issues depending on the embodiment. For example, ultra-small bends with low losses in micron-scale HIC multimode waveguides may be obtained. Both matched and generic (unmatched) bends with varying curvature may be capitalized. The applicable bandwidth may be considerably large. The designed bends feature minimal bending radii comparable to the waveguide width. Experimental results further confirm the overall effectiveness, robustness and low losses of the realized bends. As an outcome, the 'footprint', i.e. the occupied surface area, and cost of the associated circuits are reduced and previously unaffordable elements may become feasible.

For example, the size of multi-mode interferometric reflectors may be remarkably shrunk. On the other hand, bends with larger radii and lower losses may be used, for example, to design long spirals with low footprint. an area of about <NUM>. <NUM> mm2 could somewhat easily allocate an <NUM> long spiral. The proposed bends are also expected to enable the fabrication of microring resonators with high finesse. Various embodiments of the present invention are suitable for use with SOI (silicon-on-insulator) platforms including thicker SOIs and interfaceable with optical fibres. Micron-scale features of the proposed designs allow for fabrication with relaxed lithographic resolution by tools that are much less expensive than the ones usually needed for scalable production of nanophotonic devices. High confinement of light in multi-mode HIC waveguides makes the proposed solution much less sensitive to fabrication errors, wavelength changes and mode polarization than the existing nanophotonic counterparts.

Generally, waveguides with small birefringence, good fiber coupling, and robustness to fabrication errors, may be obtained in contrast to e.g. fixed curvature bends and/or nanophotonic waveguides.

The expression "a number of" refers herein to any positive integer starting from one (<NUM>), e.g. to one, two, or three.

The expression "a plurality of" refers herein to any positive integer starting from two (<NUM>), e.g. to two, three, or four.

The expression "effective bend radius" (Reff) refers herein to the radius of an arc that has the same starting and final points and the same starting and final directions with the bend of the present invention.

The term "optical waveband" refers herein to frequencies between about <NUM> and <NUM> thus including visible light and part of ultraviolet and infrared bands. The provided waveguide may be configured to operate in a number of selected sub-ranges only.

The terms "a" and "an", as used herein, are defined as one or more than one.

Various different embodiments of the present invention are also disclosed in the dependent claims.

Next the invention is described in more detail with reference to the appended drawings in which.

In <FIG> at <NUM>, by way of example only, two different embodiments of the present invention are generally illustrated at <NUM> and <NUM>. Bends such as 'U'-bends, 'S'-bends, 'L'-bends and practically any bend of a desired degree may be manufactured. Different basic bend shapes may be cleverly combined to establish more complex bends and (mirror/point) symmetry may be exploited to design the bends.

For instance, two 'U'-bends could be combined to form an 'S'-bend, and the 'U'-bend itself could be constructed from two mirror-symmetric halves, i.e. doubly symmetric structures could be established. However, a skilled reader will understand such symmetry is not obligatory for utilizing the present invention to establish bends, i.e. the bend portions preceding and following e.g. the point of maximum curvature of a bend do not have to be mirror-symmetric.

The obtained bends are optically efficient and provide small footprint due to optimized, yet small, non-constant bend radii. The order of magnitude of the waveguide width and the bend radii may be substantially the same and e.g. micrometer scale configurations are achievable.

<FIG> illustrates, at <NUM>, a cross-section (in the bend plane) of an 'L'-bend (<NUM> deg bend) forming at least part, i.e. section, of an optical multi-mode HIC waveguide in the direction of light propagation in accordance with an embodiment of the present invention and incorporating two mirror-symmetric bend sub-sections <NUM> with curvature linearly varying with length and bending radii normalized to the minimum value. According to the claimed invention, the waveguide is a strip waveguide and further contains core <NUM> and cladding <NUM> portions for transporting and confining light, respectively. It shall be noted that in some embodiments, not being part of the claimed invention, the cladding portion <NUM> may be formed by non-solid material, optionally gaseous material such as air. The point of maximum curvature <NUM> is located half way the section length at the border of the mirror-symmetric sub-sections <NUM>.

According to the claimed invention, instead of utilizing e.g. a generic prior art arc with constant radius of curvature for implementing the bend and thus abruptly changing between straight and curved (arc) portions, the radius of curvature is to be gradually and continuously varied to produce the bend with more continuous and smoother transitions, while the bend size is minimized.

For the 'L'-bend or practically any other bend of a given angle θ joining two straight waveguides, two mirror-symmetric sections may be exploited, each of them enabling bending by θ/<NUM>, which in the case of 'L' implies using two mirror-symmetric <NUM> deg bends.

<FIG> illustrates, at <NUM>, a correspondingly designed, optimized 'U'-bend for optical multi-mode HIC waveguide.

Reverting both to <FIG> and <FIG>, the linearly varying L-bend has an effective radius Reff = <NUM> Rmin, and in the case of the U-bend the effective radius is Reff = <NUM> Rmin.

<FIG> illustrates, at <NUM>, one more embodiment of a bend, in this case an 'S' bend, designed in accordance with the present invention.

With reference to <FIG>, the curvature (<NUM>/R) of a bend optimized according the teachings provided herein may change substantially linearly with the bend length as depicted. The curvature reaches a maximum value at half-length (radius R of curvature is then at minimum) and reduces back to zero (or other minimum), i.e. mirror-symmetric bend realization is shown.

As a mathematical background regarding various embodiments of the present invention, a bend with curvature that is linearly varying with path length may be characterized by means of so-called Euler spiral, which can be accurately calculated through expansion series of Fresnel integrals (for practical purposes <NUM> or <NUM> expansion terms are usually sufficient). Therefore, the associated bends are also called hereinafter as `Euler bends'.

For example, the effective or minimum radius of the applied bend curvature may substantially be in the order of magnitude of the waveguide width, preferably about <NUM> times the waveguide width or smaller, more preferably about ten times the width or smaller, and most preferably about two times the width or smaller.

<FIG> and <FIG> illustrate modeled power coupling to different modes at the output (straight) of <NUM> wide silicon strip waveguide with generic <NUM> degree arc and Euler 'L' bends, respectively, as a function of the constant bend radius (arc) or the effective bend radius (Euler bend, in which case the minimum radius is <NUM> times smaller). The wavelength is <NUM>.

As a person skilled in the art will immediately realize from the coupling curves <NUM> of <FIG> relating to a prior art arc, up to <NUM> HOMs can be excited by about <NUM>% (-<NUM> dB) or more.

At R≈<NUM> there seems to be a first resonant coupling to the fundamental (0th order) mode, but with poor suppression of coupling to 1st, 2nd and 3rd HOMs, resulting in just about <NUM>% output into the fundamental mode. The first practically useful resonance (i.e. the lowest order low-loss matched bend) corresponds to R≈<NUM>, with fundamental mode coupling > <NUM>%. For larger R values there are other matched bend occurrences and all HOMs, except 1st order, can be neglected in practice. The power oscillations between this mode and the fundamental mode slowly damp with R and for R><NUM> the maximum coupling to the HOM is suppressed by more than <NUM> dB. One could adopt e.g. such suppression level as the threshold to define the minimum R value ensuring low-loss operation of the bend. Unlike with the matched bend case, where power is significantly coupled to HOMs in the bent section and then completely coupled back to the fundamental mode at the very end of the bend, proper unmatched operation requires that coupling to HOMs is always suitably suppressed during propagation. In other words, the matched-bend is a resonant system, whereas the generic unmatched bend is not. It is clear that unmatched operation ensures broader operation bandwidth and higher tolerance to fabrication errors. In general, in any bend of any shape (i.e. with non-constant curvature) one can distinguish between two working principles: a resonant one based on matching the bend length to the beating length between fundamental and HOMs - so ensuring high coupling into the fundamental mode at the very end of the bend only - and another one simply ensuring low coupling to HOMs at any propagation step.

Reverting to the coupling curves <NUM> of <FIG>, the modeled generic, i.e. unmatched with reference to the above discussion, bend corresponds to Reff = <NUM>, i.e. more than <NUM> times smaller than the generic arc. Furthermore, the first useful matched bend occurs at Reff = <NUM>, i.e. at less than half the size of the smallest matched arc, and the second one at Reff = <NUM>, which is comparable with the arc bend, but with much better performance.

<FIG>, <FIG> illustrate power coupling in the case of a prior art type <NUM> deg arc bend, matched 'L'-bend according to an embodiment of the present invention, and generic 'L'-bend according to another embodiment of the present invention, respectively, from the standpoint of bandwidth utilization. As a motivation for such contemplation, it is typically beneficial to analyze the spectral response of the bends for various reasons. The responses reflect the associated bends' tolerance to fabrication errors since one important design parameter is the ratio between the waveguide size and the wavelength, whereupon changing the wavelength is like changing the size and vice-versa. It shall be noted that in the depicted case the matched bends were not precisely set to the transmission peak for <NUM> wavelength, but were optimized slightly off-resonance to ensure the highest operation bandwidth.

Besides the size shrinkage, the comparison between the smallest matched arc (<FIG>) and the smallest matched Euler L-bend (<FIG>) highlights an order of magnitude broader bandwidth (indicated by the shaded rectangular areas) for the Euler L-bend. Also the generic Euler L-bend (<FIG>) yields excellent performance. These simple examples show that the matched and generic Euler bends can be not only much smaller than corresponding matched and generic arc bends, but also perform great in terms of bandwidth and tolerances to fabrication errors. Similar results hold for different waveguide widths and different bend angles.

From the previous spectral analysis one may further derive a general guideline: in order to design a bend working in a given wavelength range, the bend should be targeted to the smaller wavelengths of that range, and then optimized to cover the broadest possible range of longer wavelengths.

Furthermore, a design that works at a given wavelength λ1 can be always rescaled to a different wavelength λ2 by simply rescaling waveguide width and bending radii by a factor λ2/λ1 advantageously supplemented with some minor optimization to take into account effective refractive index dispersion of the given waveguide.

Even with a highly multi-mode ≈<NUM> wide waveguide, it is possible, for example, to design low loss (<<NUM> dB per <NUM>°) matched Euler 'U'-bends with Reff ≈<NUM> like the ones shown in <FIG> at <NUM> or e.g. a generic Euler bend with Reff ≈<NUM> in the case of <NUM> wide waveguide. This is superior to the contemporary solutions in connection with standard nanophotonic circuits based on single mode waveguides, where the minimum bending radius is limited to about <NUM>, because both submicron waveguide thickness and width, required for single-mode operation, significantly lower the index contrast, also making the mode much more affected by sidewall-roughness-induced loss.

Still, the experimental results show that some of the designed bends have losses < <NUM> dB. Thus a plurality of bends may be cascaded without inducing unacceptable losses to the aggregate solution.

A skilled person may on the basis of this disclosure and general knowledge apply the provided teachings in order to implement the scope of the present invention as defined by the appended claims in each particular use case with necessary modifications, deletions, and additions, if any.

In the context of the present invention, the (radius of) bend curvature is indeed gradually and continuously changed instead of constant curvature or abrupt changes.

Curvature dependence on path length doesn't have to be the linear symmetric continuous function shown e.g. <FIG> (which defines the Euler spiral), but may be any other substantially continuous function starting from a smaller value (preferably zero), reaching a maximum value and then typically going back to a small value.

Furthermore, the waveguide width may in general vary along the bend (e.g. smaller width corresponding to smaller bending radii).

Considering the diversity of potential applications, the invention may have useful applications in connection with highly multi-mode waveguides (tens to hundreds of microns in size) proposed e.g. for low cost optical interconnects on printed circuit boards. The invention can also be applied to nanophotonic silicon waveguides both to reduce bend losses and shrink bend sizes using multimode sections with large widths.

In certain applications, the light may be coupled from an optical fibre to the input (rib) waveguide of an integrated circuit or some other predetermined target element. Then when a small bend is needed, the (rib) waveguide, which is preferably single-moded, may be converted into a strip waveguide of suitable width that can be bent with very small footprint and high performances thanks to the present invention. Furthermore, conversion to strip waveguides is anyway needed in many other devices as well (through etched MMIs, AWGs, etc.), whereupon the invented tight and low-loss bends will be also a useful alternative to the <NUM>° turning mirrors that could be used for e.g. rib waveguides.

Claim 1:
An optical multi-mode HIC, high index contrast, waveguide (<NUM>, <NUM>, <NUM>, <NUM>, <NUM>) for transporting electromagnetic radiation in the optical waveband, wherein the waveguide is a strip waveguide,
the waveguide comprising a guiding silicon core portion (<NUM>) with higher refractive index, and silica cladding portion (<NUM>) with substantially lower refractive index configured to surround the light guiding core in the transverse directions to facilitate confining the propagating radiation within the core, wherein the width of the core portion is <NUM>-<NUM> and the thickness of the core portion is <NUM>-<NUM>;
the waveguide being configured to support multiple optical modes of the propagating radiation, wherein the relative refractive index contrast between said core and cladding portions is higher than <NUM>%, and the waveguide incorporates a bent waveguide section (<NUM>) having bend curvature that is configured to gradually and continuously increase towards a maximum curvature of said section from a section end.