Broadband optical switch based on annular auxiliary Mach-Zehnder interferometer

Abstract

The invention relates to a broadband optical switch based on a ring-assisted Mach-Zehnder interferometer. Structures for broadband optical switches and methods of forming such structures are provided. The structure comprises a Mach-Zehnder interferometer, and the Mach-Zehnder interferometer comprises a first arm and a second arm. The first arm includes a first waveguide core and the second arm includes a second waveguide core. The structure also includes a ring resonator including a third waveguide core having a first thickness. A portion of the third waveguide core is adjacent to a portion of the first waveguide core over an optical coupling region. A plate layer connects the portion of the first waveguide core with the portion of the third waveguide core. The plate layer has a second thickness less than the first thickness of the first waveguide core.

Description

Technical Field

[0001] The present disclosure relates to photonic chips, and more particularly to structures for broadband optical switches and methods of forming such structures. Background Art

[0002] Photonic chips are used in many applications and systems, including but not limited to data communication systems and data computing systems. Photonic chips include photonic integrated circuits, which are composed of photonic components (such as modulators, polarizers, and optical couplers) that are used to manipulate light received from a light source (such as a laser or optical fiber).

[0003] An optical switch is a common photonic component found in photonic integrated circuits. A Mach-Zehnder interferometer can be used as the basic device for an optical switch. An optical coupler distributes the input light between a pair of arms of the Mach-Zehnder interferometer. A phase difference can be introduced between the light propagating in different arms to provide a pair of different switching conditions. The arms converge at a downstream optical coupler where the light is combined. Under one switching condition, the phase difference between the light after propagating through the arms is an odd multiple of pi, and the combined light leaves an output port of the output coupler. Under another switching condition, the phase difference between the light after propagating through the arms is an even multiple of pi, and the combined light leaves different output ports of the output coupler.

[0004] Conventional optical switches based on Mach-Zehnder interferometers may be characterized by too narrow a bandwidth, which may be unacceptable in certain applications or systems. Conventional optical switches based on Mach-Zehnder interferometers may also suffer from excessive crosstalk.

[0005] There is a need for improved structures for broadband optical switches and methods of forming such structures. Summary of the invention

[0006] In one embodiment of the present invention, a structure for an optical switch is provided. The structure includes a Mach-Zehnder interferometer, the Mach-Zehnder interferometer including a first arm and a second arm. The first arm includes a first waveguide core, and the second arm includes a second waveguide core. The structure also includes a ring resonator, the ring resonator including a third waveguide core having a first thickness. The third waveguide core includes a portion adjacent to a portion of the first waveguide core above an optical coupling region. The structure also includes a slab layer connecting the portion of the first waveguide core to the portion of the third waveguide core. The slab layer has a second thickness less than the first thickness.

[0007] In one embodiment of the present invention, a structure for an optical switch is provided. The structure includes a ring resonator including a first waveguide core having a sidewall, and a Mach-Zehnder interferometer including a first arm and a second arm. The first arm includes a second waveguide core, the second arm includes a third waveguide core, and the second waveguide core overlaps a portion of the first waveguide core above an optical coupling region.

[0008] In one embodiment of the present invention, a method of forming a structure for an optical switch is provided. The method includes forming a Mach-Zehnder interferometer including a first arm and a second arm. The first arm includes a first waveguide core, and the second arm includes a second waveguide core. The method also includes forming a ring resonator including a third waveguide core. The third waveguide core has a first thickness, and the third waveguide core includes a portion adjacent to a portion of the first waveguide core above an optical coupling region. The method also includes forming a slab connecting the portion of the first waveguide core to the portion of the third waveguide core. The slab has a second thickness that is less than the first thickness. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] The accompanying drawings, which are included in and constitute a part of this specification, illustrate various embodiments of the present invention and, together with the general description of the present invention made above and the detailed description of the embodiments made below, are used to explain the embodiments of the present invention. In the accompanying drawings, like reference numerals represent similar features in different views.

[0010] Figure 1 A top view showing a structure for an optical switch according to an embodiment of the present invention.

[0011] Figure 2 Display the approximate Figure 1 A cross-sectional view of the structure taken along line 2-2 in FIG.

[0012] Figure 2A Display the approximate Figure 1 A cross-sectional view of the structure taken along line 2A-2A in FIG.

[0013] Figure 2B Display the approximate Figure 1 A cross-sectional view of the structure taken along line 2B-2B in FIG.

[0014] Figure 3 , 3A , 3B shows that Figure 2 , 2A , a cross-sectional view of the structure at the manufacturing stage of the processing method after 2B.

[0015] Figure 4 A top view showing a structure for an optical switch according to an alternative embodiment of the present invention.

[0016] Figure 5 A cross-sectional view showing a structure for an optical switch according to an alternative embodiment of the present invention.

[0017] Figure 6 A cross-sectional view showing a structure for an optical switch according to an alternative embodiment of the present invention. DETAILED DESCRIPTION

[0018] Please refer to Figure 1 , 2 , 2A, 2B and according to an embodiment of the present invention, a structure 10 for a broadband optical switch includes a Mach-Zehnder interferometer 12, a thermos-optic phase shifter 14 embedded in the Mach-Zehnder interferometer 12, and a ring resonator 16 embedded in the Mach-Zehnder interferometer 12. The Mach-Zehnder interferometer 12 includes an input optical coupler 18, an output optical coupler 20, and arms 22, 24 routed from the input optical coupler 18 to the output optical coupler 20, respectively. The waveguide cores 26, 28 may include portions providing the input optical coupler 18 and the output optical coupler 20. The waveguide cores 26, 28 also include portions providing the arms 22, 24 connecting the input optical coupler 18 with the output optical coupler 20. The ring resonator 16 may also include a waveguide core 27 having a closed geometry.

[0019] The waveguide cores 26, 27, 28 may be disposed on and above a dielectric layer 30 and a semiconductor substrate 31 of the photonic chip. In one embodiment, the dielectric layer 30 may be composed of a dielectric material such as silicon dioxide, and the semiconductor substrate 31 may be composed of a semiconductor material such as single crystal silicon. In one embodiment, the dielectric layer 30 may be a buried oxide layer of a silicon-on-insulator substrate.

[0020] The input optical coupler 18 may receive light from the waveguide core 26 or the waveguide core 28 as an input to the Mach-Zehnder interferometer 12. In one embodiment, the input optical coupler 18 may be a directional coupler, wherein the waveguide core 26 and the adjacent portions of the waveguide core 28 are routed in a proximity characterized by a spacing that supports light transmission. In one embodiment, the input optical coupler 18 may be a 50-50 directional coupler that evenly distributes light between the arms 22, 24. In one embodiment, the output optical coupler 20 may be a directional coupler, wherein the waveguide core 26 and the adjacent portions of the waveguide core 28 are routed in a proximity characterized by a spacing that supports light transmission. In one embodiment, the output optical coupler 20 may be a 50-50 directional coupler.

[0021] Arm 22 of Mach-Zehnder interferometer 12 may include a phase delay section 33 integrated into waveguide core 26. Phase delay section 33 introduces an optical path length difference representing an unbalanced length between arm 22 and arm 24. The unbalanced length introduces a time difference between light propagating in arm 22 of waveguide core 26 and light propagating in arm 24 of waveguide core 28.

[0022] The thermo-optic phase shifter 14 is associated with a portion of a waveguide core 26 located in an arm 22 of the Mach-Zehnder interferometer 12. The thermo-optic phase shifter 14 may include a resistive heating element 32, a resistive heating element 34, and a plate layer 36 connecting the resistive heating elements 32, 34 to the portion of the waveguide core 26. The resistive heating elements 32, 34 are disposed adjacent to the portion of the waveguide core 26, with the portion of the waveguide core 26 disposed laterally between the resistive heating elements 32 and the resistive heating elements 34. The plate layer 36 has a thickness that is less than the thickness of the waveguide core 26 and the resistive heating elements 32, 34.

[0023] The resistive heating elements 32, 34 are configured to generate heat by Joule heating under the control of a variable electrical signal, and the generated heat is transferred by conduction from the resistive heating elements 32, 34 to the portion of the waveguide core 26. The plate layer 36 provides part of the heat path to conduct the heat to the portion of the waveguide core 26. The temperature of the portion of the waveguide core 26 is locally increased by the transferred heat. The local temperature change experienced by the portion of the waveguide core 26 effectively changes the refractive index of its constituent material through the thermo-optic effect, and thereby changes the phase of light propagating in the portion of the waveguide core 26. The selectively changed phase of the light provides the switching action for the optical switch at the output optical coupler 20.

[0024] The waveguide core 27 of the ring resonator 16 includes a portion disposed adjacent to a portion of the waveguide core 28 located in the arm 24 of the Mach-Zehnder interferometer 12. The portion of the waveguide core 27 of the ring resonator 16 is separated from the adjacent portion of the waveguide core 28 of the arm 24 by a notch or gap. In one embodiment, the waveguide core 27 and the adjacent portion of the waveguide core 28 across the gap define an optical coupling region characterized by a coupling length L. In one embodiment, the optical coupling region may be the physical length over which the portions of the waveguide cores 27, 28 are adjacent and juxtaposed.

[0025] In one embodiment, the ring resonator 16 may be configured to have an elliptical or racetrack shape. In one embodiment, the waveguide core 27 of the ring resonator 16 may include a curved end 48, a curved end 50, and side segments 52, 53 connecting the curved ends 48, 50 to provide the racetrack shape. In one embodiment, the waveguide core 27 of the ring resonator 16 may be elongated, with the length of the side segments 52, 53 being greater than their spacing. In one embodiment, the side segment 52 may be straight or linear so that the gap between the waveguide cores 27, 28 is constant over the coupling region. In one embodiment, the optical coupling region may extend from a junction between the curved end 48 and the side segment 52 to a junction between the curved end 50 and the side segment 52. The length of the side segment 52 may vary, among other variables, to change the coupling length L of the coupling region.

[0026] The slab layer 38 may connect the portion of the waveguide core 27 located on one side of the gap to the portion of the waveguide core 28 located on the opposite side of the gap. The slab layer 38 extends laterally on the dielectric layer 30 as a strip that spans or bridges the gap between the adjacent portions of the waveguide cores 27, 28 located on the opposite sides of the gap. In one embodiment, the slab layer 38 may be connected to the side segment 52 of the ring resonator 16 over the entire coupling region. The thickness T1 of the slab layer 38 is less than the thickness T2 of the waveguide core 27 or the waveguide core 28. The thinner slab layer 38 may be connected to the lower region of the waveguide core 27 located in the coupling region and to the lower region of the waveguide core 28 within the scope of the coupling region. In one embodiment, the waveguide cores 27, 28 may have an equal thickness T2. The waveguide cores 27, 28 include an upper region that protrudes above the slab layer 38 by a height equal to the difference between the thicknesses T1, T2.

[0027] The coupling length L of the optical coupling region may be selected to enhance the coupling strength between the adjacent portions of the waveguide cores 27, 28. In one embodiment, the plate layer 38 may extend over the entire coupling length L so that the gap separating the adjacent portions of the waveguide cores 27, 28 is coextensive with the plate layer 38. The coupling width W between the adjacent portions of the waveguide cores 27, 28 (which is the width of the gap bridged by the plate layer 38) may also be selected to enhance the coupling strength.

[0028] In one embodiment, the optical path length difference introduced by the phase delay segment 33 and the circumference of the ring resonator 16 may have a fixed ratio, which is selected to facilitate configuring the structure 10 as a broadband switch. In one embodiment where the waveguide core 26 and the waveguide core 27 are composed of the same material and have the same refractive index, the ratio of the circumference to the optical path length difference may be equal to or substantially equal to 1.5 to optimize the performance of the structure 10 as a broadband switch. If the waveguide core 26 and the waveguide core 27 are composed of different materials with different refractive indices, the fixed ratio will include an additional multiplicative factor. In one embodiment, the free spectral range of the ring resonator 16 and / or the optical path length difference introduced by the phase delay segment 33 may be selected to determine the bandwidth of the broadband optical switch. In one embodiment, by selecting a variable (e.g., coupling length L), the coupling strength between the adjacent portions of the ring resonator 16 and the waveguide core 28 may be selected to be greater than or equal to 70.

[0029] In one embodiment, the waveguide cores 26, 27, 28, the resistive heating elements 32, 34, and the slab layers 36, 38 may be composed of a semiconductor material (e.g., single crystal silicon) formed by patterning using multiple photolithography and etching processes (supporting the formation of the slab layer 36). In one embodiment, the resistive heating elements 32 and 34 may be doped with p-type dopants or n-type dopants and / or may include silicide layers. In an alternative embodiment, the waveguide cores 26, 28 may be composed of a dielectric material (e.g., silicon nitride, silicon oxynitride, or aluminum nitride), in conjunction with which the waveguide core 27 of the thermo-optical phase shifter 14 and the ring resonator 16 is composed of a semiconductor material (e.g., single crystal silicon). In an alternative embodiment, the phase delay section 33 located in the arm 22 may also be composed of a semiconductor material.

[0030] Please refer to Figure 3 , 3A , 3B and in Figure 1 , 2 , 2A, 2B, a dielectric layer 40 may be formed over the Mach-Zehnder interferometer 12, the thermo-optical phase shifter 14, and the ring resonator 16. The dielectric layer 40 may be composed of a dielectric material that is deposited and then planarized after deposition, such as silicon dioxide. A back-end-of-line stack 42 may be formed over the dielectric layer 40. The back-end-of-line stack 42 may include stacked dielectric layers, wherein each dielectric layer is composed of a dielectric material, such as silicon dioxide, silicon nitride, tetraethyl orthosilicate silicon dioxide, or fluorinated tetraethyl orthosilicate silicon dioxide.

[0031] During use, the optical switch implemented in the structure 10 can be used to switch the output of the output optical coupler 20 to route it to the downstream portion of the waveguide core 26 or the downstream portion of the waveguide core 28. Light arriving at the input optical coupler 18 in the waveguide core 26 is divided between the arm 22 and the arm 24 by the input optical coupler 18. Light propagating in the arm 22 may experience a phase delay, which can be varied under the control of the thermo-optical phase shifter 14. The output optical coupler 20 combines the light arriving at the arms 22, 24 to provide constructive or destructive interference depending on the value of the phase delay. Light leaving the output optical coupler 20 can be output to the downstream portion of the waveguide core 26 if the phase delay is zero, and output to the waveguide core 28 if the phase delay is equal to pi (i.e., half the wavelength). Similarly, light arriving at the input optical coupler 18 in the waveguide core 28 is divided between the arm 22 and the arm 24 by the input optical coupler 18. Light propagating in arm 22 may experience a phase delay that may be varied under the control of thermo-optical phase shifter 14. Output optical coupler 20 combines the light arriving at arms 22, 24 to provide constructive or destructive interference depending on the value of the phase delay. Light exiting output optical coupler 20 may be output to a downstream portion of waveguide core 28 if the phase delay is zero, and to a downstream portion of waveguide core 26 if the phase delay is equal to pi.

[0032] The optical switch can be characterized by a tunable center wavelength. The slab 38 connecting the waveguide core 27 of the ring resonator 16 with the waveguide core 28 in the arm 24 of the Mach-Zehnder interferometer 12 can allow the coupling length L to be shortened while providing a coupling power greater than 70. The enhanced coupling power of the optical coupling between the waveguide core 27 of the ring resonator 16 and the waveguide core 28 in the arm 24 of the Mach-Zehnder interferometer 12 can provide an optical switch with reduced crosstalk.

[0033] Please refer to Figure 4And according to alternative embodiments of the present invention, the input optical coupler 18 and / or the output optical coupler 20 may be configured as a multimode interference coupler. In one embodiment, the input optical coupler 18 may include a multimode interference region 44 configured to distribute light arriving from the waveguide core 26 or the waveguide core 28 between the arms 22, 24. In one embodiment, the output optical coupler 20 may include a multimode interference region 45 configured to combine the light received from the arms 22, 24. In this representative embodiment, the multimode interference region 44 of the input optical coupler 18 may have a pair of input ports coupled to the upstream portions of the waveguide cores 26, 28, respectively, and a pair of output ports coupled to the arms 22, 24. In an alternative embodiment, the multimode interference region 44 of the input optical coupler 18 may have a single input port coupled to, for example, the upstream portion of the waveguide core 26, and a pair of output ports coupled to the arms 22, 24. In this representative embodiment, the multimode interference region 45 of the output optical coupler 20 may have a pair of input ports coupled to the arms 22 , 24 and a pair of output ports coupled to the downstream portions of the waveguide cores 26 , 28 .

[0034] Please refer to Figure 5 According to an alternative embodiment of the present invention, the waveguide core 28 may be disposed on the dielectric layer 40 so that the waveguide core 28 is located at a higher height relative to the semiconductor substrate 31 than the waveguide core 27 of the ring resonator 16. A portion of the dielectric layer 40 is disposed between the waveguide core 27 and the waveguide core 28 so that the waveguide cores 27, 28 do not touch due to the intermediate dielectric material.

[0035] In one embodiment, the waveguide core 28 may be composed of a material having a refractive index greater than that of silicon dioxide. In one embodiment, the waveguide core 28 may be composed of a dielectric material, such as silicon nitride, silicon oxynitride, or aluminum nitride. In one embodiment, the waveguide core 28 may be formed by depositing a layer of a dielectric material on the dielectric layer 40 and patterning the deposited layer using a photolithography and etching process. In one embodiment, the waveguide core 27 and the waveguide core 28 may be composed of different materials. In one embodiment, the waveguide core 27 may be composed of single crystal silicon, and the waveguide core 28 may be composed of silicon nitride.

[0036] The waveguide core 28 may have a portion that overlaps a portion of the lower waveguide core 27 of the ring resonator 16 above the optical coupling region, where the portions of the waveguide cores 27, 28 are adjacent. In one embodiment, the waveguide core 28 overlaps a portion of the lower waveguide core 27 of the ring resonator 16 in the optical coupling region by a distance D. In one embodiment, the width of the waveguide core 28 may be reduced in the optical coupling region compared to the width outside of the optical coupling region to provide a closer refractive index match between the waveguide core 27 and the waveguide core 28 composed of different materials.

[0037] Please refer to Figure 6 And in accordance with an alternative embodiment of the present invention, the ring resonator 16 may be modified to add a slab layer 46 that is attached to the sidewall 47 of the waveguide core 27 in the light coupling region. The slab layer 46 (which is thinner than the waveguide core 27) may be composed of the same material as the waveguide core 27. The waveguide core 28 may overlap a portion of the waveguide core 27 over the light coupling region by a distance D, and may also overlap the slab layer 46 over the light coupling region. In one embodiment, the waveguide core 28 may completely overlap the slab layer 46 over the light coupling region. The slab layer 46 may be disposed on the dielectric layer 30, and the slab layer 46 may be connected to the lower region of the waveguide core 27 at the sidewall 47. The waveguide core 27 includes an upper region that protrudes above the slab layer 38.

[0038] The method described above is used for the manufacture of integrated circuit chips. The manufacturer can distribute the resulting integrated circuit chips in raw wafer form (e.g., as a single wafer with multiple unpackaged chips), as a bare chip, or in a packaged form. The chip can be integrated with other chips, discrete circuit elements and / or other signal processing devices as part of an intermediate product or a final product. The final product can be any product that includes an integrated circuit chip, such as a computer product or a smart phone with a central processing unit.

[0039] Terms modified by approximate language such as "about," "approximately," and "substantially" cited herein are not limited to the exact value specified. The approximate language may correspond to the precision of the instrument used to measure the value, and may represent + / -10% of the value unless otherwise dependent on the precision of the instrument.

[0040] Terms such as "vertical", "horizontal", etc. are cited herein as examples to establish a reference frame and are not limiting. The term "horizontal" as used herein is defined as a plane parallel to the conventional plane of the semiconductor substrate, regardless of its actual three-dimensional spatial orientation. The terms "vertical" and "orthogonal" refer to directions perpendicular to the horizontal plane as just defined. The term "lateral" refers to a direction within the horizontal plane.

[0041] A feature that is "connected" or "coupled" to another feature may be directly connected or coupled to the other feature, or one or more intermediate features may be present. A feature may be "directly connected" or "directly coupled" to another feature if there are no intermediate features. A feature may be "indirectly connected" or "indirectly coupled" to another feature if there is at least one intermediate feature. A feature that is "on" or "in contact with" another feature may be directly on or in direct contact with the other feature, or one or more intermediate features may be present. A feature may be directly "on" or "in direct contact with" another feature if there are no intermediate features. A feature may be "not directly" "on" or "not directly in contact with" another feature if there is at least one intermediate feature. Different features may "overlap" if one feature extends over and covers part of another feature, with or without direct contact.

[0042] The description of various embodiments of the present invention is for illustrative purposes and is not intended to be exhaustive or limited to the disclosed embodiments. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments. The terms used herein are selected to best explain the principles of the embodiments, practical applications, or technical improvements over commercially known technologies, or to enable those of ordinary skill in the art to understand the embodiments disclosed herein.

Claims

1. A structure for an optical switch, characterized in that: The structure includes: A Mach-Zehnder interferometer comprising a first arm and a second arm, the first arm comprising a first waveguide core, and the second arm comprising a second waveguide core; a ring resonator comprising a third waveguide core having a first thickness and including a portion adjacent to a portion of the first waveguide core over a light coupling region; and A slab layer connects the portion of the first waveguide core and the portion of the third waveguide core, the slab layer having a second thickness less than the first thickness.

2. The structure according to claim 1, characterized in that Also includes: A thermo-optic phase shifter is associated with a portion of the second waveguide core of the second arm.

3. The structure according to claim 1, characterized in that The second waveguide core of the second arm includes a phase delay segment defining an optical path length difference between the first arm and the second arm.

4. The structure according to claim 3, characterized in that The third waveguide core of the ring resonator has a circumference equal to about 1.5 times the optical path length difference.

5. The structure according to claim 1, characterized in that The Mach-Zehnder interferometer includes a first directional coupler and a second directional coupler, and the second directional coupler is connected to the first directional coupler through the first arm and the second arm.

6. The structure according to claim 1, characterized in that The Mach-Zehnder interferometer includes a first multi-mode interference coupler and a second multi-mode interference coupler connected to the first multi-mode interference coupler through the first arm and the second arm.

7. The structure according to claim 1, characterized in that The first waveguide core has the first thickness.

8. The structure according to claim 1, characterized in that The first and second waveguide cores of the Mach-Zehnder interferometer, the third waveguide core of the ring resonator, and the slab layer include silicon.

9. The structure according to claim 1, characterized in that The portion of the first waveguide core is separated from the portion of the third waveguide core by a gap, and the slab layer bridges the gap.

10. The structure according to claim 9, characterized in that The third waveguide core is an elliptical element having a first curved end, a second curved end, and a side section connecting the first curved end and the second curved end, and the side section is the portion of the third waveguide core connected to the slab layer.

11. The structure according to claim 10, characterized in that The ring resonator has a coupling length above the light coupling region, and the coupling length is configured to provide a coupling power greater than or equal to 70.

12. The structure according to claim 10, characterized in that The gap has a constant width over the light coupling region.

13. The structure according to claim 10, characterized in that The slab is coextensive with the side segment of the portion of the third waveguide core across the gap.

14. The structure according to claim 1, characterized in that Also includes: Semiconductor substrate; as well as a dielectric layer disposed on the semiconductor substrate, The first waveguide core and the second waveguide core of the Mach-Zehnder interferometer, the third waveguide core of the ring resonator, and the plate layer are arranged on the dielectric layer.

15. The structure according to claim 1, characterized in that The third waveguide core is an elliptical element having a first curved end, a second curved end, and a side segment connecting the first curved end to the second curved end, and the side segment is the portion of the third waveguide core connected to the portion of the slab layer.

16. A structure for an optical switch, characterized in that: The structure includes: a ring resonator comprising a first waveguide core; and The Mach-Zehnder interferometer comprises a first arm and a second arm, wherein the first arm comprises a second waveguide core, the second arm comprises a third waveguide core, and the second waveguide core overlaps a portion of the first waveguide core above a light coupling region.

17. The structure according to claim 16, characterized in that The first waveguide core has a first thickness, the first waveguide core has a sidewall, and further includes: a plate layer connected to the side wall of the first waveguide core, the plate layer having a second thickness less than the first thickness, The second waveguide core overlaps the slab layer above the optical coupling region.

18. The structure according to claim 17, characterized in that The first waveguide core is an elliptical element having a first curved end, a second curved end, and a side segment connecting the first curved end to the second curved end, and the side segment is the portion of the first waveguide core connected to the slab layer above the optical coupling region.

19. The structure according to claim 16, characterized in that Also includes: A thermo-optic phase shifter is associated with a portion of the second waveguide core of the second arm.

20. A method of forming a structure for an optical switch, characterized in that The method includes: forming a Mach-Zehnder interferometer comprising a first arm and a second arm, wherein the first arm comprises a first waveguide core and the second arm comprises a second waveguide core; forming a ring resonator including a third waveguide core, wherein the third waveguide core has a first thickness and the third waveguide core includes a portion adjacent to a portion of the first waveguide core over a light coupling region; and A slab layer is formed connecting the portion of the first waveguide core and the portion of the third waveguide core, wherein the slab layer has a second thickness that is less than the first thickness.

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