WO2021224240A1

WO2021224240A1 - Polarization selective resonator

Info

Publication number: WO2021224240A1
Application number: PCT/EP2021/061701
Authority: WO
Inventors: Chanju Kim; Minhao PU; Kresten Yvind
Original assignee: Danmarks Tekniske Universitet
Priority date: 2020-05-04
Filing date: 2021-05-04
Publication date: 2021-11-11

Abstract

An optical device comprising a resonator waveguide and a filter waveguide optically coupled with the resonator waveguide at a coupling region is disclosed. The resonator waveguide is configured to support at least a first polarization mode and a second polarization mode, the second polarization mode being an operational mode of the resonator waveguide. The resonator waveguide has a first effective index associated with the first polarization mode and a second effective index associated with the second polarization mode. The first polarization mode is in a different polarization than the second polarization mode. The filter waveguide has, in the coupling region, a filter first effective index associated with the first polarization mode, wherein the filter first effective index at least approximately matches with the first effective index of the resonator waveguide such that the first polarization mode is filtered out of the resonator waveguide.

Description

POLARIZATION SELECTIVE RESONATOR

FIELD

The present disclosure relates to an optical device comprising a resonator waveguide optically coupled to a filter waveguide which selectively filters one unwanted polarization mode from the resonator waveguide.

BACKGROUND

Optoelectronic devices such as resonators, especially dielectric micro-resonators are extensively studied subject due to their broad range of applications, such as for broadband light sources, in optical metrology, optical sensors, spectroscopy, etc. Theoretically, micro-resonators, in order to have optimal operation, need to be designed to operate in a single-polarization mode with controlled loss and dispersion characteristics for the operational polarization mode. However, in widely used channel waveguides, at least two fundamental polarization modes (quasi-TEoo and quasi-TMoo mode) are supported simultaneously. When such waveguides form a resonator, the coexistence of the two fundamental polarization modes becomes detrimental in various application scenarios. Particularly, in a low-loss resonator with non-negligible intermodal coupling between the two fundamental polarization modes, avoided mode crossing is introduced by the two polarization modes forming a hybridized mode when their resonances coincide in wavelength. The polarization-mode-coupling is influenced by waveguide cross-section dimensions, sidewall angles, radius of curvature in curved section, mechanical stress, refractive index contrast, etc. The avoided mode crossing can be observed by local resonance shift or resonance splitting due to the hybridization of the two coupled polarization modes. Such local resonance shift is especially detrimental to Kerr frequency comb generation where the local resonance shift not only introduces local loss due to the resonance detuning but also locally distorts the dispersion resulting in a perturbed parametric gain profile.

Various studies have numerically and experimentally shown the avoided mode crossing effect causing distorted amplitude envelope and unstable operation of a frequency comb. In particular, suppression of avoided mode crossing induced by high-order spatial mode coupling with fundamental spatial mode has been experimentally demonstrated by an intracavity adiabatic tapering. However, suppression of avoided mode crossing induced by polarization mode coupling has not been investigated up to this date although such avoided mode crossing is found universally in various resonator designs and material platforms.

SUMMARY

It is an object of the present invention to provide a polarization selective resonator designed to suppress avoided mode crossing induced by a polarization mode coupling. It is a further object of the present invention to provide a polarization selective resonator designed to have operational mode with low losses.

In a first aspect, disclosed is an optical device comprising a resonator waveguide and a filter waveguide optically coupled with the resonator waveguide at a coupling region, the resonator waveguide being configured to support at least a first polarization mode and a second polarization mode, the second polarization mode being operational mode of the resonator waveguide, the resonator waveguide having a first effective index associated with the first polarization mode and a second effective index associated with the second polarization mode, the first polarization mode being in a different polarization than the second polarization mode, the filter waveguide having, in the coupling region, a filter first effective index associated with the first polarization mode, wherein the filter first effective index at least approximately matches with the first effective index of the resonator waveguide such that the first polarization mode is filtered out of the resonator waveguide.

The optical device having the resonator and filter waveguides coupled to each other at the coupling region, where light is evanescently coupled there between, supresses avoided mode crossing induced by polarization mode coupling in the resonator waveguide. The optical device is a polarization selective resonator. The optical device may be utilized in a frequency comb generation, as a coupler, filter, or similar. The optical device is typically an integrated optical structure which can be fabricated together with other optical devices on a single chip. It can be fabricated with waveguide material including Aluminium gallium arsenide, Aluminium nitride, Gallium phosphide, Gallium nitride, Indium gallium phosphide, Indium phosphide, Indium arsenide, Silicon, amorphous Silicon, Silicon nitride, Silicon carbide, Diamond, High index doped silica glass, Chalcogenide glass, Lithium niobite and Tantalum pentoxide, where the waveguide may partially or wholly comprise of quantum well or quantum dot structures; and cladding or substrate material including vacuum, air, water, Silicon dioxide, Titanium dioxide, Sapphire (or Alumina), Barium titanate and dye-doped organic; where the materials comprising the optical device could have various optical functions including optical gain from stimulated emission, stimulated Raman scattering, stimulated Brillouin scattering, and nonlinear parametric process, optical modulation from Pockels effect and plasma dispersion effect; and many other enabled by electro-, magneto-, and acousto optic effects.

The resonator waveguide can be a loop waveguide or it could be an arbitrary waveguide structure with a feedback, such as a Fabry-Perot resonator with high reflection structure/coating at both ends. The loop waveguide may be an uninterrupted closed waveguide. The loop may be circular, elliptical, or have an arbitrary curved circumference. The resonant waveguide may support at least one resonant mode. The supported resonant mode may comprise two orthogonal polarization modes. The resonator waveguide may operate at one resonance wavelength, or it may be broadband, i.e. supporting a range of wavelengths. The resonance wavelength is a function of the resonator optical length defined by a physical length of the resonator waveguide and its refractive index. The resonator waveguide may be defined by a core and a cladding surrounding the core and having a refractive index lower than a refractive index of the core. Dimensions of the core may be in nm to pm range, e.g. from 200 nm up to 3 pm. It may be desired that the resonator waveguide operates at one polarization mode to thereby provide a high quality signal free from a polarization cross-talk.

The resonator coupled to the filter waveguide may be used for generating second harmonic light, optical parametric oscillation, frequency comb, squeezed light or photon- pair using spontaneous/stimulated optical nonlinear processes (i.e., parametric nonlinearity, Raman scattering, and Brillouin scattering).

The resonator coupled to the filter waveguide may be used for spectroscopy and sensing (i.e., refractive index, temperature, force/pressure, humidity, electric-/magnetic- field, molecule, single-particle, and chemical). The resonator waveguide may consist of gain material and the first polarization mode resonator net roundtrip loss may be set higher than the resonator net roundtrip gain by using the filter waveguide coupled to the resonator waveguide. Such condition may suppress unwanted lasing of the first polarization mode by selectively increasing the lasing threshold. The filter waveguide may be a waveguide with two open ends. The filter waveguide is designed such that it selectively filters an unwanted polarization mode from the resonator waveguide and maintains low loss for an operating polarization mode of the resonator. Similar to the resonator waveguide, the filter waveguide may be defined by a core and cladding. Materials used for the core and cladding of the filter waveguide may be the same as materials defining the resonator waveguide.

The filter waveguide may consist of optical structure(s) designed with inverse a design method (i.e. , topology optimization, level-set method, adjoint-based optimization, genetic algorithm, direct-binary-search, or particle swarm optimization) to assist fabrication tolerant effective index matching (mismatching) or mode matching (mismatching) of the filter and the resonator waveguide first polarization mode (second polarization mode).

The filter waveguide may not have a well-defined input and output where the input and output ports are entirely or partially coupled to non-guided modes (leaky modes or scattering modes)

The resonator and filter waveguides may be strip waveguides, ridge waveguides, rib waveguides, buried-channel waveguides, strip-loaded waveguides, diffused waveguides, or similar. The type of the resonator waveguide and the filter waveguide may not be the same, i.e. the resonator waveguide may, e.g., be a strip waveguide and the filter waveguide may, e.g., be a ridge waveguide. Both the resonator and filter waveguide may be arranged on a substrate.

The resonator waveguide and filter waveguide are optically coupled at a coupling region. Coupling of light takes place within the coupling region defined by both the resonator waveguide and the filter waveguide via evanescent field coupling. An evanescent optical field is the portion of the optical field of guided light that extends beyond the physical surface of a waveguide. For coupling to take place, an appropriate overlap between the modes in the resonator and filter waveguides at the coupling region may be required. Since the evanescent field normally does not extend far, the resonator waveguide is typically placed in close proximity to the filter waveguide to ensure efficient coupling. The light (mode) traveling along the resonator waveguide couples, over a resonator coupling length, to the filter waveguide over a filter coupling length. Coupling between the waveguides may be described by a coupling coefficient which defines a fraction of optical power that is transferred between the two waveguides. Coupling coefficient mainly depends on three factors: effective-index-matching, i.e. a phase-matching, a field overlap of the light modes, and coupling length over which the coupling takes place. When effective indices are matched the coupling efficiency is maximized and when mismatched the coupling efficiency is drastically dropped. A part of the mode field propagating in one of the waveguides leaks into the other waveguide structure. The field-overlap exponentially decreases with the distance between the waveguides. Coupling length is typically controlled to achieve a desired level of coupling at a predetermined effective index and field-overlap configuration of participating waveguides.

The coupling region is the region where main coupling occurs, i.e. where the filter waveguide approaches the resonator waveguide. Away from the coupling region, coupling between the resonator waveguide and filter waveguide becomes negligible. The coupling region may be defined by a coupling length and coupling gap. The coupling length may, in turn, be defined by the resonator coupling length and the filter coupling length, and the coupling gap may be defined by spacing between the resonator and filter waveguides. The coupling length and coupling gap serves as a figure for footprint of the coupling region. In addition, the coupling length and coupling gap together with the coupled waveguide dimension are controlled to achieve a desired coupling efficiency for a specific guided mode.

The filter coupling length may be shorter than, and/or not an odd integer multiple of the maximum power transfer coupling length of the first polarization mode to the filter waveguide. Such filter coupling length results in the filtering loss of the first polarization that are smaller than 100%, such as lower than 50% (3 dB), such as lower than 80% (7 dB). The filter coupling length shorter than the maximum power transfer length of the firs polarization mode to the filter waveguide is optimal for the present invention as unnecessarily long coupling length would increase the insertion loss of the second polarization mode in the optical device. Lower limit of the filtered power of the first polarization mode approximately can be determined by the condition \y_t — g₂ \ > 4k (viz. weak-coupling regime in two resonator coupled system), where g_ί is the first polarization mode resonator loss largely imposed by the first polarization mode filtered power, g₂ is the second polarization mode resonator loss, and k is the resonator coupling between the first and the second polarization mode, for suppression of avoided crossing, or by the single-pass net power gain of the first polarization mode, for single polarization mode lasing.

The filter coupling length shorter than the maximum power transfer length of the first polarization mode to the filter waveguide also allows for larger coupling gap since it does not require complete transfer of the first polarization mode, i.e. the first polarization mode does not have to be completely transferred out. Large coupling gap normally results in lower insertion loss, i.e. larger index mismatch.

Maximum power transfer coupling length is wavelength dependent, i.e. it depends on the wavelength of the light propagating in the optical device. Maximum power transfer is a scenario when nearly 100% of one polarization is coupled to a coupling waveguide. In the present scenario it would refer to the case when nearly 100% (with 0.01 %-1% discrepancy) of the first polarization is coupled to the filter waveguide. This would be achieved if the coupling length is set at the maximum power transfer coupling length. As explained above, the coupling length of the present invention may be shorter than the maximum power transfer coupling length thereby achieving less than 100% coupling to the filter waveguide. Given that the maximum power transfer length is wavelength dependent, if operating at a different wavelength (e.g. 1600 nm) than the design wavelength (e.g. 1550 nm), the maximum power transfer coupling length will be lower than 100%. This is due to the fact that the effective index (matching) may change with the wavelength; a different filter waveguide width should be used for a different design wavelength to ensure effective index matching of the first polarization mode. The coupling length may be 90%, 80%, 50%, 20% 10% of the maximum power transfer coupling length. Coupling power, i.e. coupling efficiency, is related to the coupling length for directional couplers through formula:

where is k-th polarization mode coupling power from the resonator waveguide to the filter waveguide; k refers to a polarization mode, 1 is for the first polarization mode and 2 for the second polarization mode; l is actual coupling length defined by the structure.

Further, A^k is the maximum power transfer intensity determined by the effective index matching of the k-th polarization mode between the resonator and filter waveguide. In the case of perfect refractive index matching, A^k =1, while, according to the present invention, A¹ = 1

is the maximum power transfer coupling length for the k-th polarization mode.

The coupling length and the second polarization mode coupling may not be in a direct correlation as they are effective index mismatched. The second polarization mode may show a fast periodic beating with very low level of maxima. Maxima may be kept sufficiently low (to a negligible level) so that the second polarization mode operation is not affected by this loss. The level of this maxima may be determined by the coupling gap (lower maxima with larger gap) and the effective index mismatch (lower maxima with more mismatching).

The resonator waveguide is configured to support at least a first polarization mode and a second polarization mode. Namely, the resonator waveguide is designed such that at least these two polarization modes are supported simultaneously. The first polarization mode may be a TEoo mode, a TMoo mode, or any other higher order polarization mode. The second polarization mode may also be a TEoo mode, a TMoo mode, or any other higher order polarization mode.

The second polarization mode is an operational polarization mode of the resonator waveguide. Namely, the second polarization mode is a preferred mode which is to be enhanced in the resonator in multiple round-trips. In other words, the second polarization mode is a dominant mode circulating in the resonator waveguide and finally out-coupled from the resonator waveguide as a use signal for possible further signal processing. The first polarization mode may be an unwanted polarization mode which is to be filtered out from the resonator waveguide. Typically, the operating mode is a TEoo polarization mode while a TMoo may be filtered out.

The first polarization mode and the second polarization mode have different polarization. The first polarization mode may have zero electric field in the propagation direction while the second polarization mode have zero magnetic field in the propagation direction, or vice versa. For instance, if the first polarization mode is TM mode, the second polarization mode may be TE_ki mode where i, j, k, and I represents arbitrary number for describing the order of each polarization mode. The reason for filtering one of the polarization modes is to avoid polarization mode coupling which has a detrimental effect on the propagation of an optical signal inside the resonator waveguide.

The first and second polarization modes may be of the same order, or they may be of a different order. In one example, the first polarization mode may be TMoo and the second may be TEoi. In another example, the first polarization mode may be TMoi and the second polarization mode may be TEoi.

The resonator waveguide has a first effective index associated with the first polarization mode and a second effective index associated with the second polarization mode. An effective index, n_efr, of a waveguide indicates how strongly one mode is confined in the waveguide, it is dependent on wavelength, and each mode has its own effective index. The effective index depends on dimensions of the waveguide, mainly a height and width of a waveguide core, a refractive index n of the core, a refractive index n of the cladding, wavelength of the light propagating in the waveguide, and a mode in which the light propagates. The effective index may also depend on other components placed in a waveguide’s close proximity. Its value can be, e.g., obtained with numerical mode calculations. The effective index is a dimensionless number which lies between the refractive index of the cladding and the refractive index of the core of the waveguide. Propagation constant which defines phase-matching in waveguides is directly proportional to the effective index. Thus, the phase-matching in waveguides is also defined by the effective index. Normally, the resonator waveguide has a constant cross-section over the entire length, i.e. the width and height of the core are constant and made of one type of material. Alternatively, the resonator waveguide may have a width which varies over the length. Thereby, the resonator waveguide having a fixed design also have one same effective index associated with a particular mode along its entire length.

The filter waveguide has, in the coupling region, a filter first effective index associated with the first polarization mode. The filter waveguide may have dimensions which vary over its length, i.e. the width and height of the core may not be constant over the filter waveguide’s length and therefore the effective indices of various modes supported by the filter waveguide may not be the same over the entire length of the filter waveguide. The filter first effective index associated with the first polarization mode relates to the coupling region mainly. If the cross-section of the filter waveguide is constant over the entire length, the effective indices will also be constant over the length.

The filter first effective index at least approximately matches with the first effective index of the resonator waveguide such that the first polarization mode is filtered out of the resonator waveguide. Ideally, matching of the effective indices of the filter and resonator waveguide associated with the first polarization mode means that these two effective indices are the same. Due to fabrication errors, small variations in a predicted effective index may occur. These small variations should not greatly influence the phase-matching conditions between the first polarization mode propagating in the resonator and filter waveguide. The main purpose of effective index matching for the first polarization mode is to cause high losses in propagation of the first polarization mode propagating in the resonator waveguide, and in particular higher losses than losses imposed on the second polarization mode.

By matching the effective indices in the coupling region, filtering of the first polarization mode from the resonator waveguide is achieved by coupling that mode to the filter waveguide. Namely, by matching the effective indices, phase-matching between the first polarization mode propagating in both the resonator and filter waveguides is achieved allowing for optical coupling of the first polarization mode from the resonator to the filter waveguide. When the first polarization mode is, to a large extent, filtered out of the resonator waveguide, interaction between the first and second polarization modes in the resonator is limited, if not completely supressed, i.e. avoided mode crossing is suppressed. The avoided mode crossing involves coupling of two or more transverse modes in the resonator waveguide. When the coupled transverse modes’ resonances approach each other in frequency, resonance-splitting appears, which indicates a lifted degeneracy by hybridization of the coupled modes. As a result, the dispersion and resonance of the resonator waveguide are locally perturbed, which may manifest as distorted spectrum in frequency combs and unstable solitons. Filtering one unwanted transverse mode out of the resonator suppresses the avoided mode crossing.

Also, in case of the resonator waveguide having comparable net optical gain for the first and second polarization modes, filtering out the first polarization mode may suppress lasing for the first polarization mode. Hence, single polarization mode lasing can be achieved.

In order to achieve index matching, the resonator waveguide is designed first depending on application requirements. Namely, the resonator waveguide design aims for a specific group velocity dispersion (GVD) and free spectral range (FSR) of the resonator. It may be desired that the resonator waveguide delivers TEoo mode, i.e. TEoo is the operational mode while TMoo mode is to be filtered out. In one example, where the resonator waveguide is a loop waveguide, the width of the resonator, W_r, is defined (i.e. spacing between side-walls of the core), the height of the resonator (spacing between the bottom and top cladding), H_r, and the radius of the resonator, R_r. In the next step, a coupling gap (spacing between the cores of the filter and resonator), G, is decided based on fabrication capability and allowed footprint of the coupling length or area in the resonator waveguide. Normally, if the coupling gap increases, the coupling length may need to be increased as well. Then, the design of the filter waveguide is approached. At first, an effective index analysis may be done based on a cylindrical coordinate system. The origin of the cylindrical system in this method is at a center of curvature of the resonator waveguide. This can be done through a numerical simulation software. The input parameters may be a refractive index of the core and cladding materials and geometric configuration of these. The first and second effective indices of the resonator waveguide, n_eff for TEoo and n_efr for TMoo mode, are analysed based on input parameters, R_r, W_r and H_r, and recorded. The effective indices of TEoo and TMoo mode of the filter is matched by choosing an appropriate filter width, W_p. Effective index analysis may be done for ranged sweep of W_p. One additional input parameter may be a radius of curvature of the filter, R_p, R_p = R_r + G + W_r/2 +W_p/2. Cross-coupling simulation performed fora coupling angle, q_r, sweeps and chooses a value that suffices a desired level of cross-coupling. Usually, filtering of a polarization mode with a lower effective index is preferred due to a lower confinement which makes it easier to cross-couple to the filter waveguide.

In some embodiments, the first polarization mode is a first fundamental polarization mode. The second polarization mode may be a second fundamental polarization mode which is preferably in a different polarization to the first fundamental polarization mode. When only TEoo and TMoo modes are supported, the resonator waveguide is single mode. It is an advantage to have a resonator waveguide which operates at a fundamental polarization mode, either TEoo or TMoo, as a number of applications require single-mode polarized signal. In some embodiments, the first and second polarization mode may be higher order polarization modes. If the first polarization mode is of the second order, then the second polarization mode will typically be of the second order as well, and effective index matching is achieved for these two polarization modes.

If one needs to efficiently cross-couple a fundamental polarization mode in a simple directional coupler configuration (two waveguides with same material, thickness and straight coordinates), an identical width should be used for the two waveguides to achieve effective index matching for the fundamental polarization mode of interest. However, this accompanies simultaneous effective-index-matching for the different fundamental polarization mode as well. If a selective cross-coupling of a fundamental polarization is required, the effective-index-matching condition may be satisfied for the mode of interest only. Such polarization beam splitting is possible in configurations such as a bent waveguide coupler, slot waveguide coupler, waveguide with different thickness, and similar. In terms of design and fabrication simplicity, the bent waveguide coupler is a preferred mode to achieve polarization mode filtering in the resonator. In some embodiments, the filter waveguide has, in the coupling region, a filter second effective index associated with the second polarization mode, n_eff-2F, and wherein the filter second effective index, is mismatched with the second effective index of the resonator waveguide, n_efr_2R, . In the present context, the term mismatched is to be interpreted such that a degree of matching of the second effective indices is lower than a degree of matching of the first effective indices (n_efr_i F and n_eft_i_R). Namely, it may be desired to have poorer effective index matching for the second polarization mode than the first polarization mode, i.e.

| n_eff_2R - n_eff_2F| > | n_eff_i R - n_eff_i

For a perfect matching n_efr_i_R - n_efr_i F is zero, i.e. the effective indices of the resonator and filter waveguides are exactly the same. When the effective indices are not matched, their absolute difference is larger than zero.

In a scenario when the filter waveguide does not have a constant cross-section in the coupling region, an average effective indices can be derived. In this case, an average mismatch of the filter second effective index and the resonator second effective index along the longitudinal direction of the coupling section is larger than the average mismatch of the filter first effective index and resonator first effective index along the longitudinal direction of the coupling region.

Mismatch in indices for the second polarization mode, i.e., the operational mode, ensures maintaining low losses for the operational polarization mode propagating in the resonator waveguide since the coupling of the second polarization mode between the resonator and filter waveguides is minimized as all power of this operational mode is maintained within the resonator.

In some embodiments, in the coupling region, the resonator waveguide comprises a resonator coupling section and the filter waveguide comprises a filter coupling section being spaced from the first resonator section by a gap. Namely, the resonator coupling section and the filter coupling section define the coupling region. These sections may either be fabricated side by side or one above the other. The gap may be filled by a cladding material of one of the waveguides. Typically, the gap forms a common cladding for the resonator and filter waveguide. In this way, the gap determines boundaries of the waveguides. A dimension of the gap is to be chosen such that efficient coupling between the waveguides is achieved. A minimum width of the gap may be dependent on fabrication limitations and low coupling requirement for the second polarization mode of the resonator. In one example, the gap may be 500 nm wide, or it may be 400 nm wide, or it may be 300 nm wide. On the other hand, a maximum width of the gap is limited by the required filtering amount. When the resonator and filter waveguides are too far apart under that the evanescent tail of the polarization mode traveling in one waveguide does not sufficiently overlap the other waveguide, coupling to the filter waveguide may not be enough within the coupling region limit.

The gap may extend in the same horizontal plane as the resonator and filter cores, or it may extend in the same vertical place as the resonator and filter cores. The gap width may influence effective index matching and field overlap and thereby evanescent coupling.

In some embodiments, the gap is filled with air or a dielectric material. The dielectric material may be chosen depending on the core material. When the optical device is fabricated on a SOI platform, the gap is typically silicon-oxide. The gap material has refractive index lower than refractive indices of the resonator and filter waveguides cores to ensure tight mode confinement. When the gap is formed of air, the resonator and filter waveguides typically do not have a top cladding.

In some embodiments, the resonator coupling section and the filter coupling section are curved, wherein preferably, the radius of curvature of the resonator coupling section and the radius of curvature of the filter coupling section have substantially the same centres. The curvature of the resonator waveguide and the curvature of the filter waveguide may have the same centres. The radius of curvature of the resonator coupling section and/or the radius of curvature of the filter coupling section may gradually change over the curve path. When this is the case, the curved coupling region may have a shape of a clothoid curve. The coupling section can be infinitely subdivided into smaller section. By having a curved coupling section where both the resonator and the filter waveguide are curved, a difference in phase matching of two different polarization modes can be achieved thanks to a design freedom of the curve. Thereby, significant losses to an unwanted polarization mode of the resonator waveguide (phase-matched mode) are selectively introduced, while low losses for an operating polarization mode of the resonator waveguide (less phase-matched) are maintained.

In some embodiments, the resonator coupling section and the filter coupling section are straight. This embodiment can be achieved by using various structures for the filter waveguide such as waveguide with different height or material, slot waveguide, subwavelength grating waveguide and adiabatically tapered waveguide. When both the resonator coupling section and the filter coupling section are straight, the coupling region can be considered as an asymmetric directional coupler or as an adiabatic/diabatic polarization mode splitter. The effective index is matched for the unwanted polarization mode and preferably mismatched for the operational mode. In some cases, large field- overlap or low optical confinement of the unwanted polarization mode may be utilized to achieve large coupling of the unwanted polarization mode. The cross-section of the filter waveguide may not be constant along the entire length of the coupling region. It is advantageous to have straight resonator and filter coupling section as it allows freedom in design where many resonators have large straight section due to practical limitation, and in some cases would allow simple fabrication and design.

In some embodiments, the resonator coupling section and the filter coupling section extend in parallel. Namely, the two waveguides run side by side in the coupling region and a distance between them, i.e. the gap, is the same along the entire length of the coupling region. The gap may be constant over the entire length of the coupling region regardless of whether the coupling region is curved or straight. Outside of the coupling region, the filter waveguide may bend away from the resonator waveguide. Alternatively, the resonator waveguide may bend away from the filter waveguide. Having the filter and resonator coupling sections being parallel to each other, fabrication steps in which the cores of the filter and the resonator are simplified.

In some embodiments, each of the resonator waveguide and the filter waveguide comprise a core. The cores of the resonator waveguide and the filter waveguide may be made of the same material. The cores of the waveguides guides major part of a mode propagating there through. Having the cores of the filter and the resonator made of the same material fabrication of the optical device is greatly simplified.

In some embodiments, the resonator waveguide and the filter waveguide are arranged in a same layer. Namely, the cores of the two waveguides may be in the same layer. If the waveguides lie in the same layer, i.e. side by side, then the mode coupling is lateral. This single layer is typically arranged on a semiconductor substrate and above a bottom cladding defining the waveguides. The bottom cladding may be formed of the same material as well. The substrate is usually the same. When the cores of the two waveguides are fabricated in the same layer, they are fabricated in the same fabrication step, resulting into the same fabrication properties of the two cores.

In some embodiments, the resonator waveguide and the filter waveguide are arranged in two different layers, allowing use of different materials for the resonator and filter waveguides. Namely, the cores of the two waveguides may be arranged one above the other, and thereby be vertically coupled. In one scenario, the resonator waveguide may be fabricated on top of the bottom cladding, top cladding is then fabricated on top of the resonator core and finally the core of the filter may be fabricated. Alternatively, the filter may be fabricated first followed by fabrication of the top cladding and resonator waveguide. Some resonator waveguides may have lateral features such as metal contact or doped region for various optical functions, and vertical coupling of the filter waveguide would prevent the case where it obstructs with the lateral feature. A vertical coupling scheme would be preferred in terms of fabrication simplicity when a different material is used for the filter waveguide.

In some embodiments, the filter waveguide is configured to cross-couple at least 20%, or 30%, or 40%, or 50%, or even more of the first polarization mode from the resonator waveguide and at most 5%, or 4%, or 3%, or 2%, or 1%, or even less, of the second polarization mode. If the resonator waveguide is designed such that the strength of the first and second polarization mode coupling is weak, even less than 20% of the first mode cross-coupling would ensure decent functioning of the optical device. In general, if the cross-coupling of the first polarization mode is sufficiently higher than the polarization mode coupling between the first polarization mode and the second polarization mode then the optical device will still provide suppression of avoided mode crossing. In a case of a resonator with optical gain, a cross-coupling of the first polarization mode larger than the net optical gain per resonator roundtrip would sufficiently suppress lasing of the first polarization mode. The cross-coupling is defined as a coupling coefficient between the filter waveguide and the resonator waveguide.

In some embodiments, in the coupling region, the filter effective index vary along a longitudinal direction of the filter waveguide. By varying at least one dimension of the filter waveguide in the coupling region, variations of the effective index can be achieved. Alternatively or additionally, variations of the gap width or height can influence the effective index of the filter waveguide, both the first and second effective index. If there are variations in the effective index of the filter waveguide, an average effective index over the coupling region can be defined and this average effective index may satisfy effective index matching with the resonator waveguide. Typically, when the effective index is varying, a very small portion of the filter waveguide may be strictly effective-index matched with the resonator waveguide. If the variation is a linear variation, it is just a single infinitesimal point in the filter where the index matching happens. Variations in the effective index is usually small and achieved with a small variation of at least one dimension, e.g. a few tens of nanometres variation. By having variations in the effective index of the filter, a broadband operation of the filter can be achieved. Namely, effective- index matching dimensions for the filter may be different for different wavelengths. For instance, if the filter waveguide has a fixed width waveguide designed for 1550 nm, it will be index-matched for 1550 nm but most likely mismatched for, e.g. 1700 nm. In order to address this issue, varying the width (tapering) allows coverage of effective-index- matching for broad wavelength region. Furthermore, variations in the effective index of the filter allow for a fabrication tolerance. Namely, if a fabrication is non-ideal that may change the actual width of the filter from the design, the filter width can be designed to sweep a certain range so that it always includes a filter portion that gives the effective- index-matching.

In some embodiments, in the coupling region, the filter waveguide has transverse dimensions that define the first filter effective index such that the first filter effective index is substantially equal to the first effective index of the resonator waveguide. In some embodiments, the filter waveguide comprises two or more sub-waveguides separated from each other by a cladding. If all the sub-waveguides have the same core, then the filter waveguide may be treated as a grating. If the cores and claddings of the sub-waveguides are different, then the filter can be treated as an array of waveguides. Such waveguides may provide broadband coverage of the cross-coupling and fabrication tolerance.

In some embodiments, the optical device is a monolithic device, i.e. fabricated in a single piece. It may be integrated with other optical or electronic devices on a same chip, or may be interconnected with other integrated circuits.

In some embodiments, the filter waveguide is integrated with a bus waveguide configured to couple input light in and out of the resonator waveguide. The bus waveguide may comprise an input port configured to couple input light into the resonator waveguide and an output port configured to couple output light out of the resonator waveguide. The input port may be coupled to a laser source generating an input signal. The filter waveguide may form part of the bus waveguide, and can be formed only at the coupling region. Sufficient bus-to-resonator coupling of the second polarization mode (operating mode) can be achieved in some portion of the bus waveguide and the first polarization mode (unwanted mode) can be over-coupled (filtered) in some portion of the bus waveguide. This may be realized with width variations over the bus waveguide. In this scenario when the filter is integrated in the bus waveguide, assuming that the resonator waveguide is designed for operating at a TEoo mode, the TEoo mode will be pumped into the bus/filter waveguide. The bus/filter waveguide is designed to couple, e.g., ~1% of the TEoo mode into/out of the resonator waveguide. This is a critical coupling condition where single pass coupling and a resonator roundtrip loss is matched. The bus waveguide may couple 2%, or 3%, or even 4% and up to 10% of the TEoo pump. TMoo mode is not excited. However, TMoo is still supported by the bus/filter waveguide. The bus/filter waveguide is designed to couple into/out of the resonator waveguide more than 50% of the TMoo mode. Since TMoo mode is not provided to the bus waveguide, i.e. no TMoo input to the resonator, the filter waveguide will only couple out of the resonator the TMoo mode, thus acting as a filter. The bus/filter waveguide integrated scheme may require a control of the TEoo mode coupling coefficient to a desired level and have TMoo coupling coefficient at an extremely high level. On the other hand, a typical bus waveguide has a similar level of coupling for TEoo and TMoo. One particular example configuration of the optical device according to the invention may have a core being AIGaAs and cladding being S1O2. A circular ring or racetrack resonator that may a width in the range between 400 nm and 600 nm, and a height in the range between 250 and 400 nm. In a particular example, a circular ring or racetrack resonator that may a width of 470 nm, and a height of 320 nm. A radius of curvature may be 17.2 pm, a coupling gap between the resonator waveguide and the bus/filter waveguide may be 450 nm, a bus/filter waveguide with a coupling angle of 145 degrees, a height of 320 nm, and the width tapering from 430 nm to 360 nm along the propagation direction. Thus, the bus/filter waveguide can be configured so that the width profile along the propagation direction includes both TEoo and TMoo effective index matching condition in relation to the resonator waveguide.

In some embodiments, the optical device further comprises a bus waveguide separated from the resonator waveguide, the bus waveguide comprising an input port configured to couple input light into the resonator waveguide and an output port configured to couple output light out of the resonator waveguide. The input light beam may travel along the bus waveguide. The bus waveguide may be a linear waveguide. The bus waveguide may be designed to optically couple to the resonator waveguide. Namely, dimensions of the bus waveguide may be chosen such that there is a phase-matching between the operational mode of the resonator waveguide, e.g. TEoo, and a mode supported by the bus waveguide, also TEoo. In other words, the propagation constant of the operational mode supported by the resonator waveguide is essentially equal to the propagation constant of the mode supported by the bus waveguide. This directly corresponds to essentially equal effective indices of the operational mode of the resonator waveguide and the mode supported by the bus at one wavelength.

In a second aspect of the invention, another optical device is disclosed. The optical device comprises a resonator waveguide and a filter waveguide, the resonator waveguide having a resonator output that is connected with a filter input of the filter waveguide, and the resonator waveguide further having a resonator input connected with a filter output of the filter waveguide, the resonator waveguide being configured to propagate at least a first polarization mode and a second polarization mode and to provide the first and second polarization mode via the resonator output and the filter input to the filter waveguide, the filter waveguide being configured to propagate the second polarization mode to the filter output and the resonator input to the resonator waveguide, and the filter waveguide being further configured to suppress propagation of the first polarization mode to the filter output and the resonator input to the resonator waveguide. The filter waveguide is configured to propagate the second polarization mode to the filter output and the resonator input to the resonator waveguide such that the second polarization mode may be circular around in the resonator waveguide and filter waveguide.

The filter waveguide is further configured to suppress propagation of the first polarization mode to the filter output and the resonator input to the resonator waveguide such that the first polarization mode is not supported by the arrangement of resonator and filter waveguide.

In one embodiment, the filter waveguide has at least a second filter output decoupled from the resonator, and wherein the filter waveguide is configured to propagate the first polarization mode to the second filter output. Any other mode except the second polarization mode may be propagated to a filter output which is decoupled from the resonator.

In one embodiment, the filter waveguide may comprise a 1 x 1 multimode interference (MMI) coupler. The MMI coupler length is designed to at least approximately match a single self-imaging length of the filter input (or resonator output) second polarization mode. The filter output of the MMI is placed at the location where the single-self image of the filter input second polarization has formed thereby guiding the filter input second polarization mode to the resonator input with low loss. The MMI coupler length is further designed not to match a single self-imaging length of the filter input (or resonator output) first polarization mode.

In one embodiment, the filter waveguide may comprise a 1 x N MMI coupler. The MMI coupler length may be designed to at least approximately match a single self-imaging length of the filter input (or resonator output) second polarization mode. A filter output of the MMI is placed at the location where the single-self image of the filter input second polarization mode has formed, thereby guiding the mode to the resonator input with low loss. The MMI coupler length is further designed not to match a single self-imaging length of the filter input first polarization mode. In case of MMI coupler length designed to at least approximately match a multiple self-imaging length of the filter input first polarization mode, the other filter outputs may be placed in the location where the multiple self-images of the filter input first polarization mode has formed. Multiple filter output ports guiding the multiple self-images of the filter input first polarization mode effectively couples out the unwanted first polarization mode from the filter waveguide and they may connect to a lossy optical structure (characterized by dominant scattering or leaky modes) to efficiently terminate the light or to an inspection channel (i.e., photodetector). In regard to the filter input first polarization mode, the multiple self imaging condition does not strictly have to be met. The output ports can be located where the arbitrary multimode interference of the filter input first polarization mode has locally high intensity.

The present invention relates to different aspects including the two optical devices described above and in the following, and corresponding devices parts, each yielding one or more of the benefits and advantages described in connection with the first mentioned aspect, and each having one or more embodiments corresponding to the embodiments described in connection with the first mentioned aspect and/or disclosed in the appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other features and advantages will become readily apparent to those skilled in the art by the following detailed description of exemplary embodiments thereof with reference to the attached drawings, in which:

Fig. 1 schematically illustrates an exemplary embodiment of an optical device, Fig. 2 schematically illustrates two exemplary embodiments of an optical device,

Fig. 3 schematically illustrates a top view of an exemplary embodiment of an optical device,

Fig. 4 schematically illustrates a cross section of a coupling region of an optical device,

Fig. 5 illustrates effective indices for two fundamental polarization modes of a resonator and filter waveguides,

Fig. 6 shows an SEM image of a fabricated optical device,

Fig. 7 illustrates a cross-section of two exemplary embodiments of a coupling region of an optical device,

Fig. 8 illustrates an electromagnetic field simulation in an exemplary embodiment of an optical device,

Fig. 9 illustrates a cross-section of five exemplary embodiments of a resonator waveguide, Fig. 10 illustrates transmission dependency on a coupling angle for respective first polarization and second polarization modes,

Fig. 11 illustrates transmission spectra, integrated dispersion and resonance deviation for respective optical devices without a filter waveguide (FIG. 11 A) and with a filter waveguide (FIG. 11 B), Fig. 12 schematically illustrates a top view of three exemplary embodiment of an optical device, and

Fig. 13 schematically illustrates an optical device according to a second aspect of the invention. DETAILED DESCRIPTION

Various embodiments are described hereinafter with reference to the figures. Like reference numerals refer to like elements throughout. Like elements will, thus, not be described in detail with respect to the description of each figure. It should also be noted that the figures are only intended to facilitate the description of the embodiments. They are not intended as an exhaustive description of the claimed invention or as a limitation on the scope of the claimed invention. In addition, an illustrated embodiment needs not have all the aspects or advantages shown. An aspect or an advantage described in conjunction with a particular embodiment is not necessarily limited to that embodiment and can be practiced in any other embodiments even if not so illustrated, or if not so explicitly described. Throughout, the same reference numerals are used for identical or corresponding parts.

Fig. 1 schematically illustrates an exemplary embodiment of an optical device 1. The optical device 1 comprises a resonator waveguide 2 optically coupled, at a coupling region 3, to a filter waveguide 4. The resonator waveguide 2 is configured to support at least a first polarization mode and a second polarization mode, the second polarization mode being an operational mode of the resonator waveguide 2. The resonator waveguide 2 has a first effective index associated with the first polarization mode and a second effective index associated with the second polarization mode. The first polarization mode is different from the second polarization mode. The filter waveguide 4 has, in the coupling region 3, a filter first effective index associated with the first polarization mode and a filter second effective index associated with the second polarization mode. The filter first effective index at least approximately matches with the first effective index of the resonator waveguide 2 such that the first polarization mode is filtered out of the resonator waveguide.

Fig. 2 schematically illustrates another exemplary embodiment of an optical device. The optical device 10 shown in Fig. 2 in addition to the filter and resonator waveguides 4, 2 comprises a bus waveguide 12. The bus waveguide 12 may serve to couple input light 6 and out-couple output light 8 of the resonator waveguide 2. In this embodiment, the filter waveguide may then only serve as a polarization filter selectively filtering a polarization mode undesired in the resonator waveguide 2. Such a design relaxes requirements on the filter waveguide. Namely, when designing the filter waveguide 4, only considerations are related to the filtering function. Fig. 3 schematically illustrates a top view of an exemplary embodiment of an optical device 200 of the present invention. The optical device comprises a resonator waveguide 2, a filter waveguide 4, and a bus waveguide 12. The resonator waveguide 2 is a loop waveguide having two possibly symmetrical curved sections 24 and two substantially straight sections 22 with varying dimensions. Input light 6 is pumped into the bus waveguide 12 at an input port. The bus waveguide 12 may be designed to couple a part of input light 6 into the resonator waveguide 2. This input light then builds up in intensity over multiple round-trips through the resonator waveguide 2 due to constructive interference and is output to the output port of the bus waveguide 12 as output light 8. Optical coupling between the resonator waveguide 2 and the bus waveguide 12 is achieved by evanescent field which extends outside of the resonator and bus waveguides 2, 12. The two waveguides are physically separated by a certain distance designed to provide an optimal coupling coefficient. The optical device 200 defines a coupling region 3 where an unwanted polarization mode is selectively coupled out from the resonator waveguide 3 to a filter coupling section 48 of the filter waveguide 4 while coupling of an operational polarization mode is kept at a negligible level. Bending section 47 may be introduced to guide the out-coupled polarization mode away from the resonator waveguide 2. The bending section 47 further connects to an adiabatic taper 46, to a narrow waveguide width 44, and to a curved waveguide tip 42 in order to terminate the extracted polarization mode with high loss and reduce back-reflection. The coupling region 3 may need to be designed to achieve maximum cross-coupling from the resonator waveguide 2 to the filter waveguide 4 of the unwanted polarization mode and minimum cross-coupling of the operational polarization mode. This condition can be realized by matching of the effective indices for the unwanted polarization mode of the resonator waveguide 2 and the filter waveguide 4, i.e. making the indices substantially equal, and mismatching of the effective indices for the operational polarization mode. The unwanted polarization mode may be TMoo mode and the operational mode may be TEoo mode. The filter waveguide parts 42, 44, 46, and 47 that are separated away from the resonator waveguide do not require effective index matching. These parts may only be relevant for back reflection of the light which should be avoided. In some embodiments, it is possible to use the bus waveguide for coupling light into the resonator waveguide, and the filter waveguide for output light from the resonator.

Fig. 4 schematically illustrates a cross-section of a coupling region 3 of the filter waveguide 4 and resonator waveguide 2. More precisely, Fig. 4 illustrates the coupling region 3 defined by the filter coupling section 48 and the resonator coupling section 24. The coupling region 3 is defined by a resonator height H_r, resonator width W_r, resonator radius of curvature R_r, a filter height H_p, filter width W_p, filter radius of curvature R_p, a coupling gap G, and coupling angle q_r.

The bottom inset shows a cross-section of the resonator waveguide 2 arranged on a substrate. The resonator waveguide is defined by a bottom cladding, core having height H_r, and a top cladding. The top inset shows a cross-section where the filter waveguide is physically distanced from the resonator waveguide 2 with a coupling gap G. The filter waveguide 4 is, similar to the resonator waveguide 2, defined by the bottom cladding, a core having height H_p, and the top cladding. Refractive indices of a core material, bottom cladding material, and top cladding material, together with dimensions of the core, define effective indices of the waveguides.

Fig. 5 illustrates simulated effective indices for two fundamental polarization modes of a resonator and filter waveguides with respect to a filter waveguide width. Since the effective index of a waveguide is wavelength dependent, for this simulation, commonly used telecom wavelength of 1550 nm has been selected. In this simulation, the resonator waveguide dimensions are fixed at R_r = 17.2 pm, W_r = 470 nm, and H_r = 320 nm, resulting in the effective index for TEoo mode to be 2.42 and the effective index for TMoo mode to be 2.18. The coupling gap G is fixed at 500 nm. Height of the filter waveguide H_f is fixed at 320 nm and R_p = R_r + W_r/2 + G + W_p/2. The effective indices were simulated separately for the resonator waveguide and the filter waveguide with finite-difference eigenmode (FDE) solver where Maxwell’s equations were solved in a cylindrical coordinate system sharing the same origin for the resonator and filter waveguides. From the graph it can be seen that for TMoo mode, effective indices of the filter and resonator are matched for the filter width around 374 nm. For this filter width, effective indices for TEoo are mismatched. Therefore, for this filter width the operational polarization mode of the optical device is TEoo and TMoo is the unwanted polarization mode. The coupling region will achieve maximum cross-coupling from the resonator to the filter for the TMoo mode, and minimum cross-coupling for the TEoo mode. If it is desired to have TMoo mode as the operational mode and TEoo as unwanted mode, filter width of around 420 nm can be selected as for this W_p, TMoo effective indices are mismatched while TEoo effective indices are matched.

Fig. 6 shows an SEM image of a fabricated optical device 1 comprising a resonator waveguide 2 and a filter waveguide 4.

Fig. 7 illustrates a cross section of two exemplary embodiments of a coupling region of an optical device. Fig. 7 A illustrates an optical device comprising a resonator waveguide and a filter waveguide comprising one or more cores. The cores are separated with the top cladding. The cores may be made of the same material or they may be made of different materials. Fig. 7B illustrates an optical device where the resonator waveguide 2 and the filter waveguide 4 are arranged in two different layers. Namely, the core of the filter waveguide 4 is fabricated above the core of the resonator waveguide 2 and fully embedded in the top cladding. The resonator waveguide may have different bottom and top cladding. In this embodiment, the resonator 2 and filter 4 waveguides are vertically coupled. Alternatively, the resonator waveguide may be placed above the filter waveguide.

Fig. 8 illustrates an electromagnetic field simulation in an exemplary embodiment of an optical device. Fig. 8A shows a simulation structure of a resonator waveguide 2 represented by a lower curved path and a filter waveguide 4 represented by a path that partially and concentrically wraps the lower curved path of the resonator waveguide 2 in the coupling region. The filter waveguide 4 is distanced from the resonator waveguide 2 by a coupling gap and separated away from the curved region of the resonator waveguide 2 at both ends. The resonator waveguide 2 dimensions in the simulation is fixed by R_r = 17.2 pm, W_r = 470 nm, and H_r = 320 nm; and the filter waveguide dimension is fixed by G = 500 nm, q_r = 90 °, W_p = 374 nm, H_p = 320 nm, and R_p = 18.122 pm. The filter waveguide is designed to couple TMoo mode out of the resonator waveguide 2. A three-dimensional Finite-difference-time-domain (FDTD) simulation was performed for two different polarization modes, TEoo and TMoo, launched into the resonator waveguide 2 at 1550 nm. An input port is denoted by a dotted arrow in the lower left corner and an output port is denoted by a dotted arrow in the lower right corner. Resulting field obtained at the output port is used for acquiring single-pass transmission of each input polarization mode after propagating through the coupling section of the resonator waveguide 2. Fig. 8B and Fig. 8C show electric field intensity for TEoo mode and TMoo mode injected to the input port, respectively. The cross-coupling is visually negligible for the operational TEoo mode and significant for the unwanted TMoo mode in the given configuration.

Fig. 9 illustrates a cross section of five exemplary embodiments of a resonator waveguide. These waveguides may be selected from a group of waveguides such as: Fig. 9A, a buried channel waveguide, Fig. 9B, a strip-loaded waveguide, Fig. 9C, a ridge waveguide, Fig.9D, a rib waveguide, and Fig. 9E, a diffused waveguide. Fig. 9A, a buried channel waveguide is configured with a high-index core in a low-index surrounding r\2. Fig. 9B, a ridge waveguide is configured with a high-index core _, low-index surrounding n2on one side and low-index air on three sides allowing strong optical confinement. Fig. 9C, a rib waveguide configured by super-positioning of a ridge waveguide and a slab structure, where partial etching depth h of original core material thickness d is determined for optimal optical confinement and additional functionalities such as optical modulation or carrier sweep-out. Fig. 9D, a strip-loaded waveguide is configured by loading a planar waveguide with high-index ni for optical confinement in y direction and strip waveguide with an index of n3 lower than providing optical confinement in x direction which allows convenient fabrication and flexible configuration of waveguide with various material combinations where strip height h and width w may be increased to support and guide higher order modes, strip height h and planar waveguide thickness d can be adjusted to achieve a desired mode field distribution. Fig. 9E, a diffused waveguide is configured by a high-index m core defined by dopant diffusion or ion implantation.

Fig. 10 illustrates transmission dependency on a coupling angle for respective first polarization and second polarization modes, i.e. TMoo mode and TEoo mode. The resonator waveguide and the filter waveguide dimensions are identical to the embodiment described in Fig. 8 but with varying coupling angle from 0° to 180° for the simulation. The transmission dependent on the coupling angle of the filter waveguide is shown, where solid line represents TEoo mode and dotted line represents TMoo mode obtained by Finite Difference Equation (FDE) simulation. FDTD simulation result from Fig. 8 is also plotted for verification of simulation where square marker represents TEoo mode and circle marker represents TMoo mode with values of -0.0055 dB and -1.849 dB respectively. Fig. 10B plots the same simulation result as Fig. 10A but has a magnified secondary axis to accurately show the TEoo mode transmission. Hence, for exemplary transmission plots with varying coupling angle exhibit negligible loss in TEoo mode propagation and significant loss in TMoo mode.

Fig. 11 illustrates transmission spectra, integrated dispersion, Di_nt, and resonance deviation for respective optical devices without a filter waveguide (FIG. 11 A) and with a filter waveguide (FIG. 11 B). The two optical devices’ nominal dimension for the resonator waveguide is fixed by R_r = 17.2 pm, W_r = 470 nm, H_r = 320 nm and total resonator length of 808 pm; a bus waveguide is fixed by width of 470 nm, height of 320 nm; and coupling gap between the bus waveguide and the resonator waveguide is fixed by 225 nm at one side of a curved section of the resonator waveguide. The optical device shown in Fig. 11 B has the filter waveguide dimension fixed by G = 500 nm, q_r = 150 °, W_p= 374 nm, H_p = 320 nm, and R_p = 18.122 pm. Plots presented in the left side show transmission spectra from different polarization input to the optical devices where solid line represents TE mode and dotted line represents TM mode input. Plots in the upper right side show measured integrated dispersion represented by solid circle where Di_nf = w_m- (wo + Oy), Oi/2p is the free spectral range, m is the relative mode number, w_m is the resonance frequency of the m-th mode, and wo is the center resonance frequency; and fitted Di_nt curve represented by solid line where the curve is fitted to a Taylor series described by V2 D^² + 1/6Ό₃m³ + ·. Plots in the lower right side shows dispersion deviation that is derived by subtracting the fitted D_mffrorn the measured Di_nt. Transmission spectra in Fig. 11A show that TEoo and TMoo mode resonances have comparable extinction ratio with the TEoo mode in slightly under-coupled condition and the TMOO mode in over-coupled condition. In addition, resonance splitting is visible indicating avoided mode crossing due to the polarization mode coupling. In comparison, transmission spectra in Fig. 11 B show insignificant TMoo mode resonance extinction indicating extremely under coupled condition due to the high loss of the TMoo mode in the optical device. Median intrinsic quality factor of the TEoo mode was around 110,900 for the optical device in Fig. 11 B and 113,900 for the optical device in Fig. 11A where up to 170 resonances of TEoo modes in both optical devices were evaluated. Hence, we confirm low loss optical performance in operational TEoo mode with filtering of the unwanted TMoo mode for the exemplary optical device described in Fig. 11 B. From the Dim we obtain dispersion parameter D_å being 3.06 MHz and 3.02 MHz, and root mean squared error of the dispersion deviation being 241 MHz and 70 MHz respectively for the optical device described in Fig. 11A and Fig.11 B. Hence, we confirm unperturbed dispersion characteristics and significant suppression of deviated dispersion in the optical device described in Fig. 11 B.

Fig. 12 schematically illustrates a top view of three exemplary embodiment of an optical device. The illustrations of the embodiments are presented with both Cartesian (x, y) and polar coordinate system (r, Q) axes to show that the illustration may be projected into an arbitrary coordinate system. Fig. 12A illustrates an optical device comprising a resonator waveguide 2 and a filter waveguide 4 having variation in width W_p and coupling gap G in longitudinal direction. Fig. 12B illustrates an optical device comprising a resonator waveguide 2 and a filter waveguide 4 comprising two or more cores separated by an arbitrary gap in secondary axis direction. Fig. 12C illustrates an optical device comprising a resonator waveguide 2 and a filter waveguide 4 comprising two or more cores with arbitrary length separated by arbitrary gap in primary axis direction.

Fig. 13 illustrates another optical device according to a second aspect of the present invention. The optical device 300 comprises a resonator waveguide 302 and a filter waveguide 304. The filter waveguide 304 may support multiple polarization and spatial modes. The resonator waveguide 302 has a resonator output 305 that is connected with a filter input 306 of the filter waveguide 304, and the resonator waveguide 302 further has a resonator input 307 connected with a filter output 308 of the filter waveguide 308. The resonator waveguide 302 is configured to propagate at least a first polarization mode and a second polarization mode and to provide the first 311 and second 312 polarization mode via the resonator output 305 and the filter input 306 to the filter waveguide 304. The first 311 and second 312 polarization mode propagating from the resonator input 305 past the filter input 306 excites the multiple polarization and spatial modes in the filter waveguide 304.

The multiple modes propagating in the filter waveguide 304 (from the filter input 306 to the filter output 308) excited by the second polarization mode 312 from the resonator input 305 generate interference pattern in the plane normal to the propagation direction. The multimode interference pattern at the (or in the vicinity of) filter output 308, originating from second polarization mode 312, matches the electromagnetic field profile of the second polarization mode 312 at the resonator input 307. Such mode matching condition guarantees low loss propagation of the second polarization mode 312 through the resonator output 305, filter input 306, filter waveguide 304 and filter output 308 to resonator input 307. The same operation can be realized by, for example, using a multimode interference waveguide for the filter waveguide 304 where the single self imaging condition is met at the filter output 308 for the second polarization mode 312. Single self-imaging is a property of multimode waveguides by which an input field profile is reproduced in single image at periodic intervals along the propagation direction of the guide. Specifically, the filter waveguide can be set as a rectangular multimode waveguide with a side parallel to the propagation direction L_s (single self imaging length) and a side orthogonal to the propagation direction W (width). nW_e 2 e

Is — k o where n is effective refractive index of the multimode waveguide, W_e is multimode waveguide effective width, l₀ is operation wavelength, and k is a positive integer. The single self imaging field profile at the filter output 308 can have an arbitrary magnification factor in respect to the filter input 306. Such mode mismatch (field profile mismatch) between the filter output 308 and the resonator input 307 relating to the second polarization mode 312 can be addressed by placing an intermediate structure in between the filter output 308 and the resonator input 307. For example, a tapered structure smoothly connecting the filter output 308 and the resonator input 307 would de-magnify or magnify the field profile of the filter output 308 with low loss and matching the field profile of the resonator input 307 relating to the second polarization mode 312. The multiple modes propagating in the filter waveguide 304 excited by the first polarization mode 311 from the filter input 306 also generate interference pattern at the filter output 308 which the field profile does not match that of the first polarization mode at the resonator input 307. This results in high loss of the first polarization mode 311 propagating through the resonator output 305, filter input 306, filter waveguide 304 and filter output 308 to resonator input 307. Thus, the filter waveguide 304 is configured to propagate the second polarization mode 312 to the filter output 308 and the resonator input 307 to the resonator waveguide 302. The filter waveguide 304 is further configured to suppress propagation of the first polarization mode 311 to the filter output 308 and the resonator input 307 to the resonator waveguide 302.

The filter waveguide 304 can be segmented in the propagation direction so that the number of the modes and the energy distribution in the modes are altered during the propagation. Here modes in the filter waveguide 304 are not confined to guided modes, where leaky and scattered modes (including loss) are also considered. The filter waveguide 304 can be segmented in continuous or discrete manner where each segment may consist of different refractive index, and cross-sectional dimension (i.e., width, height).

The filter output 308 may consist of multiple ports where one port outputs the second polarization mode 312 originating from the resonator output 305 to the resonator input 307 according to principle noted in the claim 14; the other ports may propagate the entirety or the part of the first polarization mode 311 originating from the resonator output 305. Thus, efficiently removing the modes in the filter waveguide 304 excited from the first polarization mode 311 from the resonator output 305.

Although particular features have been shown and described, it will be understood that they are not intended to limit the claimed invention, and it will be made obvious to those skilled in the art that various changes and modifications may be made without departing from the scope of the claimed invention. The specification and drawings are, accordingly to be regarded in an illustrative rather than restrictive sense. The claimed invention is intended to cover all alternatives, modifications and equivalents. LIST OF REFERENCES

1 , 10 optical device

2, 302 resonator waveguide

3 coupling region 4, 5, 304 filter waveguide

6 input light

8 output light

12 bus waveguide

22 resonator straight section 24 resonator coupling section, resonator curved section

42 filter curved waveguide tip

44 filter narrow waveguide width

46 adiabatic taper

47 bending section 48 filter coupling section

100, 200 optical device

300 optical device, second aspect

305 resonator output

306 filter input 307 resonator input

308 filter output

311 first polarization mode

312 second polarization mode

Claims

1. An optical device comprising a resonator waveguide and a filter waveguide optically coupled with the resonator waveguide at a coupling region, the resonator waveguide being configured to support at least a first polarization mode and a second polarization mode, the second polarization mode being an operational mode of the resonator waveguide, the resonator waveguide having a first effective index associated with the first polarization mode and a second effective index associated with the second polarization mode, the first polarization mode being in a different polarization than the second polarization mode, the filter waveguide having, in the coupling region, a filter first effective index associated with the first polarization mode, wherein the filter first effective index at least approximately matches with the first effective index of the resonator waveguide such that the first polarization mode is filtered out of the resonator waveguide.

2. An optical device according to claim 1, wherein the first polarization mode is a first fundamental polarization mode and/or wherein the second polarization mode is a second fundamental polarization mode, and/or wherein the filter waveguide has, in the coupling region, a filter second effective index associated with the second polarization mode, and wherein the filter second effective index is mismatched with the second effective index of the resonator waveguide.

3. An optical device according to any of the preceding claims, wherein in the coupling region, the resonator waveguide comprises a resonator coupling section and the filter waveguide comprises a filter coupling section being spaced from the first resonator section by a gap, wherein, optionally, the gap is filled with air or a dielectric material.

4. An optical device according to claim 3, wherein the resonator coupling section and the filter coupling section are curved, wherein preferably, the curvature of the resonator coupling section and the curvature of the filter coupling section have substantially the same centres.

5. An optical device according to claim 3, wherein the resonator coupling section and the filter coupling section are straight.

6. An optical device according to claims 3 to 5, wherein the resonator coupling section and the filter coupling section extend in parallel.

7. An optical device according to any of the preceding claims, wherein each of the resonator waveguide and the filter waveguide comprise a core, the cores of the resonator waveguide and the filter waveguide are made of the same material.

8. An optical device according to any of the preceding claims, wherein the resonator waveguide and the filter waveguide are arranged in a single layer, or wherein the resonator waveguide and the filter waveguide are arranged in two different layers.

9. An optical device according to any of the preceding claims, wherein the filter waveguide is configured to cross-couple at least 20%, or 30%, or 40%, or 50% of the first polarization mode from the resonator waveguide and at most 5%, or 4%, or 3%, or 2% of the second polarization mode.

10. An optical device according to any of the preceding claims, wherein, in the coupling region, the filter first effective index vary along a longitudinal direction of the filter waveguide, and/or wherein, in the coupling region, the filter waveguide has transverse dimensions that define the first filter effective index such that the first filter effective index is substantially equal to the first effective index of the resonator waveguide.

11. An optical device according to any of the preceding claims, wherein the filter waveguide comprises two or more sub-waveguides separated from each other by a cladding.

12. An optical device according to any of the preceding claims, wherein the optical device is a monolithic device.

13. An optical device according to any of the preceding claims, wherein the filter waveguide is integrated with a bus waveguide configured to couple input light in and out of the resonator waveguide, or wherein the optical device further comprises a bus waveguide separated from the resonator waveguide, the bus waveguide comprising an input port configured to couple input light into the resonator waveguide and an output port configured to couple output light out of the resonator waveguide.

14. An optical device according to any of the preceding claims, wherein the coupling region is defined by a coupling length, the coupling length being defined by a resonator coupling length and a filter coupling length, and wherein the filter coupling length is shorter than the maximum power transfer coupling length of the first polarization mode to the filter waveguide, the coupling length being approximately 90%, 80%, 50%, 20% 10% of the maximum power transfer coupling length.

15. An optical device comprising a resonator waveguide and a filter waveguide, the resonator waveguide having a resonator output that is connected with a filter input of the filter waveguide, and the resonator waveguide further having a resonator input connected with a filter output of the filter waveguide, the resonator waveguide being configured to propagate at least a first polarization mode and a second polarization mode and to provide the first and second polarization mode via the resonator output and the filter input to the filter waveguide, the filter waveguide being configured to propagate the second polarization mode to the filter output and the resonator input to the resonator waveguide, and the filter waveguide being further configured to suppress propagation of the first polarization mode to the filter output and the resonator input to the resonator waveguide.

16. The optical device according to claim 15, wherein the filter waveguide has at least a second filter output decoupled from the resonator, and wherein the filter waveguide is configured to propagate the first polarization mode to the second filter output.