TECHNICAL FIELD

[01] The present disclosure relates generally to optics and photonics— including at wavelengths from the ultraviolet, through the visible, the near infrared, and the mid- infrared, to the far infrared and THz bands, i.e., wavelengths from 300 nanometers (nm) to 100 micrometers (um)— including to silicon photonics ("SiPh"), including to resonators for optical and SiPh applications.

BACKGROUND

[02] Optical resonators are critical functional building blocks in optical and photonic devices, including in silicon photonics ("SiPh"), i.e., photonic systems that use silicon as an optical medium, e.g., silicon lying on an insulator (silica), known as silicon- on-insulator (SOI).

[03] However, existing optical and SiPh resonators may be difficult and expensive to manufacture, and/or difficult to design using existing design tools, at least for some applications in photonic circuits.

[04] It is desired to address or ameliorate one or more disadvantages or limitations associated with the prior art, or to at least provide a useful alternative.

SUMMARY

[05] Described herein is an optical resonator including: a. a slab waveguide (SWG), with a slab that supports an optical slab mode; and b. a ridge waveguide (RWG), with a main ridge that supports an optical ridge mode, wherein the RWG is coupled to the SWG such that light in the optical slab mode couples to the optical ridge mode, c. wherein the optical resonator includes a plurality of geometric features with selectable dimensions that independently control a plurality of electromagnetic (EM) properties of the optical resonator.

[06] The plurality of the geometric features with selectable dimensions includes a plurality of types of geometric features, the types including: a. slab-mode geometric features that interact predominantly with light in the slab mode; b. ridge-mode geometric features that interact predominantly with light in the ridge mode; and c. coupling geometric features that predominantly affect the coupling of the light between the slab mode and the ridge mode.

[07] The slab-mode geometric features include a trench under the main ridge and above the slab.

[08] The ridge-mode geometric features include the main ridge and a loading above the main ridge.

[09] The coupling geometric features include coupling ridges (also referred to as

"steps") to affect the coupling of the light between the slab mode and the ridge mode, wherein the coupling ridges. The coupling ridges are at least partially perpendicular to the slab of the SWG and at least partially parallel to a longitudinal axis of the RWG. The coupling ridges include sides of the main ridge. The main ridge includes a pedestal with at least partially mutually parallel sides forming two of the coupling ridges. The main ridge includes a core, on the pedestal, also with at least partially parallel sides forming two of the coupling ridges. [10] The selectable dimensions are at least partially parallel to the slab of the SWG and at least partially perpendicular to the longitudinal axis of the RWG. The longitudinal axis of the RWG is parallel to a propagation direction of the optical ridge mode.

[11] The optical resonator includes a low-refractive index gap ("low-n gap") between the slab and the main ridge. The low-n gap is formed by the trench under the main ridge. A width WT of the trench is selected to control (or "tune") electromagnetic (EM) properties of the optical resonator, including back reflectivity of light in the slab mode from the RWG. The width WT is one of the selectable dimensions.

[12] The RWG includes the loading separate from the main ridge to control electromagnetic (EM) properties of the optical resonator. A width WL of the loading is selected to control (or "tune") the electromagnetic (EM) properties of the optical resonator, including the resonant wavelength of the optical resonator. The width WL is one of the selectable dimensions.

[13] The ridge waveguide includes the pedestal and the core in the main ridge. A width WP of the pedestal, and a width WC of the core, are both selected to control (or "tune") electromagnetic (EM) properties of the optical resonator, including a quality (Q) factor of the optical resonator, which is based on the degree to which the resonant ridge mode couples to the unguided slab mode. The width WP and the width WC are both ones of the selectable dimensions.

[14] Described herein is a method of manufacturing the optical resonator above.

[15] Described herein is a method including: a. supporting an optical slab mode with a slab of a slab waveguide (SWG); b. directing light in the optical slab mode to a ridge waveguide (RWG) with a main ridge and a selected resonant wavelength; c. coupling light at the resonant wavelength in the optical slab mode to an optical ridge mode supported by the ridge waveguide (RWG); and d. transmitting light not at the resonant wavelength in the optical slab mode past the RWG by means of a gap between the slab and the main ridge.

[16] Described herein is a method including: a. supporting an optical slab mode with a slab of a slab waveguide (SWG); b. directing light in the optical slab mode to a ridge waveguide (RWG) with main ridge and a loading above the main ridge that defines a resonant wavelength; and c. coupling light at the resonant wavelength in the optical slab mode to an optical ridge mode supported by the ridge waveguide (RWG).

BRIEF DESCRIPTION OF THE DRAWINGS

[17] Some embodiments are hereinafter described, by way of non-limiting example only, with reference to the accompanying drawings, in which: a. Figure 1 is a schematic diagram of a transverse cross-section of an optical resonator; and b. Figure 2 is a cross-sectional picture of an example filter with three (3) examples of the optical resonator.

DETAILED DESCRIPTION

Overview

[18] As shown in Figure 1, an optical resonator 100 includes: a. a slab waveguide (SWG) 102, and b. a ridge waveguide (RWG) 104 coupled to the SWG 102. [19] The SWG 102 supports an optical slab mode that is confined in one dimension

(e.g., vertically, Y) and unguided (or unconfined) in two dimensions (e.g., in a horizontal plane, X and Z). The slab mode is a transverse electric (TE) mode.

[20] The SWG 102 may include: a. a high-refractive index ("high-n") slab 106 of a high-n material, which can be silicon (Si) with a refractive index of about 3.5 at an operational wavelength of about 1.5um (micrometers); and b. low-n slabs 108, 110 (of at least one low-n material, which can be silicon dioxide, Si02 with a refractive index of about 1.45 at an operational wavelength of about 1.5um) on the lateral sides (i.e., above and below in the Y direction) of the high-n slab 106 and at least partially plane parallel with the high-n slab 106— " at least partially plane parallel" means the slabs are "essentially plane parallel", meaning: (i) in the vertical (Y) direction, the slabs are of uniform thickness and etching is uniformly deep within fabrication tolerances, e.g., a few nm over 1cm for infrared or visible operational wavelengths; and (ii) in the horizontal (X,Z) directions, the slabs are longitudinally unvarying enough to support the optical modes at the operational wavelengths but can include perturbations, i.e., variations in the lateral dimensions (by about 1%) that apodize a filter formed by the optical resonator 100 (by reducing ripples in the pass band and the stop band).

[21] The RWG 104 includes a longitudinal ridge axis (or "RWG axis"), i.e., an axis running generally along a centre of the RWG 104 (in the Z direction, i.e., into the page in Figures 1 and 2). The RWG 104 supports an optical ridge mode that is confined in two dimensions (e.g., vertically, Y, and in one horizontal direction, X) and propagating (or unconfined) along one dimension (e.g., the other horizontal direction, Z). The ridge mode is a transverse magnetic (TM) mode. [22] The resonator 100 may be referred to as a resonator system, or just a "system", because it includes interacting components in the form of the SWG 102 and the RWG 104.

[23] The resonator 100 is part of an optical apparatus that includes: a. an input port (which can be a single-mode input waveguide) for a beam of light in the slab mode (which is referred to as the "slab beam"); and b. two output ports (to collect transmitted and reflected beams from the optical resonator 100).

[24] The input port directs the light beam to the optical resonator 100 at a selected incident angle (THETA) relative to the longitudinal ridge axis. The optical apparatus includes a beam expander or condenser to convert light from the input port into an unguided beam in the slab mode. The selected incident angle (THETA) includes a range of angles around a central angle, and this angular range depends on how narrow the filter (formed by the optical resonator 100) is designed to be: the incident angle (THETA) determines the operational wavelength of the filter, and hence the range of angles is selected to be sufficiently narrow to match a desired width in wavelengths of the filter.

[25] As a filter, the resonator 100 can have multiple operational wavelengths, including the resonant wavelength and off-resonance wavelengths (or "non-resonant wavelengths", i.e., wavelengths that differ from the resonant wavelength to not resonate). The "resonant wavelength" refers to a range of resonant wavelengths, and the width of this range depends on the selected width of the resonator. Light at the resonant wavelength is reflected due to an electromagnetic coupling effect that may be referred to as

electromagnetic "lateral leakage", which is described in the specification of Patent Cooperation Treaty Application No. PCT/AU2016/050201 (published as

WO/2016/149749A1), which is hereby incorporated by reference herein in its entirety. Light at the off-resonance wavelengths is transmitted due to no coupling.

[26] As set out in WO/2016/149749A1, when the slab beam is incident on the RWG

104, at the angle THETA to the longitudinal ridge axis, at least a portion of the slab beam couples electromagnetically to the ridge mode to form ridge light. This electromagnetic coupling effect (also referred to as "conversion") occurs due to, and at, coupling ridges (also referred to as coupling "steps", "surfaces" or "edges") in the optical resonator 100 where the slab mode overlaps with the ridge mode. The coupling ridges affect the coupling of the light between the slab mode and the ridge mode (including from the slab mode to the ridge mode, and from the ridge mode to the slab mode) because they are at least partially perpendicular to the slab of the SWG 102 and at least partially parallel to the longitudinal axis of the RWG 104. The coupling ridges include the sides of the main ridge, including the sides of a pedestal 128 and the sides of the core 126. The coupling ridges can include portions that are not perpendicular to the slab so long as the coupling ridges provide respective discontinuities in the plane of the slab mode, e.g., by rising from the slab of the SWG 102 as a slant/slope, or staircase, or step, or presenting a face that is at least partially perpendicular to the slab of the SWG 102. The coupling ridges can include portions that are not parallel to the longitudinal axis of the RWG 104 so long as the coupling ridges provide respective extensions in the direction of the longitudinal axis of the RWG 104, e.g., by following the RWG 104 substantially longitudinally to support the optical modes at the operational wavelengths while able to include perturbations, i.e., variations in the lateral dimensions (by about 1%) that apodize a filter formed by the optical resonator 100 (by reducing ripples in the pass band and the stop band).

[27] The optical resonator 100 can be used in integrated optical systems, i.e., silicon photonics ("SiPh"), and the optical apparatus can be referred to as an optical or photonic device, apparatus or module.

[28] The slab 106 can be a pristine polished silicon on insulator wafer with no etched features, meaning that propagation loss of the slab mode can be very low due to the minimal number of scattering defects.

[29] The optical resonator 100 can be used for known applications, e.g., including applications described in WO/2016/ 149749A1.

Trench 112 [30] As shown in Figure 1, the optical resonator 100 includes a trench 112. The trench 112 may be described as part of the SWG 102 because it affects the slab beam. The trench 112 may also be described as part of the RWG 104 because it lies parallel to, and beneath, the other components of the RWG 104; however, it affects the slab beam more strongly than the ridge light. The trench 112 is at least partially parallel to the RWG 104, meaning "essentially parallel", which means: (i) in the vertical (Y) direction, the separation between the trench 112 and the slab 106 is uniform within fabrication tolerances, e.g., a few nm over 1cm for infrared or visible operational wavelengths; and (ii) in the horizontal (Z) directions, the separation between the trench 112 and the slab 106 is longitudinally unvarying enough to support the optical modes at the operational wavelengths but can include perturbations, i.e., variations in the lateral dimensions (by about 1%) that apodize a filter formed by the optical resonator 100 (by reducing ripples in the pass band and the stop band).

[31] The trench 112 includes: a. a downward step 114, i.e., a step perpendicular to the plane of the SWG 102, that is parallel to the RWG axis, that lies between the input port and the RWG 104 so that the slab mode is incident on the downward step 114 at the angle THETA before it couples to the RWG 104 ; b. a floor 116 that is generally parallel to the plane of the SWG 102, albeit down the downward step 114, and that extends beneath the RWG 104; c. an upward step 118, i.e., another step perpendicular to the plane of the SWG 102 in an opposite direction from the downward step 114, that is also parallel to the RWG axis, and that lies on the far side of the RWG 104 from the input port, so that the slab beam is incident on the upward step 118 at the angle THETA after it passes the RWG 104; and d. a separation volume 120 between a base 122 of the RWG 104 and the floor 116. [32] The separation volume 120 is filled with a low-n material, which can be the low-n material of the SWG 102. The downward step 114, the upward step 118 and the floor 116 are formed by the high-n material of the SWG 102.

[33] The separation volume 120 provides a separation gap ("gap") 124 between the high-n material of the SWG 102 and high-n material of the RWG 104 described hereinafter. The gap distance is selected based on the desired resonant wavelength. The gap 124 is selected to be small enough so that the ridge mode couples strongly to both a main ridge and to the slab, and so that the slab mode does not couple strongly to the main ridge, except for portions of the slab mode with a wavelength equal to the resonant wavelength (i.e., when the resonator system is resonant).

[34] The width of the trench 112 (i.e., "WT" in the plane of the slab 106 perpendicular to the RWG axis, e.g., in the X direction shown in Figure 1) is selected to control resonance properties (i.e., electromagnetic operational characteristics) of the optical resonator 100 as described hereinafter.

Main Ridge - Pedestal 128 and Core 126

[35] As shown in Figure 1, the optical resonator 100 includes the main ridge, which includes: a. a core ridge (or "core") 126; and b. a pedestal ridge (or the "pedestal") 128.

[36] The core 126 and the pedestal 128 are formed of a high-n material, which is referred to as the high-n material of the RWG 104. The high-n material of the RWG 104 can be the same as the high-n material of the SWG 102. Alternatively, the high-n material of the RWG 104 can be polysilicon with a refractive index of about 3.5. The separation volume 120 of the trench 112 forms the gap 124 between the high-n material of the main ridge and the high-n material of the SWG 102.

[37] The width of the pedestal 128 (i.e., "WP" in the plane of the slab 106 perpendicular to the RWG axis, e.g., in the X direction shown in Figure 1) is selected to control the resonance properties of the optical resonator 100 as described hereinafter. The width of the core 126 (i.e., "WC", in the X direction, as shown in Figure 1) is selected to control the resonance properties of the optical resonator 100 as described hereinafter.

Loading 130

[38] As shown in Figure 1, the optical resonator 100 includes at least one loading

130 that is: a. separated from the main ridge by a spacer 132 of low-n material (which can be Si02); b. above the main ridge (i.e., separated radially from the RWG axis, e.g., in the Y direction shown in Figure 1) for maximum overlap with the TM mode (the strength of the TM mode falls off sharply with distance from the main ridge); and c. generally rectangular in cross-section, where "generally rectangular" refers to having loading sides that include portions at least partially perpendicular to the slab of the SWG 102 and at least partially parallel to the longitudinal axis of the RWG 104 within the same ranges / tolerances (parallel and perpendicular) as the coupling ridges described hereinbefore, and can include sloped loading sides providing a trapezoidal cross-section.

[39] The loading 130 extends with generally constant cross-section (where

"generally constant cross-section" means as constant as provided by the fabrication process) generally parallel to the longitudinal axis of the RWG 104, where "generally parallel" parallel within fabrication tolerances, e.g., a few nm over 1cm for infrared or visible operational wavelengths.

[40] The loading 130 has an intermediate refractive index, i.e., is formed of an intermediate-n material, which can be silicon nitride (Si3N4) with a refractive index of about 2, which is between (i.e., intermediate) the refractive index of the high-n material(s) and the low-n material(s) that form the SWG 102 and the RWG 104 as described herein. [41] The loading 130 can be about 200nm thick (i.e., in a direction radially between the RWG axis and a longitudinal axis of the loading 130— the "loading axis", e.g., in the vertical Y direction shown in Figure 1).

[42] The width of the loading 130 (i.e., "WL" in the plane of the slab 106 perpendicular to the RWG axis, e.g., in the X direction shown in Figure 1) is selected to control the resonance properties of the optical resonator 100 as described hereinafter.

Control of Resonator Properties

[43] The optical resonator 100 includes a plurality of geometric features with selectable dimensions (in a direction parallel to the slab of the SWG 102 and perpendicular to a longitudinal axis of the RWG 104) that independently control a plurality of electromagnetic (EM) properties of the optical resonator 100.

[44] From an electromagnetic point of view, the optical resonator 100 includes a plurality of types of geometric features with selectable dimensions, the types including: a. slab-mode geometric features that interact predominantly with light in the slab mode; b. ridge-mode geometric features that interact predominantly with light in the ridge mode; and c. coupling geometric features that predominantly affect the coupling of the light between the slab mode and the ridge mode.

[45] The slab-mode geometric features include the trench 112 under the main ridge and above the slab. The ridge-mode geometric features include the main ridge and the loading 130 above the main ridge. The coupling geometric features include the coupling ridges (also referred to as "steps") that are perpendicular to the slab of the SWG 102 and parallel to the longitudinal axis of the RWG 104. The coupling ridges are provided by sides 134 of the main ridge. The main ridge includes the pedestal 128 with at least partially mutually parallel sides 134 forming two of the coupling ridges. The main ridge includes the core 126, on the pedestal 128, also with at least partially mutually parallel sides 134 forming two of the coupling ridges. The at least partially mutually sides 134 form the coupling ridges, and are essentially parallel meaning they can include portions that are not perpendicular to the slab so long as they provide respective discontinuities in the plane of the slab mode, e.g., by rising from the slab of the SWG 102 as a slant/slope, or staircase, or step, or presenting a face that is at least partially perpendicular to the slab of the SWG 102. Furthermore, the essentially parallel sides 134 can include portions that are not parallel to the longitudinal axis of the RWG 104 so long as they provide respective extensions in the direction of the longitudinal axis of the RWG 104, e.g., by following the RWG 104 substantially longitudinally to support the optical modes at the operational wavelengths while able to include perturbations, i.e., variations in the lateral dimensions (by about 1%) that apodize a filter formed by the optical resonator 100 (by reducing ripples in the pass band and the stop band).

[46] For a filter including the optical resonator 100, the hereinbefore-mentioned separate control of the slab-mode properties from the ridge-mode properties may provide: a. flexible, independent control of the filter' s stop-band properties (including filter Q and resonant wavelength); b. flexible, independent control of the filter's stop-band and pass-band properties (including back reflection); c. control of the electromagnetic properties of the resonator over a broader wavelength range than pre-existing resonators; d. control of dispersion of the ridge mode independent of other filter properties, which can enable phase matching of multiple wavelength components within the resonator for applications in nonlinear wavelength conversion, generation or pulse manipulation; e. compatibility with scalable mass manufacture using known techniques; and/or f. high-performance, low-cost, mass-manufacturable SiPh filters. [47] As shown in Figure 1 (and mentioned hereinbefore), the optical resonator 100 has at least four (4) geometric features (also referred to as "variable parameters" or "variables") with selectable values: WT, WP, WC, and WL. The selectable values can be selected within significant ranges while remaining compatible with scalable photonic mass manufacture techniques. The at least 4 selectable values can be selected independently of each other (i.e., mutually independently) to control the plurality of optical properties independently of each other (i.e., mutually independently), or at least partially

independently, and in some cases substantially independently, while maintaining compatibility with known low-cost silicon photonic manufacturing techniques.

[48] Selection of the selectable values (WT, WP, WC and WL) enables

simultaneous mutually independent control of a plurality of desired electromagnetic (EM) properties of the optical resonator 100, including: a desired resonant wavelength, a desired coupling strength (leading to resonator quality factor, Q), and a desired level of back reflection (e.g., ensuring that any reflection achieved is due only to the designed resonator interaction and not incidental Fresnel reflections that are TE-TE back-reflections). The back reflection is a non-resonant property, i.e., the reflected light includes wavelengths other than the resonant wavelength for which the optical resonator 100 has been formed.

[49] The ridge mode predominantly responds to (or "sees") three (3) of the selectable geometric features: WP, WC, and WL. In this context, "predominantly" refers to the interaction of the ridge mode with these geometric features being substantially stronger than the interaction of the slab mode with these geometric features, including one or two or three orders of magnitude stronger, e.g., 100 times stronger. In contrast, the slab mode predominantly responds to (or "sees") only two (2) of the selectable geometric features: WT and WP, the trench width and the pedestal width. In this context,

"predominantly" refers to the interaction of the ridge mode with these geometric features being substantially weaker than the interaction of the slab mode with these geometric features, including one or two or three orders of magnitude weaker, e.g., 100 times weaker for WT. The coupling between the slab mode and the ridge mode, which depends on the lateral leakage, requires both modes to be supported at the same position, and the ridge mode is only very weakly present (if at all) at the sides (or steps) of the trench 112, so the trench width value WT does not greatly affect the ridge mode. In contrast, both the slab mode and the ridge mode are present at the sides (or steps) of the main ridge (including the sides of the pedestal 128 and of the core 126), so most of the coupling between the mode occurs along these sides, and the values of WP and WC predominantly affect the coupling. In this context, "predominantly" refers to the coupling being affected by these geometric features substantially more strongly than by the other geometric features, including one or two or three orders of magnitude more strongly. The sides (or steps) of the loading 130 are so far (i.e., so distant) from the slab mode that there is little overlap between the slab mode and the ridge mode at the sides of the loading 130, so the sides and width WL of the loading 130 have little effect on the coupling between the slab mode and the ridge mode.

[50] In summary, the width WT and the width WP most strongly affect the back reflection of the slab mode due to traditional Fresnel reflection, i.e., TE-TE reflections, i.e., direct reflection of light in the slab mode without conversion to the ridge mode. The width WC and the width WL have minimal impact on the background reflection. The width WP and the width WC most strongly affect the coupling between the slab mode and the ridge mode. The width WT and the width WL have minimal impact on the coupling between the slab mode and the ridge mode. The widths WP, WC and WL all affect the phase matching frequency of the resonator (while WT has minimal impact). These isolated dependencies may greatly aid design of suitable resonators for filter applications.

[51] A shortcoming of previous optical resonators may have been that it was difficult to select geometrical values that achieved high performance over a wide wavelength range due to the limited number of variable geometrical values available, and constraints placed on these variable geometrical values by certain fabrication processes, e.g., low-cost mass manufacture. For example, filters based on previous optical resonators, in which there was flexible control of the resonator's stop-band properties (i.e.,

independent control of Q and resonant wavelength)— e.g., using selected etch depths, or independent control of the filter's stop-band and pass-band properties (back reflection), were often not compatible with low-cost mass -manufacturing design rules. [52] Compared to example prior resonator designs, e.g., described in

WO/2016/149749A1, the geometric features described herein are more independent in their control of or effect on the EM properties. For example, the slab mode in the optical resonator 100 described herein interacts with the trench 112 but not with the loading 130; in contract, in the optical resonator 100 described in Figure 9(b) of WO/2016/149749A1, the slab mode may undesirably interact with the described dielectric loading strips, and furthermore the dielectric loading strips in WO/2016/149749A1 may be high-n and have a very strong effect on one or both modes, which can then be hard to control accurately in design.

Operational Method

[53] The resonator 100 operates according to the following method: a. the slab 106 supports the optical slab mode; b. the input waveguide directs light into the optical slab mode and towards the RWG 104, which has its selected resonant wavelength defined by the main ridge and the loading 130; c. the coupling ridges couple light at the resonant wavelength in the optical slab mode to the optical ridge mode; and d. the trench 112, with the selected WT, transmits light not at the resonant wavelength (i.e., off-resonant light) in the optical slab mode past the RWG 104 by means of the gap 124 between the slab 106 and the base 122 of the main ridge.

Manufacturing Method

[54] For manufacturing, the trench width (WT) is selected such that the slab beam passing under the main ridge is approximately an integer multiple of half wavelengths between the edges of the trench 112, which leads to a minimum in reflection in the absence of the TE-to-TM conversion effect. The pedestal width (WP) and the core width (WC) are selected (or adjusted) to optimize coupling between the slab beam and ridge mode to provide a selected resonator quality factor (Q) required for a desired filter design. The loading width (WL) is selected (or adjusted) so that, for a specific incident angle THETA, the slab beam and the ridge mode are phase matched at the desired wavelength.

[55] The optical resonator 100 can thus be formed or manufactured by the following method: a. receiving or defining desired electromagnetic (EM) properties, including the resonant wavelength, the Q, the reflectivity, the angle THETA etc., based on an application of the resonator; b. selecting the values of the geometric features (WT, WP, WC, and WL) based on the desired electromagnetic properties, including: i. selecting WP and WC based on the desired Q and desired resonant wavelength, ii. selecting WT based on the desired wavelength such that an EM

trench width at the resonant wavelength (which depends on the selected WL and WP, and in some cases WC, and so requires the prior selected WP and WC) is an integer multiple of half the resonant wavelength so that the trench 112 is antireflective at the resonant wavelength, i.e., so that Fresnel reflections of the slab mode are minimised at the desired wavelength, and iii. selecting WL (or equivalently the cross-sectional area of the loading 130) based on desired phase velocity of the ridge mode, which is determined based on the resonant wavelength and the angle

THETA; c. building a simulation of the optical resonator 100 with the selected values (WT, WP, WC, and WL) of the geometric features, and default values of other features, including the material properties, e.g., using the REME simulator in the IPKISS design framework from Luceda Photonics; d. numerically simulating electromagnetic properties of the simulated optical resonator 100 to determine simulated values of the electromagnetic properties, which can include the resonant properties, the stop-band properties, and the pass-band properties; e. if the simulated electromagnetic properties are insufficiently close to the desired electromagnetic properties, adjusting the selected values of the geometric features following a similar procedure to the procedure of step (b) above; f. forming the slab 106 as a single layer of high-index material which can be single crystal silicon; g. etching the one or more trenches into the slab 106, each with a selected WT (which can differ from each other, e.g., for different resonant wavelengths); h. filling the trench 112 with low index material, which can be silicon dioxide; i. planarising the filled trench(s) 112; j. coating a middle strip along each trench 112 with an additional layer of high index material which can be polycrystalline silicon; k. patterning the middle strip and etching to two etch depths to form the main ridge, including: i. a full etch patterned to form the pedestal of width WP, and ii. a partial etch patterned to form the core of width WC;

1. coating the main ridge with an additional layer of low index material which can be silicon dioxide; m. planarising the additional low index layer over the main ridge to leave the low-n spacer 132; n. depositing an intermediate index layer, having a refractive index between the high and low index materials, which can be silicon nitride, over the planarised additional low-n layer; and o. patterning and etching the intermediate index layer to leave the loading 130 with width WL and selected thickness.

[56] WT is selected to be larger than WP, and WC is selected to be smaller than

WP, to make the fabrication process simpler. WL can be selected independently of WT, WP and/or WC because it is separated vertically from the other geometric features.

[57] The step of selecting WP and WC based on the desired Q in Step (b)(i) above is done by: simulating eigenvalues of the ridge mode (i.e., the TM mode supported by the ridge) using a mode-matching eigenmode simulator. The Q of the resonator can be calculated using the following relationship:

|ω ₂ - 6>i |

ω ₀

γ =—lmag(n _TM )

where coo is the resonant frequency, O∑E and O∑M are the dispersion of the phase velocity of the TE slab mode and TM ridge mode respectively, and n _TM is the complex effective index of the TM mode of the RWG 104. [58] The step of selecting WT based on the desired wavelength in Step (b)(ii) above is done by: simulating the transmission response of the resonator 100 and the apparatus using a mode-matching propagation tool, and observing the transmitted and reflected power in the fundamental TE slab mode.

[59] The step of selecting W4 based on the desired phase velocity in Step (b)(iii) above is done by: simulating the eigenvalues of the TM mode supported by the RWG 104 using a mode-matching eigenvalue simulator. The real part of the eigenvalue is proportional to the phase velocity.

Examples

[60] In an example, a silicon-on-insulator wafer has silicon (n = 3.5) of thickness

140nm. The wafer can be etched partially to form the trench 112 with WT, and then this can be coated with low index material (typically silicon dioxide), and then planarised, leaving a very thin oxide in the trench 112. A high index layer (typically polysilicon, n = 3.5) of thickness 120nm can be deposited over the top. This can then be etched partially to form the core 126 with width WC, and then etched fully to form the pedestal 128 with width WP. This can then be coated again with low index material (typically silicon dioxide), and then planarised again, and then a further layer of material, with intermediate index (typically silicon nitride, n = 2), could be deposited and fully etched to form the loading 130 with width WL.

[61] In an example, the minimum width WL of the loading 130 may be set by the fabrication process, e.g., to around 200nm (nanometer). The maximum width WL of the loading 130 may be unconstrained by the other geometric features and the fabrication process, leaving it as a free tuning variable to tune the phase velocity of the ridge mode. The depth of the loading 130 may be set by the fabrication process, e.g., to around lum (micrometer).

[62] In an example, the loading 130 may be implemented as a plurality of separated portions, e.g., with high-n material or low-n material between the portions; however, the ridge mode sees the plurality of separated portions as a single loading, in particular where the separated portions are substantially closer than the optical wavelength.

[63] An example filter, as shown in Figure 2, can include three or more optical resonators 100 (e.g., 5 or 7 resonators for higher-order filters) with selected values for the geometric properties that differ between the optical resonators 100 to ensure that the resonators all have the same resonant wavelength but appropriately chosen Q values to form the desired coupled resonator filter function, based on known filter-design

techniques. An example first resonator in the example filter can have the following selected values: loading width = 700nm (WL), core width = 640nm (WC), pedestal width = 1700nm (WP), and trench width = 2850nm (WT). An example second resonator in the example filter can have the following selected values: loading width = 1500nm (WL), core width = 580nm (WC), pedestal width = 1700nm (WP), trench width = 2850nm (WT). The separation between the example first resonator and the example second resonator can be 200nm (between the trench walls of the adjacent resonators).

Alternatives

[64] In some embodiments: a. any selected number of the resonators 100 can be coupled together to form a filter, or filters; b. the trench 112 could continue uninterrupted under the main ridges of a plurality of adjacent resonators 100, i.e., there does not need to be an upward step 118 (or "step up") and a downward step 114 ("step down") between each pair of resonators 100; c. the main ridge could be implemented as a plurality of sub-ridges that

together carry the ridge mode; d. the loading 130 could be implemented as a plurality of sub-loadings that together interact with the ridge mode— e.g., the loading 130 could be split into 2 or 3 sub-loadings in the form of loading pieces; e. the trench 112 could also be split longitudinally into a plurality of at least partially (or "essentially") parallel trenches: including 2 trenches, one on each side with a spatial separator (which can be formed of the high-n material, such as a pillar of silicon) connecting the slab to the ridge, or more than 2 trenches, with adjacent ones of the trenches being

electromagnetically coupled (to carry the slab mode) and yet being spatially separated by a spatial separator— this plurality of essentially parallel trenches can be used to engineer dispersion in the resonator 100, e.g., to make the filter work over a broad wavelength range or to use the filter in a nonlinear optic configuration (the meaning of "essentially parallel" is set out hereinbefore); f. the materials could include different low-n materials, high-n materials

and/or intermediate-n materials, e.g., Indium Phosphide or Lithium Niobate, etc.; and g. the resonant wavelength can differ based on the photonic system, and the materials used, e.g., visible light, i.e., 400nm to 800nm with different materials; near infrared (NIR), i.e., 800nm to 1600nm, including around 1550nm, around 1300nm; or mid infrared (MIR), i.e., 1600nm to 3000nm, or to 10,000nm with different materials.

[65] The plurality of the sub-ridges that together carry the ridge mode could be formed of electromagnetically coupled, thin-ridge waveguide elements, aligned at least partially (or "essentially") parallel with the RWG axis, as described in

WO/2016/ 149749 A 1— this plurality of essentially parallel thin-ridge waveguide elements can be used to engineer dispersion in the resonator 100, e.g., to make the filter work over a broad wavelength range or to use the filter in a nonlinear optic configuration (the meaning of "essentially parallel" is set out hereinbefore), and spacing between the thin-ridge waveguide elements can be selected to differ subtly (on the order of 1%) to apodize the filter (as described hereinbefore); [66] The plurality of the sub-loadings that together form the loading 130 could be formed of electromagnetically coupled, spatially separated, thin longitudinal loading elements, aligned at least partially (or "essentially") parallel to the loading axis this plurality of essentially parallel loading elements can be used to engineer dispersion in the resonator 100, e.g., to make the filter work over a broad wavelength range or to use the filter in a nonlinear optic configuration (the meaning of "essentially parallel" is set out hereinbefore), and spacing between the loading elements can be selected to differ subtly (on the order of 1%) to apodize the filter (as described hereinbefore).

[67] The low-n materials can include: air, Si02, BCB, SU8, silicon nitride, and

MgF. The intermediate-n materials can include SiN2, any soft glass such as AsS3, Ta205, Ti02, A1N or high-index glass, and Lithium Niobate. The high-n material can include most semiconducting materials, e.g. III-V materials, Silicon, Lithium niobate, etc. The index contrast between the low-n material and the intermediate-n material is around 15- 20%, and the index contrast between intermediate-n material and the high-n material is around 15-20%.

Interpretation

[68] Many modifications will be apparent to those skilled in the art without departing from the scope of the present invention as hereinbefore described with reference to the accompanying drawings.

[69] The reference in this specification to any prior publication (or information derived from it), or to any matter which is known, is not, and should not be taken as an acknowledgment or admission or any form of suggestion that that prior publication (or information derived from it) or known matter forms part of the common general knowledge in the field of endeavour to which this specification relates.