GB2612030A

GB2612030A - Dual waveguide polarization rotator

Info

Publication number: GB2612030A
Application number: GB2114900.0A
Authority: GB
Inventors: Stroganov Anton; Aamer Benalfaquih Mariam; Sacchetto Davide
Original assignee: Ligentec SA
Current assignee: Ligentec SA
Priority date: 2021-10-19
Filing date: 2021-10-19
Publication date: 2023-04-26
Also published as: GB202114900D0

Abstract

A polarisation rotator, comprising: a substrate; a first waveguide disposed on the substrate, configured to support a first mode and a second mode, wherein a first polarisation of the first mode and a second polarisation of the second mode are orthogonal to each other; and a second waveguide disposed over the first waveguide. In an asymmetric region, the second waveguide is evanescently coupled to the first waveguide and laterally displaced with respect to the first waveguide by a first offset in plan view, such that in response to the first mode or the second mode on the first waveguide input into the asymmetric region, the second mode or the first mode, respectively, is output out of the asymmetric region on the first waveguide. The offset may be determined such that the waveguides support first and second hybrid modes. The length of the asymmetric region may be determined by simulations, such that the accumulated phase difference between hybrid modes is 180 degrees.

Description

Dual waveguide polarization rotator

Technical Field

This specification relates to photonic integrated circuits.

Background

In integrated photonic circuits or in photonies platforms, an integrated device for polarisation rotation implemented in a compact and robust fashion is required.

Summary

According to an aspect of the present invention, there is provided a polarisation rotator, which comprises a substrate and a first waveguide disposed on the substrate, the first waveguide configured to support a first mode and a second mode. A first polarisation of the first mode and a second polarisation of the second mode are orthogonal to each other. The polarisation rotator comprises a second waveguide disposed over the first waveguide. In an asymmetric region, the second waveguide is evanescently coupled to the first waveguide and laterally displaced with respect to the first waveguide by a first offset in plan view. The polarisation rotator is such that in response to the first mode or the second mode on the first waveguide input into the asymmetric region, the second mode or the first mode, respectively, is output out of the asymmetric region on the first waveguide.

In some implementations, the first offset is determined such that the first waveguide and the second waveguide support a first hybrid mode and a second hybrid mode and such that a third polarisation of the first hybrid mode and a fourth polarisation of the second hybrid mode are orthogonal to each other.

In some implementations, the third polarisation and the fourth polarisation are at 45 degrees angle from the first polarisation and the second polarisation, respectively.

In some implementations, a length of the asymmetric region is arranged such that a phase difference between the first and second hybrid modes accumulated over the asymmetric region is i8o degrees.

In some implementations, the first offset is determined such that a line connecting a first centre of a cross-section of the first waveguide and a second centre of a cross-section of the second waveguide is at 45 degrees angle from a line parallel to a plane of the substrate and orthogonal to the propagation direction of the first waveguide.

In some implementations, the polarisation rotator further comprises a gap layer disposed between the first waveguide and the second waveguide in the asymmetric region.

In some implementations, the thickness of the gap layer is less than 1micron.

In some implementations, the first waveguide comprises a first section within the asymmetric region and a second section outside the asymmetric region, and a width of the first section is different from a width of the second section.

In some implementations, a width of the first section is larger than a width of the second section.

In some implementations, a width of the first section is smaller than a width of the second section.

In some implementations, the second waveguide does not overlap the first waveguide in plan view.

According to another aspect of the present invention, there is provided a method of designing a polarisation rotator which comprises a first waveguide and a second waveguide disposed over the first waveguide, wherein in an asymmetric region, the second waveguide is evanescently coupled to the first waveguide and laterally displaced with respect to the first waveguide by a first offset in plan view. The method comprises: determining a wavelength of operation; determining a first width and a first height of the first waveguide based on the wavelength of operation such that the first waveguide supports a first mode and a second mode, wherein a first polarisation of the first mode and a second polarisation of the second mode are orthogonal to each other; determining a second height of the second waveguide and a gap between the first waveguide and the second waveguide; determining a second width of the second waveguide; calculating the first offset, wherein the first offset is a degree of lateral displacement of the second waveguide with respect to the first waveguide; and calculating a length of the asymmetric region, such that in response to the first mode or the second mode input into the asymmetric region, the second mode or the first mode, respectively, is output out of the asymmetric region.

In some implementations, calculating the first offset comprises performing mode simulations by varying the first offset such that the first waveguide and the second waveguide support a first hybrid mode and a second hybrid mode.

In some implementations, a third polarisation of the first hybrid mode and a fourth polarisation of the second hybrid mode are orthogonal to each other, and the third polarisation and the fourth polarisation are at 45 degrees angle from the first polarisation and the second polarisation, respectively. -3 -

In some implementations, calculating a length of the asymmetric region comprises performing simulations such that at the length, a phase difference between the first and second hybrid modes accumulated over the asymmetric region is 180 degrees.

Brief Description of the Drawings

Certain embodiments of the present invention will now be described, by way of examples, with reference to the accompanying drawings, in which: FIG. la is a schematic transverse cross-section of the double waveguide rotator. FIG. lb is a top view schematic of the double waveguide rotator which can be implemented over various bottom waveguide geometries.

FIG. 2 is a process flow diagram defining the geometry of the different parts composing the polarisation rotator.

FIG. 3 is a plot of an effective index of supported modes as a function of width of a silicon nitride waveguide in silicon dioxide cladding.

FIG. 4a is a plot of a mode profile of a first hybrid optical mode in the transverse plane.

FIG. 4b is a plot of a mode profile of a second hybrid optical mode in the transverse plane.

Detailed Description

Polarisation rotating devices on waveguides or on a photonic circuit, or an integrated polarisation rotator, are implemented based on similar concepts -at least two optical modes are excited from an incident beam. These two optical modes are supported with two orthogonal principal polarisations and with different propagation velocities within the polarisation rotating device. The difference in velocities introduces a relative phase shift between the two optical modes during the propagation in the device. When the two optical modes are recombined after propagation, the resulting polarisation state vector is altered depending on the relative phase shift. The -4 -recombined output optical mode with the altered polarisation state is outputted from the polarisation rotating device.

Conventional implementations of an integrated polarisation rotator are based either on directional couplers or partially etched waveguides.

In the directional couplers used for polarisation rotation, polarisations are split and one of them is rotated. Since a fundamental mode and a higher-order mode with two different polarisations should be phase-matched, the design and fabrication process tends to be complicated due to additional requirements on the waveguides and supported modes, and occasionally requires additional material layers. Moreover, often the rotation is limited to only one of the polarisations.

For a partially etched waveguide, an important parameter to consider is the refractive index contrast, defined as: An 2,2 where ni is the refractive index of the waveguide or the core, lid is the refractive index of the cladding. In silicon photonics where silicon is used for the waveguide, wg 3.5 whereas in photonic circuits where silicon nitride is used for the waveguide, kf, 2,0. In both platforms, typically silicon dioxide (Si02) is used as the cladding, which has 71,1 1.44.

Thanks to a large refractive index contrast An in silicon photonics, polarisation beam rotation can be achieved by modifying a waveguide to be asymmetric, for instance, by introducing a shallow etch to a channel waveguide. A short conversion length, a length over which the polarisation rotation is completed, can be obtained as a consequence of a large difference in propagation constants of the two beating modes within the asymmetric waveguide.

Since photonic-grade silicon nitride waveguides have a moderate refractive index contrast, a compact design of an efficient polarisation beam rotator in silicon nitride waveguides raises a considerable challenge.

The implementation of the polarisation beam rotator in silicon nitride waveguides may require wider and/or thicker dimensions compared to the equivalent implementations in silicon waveguide circuits. For the case of the silicon nitride waveguides, a thicker silicon nitride layer requires a greater level of accuracy in relation to the etching depth. Therefore, a design that does not require single waveguides would be preferred. in addition, due to the mechanical stress related to a thick silicon nitride layer, there is a limitation on the thickness of a silicon nitride waveguide. -5 -

To address these issues, this specification provides a design of a polarisation beam rotator implemented with silicon nitride vvaveguides in a silicon dioxide cladding to achieve an efficient polarisation beam rotation with a greater accuracy and at the same time to overcome the limits on the thickness of a silicon nitride layer.

FIG. la illustrates a cross section of a polarization rotator.

The polarization rotator 100 includes a first waveguide no and a second waveguide 120. In this specification, the term "waveguide" will be used to refer to the core in a typical core/cladding geometry of optical waveguide. Also throughout the specification, the material of the first waveguide no and the second waveguide 120 is assumed to be photonic-grade silicon nitride. However, the main concept of the invention applies to other materials used for the first waveguide no and the second waveguide 120.

The polarisation rotator loo is implemented on a substrate 101. The substrate 101 is assumed to be a silicon wafer. A BOX (buried oxide) layer 102, or an oxide layer 102, is formed on the surface of the substrate 101 by oxidising the substrate 101. The thickness of the oxide layer 102 varies depending on the application and typically ranges from 5onm to several micrometres. Since the first waveguide no is formed on the oxide layer 102, it is understood that the thickness of the oxide layer 102 is determined to be large enough such that the supported optical mode profile is not significantly distorted by the substrate 101.

The polarisation rotator loo can be constructed as a stand-alone device. Alternatively, the polarisation rotator loo can be constructed as part of larger photonic circuits. In that case, the polarisation rotator loo refers to a part of such photonic circuits which serve the function of the polarisation rotation. The polarisation rotator 100 can be the part of the photonic circuit comprising the first waveguide no, where the second waveguide 120 is disposed in parallel to but laterally offset with respect to the first waveguide no, as described in more detail below.

In some implementations, within the polarisation rotator loo, the cross section of the first waveguide no has a constant width 111 in the x-direction, parallel to the plane of the substrate 101, and a constant height 112 in the y-direction, normal to the plane of the substrate 101.

In some implementations, within the polarisation rotator loo, the cross section of the second waveguide 120 has a constant width 121 in the x-direction, parallel to the plane of the substrate 101, and a constant height 122 in the y-direction, normal to the plane of the substrate 101. -6 -

Within the polarisation rotator loo, the first waveguide no and the second waveguide 120 are disposed parallel to each other. The second waveguide 120 is disposed over the first waveguide no with a gap 1,3o or a first distance 130. The gap 130 is defined to be the shortest distance between the bottom surface of the second waveguide 120 and the top surface of the first waveguide no. The top surface of the first waveguide no and the bottom surface of the second waveguide 120 are parallel to each other and the gap is the shortest distance between the two surfaces.

The second waveguide 120 is offset laterally in the x-direction with respect to the first waveguide no. The direction of the offset is defined to be in x-direction in FIG. la, which is normal to the propagation direction, the z-direction, and parallel to the plane of the substrate no, the y-direction.

In some implementations, at least part of the bottom surface of the second waveguide 120 faces part of the top surface of the first waveguide no and at least part of the bottom surface of the second waveguide 120 does not face the top surface of the first waveguide no. Alternatively, in some implementations, although not depicted in the Figures, the entire bottom surface of the second waveguide 120 faces part of the top surface of the first waveguide no. Aline through the centre of the cross section of the first waveguide no and a line through the centre of the cross section of the second waveguide 120 are therefore parallel to each other but displaced in the x-direction and the y-direction. The degree of offset 140 or an overlay offset 140 or a lateral offset 140 is defined to be the shortest distance, in the xz-plane or in the x-direction, between the centre of the cross section of the first waveguide no and the centre of the cross section of the second waveguide 120.

In some implementations, the degree of offset 140 is constant throughout the polarisation rotator loo.

Alternatively, in some implementations, the degree of offset 140 may vary. In this case, either the first waveguide no or the second waveguide 120 or both of the first waveguide no and the second waveguide 120 may be curved in the xz-plane to change direction. Once the first waveguide no is deposited and patterned on the oxide layer 102, the first waveguide no is deposited and patterned. Subsequently, a cladding 103 is deposited on the oxide layer 102 and the first waveguide no. In some implementations, the cladding 103 may be etched or polished. Subsequently the second waveguide 120 is deposited and patterned on the cladding 103. -7 -

In some implementations, the gap 130 may be filled with the material of the cladding 103. Therefore, the gap 130, or the first distance 130, is controlled with the thickness of the cladding 103 deposited on the top surface of the first waveguide no. In some implementations, the cladding 103 deposited on the top surface of the first waveguide no may be etched or polished such that the gap 130 is minimised.

In some implementations, a material for the cladding 103 may be additionally deposited on the second waveguide 120 and the cladding 103 deposited to define the gap 130.In some implementations, although not depicted in the Figures, the first waveguide no and the second waveguide 120 do not overlap in the xz-plane, the plane parallel to the substrate. in this case, the offset izto and the gap 130 are determined such that the second waveguide 120 can interact efficiently with the first waveguide no to rotate the polarisation.

Figure ib shows exemplary arrangements of the waveguides of the polarization rotator.

The three panels 100-1, 100-2, 100-3 correspond to the top-views of three arrangements of the first waveguide 110-1, 110-2, 110-3 and the second waveguide 120- 1, 120-2, 120-3 of the polarisation rotator 100. At least the first waveguide 110-1, 110-2, 110-3 is frilly embedded within the cladding 103. These diagrams show simultaneously the first waveguide 110-1, 110-2, 110-3 and the second waveguide 120-1, 120-2, 120-3 are for illustrations only.

In all of the three panels, 100-1, 100-2, 100-3, the second waveguide 120-1, 120- 2, 120-3 is offset in the x-direction, which is normal to the propagation direction and parallel to the substrate mi.

The region where the first waveguide 110-1, 110-2, 110-3 and the second waveguide 120-1, 120-2, 120-3 overlap will be referred to as asymmetric region woa. As discussed above, the polarisation rotator 100 can be part of a larger photonic circuit. The asymmetric region boa corresponds to the key part of the polarisation rotator 100 in that case. The first waveguide 110-1, 110-2, 110-3 on each side of the asymmetric region boa at the boundary of the asymmetric region boa, marked as two horizontal dotted lines in FIG. ib, serves as the input/output of the polarisation rotator loo.

in some implementations, the second waveguide 120-1, 120-2, 120-3 is a single strip which is present only within the asymmetric region iooa. In this case, the length of the asymmetric region looa is determined by the length of the second waveguide 120-1, 120-2, 120-3 in the z-direction, the propagation direction. -8 -

In the leftmost panel 100-1, the width 111 of the first waveguide 110-1 as a constant width in within the asymmetric region inoa. The portion of the first waveguide 100-1 outside the asymmetric region lc:ma, used for input and output of the polarisation rotator 100-1, also has a constant width along its length, which is the same as the width 111 of the first waveguide 100-1 within the asymmetric region low.

In the middle panel 100-2, the first waveguide no-2a has a constant width in in the asymmetric region bow. In this example, the width in of the first waveguide of the asymmetric region no-2a is larger than the width of the first waveguide 110-2 outside the asymmetric region no-2a. The first waveguide 100-2 of the asymmetric region no-2a is connected to the first waveguide 110-2 via a transition region 110-2t on either side of the first waveguide of the asymmetric region no-2a.

The first waveguide 110-2 is configured to support at least two fundamental modes, for example, TMo mode and TEo mode. The first waveguide of the asymmetric region no-2a and the transition region no-2t are configured such that the same two modes are supported within the asymmetric region moil.

For example, the first waveguide 110-2 outside the asymmetric region low can be configured to support only TMo and TEo modes and the first waveguide no-2a inside the asymmetric region inoa can be configured to support TMo, TEo and TEl modes. For another example, the first waveguide 110-2 outside the asymmetric region vim can be configured to support only TMo and TEo modes and the first waveguide lio-2a inside the asymmetric region boa can be configured to support also TMo and TEo modes.In the rightmost panel 100-3, the first waveguide no-3a has a constant width 111 in the asymmetric region inoa. In this example, the width in of the first waveguide of the asymmetric region no-3a is smaller than the width of the first waveguide 110-3 outside the asymmetric region 110-3a. The first waveguide 100-3 of the asymmetric region no-3a is connected to the first waveguide 110-3 via a transition region no-3t on either side of the first waveguide of the asymmetric region no-3a.

The first waveguide 110-3 is configured to support at least two fundamental modes, for example, TMo mode and TEo mode. The first waveguide of the asymmetric region no-3a and the transition region no-3t are configured such that the same two modes are supported within the asymmetric region looa. The transition region no-3t is introduced to alleviate the insertion loss and output coupling loss.

For example, the first waveguide 110-3 outside the asymmetric region low can be configured to support only TMo and TEo mode and the first waveguide no-3a inside the asymmetric region inoa can be configured to support also TMo and TEo modes. -9 -

In some implementations, although not shown in the FIG. 1b, when the width of the first waveguide of the asymmetric region 110-2a, no-3a is different from the width of the first waveguide 110-2, 110-3 on either side, the waveguides within and outside the asymmetric region bow maybe connected without the transition region no-2t, no-3t, such that there is a step in the width 111 of the first waveguide 110-2, 110-3 at the boundary of the asymmetric region 100a. In this case, the first waveguide of the asymmetric region no-2a, no-3a is configured to support at least the two optical modes supported by the first waveguide 110-2, 110-3 on either side.

Although the second waveguide 120-1, 120-2, 120-3 are shown to be a single strip in FIG. ib, the invention is not limited to these cases. In some implementations, the second waveguide 120-1, 120-2, 120-3 may include connecting waveguides or input/output waveguides connected to each end of the strip of the second waveguide 120-1, 120-2, 120-3. For example, the first and second waveguides lio, 120 may be arranged as directional couplers, in which case the second waveguide 120-1, 120-2, 1203 may include input and output waveguides approaching the second waveguide 120-1, 120-2, 120-3.

In some implementations, the connecting waveguides to the second waveguide 120-1, 120-2, 120-3 may approach one end of the second waveguide 120-1, 120-2, 120-3 within the same plane as the second waveguide 120-1, 120-2, 120-3.

In some implementations, the connecting waveguides may approach one end of the second waveguide 120-1, 120-2, 120-3 from out-of-plane or at an angle with respect to the xz-plane, the plane parallel to the substrate 101. For example, the connecting waveguides may approach the second waveguide 120-1, 120-2, 120-3 in a slope within a vertical plane that is normal to the second waveguide 120-1, 120-2, 120-3 and parallel to the propagation direction.

The first waveguide 110-1, 110-2, 110-3 is configured to support at least two fundamental optical modes.

For example, the first waveguide 110-1, 110-2, 110-3 is configured to support TE0 and TIVI0 modes. The principal polarisation of the TE0 mode is horizontal, in x-direction, normal to the propagation direction and parallel to the plane of the substrate 101. The principal polarisation of the TIVIo mode is vertical, in y-direction, normal to the propagation direction and to the plane of the substrate 101.

When the first waveguide 110-1, 110-2, 110-3 is excited with either TE0 mode or TA40 modes or any superposition of the TE0 and TM0 modes, two hybrid modes are excited in the asymmetric region boa or the polarisation rotator 100. Within the -10 -asymmetric region low., two hybrid modes are supported by the first waveguide 110-2a, no-3a, the second waveguide 120-1, 120-2, 120-3 and the cladding 103.

A transverse electric (TB) mode has Ez = o and Hz * o. A transverse magnetic (TM) mode has Hz = o and Ez * o. A hybrid mode has both Ez * o and Hz * o. Therefore, the hybrid mode refers to a superposition of TE and TM modes and the principal polarisation axes are rotated with respect to fundamental modes within the first waveguide 110-1, 110-2, 110-3. Since the distribution of the refractive indices is asymmetric within the cross section of the asymmetric region woa, the effective refractive indices or group velocities of the two hybrid modes are different, which effectively leads to the rotation of the polarisations.

In some implementations, either of TEo or TMo modes is launched outside the asymmetric region woa and input into the asymmetric region row.. The asymmetric region rooa is configured to rotate the polarisation of the input TEo/TMo mode into TMo/lEo mode over the course of the asymmetric region rooa. The principal polarisation of a TEo mode is in the horizontal direction or x-direction or parallel to the plane and normal to the propagation direction. The principal polarisation of a TMo mode is in the vertical direction or y-direction or normal to the plane and the propagation directions. The asymmetric region tow, or the polarisation rotator 100 in effect rotates a horizontal polarisation of TEo mode to a vertical polarisation of TMo mode and vice versa.

Even if higher order modes are present within the first waveguide 110-1, 110-2, 110-3, the polarisation rotator 100-1, 100-2, 100-3 can operate according to this principle.

FIG. 2 shows a flowchart of the process for designing a polarisation rotator. An example of the design process are as follows: At step 210, the wavelength of operation is determined. Since the polarisation rotator too can be part of a photonic circuit, the wavelength of operation can be determined from the purpose of the intended photonic circuit. For example, the operation wavelength is typically 15500m.

At step 220, the width in and the height 112 of the first waveguide no within the polarisation rotator roo are determined. For example, these can be determined to support only two fundamental optical modes, TEo and TMo. This win be explained in more detail in FIG. 3. When the polarisation rotator roo is embedded in a photonic circuit, the width in and the height 112 of the first waveguide no may be determined to be those of the connected photonic circuit.

In some implementations, a cross-section of the first waveguide no provides the same effective refractive index/group velocity for the two fundamental modes: for example symmetric 800nm x 800nm.

In some implementations, a height 112 of the first waveguide no is set to be 800nm and the width 111 of the first waveguide no is set between 5oonm and 800nm.

At step 230, the height 122 of the second waveguide 120 and the gap 130 are determined. The height 122 of the second waveguide 120 and the gap 130 are determined to be as thin as possible to reduce fabrication load. Since a smaller size of the gap 130 leads in general to a higher coupling efficiency between the first waveguide no and the second waveguide 120, the gap 130 may be determined as small as possible within the fabrication tolerance. Practically, loonm target value can be set for the size of the gap 130. The height 122 of the second waveguide 120 is set to be 200nm.

At step 240, the width 121 of the second waveguide 120 is determined. The width 121 of the second waveguide 120 is determined such that the disruption of the symmetry of the mode supported by the first waveguide no is large enough to support a hybrid mode.

In some implementations, the width 121 of the second waveguide 120 is determined such that, in view of the height 122 of the second waveguide 120 determined at step 230, the second waveguide 120 supports a single guided mode or the second waveguide 120 is near a cutoff condition.

At step 250, the offset 140 is calculated. The offset 140 is a degree of lateral displacement of the second waveguide 120 with respect to the first waveguide no. The offset 140 is defined as the distance in the x-direction between the centres of the cross-sections of the first waveguide 110 and the second waveguide 120 so that the hybrid mode is rotated by 45 degrees from either TM or TE polarisations.

The offset 140 is calculated by performing mode simulations repeatedly by varying the offset 140 to find a value of the offset 140 at which supported hybrid modes has a polarisation at 45 degrees from either 'FE or TM polarisation of the first waveguidc no. In some implementations, the offset 140 may be determined such that a line connecting a first centre of a cross-section of the first waveguide and a second centre of a cross-section of the second waveguide is at 45 degrees angle from a line parallel to a plane of the substrate and orthogonal to the propagation direction of the first waveguide. In this case, starting from the fixed values of the width in and the height 112 of the first waveguide no, the height 122 of the second waveguide 120, the gap 130 and the offset 140, to determine the width 121 of the second waveguide 120, mode -12 -simulations are performed by varying the width 121 of the second waveguide 120 within a predetermined range. For example, a parameter sweep of the width 121 of the second waveguide 120 can be performed.

In some implementations, the initial value of the offset 140 may be determined such that a line connecting a first centre of a cross-section of the first waveguide and a second centre of a cross-section of the second waveguide is at 45 degrees angle from a line parallel to a plane of the substrate and orthogonal to the propagation direction of the first waveguide. In this case, mode simulations are performed by varying the offset 140 within a predetermined range. For example, a parameter sweep of the offset 140 starting from the initial value of the offset 140.

In some implementations, starting from the fixed values of the width in and the height 112 of the first waveguide no, the height 122 of the second waveguide 120, the gap 130, to determine the offset 140 and the width 121 of the second waveguide 120, mode simulations are performed by varying the offset 140 and the width 121 of the second waveguide 120 within a predetermined range. For example, a parameter sweep of the offset 140 and the width 121 can be performed. This case corresponds to the steps 240 and 250 being performed simultaneously.

In performing the parameter sweep, mode solutions for the two hybrid modes are calculated for the cross section of the polarisation rotator 100 shown in FIG. la by varying the parameters starting from initial values.

The initial values of the width 121 of the second waveguide 120 or the offset 140 can be determined based on past simulation results and/or fabrication considerations. In absence of prior information, various trial values of the width 121 can be tried, for example, between 200 nm to 2 microns, if the first waveguide no and the second waveguide 120 are silicon nitride.

If the two hybrid mode solutions cannot be found, both the width 121 of the second waveguide 120 and the offset 140 can be sweeped in mode simulations to find two hybrid mode solutions.

A smaller value of the width 121 of the second waveguide 120 generally leads to a weaker interaction between the first waveguide no and the second waveguide 120 or a small tilt of the polarisations from the input beam. A larger value of the width 121 generally leads to a stronger interaction between the first waveguide no and the second waveguide 120 or a larger tilt of the polarisations from the input beam.

If the offset 140 is too small, the tilt of the polarisations of the hybrid modes with respect to the input polarisations will be low. If mode solutions are not found by -13 -varying only the width 121 of the second waveguide 120, the offset 140 can be made larger than the current value.

The width 121 of the second waveguide 120 and the offset 140 are the main control parameters in designing the polarisation rotator loo. In order to achieve the 45 degrees polarisations inclination angle within the polarisation rotator loo, a small value of the offset 140 can be compensated with a larger value of the width 121 and vice versa.

In order for an efficient coupling between the first waveguide no and the second waveguide 120, the offset 140 can be kept as small as practically possible considering the fabrication tolerance and the required inclination angle of polarisations.

In some implementations, if the target specifications are not met by a parameter sweep of the width 121 of the second waveguide 120 and the offset 140, the width in of the first waveguide 120-2a, 120-3a within the asymmetric section boa can be varied in addition. This corresponds to the case shown in FIG. lb in the middle panel 100-2 and the rightmost panel 100-3.

In some implementations, if the target specifications are not met by a parameter sweep of the width 121 of the second waveguide 120, the offset 140, and the width in of the first waveguide 110-2a, no-3a within the asymmetric section low., the height 112 of the first waveguide 120-2a, 120-3a can also be varied.

At step 260, the length of the polarisation rotator low is determined by performing a full device simulation. The examples of the full device simulation include 2D/3D FDTD or varFDTD simulations, although the examples are not limited to these. By performing a detailed simulation of the propagation of the electromagnetic wave at the operating wavelength, the length of the asymmetric region looa can be determined and the evaluation of the performance can be made.

In some implementations, the length of the asymmetric section woa is determined such that an accumulated phase difference of the two hybrid optical modes leads to one of the fundamental modes of the output waveguide, TMo or TE0 respectively.

The effective beat length, cr,, which corresponds to the length of the asymmetric region 100a, can be estimated with the following approximation, which is given by the formula LT, -

A

-14 -where n, and n, are the effective indices for the hybrid mode 1 and the hybrid mode 2 inside the asymmetric region woa and A is the wavelength of the optical signal. Important to note that the total length can be chosen as odd multiple of this value, namely Lam = La * (2n-1), where n is integer.

However, the exact length of the polarisation rotator loo is determined by the numerical simulations. The beat length obtained as discussed above can be used as the initial value for these simulations.

The target specifications include the following:

The target specifications are determined to facilitate efficient conversion between the fundamental modes (TEo to TMo and vice versa).

At least two hybrid modes are supported in the asymmetric section low. The hybrid modes have high coupling efficiencies, typically with less than 0.5dB insertion loss, to the first waveguide no outside the asymmetric region low.

In some implementations, the dimensions of the asymmetric region woa may be determined such that the coupling efficiencies of the two hybrid modes are equal. Alternatively, in some implementations, the dimensions of the asymmetric region low may be determined such that the coupling efficiency of each of the hybrid modes are maximised but to different values.

In some implementations, within the asymmetric region boa, the principal polarisation axes of the hybrid modes should be rotated by 45 degrees, or as close to 45 degrees as possible, with respect to the horizontal and vertical polarisations of the TEo and TMo modes, respectively.

In some implementations, the asymmetric region boa of the polarisation rotator boo may be designed such that at least two such hybrid modes are supported and the two hybrid modes are excited as equally as possible in response to the incidence of TEo and TMo modes. In this case, the target specifications include the tolerance from the ideal 45 degrees rotation and equal excitation of the two hybrid modes.

If target specifications are met, the parameters are used for a final design. If target specifications are not met the steps are iterated.

In a typical implementation of rib-based polarisation rotators or partially etched polarisation rotators, the hybrid modes are generated in a single asymmetric waveguide. Taking into account the typical thickness and required width, these devices are very sensitive to the etching mask misalignments and lithographic accuracy. Moreover, such polarisation rotators require a certain level of thickness of the silicon nitride layer.

-15 -By employing two separate waveguides, stringent requirements for the thickness of the layers and respective alignment tolerances can be alleviated. Moreover, the second waveguide 120 can be in a second photonic layer or within a separate layer of photonic circuits, so there is no need for an additional "module" to form such polarisation rotators.

Example case study: Dual waveguide polarisation rotator for C-band For silicon nitride (Si3N4) waveguides of 800 nm thickness and surrounded by silicon dioxide (Si02) cladding, single mode conditions in the C-band (wavelengths ranging from 153onm to 1565nm) are satisfied when the width of the silicon nitride waveguide is less than 1 micron.

In order to excite a single mode which is excitable in both TE and TM polarization within the first waveguide no, a typical choice is to keep the first width in of the bottom waveguide same as its height 112, for example, 800 nm. Since variation of the optical constants or the refractive indices of both silicon nitride and silicon dioxide are negligible within this wavelength range defined by the C-band, input optical signals in the C-band travels within the first waveguide no without any polarisation rotation.

The polarisation rotator 100 in this specification relates to achieving polarisation rotation by disrupting the symmetry of the configuration of the first waveguide no by introducing the second waveguide 120, which also extends along the signal propagation direction of the first waveguide no and laterally displaced with respect to the first waveguide no. The lateral offset 140 is determined large enough to disrupt the symmetry and at the same time small enough to ensure an efficient interaction between the first waveguide no and the second waveguide 120.

In order to reduce the overall footprint of the polarisation rotator loo, one of the options is to reduce the width of the first waveguide lio, as shown in the rightmost panel 100-3 of FIG. lb and FIGs. 4a and 4b. As the width of the first waveguide no is reduced, the optical mode is less confined around the first waveguide no and the mode-field diameter is expanded, which enables a stronger interaction with the second waveguide 120. Under such conditions, the tail of the optical single mode confined in the first waveguide no can "see" the higher refractive index of the top waveguide more easily, thereby disrupting the mode symmetry. The narrower the widths of the first waveguide no and second waveguide 120, the less the confinement of the optical modes within the first waveguide no and second waveguide 120, thereby creating a collective propagation mode or a hybrid mode. The smaller the lateral offset 140 becomes, the stronger the -16 -coupling becomes between the first waveguide 110 and the second waveguide 120, but at the cost of less degree of disruption of the symmetry of the optical mode.

A plot 300 shows an effective index of supported modes as a function of width of the first waveguide no. The choice of the design parameters will be explained with reference to the plot 300, such as the width in of the first waveguide no, the width 121 of the second waveguide 120, and the height 122 of the second waveguide 120. In the plot 300, the thickness of the waveguide is assumed to be 800nm. For example, the thickness 112 of the first waveguide no is typically set to be 800nm. The material of the waveguide is assumed to be silicon nitride and the cladding 103 is assumed to be silicon dioxide. The operation wavelength is 155onm.

A horizontal axis 301 of the plot 300 represents the width of the waveguide and a vertical axis 302 represents the effective index of guided modes.

A first curve 310 represents the fundamental TM mode supported by the waveguide. A second curve 320 represents the fundamental TE mode supported by the waveguide. A third curve 330 represents a next higher order TM mode supported by the waveguide. A fourth curve 340 represents a next higher order '1E mode supported by the waveguide.

A cutoff line 303, a dotted horizontal line at the effective index of 1.45, represents the cutoff condition, where the effective index of the mode is the same as the refractive index of the cladding 103.

At the width of 800nm, marked by a vertical dotted line 304, the effective indices of the fundamental TM mode 310 and the fundamental '1E mode 320 are the same. Also at the width of 800nm, the higher order TM mode 330 and the higher order TE mode 340 are at a cutoff condition. For a width larger than Soo nm, a second TE mode is present, as well as a second TM mode. At the width of 800nm, there is a mode crossing: below 800 nm width, the 1E mode 320 is the second supported mode, whereas above 800 nm, the TM mode 310 becomes the second supported mode.

At the width of 500nm, marked by a vertical line 305, the fundamental TE mode 320 has an effective index, 1.59, much smaller than that of the fundamental one of TM mode 310, 1.63.

In some implementations, the width in of the first waveguide no in silicon nitride in silicon dioxide cladding is between 500 nm and 800 nm.

-17 -In some implementations, the width in of the first waveguide no in silicon nitride in silicon dioxide cladding is between 200 nm and 500 nm in case a stronger interaction between the first waveguide no and the second waveguide 120 is desired.

The gap 130 between the first waveguide no and the second waveguide 120 is filled with a silicon dioxide spacer. In some implementations, the gap 130 is set at ioo nm.

To reduce fabrication burdens, the thickness of the second waveguide 120 is set as small as possible, typically smaller than 300 nm. In some implementations, the width 121 of the second waveguide 120 is chosen such that the second waveguide 120 supports a single mode operation or such that the second waveguide izo is near the cutoff condition. For example, when the thickness 122 of the second waveguide 120 is set at loo nm, the width 121 of the second waveguide 120 is kept at Soo nm to be near cutoff condition. For another example, when the thickness 122 of the second waveguide 120 is set at zoo nm, the width 121 of the second waveguide 120 is set at 600 nm or above, at which conditions a single mode operation is supported.

FiGs. 4a and 4b show exemplary simulation results of a polarisation rotator.

A transverse mode profile of a hybrid mode is shown with a cross section, the xyplane, of the polarisation rotator loo, comprising the first waveguide 410 and the second waveguide 420, both silicon nitride, embedded in the cladding material 103, silicon dioxide. The numbers on the axes are microns.

In this simulation, the thickness 112 of the first waveguide no, 410 is 8 oonm, the width in of the first waveguide no, 410 is 225 nm. The width 121 of the second waveguide 120,420 is 900nm, the thickness 122 of the second.waveguide 120,420 is 200 nm, and the gap 130 is ioo nm. The operation wavelength is assumed to be 155onm.

In relation to the width in of the first waveguide no, 410, although the difference between the effective indices of the TM mode 310 and the TE mode 320 become significant below 500 nm as discussed in FIG. 3, in this example, the width 111 was chosen to be 225nm due to the requirements of a specific application. As discussed in FIG. 3, a narrow width of the first waveguide 110, 410 renders the optical mode supported by the first waveguide no less confined thereby enhancing the interaction between the first waveguide no and the second waveguide 120.

Mode simulations were performed repeatedly by varying the value of offset 140 looking for a value of the offset 140 that enables two hybrid modes each with inclined polarisations at or as near as 45 degrees, or equal fractions of TE and TM mode.

-18 -Table I shows the summary of supported modes. Mode number 1 and 2 correspond to the two hybrid modes which are tightly guided around the first waveguide 410 and the second waveguide 420 with an effective area less than 3 micron squared. The transverse mode profile of mode number 1 is shown in FIG. 4a and the transverse mode profile of mode number 2 is shown in FIG. 4b. Mode number 1 has 45% of TE polarisation and mode number 2 has 55% of TE polarisation.

FIGs. 4a and 4h show that the mode profile for mode number 1491 and the guided mode profile for mode number 2 492 are both heavily distorted with respect to the centre of the cross-section of the first waveguide no, 410. In particular, the guided mode profiles 491, 492 are elongated approximately along 45 degrees angle. As explained above, this is due to the influence of the second waveguide 120, 420 laterally offset 140 with respect to the first waveguide no, 410.

mode number Effective index Group index TE Effective area (micron squared) polarisatio n fraction (%) 1 1.509666 1.694144 45 2.04119 2 1.504173 1.689244 55 2.51637 TABLE I. Summary of the solutions of the mode simulations Using the effective index values for these two modes, the required beat length can be calculated. The beat length is given by: A A 1.55 Lit= -141.09 pm 2*(nl-n2) 2*(1.509666-1.504173) 2*(0.005493) When the length of the second waveguide 120,420 is set to be this beat length, the polarisation rotator loo is expected to induce close to 90° polarisation rotation of the input signal.

The embodiments of the invention shown in the drawings and described above are exemplary embodiments only and are not intended to limit the scope of the invention, which is defined by the claims hereafter. It is intended that any combination of non-mutually exclusive features described herein are within the scope of the present invention.

Claims

-19 -Claims 1. A polarisation rotator, comprising: a substrate; a first waveguide disposed on the substrate, configured to support a first mode and a second mode, wherein a first polarisation of the first mode and a second polarisation of the second mode are orthogonal to each other; and a second waveguide disposed over the first waveguide, wherein in an asymmetric region, the second waveguide is evanescently coupled to the first waveguide and laterally displaced with respect to the first waveguide by a first offset in plan view, such that in response to the first mode or the second mode on the first waveguide input into the asymmetric region, the second mode or the first mode, respectively, is output out of the asymmetric region on the first waveguide.
2. The polarisation rotator of claim 1, wherein the first offset is determined such that: the first waveguide and the second waveguide support a first hybrid mode and a second hybrid mode; and a third polarisation of the first hybrid mode and a fourth polarisation of the second hybrid mode are orthogonal to each other;
3. The polarisation rotator of claim 2, wherein the third polarisation and the fourth polarisation are at 45 degrees angle from the first polarisation and the second polarisation, respectively.
4. The polarisation rotator of claim 2 or 3, wherein a length of the asymmetric region is arranged such that a phase difference between the first and second hybrid modes accumulated over the asymmetric region is 180 degrees.
5- The polarisation rotator of any preceding claim, wherein the first offset is determined such that a line connecting a first centre of a cross-section of the first waveguide and a second centre of a cross-section of the second waveguide is at 45 degrees angle from a line parallel to a plane of the substrate and orthogonal to the propagation direction of the first waveguide.-20 -
6. The polarisation rotator of any preceding claim, further comprising: a gap layer disposed between the first waveguide and the second waveguide in the asymmetric region.
7. The polarisation rotator of claim 6, wherein the thickness of the gap layer is less than 1 micron.
8. The polarisation rotator of any preceding claim, wherein the first waveguide comprises a first section within the asymmetric region and a second section outside the asymmetric region, and wherein a width of the first section is different from a width of the second section.
9. The polarisation rotator of claim 8, wherein a width of the first section is larger than a width of the second section.
10. The polarisation rotator of claim 8, wherein a width of the first section is smaller than a width of the second section.
The polarisation rotator of any preceding claim, wherein the second waveguide does not overlap the first waveguide in plan view.
12. A method of designing a polarisation rotator comprising: a first waveguide; and a second waveguide disposed over the first waveguide, wherein in an asymmetric region: the second waveguide is evanescently coupled to the first waveguide and laterally displaced with respect to the first waveguide by a first offset in plan view, the method comprising: determining a wavelength of operation; determining a first width and a first height of the first waveguide based on the wavelength of operation such that the first waveguide supports a first mode and a second mode, wherein a first polarisation of the first mode and a second polarisation of the second mode are orthogonal to each other; determining a second height of the second waveguide and a gap between the first waveguide and the second waveguide; -21 -determining a second width of the second waveguide; calculating the first offset, wherein the first offset is a degree of lateral displacement of the second waveguide with respect to the first waveguide; and calculating a length of the asymmetric region, such that in response to the first mode or the second mode input into the asymmetric region, the second mode or the first mode, respectively, is output out of the asymmetric region.
13. The method of claim 12, wherein calculating the first offset comprises performing mode simulations by varying the first offset such that the first waveguide and the second waveguide support a first hybrid mode and a second hybrid mode.
14. The method of claim 13, wherein a third polarisation of the first hybrid mode and a fourth polarisation of the second hybrid mode are orthogonal to each other, and wherein the third polarisation and the fourth polarisation are at 45 degrees angle from the first polarisation and the second polarisation, respectively.
15. The method of any one of claims 12 to 14, wherein calculating a length of the asymmetric region comprises performing simulations such that at the length, a phase difference between the first and second hybrid modes accumulated over the asymmetric region is 180 degrees.
16. The method of any one of claims 12 to 15, wherein the first offset is determined such that a line connecting a first centre of a cross-section of the first waveguide and a second centre of a cross-section of the second waveguide is at 45 degrees angle from a line parallel to a plane of the substrate and orthogonal to the propagation direction of the first waveguide.