Waveguide for Low-Loss High-Speed Electro-Optic Modulator

Abstract

To provide a low-voltage and low-insertion-loss electro-optical modulator.SOLUTION: A waveguide device includes: a base material including an electro-optical material; a waveguide formed in the electro-optical material; and a plurality of electrodes formed near the waveguide. The electro-optical material has a first index of refraction. The waveguide has a plurality of tracks. The tracks have a second index of refraction lower than the first index of refraction, are parallel to one another in a common direction that defines the direction of the waveguide, and form a structure in a plane vertical to the direction of the waveguide. The structure has at least 40 regular triangles with the same length of sides. Three angles of each regular triangle are the same as those of different ones of the tracks in the plane vertical to the direction of the waveguide.SELECTED DRAWING: Figure 4

Description

Technical Field

[0001] The present disclosure relates to optical waveguide devices, particularly concave clad waveguide devices, and more particularly to optical waveguide devices having electrodes adapted to provide an electro-optic modulator.

Background Art

[0002] Low-voltage, low-insertion-loss electro-optic modulators (EOMs) are important elements for high-speed optical switching. Quantitatively, an insertion loss of 3 dB or less is desirable. For switching of electro-optic modulators in the GHz frequency range, a control voltage lower than 20 V is beneficial, but this is because it becomes increasingly difficult to provide a larger control voltage at such high frequencies. To achieve a control voltage of less than 20 V using known optoelectronic materials, an optical path within several centimeters of electro-optic material, the distance between the optical path and the electrodes of the EOM, and an optical path of several tens of micrometers are simultaneously required. These can be achieved using a waveguide architecture for an electro-optic modulator. Planar waveguides fabricated from LiNbO3 films are typical main components in high-speed modulators. However, such waveguides typically have a high propagation loss exceeding 3 dB / cm. Waveguides fabricated from electro-optic crystals (or crystal films) with a propagation loss of less than 0.5 dB / cm can provide an important element for optical switching operations in the GHz frequency range.

Summary of the Invention

Problems to be Solved by the Invention

[0003] In view of the above technical problems, there is a need for a waveguide device having a propagation loss of less than 0.5 dB / cm and a control voltage of at most 20 V to facilitate high-speed (≧1 GHz) switching. In particular, these operating parameters should be achieved in electro-optic modulators, such as phase shifters, for example, π-phase shifters.

Means for Solving the Problems

[0004] This object is achieved by the waveguide device according to claim 1. Claim 8 provides an electro-optical modulator comprising the waveguide device. Claim 9 relates to a method of manufacturing a waveguide device suitable for providing the above important parameters. The dependent claims relate to preferred embodiments.

[0005] In a first aspect, the waveguide device comprises a substrate including an electro-optic material, a waveguide formed in the electro-optic material, and a plurality of electrodes formed in the vicinity of the waveguide. The electro-optic material has a first refractive index. The waveguide comprises a plurality of tracks. The tracks include a second refractive index smaller than the first refractive index, are parallel to each other in a common direction defining the direction of the waveguide, and form a configuration in a plane perpendicular to the direction of the waveguide. This configuration comprises at least 40 equilateral triangles of the same side length, and all three corners of each equilateral triangle respectively coincide with different tracks of the plurality of tracks in a plane perpendicular to the direction of the waveguide.

[0006] In the context of the present disclosure, the equilateral triangle can function as a reference for the configuration of the tracks, but does not add any physical structure to the waveguide device.

[0007] The corresponding waveguide can provide a propagation loss 0.15 dB / cm or 0.45 dB lower than that of a waveguide having a length of 30 mm each, which corresponds to a length typically applicable to an electro-optical modulator suitable for providing a π-phase shifter. The low propagation loss is a result of the configuration of the tracks of the waveguide and the track manufacturing method. Together with the low refractive index of the tracks, this configuration provides an embedded cladding for the waveguide. The waveguide shape can support a low control voltage that can be less than 20 V according to the embodiment. A particularly beneficial configuration of the electrodes can further reduce the control voltage.

[0008] At least 30, particularly at least 40, or particularly at least 50 equilateral triangles may form a lattice, and at least one corner of each equilateral triangle of the lattice coincides with a corner of another equilateral triangle of the lattice. Any triangle of the lattice may be interconnected with any other triangle of the lattice through the triangles of the lattice, particularly through the sides of the triangles of the lattice. The sides of the triangles of the lattice may connect the corners of the triangles of the lattice. The lattice may be hexagonal and / or may form a cross-section of a hexagonal lattice. In particular, at least two corners of each equilateral triangle of the lattice may coincide with the corners of different equilateral triangles of the lattice respectively. In particular, all three corners of each equilateral triangle of the lattice may coincide with the corners of different equilateral triangles of the lattice respectively.

[0009] Any pair of two different equilateral triangles can share at most one same track. Any pair of two different corners of an equilateral triangle can share at most one same track. According to an embodiment, when a corner of a first equilateral triangle coincides with a first track, a second track, and a third track, at most one corner of any other equilateral triangle coincides with the first track, the second track, or the third track.

[0010] The configuration may include at least 50 or at least 60 equilateral triangles having the same side length.

[0011] The same side length may be at least 2 μm or at least 3 μm.

[0012] Alternatively or additionally, the same side length may be at most 8 μm, particularly at most 7 μm or at most 6 μm.

[0013] In an embodiment, each of the equilateral triangles shares their orientation in space, particularly in a plane perpendicular to the direction of the waveguide.

[0014] According to an embodiment, each of the equilateral triangles within the configuration may be interpreted as a shifted image of any other equilateral triangle within the configuration, and the shift may be a translation within a plane perpendicular to the direction of the waveguide. The shifted image may be a non-rotated image that is linearly translated within a plane perpendicular to the direction of the waveguide.

[0015] The configuration within a plane perpendicular to the direction of the waveguide may refer to the center of the cross-section of the track within a plane perpendicular to the direction of the waveguide.

[0016] The configuration may include an outer boundary of a substantially hexagonal shape.

[0017] This configuration may include at least 30 tracks, particularly at least 35 or at least 40 tracks, preferably each being located at the center of a regular hexagon formed by other tracks within a plane perpendicular to the direction of the waveguide, and each regular hexagon having the same side length.

[0018] According to an embodiment, the waveguide device may have translational symmetry along the direction of the waveguide.

[0019] According to an embodiment, a plurality of planes perpendicular to the direction of the waveguide, particularly all planes perpendicular to the direction of the waveguide, form a configuration having some or all of the features described above or further detailed below.

[0020] The tracks may form a configuration within any plane perpendicular to the direction of the waveguide along the length of the waveguide device.

[0021] The electro-optic material may include or may be a non-linear optical material and / or a crystalline material without inversion symmetry, such as RbTiOPO4 or KTiOPO4.

[0022] Such electro-optical materials can provide a high electro-optical coefficient, which can be beneficial for establishing electro-optical modulators such as π-phase shifters having a short optical path within the electro-optical material. The short optical path within the electro-optical material can reduce propagation loss and the capacitance of the waveguide device, which can facilitate a high switching speed.

[0023] The waveguide can be adapted to operate as a single-mode waveguide. The waveguide may have an extension of less than 200 μm, particularly less than 100 μm or less than 50 μm, along at least one direction in a plane perpendicular to the direction of the waveguide. In particular, the extension of the waveguide may be less than 200 μm, particularly less than 100 μm or less than 50 μm, along any direction in a plane perpendicular to the direction of the waveguide.

[0024] The first refractive index may be the refractive index of the electro-optical material for light having a polarization perpendicular to the direction of the waveguide. The first refractive index may be the refractive index of the electro-optical material for an electromagnetic wave having an optical communication wavelength, for example, an electromagnetic wave having a wavelength of 1.55 μm or 1.3 μm in vacuum.

[0025] Therefore, the electro-optical modulator to which the waveguide device is applied can be adapted to operate at an optical communication wavelength that is beneficial for communication applications.

[0026] The second refractive index may be at least 0.3%, particularly at least 0.4%, particularly at least 0.5% or at least 0.6% smaller than the first refractive index.

[0027] The second refractive index may be the refractive index of the track for an electromagnetic wave having an optical communication wavelength.

[0028] The second refractive index may be the refractive index of the track for light having a polarization perpendicular to the direction of the waveguide.

[0029] Each track of the plurality of tracks can have an extension less than 5 μm, particularly less than 2 μm or less than 1 μm, along at least one direction in a plane perpendicular to the direction of the waveguide. Each track of the plurality of tracks can have an extension of at least 5 μm, particularly at least 6 μm or at least 7 μm, along a second direction in a plane perpendicular to the direction of the waveguide, and the second direction in the plane perpendicular to the direction of the waveguide is perpendicular to at least one direction in the plane perpendicular to the direction of the waveguide. Each track of the plurality of tracks can have an extension of at most 10 μm, particularly at most 9 μm or at most 8 μm, along a second direction in a plane perpendicular to the direction of the waveguide.

[0030] The plurality of tracks may form at least a part of the outer boundary of the waveguide.

[0031] The waveguide may include a first end, and the waveguide device may include a first optical fiber optically coupled to the first end of the waveguide. The waveguide may include a second end, and the waveguide device may include a second optical fiber optically coupled to the second end of the waveguide.

[0032] At least one electrode or all of the plurality of electrodes of the plurality of electrodes can include a noble metal such as copper or gold, or can be composed of a noble metal.

[0033] The waveguide can include a core. The core may be defined by a first interruption of a track configuration including an equilateral triangle in a plane perpendicular to the direction of the waveguide.

[0034] The minimum distance between the center of the core and the closest electrode of the plurality of electrodes may be at most 60 μm, particularly at most 40 μm, particularly at most 30 μm or at most 20 μm.

[0035] The shortest distance between the center of the core and the nearest electrode can reduce the control voltage required to establish an electro-optic modulator having a waveguide device, such as a phase shifter having a waveguide device, for example, a π-phase shifter. The reduced control voltage can improve the switching speed of the electro-optic modulator.

[0036] The first interruption can include an electro-optical material without tracks.

[0037] The center of the core can refer to the center of the core in a plane perpendicular to the direction of the waveguide.

[0038] The nearest electrode can be the electrode among a plurality of electrodes having the smallest distance from the center of the core in a plane perpendicular to the direction of the waveguide.

[0039] The core may be surrounded by a configuration in a plane perpendicular to the direction of the waveguide with at least two sides, particularly at least three sides. The sides may correspond to directions, and the angle between any two of the directions may be an integer multiple of 90°.

[0040] The configuration of the tracks surrounding the core can be suitable for confining electromagnetic waves to the core and reducing propagation losses associated with leakage of electromagnetic waves to regions with increased dissipation, such as absorption regions and / or metal regions.

[0041] The core can have an outer boundary that is substantially hexagonal.

[0042] The cladding thickness can be the thickness of the track configuration in a plane perpendicular to the direction of the waveguide. In particular, the cladding thickness can refer to the distance in a plane perpendicular to the direction of the waveguide from the core of the waveguide to the outer boundary of the track configuration. The outer boundary of the track configuration may be defined as a polygon, particularly a polygon of the smallest size, such as a hexagon of the smallest size, including all the tracks of the configuration in a plane perpendicular to the direction of the waveguide.

[0043] The cladding thickness may be asymmetric such that a portion of the track configuration in a plane perpendicular to the direction of the waveguide having the minimum cladding thickness is configured between the core and an electrode among the plurality of electrodes, particularly between the core and the electrode closest to the core. The minimum cladding thickness can correspond to one track. The portion of the configuration having the minimum cladding thickness can include or be an interruption of the hexagonal symmetry of the track configuration.

[0044] The minimum thickness of the waveguide and / or the minimum thickness of the track configuration between the core and the electrode can reduce the distance between the two. When the distance is shortened, a large electric field can be promoted, and thus the operation of the waveguide device as a phase shifter, such as a π-phase shifter, with a moderate control voltage applied to the electrode can be promoted. The moderate control voltage can improve the switching speed of the waveguide device.

[0045] The minimum cladding thickness may be less than 30 μm, particularly less than 25 μm or less than 20 μm.

[0046] According to an embodiment, the minimum cladding thickness may be at least 10 μm, particularly at least 12 μm or at least 15 μm.

[0047] This thickness range enables a short distance between the waveguide and / or its core and the closest electrode, while providing sufficient confinement of electromagnetic waves to the waveguide and / or its core to avoid losses associated with leakage of electromagnetic waves to the electrodes.

[0048] The minimum cladding thickness may be zero, and / or the track configuration may not be present in the portion of the configuration having the minimum cladding thickness.

[0049] The configuration of the track and the plurality of electrodes can surround the core together within a plane perpendicular to the direction of the waveguide. In particular, the configuration of the track and the closest electrode can surround the core together within a plane perpendicular to the direction of the waveguide. For example, any half-line within a plane perpendicular to the direction of the waveguide starting from the center of the core can intersect the plurality of electrodes, particularly the track or the configuration of the closest electrode of the electrodes.

[0050] The absence of the waveguide cladding and / or the configuration of the track in the portion with the minimum thickness can further reduce the distance between the waveguide and / or its core and the closest electrode, and thus the control voltage. However, in such embodiments, there may be an increase in propagation loss due to the leakage of electromagnetic waves from the waveguide and / or its core to the electrodes.

[0051] At least one of the plurality of electrodes may be configured on the first surface, and the first surface may be the surface of the substrate and / or the surface of the electro-optic material.

[0052] Configuring electrodes on the surface of the substrate and / or the electro-optic material can provide a device design that can be easily and economically implemented using available technologies.

[0053] Alternatively, at least one of the plurality of electrodes may be at least partially embedded in the substrate and / or the electro-optic material. In such embodiments, at least one electrode may be at least partially configured below the first surface, and the first surface is the surface of the substrate and / or the surface of the electro-optic material.

[0054] The first electrode among the plurality of electrodes and the second electrode among the plurality of electrodes may be configured on both sides of the waveguide.

[0055] At least a part of the first electrode and / or at least a part of the second electrode may be concentric with the outer shape and / or the core of the waveguide.

[0056] Embedding at least one electrode into the substrate and / or the electro-optical material can bring the electrode closer to the waveguide or its core, and thus, although it may sacrifice more complex and potentially more expensive manufacturing of the electrode in some cases, the control voltage can be further reduced.

[0057] The minimum distance between the center of the core and the first surface can be up to 60 μm, particularly up to 40 μm, particularly up to 30 μm, particularly up to 20 μm or up to 15 μm.

[0058] In an embodiment having a portion of the waveguide with a minimum thickness, the portion of the waveguide with the minimum thickness may be partially or completely configured between the core of the waveguide and the first surface.

[0059] At least one electrode can have an extension along the direction of the waveguide of at least 10 mm, particularly at least 15 mm, at least 20 mm, or at least 25 mm.

[0060] The corresponding extension can facilitate the application as an electro-optic modulator of the waveguide device, such as a phase shifter, for example, a π-phase shifter.

[0061] At least one electrode may be in direct contact with the electro-optical material.

[0062] The direct contact can minimize the distance between the electrode and the waveguide and / or its core, thereby minimizing the control voltage of the electro-optic modulator applying the waveguide device.

[0063] At least one electrode may include the closest electrode.

[0064] The plurality of electrodes may further include at least one counter electrode different from at least one electrode, and at least one counter electrode is configured on the first surface.

[0065] Constructing a counter electrode on the first surface can provide a device design that can be easily and economically implemented using known techniques.

[0066] At least one counter electrode may be in direct contact with the electro-optic material.

[0067] At least one counter electrode can have an extension along the direction of the waveguide of at least 10 mm, particularly at least 15 mm, at least 20 mm, or at least 25 mm.

[0068] At least one counter electrode may be configured parallel to at least one electrode.

[0069] In some embodiments, the minimum distance between at least one counter electrode and at least one electrode does not exceed 300 μm, particularly does not exceed 150 μm, particularly does not exceed 100 μm or 80 μm.

[0070] At least one counter electrode may include at least two counter electrodes.

[0071] At least two counter electrodes may be configured on both sides of at least one electrode on the first surface. Alternatively or additionally, at least two counter electrodes may be configured symmetrically with respect to a mirror surface near at least one electrode on the first surface, particularly intersecting at least one electrode and / or the core of the waveguide.

[0072] At least two counter electrodes may be configured parallel to each other.

[0073] At least two counter electrodes may be configured parallel to at least one electrode.

[0074] The minimum distance between any of at least two counter electrodes and at least one electrode shall not exceed 300 μm, particularly shall not exceed 150 μm, particularly shall not exceed 100 μm or 80 μm.

[0075] The first surface may be a flat surface. The surfaces of at least one electrode and at least one counter electrode may be in the same plane as each other, and in particular, may be in the same plane as the first surface.

[0076] In a second aspect, the electro-optical modulator comprises a waveguide device as described above. In particular, the electro-optical modulator can be a phase shifter, in particular a π-phase shifter.

[0077] The electro-optical modulator can be adapted to operate at a frequency of at least 1 GHz.

[0078] The electro-optical modulator can be adapted such that the control voltage between at least one electrode and at least one counter electrode operates at a maximum of 20 V.

[0079] The electro-optical modulator can comprise a first lead connected to at least one electrode and a second lead connected to at least one counter electrode, and the first lead and the second lead can be adapted to connect at least one electrode and at least one counter electrode to a voltage source adapted to provide a control voltage.

[0080] In a third aspect, a method for manufacturing a waveguide device includes providing a substrate including an electro-optic material having a first refractive index and forming a waveguide in the electro-optic material. Forming the waveguide includes forming a plurality of tracks of the waveguide such that the tracks are parallel to each other in a common direction defining the direction of the waveguide and the tracks include a configuration in a plane perpendicular to the direction of the waveguide. This configuration includes at least 40 equilateral triangles of the same side length. All three corners of each equilateral triangle respectively coincide with different tracks among the plurality of tracks in a plane perpendicular to the direction of the waveguide. Forming each track of the plurality of tracks includes focusing a laser beam into the electro-optic material to permanently reduce the refractive index at the focus of the laser beam from the first refractive index to a second refractive index smaller than the first refractive index, and propagating the focus of the laser beam along the direction of the waveguide to form a track having the second refractive index in the electro-optic material.

[0081] The method of the present disclosure can provide a technique for laser writing a waveguide having tracks with a reduced refractive index, also called an embedded clad waveguide. The embedded clad waveguide can provide low propagation loss. The configuration of the tracks having equilateral triangles can further reduce the propagation loss.

[0082] The method can further include using a laser to generate a laser beam. The laser may be a pulsed laser that provides a laser beam having a pulse duration of less than 1 ps, particularly less than 0.5 ps. The laser may be an infrared laser that provides a laser beam having a wavelength of, for example, up to 11 μm, particularly up to 1100 nm.

[0083] The repetition rate of the pulsed laser may be at least 1 kHz. The repetition rate of the pulsed laser may be 200 kHz or less.

[0084] Propagating the focus of the laser beam can include, in particular, translating the substrate while keeping the position of the laser fixed. Translating the substrate can be done using a translation stage, in particular an at least partially automated translation stage. Alternatively or additionally, propagating the focus of the laser beam may include translating the position of the laser beam.

[0085] The waveguide device, the substrate, the electro-optic material, the plurality of tracks, and the configuration in a plane perpendicular to the direction of the waveguide can be characterized by features corresponding to those described above in the context of the waveguide device.

[0086] The polarization of the laser beam can be linear and perpendicular to the direction of the waveguide.

[0087] The focus can refer to a plane perpendicular to the direction of the laser beam, in particular the focal plane.

[0088] At the focus, the width of the laser beam can be minimum along at least one direction perpendicular to the direction of the laser beam.

[0089] Focusing the laser beam within the electro-optic material can include generating a longitudinal width of the laser beam within a focus perpendicular to the direction of the laser beam along the direction of the waveguide, and generating a transverse width of the laser beam within a focus perpendicular to the direction of the waveguide and perpendicular to the direction of the laser beam, where the longitudinal width is greater than the transverse width.

[0090] The longitudinal width and the transverse width can each refer to the width of the laser beam perpendicular to the direction of the laser beam.

[0091] The longitudinal width and the transverse width can each refer to the width of the laser beam at the focus, in particular at the focal plane perpendicular to the direction of the laser beam.

[0092] The longitudinal width can refer to the width of the laser beam along the direction of the waveguide. The transverse width can refer to the width of the laser beam perpendicular to the direction of the waveguide. The laser beam can have a non-circular or asymmetric cross-section at the focus.

[0093] In particular, the laser beam can have an elliptical cross-section at the focus. The major axis of the elliptical cross-section may be parallel to the direction of the waveguide. The minor axis of the elliptical cross-section may be perpendicular to the direction of the waveguide.

[0094] The non-circular or asymmetric cross-section of the laser beam at the focus can result in a reduction in the roughness of the formed track and a further reduction in the propagation loss of the waveguide.

[0095] The longitudinal width and / or the transverse width can each refer to an extension perpendicular to the direction of the laser beam at the focus of the laser beam.

[0096] The method can further include providing, before focusing, the laser beam as a substantially parallel beam having a first extension along the direction of the waveguide and a second extension along a direction perpendicular to both the direction of the waveguide and the direction of the laser beam, where the second extension exceeds the first extension.

[0097] The substantially parallel beam having the first extension and the second extension can be easily converted into a laser beam at a focus having a longitudinal width that exceeds the transverse width by focusing.

[0098] Alternatively or additionally, the method may include introducing an anisotropic focusing element, such as a cylindrical lens or mirror and / or an elliptical lens or mirror and / or a tilted lens, into the laser beam to generate a longitudinal width that is greater than the transverse width. In such embodiments, the method can include generating a second focus in addition to the focus.

[0099] In such an embodiment, the laser beam can have a second longitudinal width at a second focus along the direction of the waveguide and a second transverse width at the second focus along a direction perpendicular to both the direction of the waveguide and the direction of the laser beam, and the second transverse width is greater than the second longitudinal width.

[0100] The method can further include providing the laser beam as a substantially parallel beam having a substantially circular cross-section before providing the laser beam as a beam substantially parallel to the first extension and the second extension, and shaping the substantially parallel beam having a substantially circular cross-section into a substantially parallel beam having the first extension and the second extension.

[0101] The substantially parallel beam can include a cross-section that substantially corresponds to an ellipse. The first extension can correspond to the minor axis of the ellipse, and the second extension can correspond to the major axis of the ellipse.

[0102] Shaping the substantially parallel beam having a substantially circular cross-section into a substantially parallel beam having the first extension and the second extension can include introducing a collimator, such as a slit, into the substantially parallel beam. The collimator may be introduced into the substantially parallel beam along one direction perpendicular to the direction of the substantially parallel beam.

[0103] A collimator, such as a slit, can have a width of at least 0.2 mm. A collimator, such as a slit, can have a width of up to 1.5 mm.

[0104] The method can further include forming a plurality of electrodes in the vicinity of the waveguide.

[0105] The plurality of electrodes can be characterized by features corresponding to those described above in the context of a waveguide device.

[0106] Focusing a laser beam on an electro-optical material may include transmitting the laser beam through a first surface, which is the surface of the substrate and / or the surface of the electro-optical material.

[0107] Forming a plurality of electrodes may further include forming at least one of the plurality of electrodes on the first surface.

[0108] The first surface can be characterized by features corresponding to the features described above in the context of a waveguide device.

[0109] Forming a plurality of tracks of a waveguide can include forming tracks of a plurality of tracks configured further away from the first surface before forming tracks of a plurality of tracks configured closer to the first surface.

[0110] In particular, for any pair of tracks of a plurality of tracks having different distances from the first surface, forming a plurality of tracks of a waveguide can include forming a pair of tracks having a greater distance from the first surface before forming a pair of tracks having a smaller distance from the first surface.

[0111] Forming a plurality of tracks of a waveguide can include forming tracks of a plurality of tracks located closer to the center of the waveguide in a plane parallel to the first surface before forming tracks of a plurality of tracks located further away from the center of the waveguide in a plane parallel to the first surface.

[0112] In particular, for any pair of tracks of a plurality of tracks having different distances from the center of the waveguide in a plane parallel to the first surface, forming a plurality of tracks of a waveguide can include forming a pair of tracks having a smaller distance from the center of the waveguide in a plane parallel to the first surface before forming a pair of tracks having a greater distance from the center of the waveguide in a plane parallel to the first surface.

[0113] Forming a plurality of electrodes can further include forming at least one counter electrode of the plurality of electrodes on the first surface, and the at least one counter electrode is different from the at least one electrode.

[0114] The at least one counter electrode can be characterized by features corresponding to those described above for the waveguide device.

Brief Description of Drawings

[0115] The technology of the present disclosure and its related advantages will be most clearly revealed from the description of exemplary embodiments related to the accompanying drawings.

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Best Mode for Carrying Out the Invention

[0116] FIG. 1a is a schematic view of a waveguide device 120. The waveguide device 120 is formed on and in a substrate 102. It includes a waveguide 100 and a plurality 300 of electrodes 302, 304. The waveguide 100 is formed in an electro-optic material 104 such as rubidium titanyl phosphate (RTP, RbTiOPO4) contained in the substrate 102.

[0117] The substrate 102 may be entirely composed of RTP 104, or may include additional structures for, for example, optical or plasmonic waveguides, or for establishing electronic functions. For this purpose, the additional structure can comprise portions made of a linear dielectric, semiconductor, and / or metallic structure. Instead of or in addition to RTP, other electro-optic materials 104 such as potassium titanyl phosphate (KTP, KTiOPO4) can be applied to the substrate 102.

[0118] Applying a control voltage between the plurality 300 of electrodes 302 and the counter electrode 304 enables modulating the refractive index of the core 110 of the waveguide 100 and operating the waveguide device 120 as an electro-optic modulator. The waveguide 100 and the electrodes 302, 304 overlap along a distance L that defines the length L of the waveguide device 120. Light can be coupled into and out of the waveguide device 120 by coupling an optical fiber (not shown) to the first end 100a and the second end 100b of the waveguide device 120.

[0119] The detailed view of FIG. 1a shows a cross-section of waveguide 100 of waveguide device 120 in a plane perpendicular to waveguide 100. Waveguide 100 can have a similar cross-section in any plane perpendicular to waveguide 100. In particular, waveguide 100 can have a similar cross-section in any plane perpendicular to the waveguide along the length L of waveguide device 120. The cross-section can deviate slightly along the length L of waveguide device 120, for example, when waveguide device 120 is curved or when additional structures of substrate 102 are formed in the vicinity of waveguide device 120.

[0120] Waveguide 100 is formed by configuration 108 of tracks 106 within electro-optic material 104. Tracks 106 include modified RTP having a refractive index lower than that of RTP 104. Those configurations 108 can be characterized with respect to adjacent tracks 106 that intersect the corners of equilateral triangles having the same size and orientation. Thus, configurations 108 and / or tracks 106 can form a portion of a hexagonal lattice, although in some embodiments they deviate from a complete hexagonal lattice. In the central region 110 of the waveguide, the configuration 108 of the tracks has interruptions 112 where tracks 116 are absent, and the central region 110 consists of substantially unmodified RTP 104.

[0121] Since central region 110 has a higher refractive index than tracks 106, waveguide 100 is suitable for confining electromagnetic waves in central region 110 within the x-y plane 114. Thus, the central region acts as the core 110 of waveguide 100. Waveguide 100 may be referred to as an embedded clad waveguide 100. Embedded clad waveguide 100 induces electromagnetic waves along direction z of waveguide 100 perpendicular to the x-y plane 114. Along direction z of waveguide 100, waveguide 100 has translational symmetry along its length and, in some cases, has a constant cross-sectional structure except for slight variations, for example, due to the curvature or bending of waveguide 100.

[0122] Embedded-cladding waveguides have been previously implemented in materials with garnet-type structures such as cubic YAG:Nd (propagation loss of 0.7 dB / cm at 1064 nm) and orthorhombic YAP:Nd (propagation loss of 0.52 dB / cm at 1064 nm), as described in Y. Jia, C. Cheng, J. R. Vazquez de Aldana, G. R. Castillo, B. del R. Rabes, Y. Tan, D. Jaque, and F. Chen, "Monolithic crystalline cladding microstructures for efficient light guiding and beam manipulation in passive and active regimes", Sci. Rep. 4, 5988 (2014) and W. Nie, R. He, C. Cheng, U. Rocha, J. Rodriguez Vazquez de Aldana, D. Jaque, and F. Chen, "Optical lattice-like cladding waveguides by direct laser writing: fabrication, luminescence, and lasing", Opt. Lett. 41, 2169-72 (2016). These embedded-cladding waveguides provide low propagation losses. However, for waveguide devices such as electro-optic modulators, waveguides of electro-optic materials with large electro-optic coefficients, and thus crystal materials without inversion symmetry such as RTP or KTP, are desirable.

[0123] Figures 1b and 1c show the configuration 108 of the track 106 in more detail. The configuration 108 can strongly affect the propagation loss of an electromagnetic wave propagating within the core 110 along the waveguide direction z. The waveguide 100 according to this description has minimized propagation loss, which is achieved using the configuration 108 of the track 106 shown. The configuration 108 may be represented by equilateral triangles 116 of the same size or side length. These equilateral triangles 116 are introduced for illustration and reference and do not add any physical structure to the waveguide 100 of FIG. 1a.

[0124] Any one of the equilateral triangles 116 is configured such that each of its corners is located within the cross-section of a different track 106 in the x-y plane 114 perpendicular to the direction z of the waveguide. Any pair of two different equilateral triangles share at most one cross-section of the same track 106. In other words, if a corner of a first equilateral triangle 116 is located in the same cross-section of the same track 106 as a corner of a second equilateral triangle 116, the other two corners of the first equilateral triangle 106 are located in cross-sections of tracks different from the cross-sections of the tracks in which the other two corners of the second equilateral triangle are located.

[0125] Figures 1b and 1c also show alternative features of the configuration 108 using the lattices 118a, 118b, 118c, 118d of equilateral triangles 106. In contrast to the individual equilateral triangles 116 described above that can be respectively identified at any position of the configuration 108 (except for the above limitations), the lattices 118a, 118b, 118c, 118d include a plurality of mutually related equilateral triangles 116.

[0126] According to a first definition, any equilateral triangle 116 of the lattices 118a, 118b, 118c, 118d shares at least one corner with an adjacent triangle 116 of the lattices 118a, 118b, 118c, 118d. For example, the lattices 118a, 118b, 118c, 118d include 3, 6, 52, and 11 such equilateral triangles 116.

[0127] Alternatively, the lattices 118a, 118b, 118c, 118d may be defined such that any equilateral triangle 116 of the lattices 118a, 118b, 118c, 118d shares at least two corners with an adjacent triangle of the lattices 118a, 118b, 118c, 118d. According to this definition, for example, the lattices 118a, 118b, 118c, 118d include 1, 4, 52, and 9 equilateral triangles 116.

[0128] The cells 118a, 118b, 118c, 118d may also be defined such that any equilateral triangles 116 of the cells 118a, 118b, 118c, 118d share all of their corners with adjacent triangles of the cells 118a, 118b, 118c, 118d. According to this definition, for example, the cells 118c, 118d include 35 and 3 equilateral triangles 116. The portions 118a, 118b of the configuration 108 of FIG. 1b do not include such equilateral triangles 116 and thus are not cells according to this definition.

[0129] The configuration 108 having the equilateral triangles 116 corresponds to at least a locally and / or approximately hexagonal configuration. In other words, the configuration 108 exhibits at least a locally and / or approximately hexagonal symmetry. In particular, any set of equilateral triangles 116 that can be described as the cells 118a, 118b, 118c, 118d forms a cross-section of a hexagonal lattice and exhibits an exact local hexagonal symmetry. Thus, each of the cells 118a, 118b, 118c, 118d of the equilateral triangles 116 corresponds to a cross-section of a hexagonal lattice and has a local hexagonal symmetry. However, this does not necessarily apply to the tracks 106 corresponding to the cells 118a, 118b, 118c, 118d. As long as the corners of the equilateral triangles 116 are located within the cross-section of the track 106, the track 106 may have a shape that reduces symmetry and / or the center of the track 106 may be offset from the corners of the equilateral triangles 116.

[0130] The configuration 108 having the equilateral triangles 116 optimizes the confinement of electromagnetic waves propagating along the direction z of the waveguide and minimizes the propagation loss. This is particularly important for the embedded clad waveguide 100 because the relative difference between the refractive index of the modified RTP of the track 106 and the unmodified RTP 104 is only 0.006 - 0.009. The configuration 118 having the equilateral triangles 116 is at least locally and / or approximately hexagonal and thus provides an optimized (nearly close-packed) filling density of the track 106. Thus, the configuration 108 enables the maximum utilization of the limited refractive index difference to achieve the strongest possible confinement and the lowest possible propagation loss.

[0131] Figures 2a, 2b, 2c, 2d, 2e, 2f, 2g, 2h, and 2i show an apparatus and method for manufacturing waveguide 100. The apparatus comprises a laser system 200 having a laser. The laser device 200 emits a substantially parallel laser beam 202 at a wavelength of 1030 nm with a pulse duration of 180 fs, a pulse energy in the range of 250 to 400 nJ, and a diameter of 4.5 mm at a repetition rate of 5 kHz. The laser beam 202 is focused into the substrate 102 of KTP 104 through the surface 208 using a microscope objective lens 204 with a numerical aperture of 0.65. Under such conditions, a modified RTP for the track is formed within the focus 206 of the laser beam 202 having a refractive index reduced by 0.006 to 0.009 with respect to the refractive index of the unmodified RTP. The extension of the focus 206 along the direction y of the laser beam 202 is in the range of 8 to 12 μm. Thus, the region of the modified RTP, and ultimately the extension of the track 106 in FIGS. 1a, 1b, and 1c along this direction y are also in the range of 8 to 12 μm.

[0132] The substrate 102 is configured on a translation stage 210 having a translation direction 212, z for propagating the focus 206 within the electro-optic material 104 to write the track 106. FIGS. 2a and 2c show the apparatus as viewed along the translation direction 212, z, and FIGS. 2b and 2d show the apparatus as viewed along a direction perpendicular to the translation direction 212, z. The translation direction 212, z of the translation stage 210 corresponds to the direction z of the generated waveguide 100.

[0133] Since this geometry is known to give the strongest reduction in the refractive index of the modified RTP, the polarization of the laser beam 202 is perpendicular to the translation direction 212, z.

[0134] As shown in FIGS. 2a and 2c, along the direction x perpendicular to the direction 212, z of the translation stage 210, the laser beam 202 is focused to the lateral width w2 of the focus 206.

[0135] As shown in FIGS. 2b and 2d, along the direction 212 of the translation stage 210, the direction z parallel to the z-direction, the laser beam 202 is focused at the focal point 206 with a longitudinal width w1. The longitudinal width w1 and the transverse width w2 respectively refer to the width of the laser beam 202 within the focal point 206 along the direction 212 of the translation stage and the waveguide and the width perpendicular thereto, both being perpendicular (transverse) to the direction of the laser beam 202. The longitudinal width w1 is larger than the transverse width w2.

[0136] As shown in FIGS. 2a and 2b, in order to achieve a larger longitudinal width w1, a spectral slit 214 having a width of 1 mm can be introduced into the substantially parallel laser beam 202 emitted by the laser system 200. The spectral slit 214 results in a reduced extension of the substantially parallel laser beam 202 along one direction 212 perpendicular to the direction y of the laser beam 202, the z-direction. As a result, when the laser beam 202 is focused using the microscope objective lens 204, a larger longitudinal width w1 is obtained along this direction 212, the z-direction.

[0137] As an alternative to the spectral slit 214, an anisotropic focusing element 222 such as a cylindrical lens 222 can be introduced into the laser beam, particularly the substantially parallel laser beam 202, to generate a longitudinal width w1 along the direction 212, the z-direction, that exceeds the transverse width w2 along the vertical direction y.

[0138] The corresponding embodiments are shown in FIGS. 2c and 2d. In such embodiments, the focus 206 points to a plane 216g perpendicular to the direction of the laser beam 202 at a position along the direction of the laser beam 202 where the width w2 of the laser beam 202 along the lateral direction (the translation direction 212 or with respect to the direction of the waveguide 100, respectively) is minimized. Thus, at the focus, the laser beam 202 exhibits a beam waist w2 along the lateral direction x. Further, the second focus 206' is formed at the position of the waist of the laser beam 202 along the translation direction 212 corresponding to a plane 216h perpendicular to the direction of the laser beam 202. At the second focus 206', contrary to the focus 206, the order of the beam widths is reversed, i.e., the lateral width of the laser beam 202 exceeds the longitudinal width. The fact that the longitudinal width within the focus is large compared to the lateral width results in a smoother track formation and a reduction in the propagation loss of the formed waveguide, and is thus desirable. Therefore, the focus 206 is used to form the waveguide rather than the second focus 206'. For details regarding focusing by an anisotropic focusing element such as a cylindrical lens, see, for example, A.G. Okhrimchuk, "Femtosecond Fabrication of Waveguides in Ion-Doped Laser Crystals", DOI: 10.5772 / 12885, in: "Coherence and Ultrashort Pulse Laser Emission", Nov. 2010.

[0139] The writing of tracks into YAG:Nd using a laser beam with an elliptical cross-section has been demonstrated previously by S.S. Fedotov and A.G. Okhrimchuk, "Smooth Writing In YAG Single Crystal with Beam Waist of an Elliptical Cross-Section", Frontiers in Optics / Laser Science, p. JTh4B.40 (OSA, 2020). However, the question of whether such a technique can be applied to electro-optic materials and / or whether it can be applied to generate a triangular configuration has remained difficult thus far.

[0140] FIG. 2e shows a cross-section of an apparatus for manufacturing waveguide 100 along plane 216e of FIGS. 2a, 2b, 2c, and 2d. In this plane 216e, the laser beam 202 has a substantially circular cross-section 218.

[0141] FIG. 2f shows a cross-section of an apparatus for manufacturing waveguide 100 along plane 216f of FIGS. 2a, 2b, 2c, and 2d. In this plane 216f, the laser beam 202 has a cross-section 220 corresponding to an ellipse. The extension e2 along direction x perpendicular to the translation direction 212, z exceeds the extension e1 along the translation direction 212, z.

[0142] FIG. 2g shows a cross-section of an apparatus for manufacturing waveguide 100 along plane 216g of FIGS. 2a, 2b, 2c, and 2d. This plane 216g corresponds to the focus 206 of the laser beam. In this plane 216g, 206, the laser beam 202 has a longitudinal width w1 along direction 212, z of the translation stage 210 and a transverse width w2 along direction x perpendicular to the direction 212, z of the translation stage 210. The longitudinal width w1 along the direction 212, z of the translation stage 210 exceeds the transverse width w2 along the direction x perpendicular to the direction 212, z of the translation stage 210.

[0143] FIG. 2h shows a cross-section of an apparatus for manufacturing waveguide 100 along plane 216h of FIGS. 2c and 2d. This plane 216h corresponds to the second focus of the laser beam. In this plane 216h, 206’, the laser beam 202 has a longitudinal width along direction 212, z of translation stage 210 and a transverse width along direction x perpendicular to direction 212, z of translation stage 210. The longitudinal width along direction 212, z of translation stage 210 is smaller than the transverse width along direction x perpendicular to direction 212, z of translation stage 210.

[0144] The flow diagram of FIG. 2i summarizes the essential process steps of method 230 for forming a waveguide device. The method begins with providing 232 a substrate 102 including an electro-optic material 104 having a first refractive index and proceeds to forming 234 a waveguide 100 within electro-optic material 104. Forming 234 the waveguide 100 includes forming 236 a plurality of tracks 106 of the waveguide 100. Forming 236 any of the tracks 106 includes focusing 238 a laser beam 202 onto electro-optic material 104 to reduce the refractive index within focus 206. Forming 236 any of the tracks 106 further includes propagating 240 the focus 206 of the laser beam 202 along direction z of the waveguide 100 to form the track 106.

[0145] FIG. 3 shows a preferred embodiment of a method for manufacturing a waveguide. The numerals 106’ in FIG. 3 give the order in which the tracks 106 are written using the method described in the context of FIGS. 2a through 2i. The smaller numbered tracks 106’ are written first and the larger numbered tracks 106’ are written later. Tracks located further away from surface 208 are written before tracks located closer to surface 208. In this way, reflection and scattering of the laser beam 202 by tracks 106 already written in substrate 102 are minimized. When a set of tracks 106, 106’ have the same distance from surface 208, the set of tracks 106, 106’ located closer to the center 110 of the waveguide are written first.

[0146] Figure 4 shows a waveguide device having a waveguide 100 within an electro-optic material 104 of a substrate 102. The waveguide 100 may be similar to that described in the context of FIGS. 1a, 1b, 1c, 2a through 2i and / or FIG. 3. Further, a plurality 300 of electrodes 302, 304 are formed on a surface 208 of the substrate 102. A distance h separates the center 402 of the core 110 of the waveguide 100 from the nearest electrode 302 having a width w. Two opposing electrodes 304 are symmetrically configured at a distance g in the vicinity of the electrodes 302 on the surface 208. Along the direction z of the waveguide 100, the waveguide 100 and the plurality 300 of electrodes 302, 304 have translational symmetry along their respective lengths and have the same cross-section, except for slight variations due to, for example, curvature or bending of the waveguide device.

[0147] A control voltage is applied between the electrode 302 and the opposing electrode 304 to operate the waveguide device. Applying the control voltage induces an electric field at the position of the core 110 and changes the refractive index of the core 110. Accordingly, the waveguide device functions as an electro-optic modulator for modulating an electromagnetic wave confined to the core 110 and propagating along the direction z of the waveguide.

[0148] The degree of modulation depends on the magnitude of the electric field at the position of the core 100 induced by applying a control voltage to the electrodes 302, 304. A greater degree of modulation is desirable to enable achieving a preselected change in the electromagnetic wave, such as a π-phase shift, using a waveguide device having a shorter length. The shorter the length of the waveguide device, the lower the propagation loss suffered by the electromagnetic wave as it propagates within the waveguide 100 while the preselected change is being effected.

[0149] Generally, providing a waveguide device with a shorter distance h between the core 110 and the nearest electrode 300 improves the degree of the electric field and modulation at the position of the core 100. In the embodiment of FIG. 4 where the thickness t of the waveguide 100 formed by the configuration 108 of the track 106 is substantially the same (isotropic) in each direction, the minimum distance h between the center 402 of the core 110 and the nearest electrode 300 is determined by the thickness t of the waveguide 100. According to the illustrated embodiment, the minimum minimum distance h is given by the sum of the thickness t and the radius of the core 110.

[0150] FIG. 5a shows an electric field 500 induced by applying a control voltage between the electrode 302 and the counter electrode 304. At the position of the core 110, the electric field 500 is directed substantially perpendicular to the surface 208 and / or the interface between the electrode 208 and the substrate 102 (or the electro-optic material 104). Therefore, the electric field 500 at the position of the core 110 can be characterized by its y-component Ey. The y-component Ey is maximum at the interface between the electrode 302 and the substrate 102 and decreases as the distance d to the electrode 302 increases.

[0151] FIG. 5b shows the maximum y-component max(Ey) and the minimum y-component min(Ey) of the electric field in the core region 110 for different widths w of the electrode 302. A small deviation between the maximum y-component max(Ey) and the minimum y-component min(Ey) is desirable to facilitate uniform modulation of the electromagnetic wave confined within the core 110. FIG. 5b shows that the deviation is generally small for the waveguide device and can be further minimized using an electrode 302 width w of about 60 to 100 μm.

[0152] FIG. 6 shows the change Δn in the refractive index for light having polarization along the direction y perpendicular to the surface 208, obtained by applying a control voltage of 37 V between the electrode 302 and the counter electrode 304. yy For a waveguide device where the width w of the electrode 302 is 50 μm and the distance g between the electrode 302 and the counter electrode 304 is 10 μm, the change Δn in the refractive index yy was determined.

[0153] Using the change in refractive index, the length L of the waveguide device suitable for operating the waveguide device as a π-phase shifter is calculated. FIG. 7 shows the corresponding length L for different widths w of the electrode 302. The distance g between the electrode 302 and the counter electrode 304 is 30 μm, and the distance h between the center 402 of the core 110 and the closest electrode 302 is 50 μm. For an optimized width w of the electrode of about 50 to 100 μm, such as 70 μm, the length L of the 30 mm waveguide device is sufficient to establish a π-phase shifter. The short length minimizes the propagation loss of the electro-optic modulator because it reduces the optical path length of the electromagnetic wave propagation in the core 110 as it undergoes a π-phase shift.

[0154] The length L of the waveguide device for an electro-optic modulator, such as a π-phase shifter, can be further reduced by increasing the electric field 500 at the position of the core 110, or by increasing the overlap between the electric field 500 and the electromagnetic wave confined in the core.

[0155] FIG. 8a shows an embodiment of a waveguide device having a reduced distance h between the center 402 of the waveguide 100 and the nearest electrode 302. The reduced distance h is achieved by forming a configuration 108 of a track 106 having an anisotropic thickness, i.e., having different thicknesses t, t' along different directions. The thicknesses t, t' are minimum in the region between the core 110 and the nearest electrode 302. Thus, the minimum thickness t' of the waveguide 100 determines the minimum distance h between the center 402 of the core 110 and the nearest electrode 302, rather than being an isotropic thickness t as in the embodiment of FIG. 4. The minimum thickness t' of the waveguide 100 is smaller than the isotropic thickness t of the embodiment of FIG. 4. This enhances the electric field induced at the position of the core 110 by applying a control voltage between the electrode 302 and the counter electrode 304. Thus, an electro-optic modulator such as a π-phase shifter can be implemented with a reduced length L and / or control voltage of the waveguide device. Accordingly, the propagation loss of the electro-optic modulator is reduced and / or the switching frequency of the electro-optic modulator is increased. For example, the waveguide device according to the embodiment of FIG. 8a is formed with a length of 30 mm and can operate as an electro-optic modulator in the form of a π-phase shifter when a control voltage of 13.5 V is applied. Thus, the waveguide device according to the embodiment of FIG. 8a provides a low-loss and high-speed electro-optic modulator.

[0156] FIG. 8b shows equipotential lines 600 of an electromagnetic wave propagating within the waveguide 100 for a waveguide device corresponding to the embodiment of FIG. 8a. In this embodiment, the minimum thickness t' of the configuration 108 of the track 106 corresponds to a single track. In this geometry, the equipotential lines 600 are limited to the core 110 and the overlap with the electrode 302 can be ignored. As a result, the configuration 108 of the track 106 according to the embodiments of FIGS. 8a and 8b provides a functional waveguide with low propagation loss while minimizing the distance h and the length L.

[0157] Figures 9a and 9b show an embodiment in which the minimum thickness t' of the waveguide 100 is further reduced, resulting in a further reduction in the minimum distance h between the core 110 and the closest electrode 302. In this embodiment, the minimum thickness t' is approximately zero, and there is no track in the region between the core 110 and the closest electrode 302. The distance between the center 402 of the core 110 and the electrode 302 is minimized and approximately corresponds to the radius of the core 402. Therefore, the electric field 500 at the position of the core 110 induced by applying a control voltage between the electrode 302 and the counter electrode 304 is further enhanced, and the modulation of the electromagnetic wave propagating through the core 110 is enhanced.

[0158] However, the absence of the track 106 in the region between the core 110 and the closest electrode 302 results in leakage of electromagnetic waves from the core 110 to the electrode 302. This is shown in FIG. 9b, which shows the equipotential lines 600 of the electromagnetic wave for such an embodiment. The overlap between the electromagnetic wave and the electrode 302 results in an increase in the absorption and propagation loss of the electromagnetic wave at the electrode 302.

[0159] In summary, the embodiments of FIGS. 9a and 9b can provide enhanced electric field 500 and modulation of the refractive index at the position of the core 110, although at the expense of potentially stronger distortion of the electromagnetic field and greater propagation loss in some cases.

[0160] The graph of FIG. 10 shows the propagation losses 700a, 700b, 702a, 702b, 704a, 704b of waveguide devices having a minimum thickness t' corresponding to one track 116 (embodiments of FIGS. 8a, 8b) and a minimum thickness t' of approximately zero (embodiments of FIGS. 9a, 9b).

[0161] Specifically, the individual data sets 700a, 700b, 702a, 702b, 704a, 704 show the propagation losses of devices having the following characteristics: 700a: Minimum thickness t' of one track 116, copper electrode, control voltage 37V; 700b: Minimum thickness t' of one track 116, copper electrode, control voltage 0V; 702a: Minimum thickness t’ of one track 116, gold electrode, control voltage 37V; 702b: Minimum thickness t’ of one track 116, gold electrode, control voltage 0V; 704a: Minimum thickness t’ = 0, copper electrode, control voltage 37V; 704b: Minimum thickness t’ = 0, copper electrode, control voltage 0V.

[0162] FIG. 10 shows that for the optimized distance h between the center 402 of a 14μm core and the closest electrode 302, a device having a minimum thickness t’ corresponding to one track 116 (embodiments of FIGS. 8a and 8b) provides a low propagation loss of 0.15 dB / cm (copper electrode) or 0.2 dB / cm (gold electrode). Thus, a corresponding waveguide device with a length L of 3 cm has a total propagation loss of 0.45 dB (copper electrode) or 0.6 dB (gold electrode). In contrast, for a device having a minimum thickness t’ of approximately zero (embodiments of FIGS. 9a and 9b), the propagation loss is about 0.65 dB / cm.

[0163] FIGS. 11 and 12 show waveguide devices according to alternative embodiments. The waveguide 100 of the embodiments shown in FIGS. 11 and 12 is similar to the waveguide described in the context of the embodiments of FIGS. 1a, 1b, and 1c and is fabricated using the devices and methods described in the context of FIGS. 2a through 2i and FIG. 3. Each of the waveguide devices also includes a plurality 300 of electrodes 302, 304.

[0164] However, the waveguide devices according to the embodiments of FIGS. 11 and 12 have different geometric configurations of the electrodes 300, 302, 304 from each other and different from the embodiments described above. In particular, the electrodes 302 and the opposing electrode 304 of the embodiments of FIGS. 11 and 12 are at least partially configured below the surface 208. In other words, the surface 208 is a position along the direction y perpendicular to the surface 208 and is located above at least a portion of the electrodes 302 and the electrode 304.

[0165] In the embodiment of FIG. 11, the electrodes 302 and the counter electrode 304 are located on both sides of the waveguide 100. The electrodes 300, 302, 304 are parallel to the waveguide 100 and are substantially flat in the plane y, z perpendicular to the surface 208. Such electrodes are manufactured by first forming the waveguide 100 in the electro-optic material 104 of the substrate 102, as described in the context of FIGS. 2a through 2i and FIG. 3. Thereafter, an etching or laser cutting step is performed to selectively remove a portion of the substrate 102 and generate a void structure having the shape of the formed electrodes 300, 302, 304. The etching or laser cutting step can use a photolithographic etching step, particularly an anisotropic etching step, or a maskless laser cutting step, or a combination of the two. Thereafter, the structured voids are filled with a conductive material such as titanium, tantalum, gold or copper or a combination thereof deposited from the gas phase within, for example, a vacuum chamber.

[0166] The embodiment of FIG. 12 is similar to the embodiment of FIG. 11, but has curved electrodes 300, 302, 304. The curved electrodes 300, 302, 304 further improve the overlap between the electric field induced by the control voltage applied between the electrode 302 and the counter electrode 304 and the electromagnetic wave propagating through the core 110. The curved electrodes 300, 302, 304 are manufactured using at least one photolithographic etching step, particularly a combination of an anisotropic etching step and an isotropic etching step, and / or a maskless laser cutting step. Compared to the electrodes 300, 302, 304 described above, the more complex shape of the electrodes 300, 302, 304 in the embodiment of FIG. 12 can make the manufacture of the waveguide device of FIG. 12 more difficult and expensive.

[0167] The description and drawings are only useful for explaining the present disclosure and the numerous advantages associated therewith and should not be construed as meaning any limitation. The scope of the present disclosure should be determined from the appended claims.

Description of the Reference Numerals

[0168] 100 Waveguide 100a, 100b First end of the waveguide, second end of the waveguide 102 Substrate 104 Electro-optic material 106, 106’ Track 108 Configuration in a plane perpendicular to the direction of the waveguide 110 Central region, core of the waveguide 112 First interruption of the track configuration 114 Plane (xy plane) perpendicular to the direction of the waveguide 116 Equilateral triangle 118a - d Lattice of equilateral triangles 120 Waveguide device z Direction of the waveguide t, t’ Thickness of the waveguide 200 Laser device having a laser 202 Laser beam 204 Microscope objective lens 206 Focus 206’ Second focus 208 First surface 210 Translation stage 212 Translation direction 214 Slit 216e, 216f, 216g, 216h Reference plane 218 Approximately circular cross-section 220 Cross-section corresponding to an ellipse 222 Anisotropic focusing element, cylindrical lens e1 First extension e2 Second extension 230 Method for manufacturing a waveguide device 232 Provide a substrate 234 Form a waveguide 236 Form a plurality of tracks 238 Focus a laser beam into the electro-optic material 240 Propagate the focus of the laser beam w1 Longitudinal width of the laser beam at the focus (with respect to the translation direction of the translation stage) Lateral width of the laser beam at the w2 focus (with respect to the translation direction of the translation stage) 300 A plurality of electrodes 302 Electrode 304 Opposing electrode 402 Center of the core g Distance between the electrode and the opposing electrode h Distance between the core center and the closest electrode w Width of the electrode 500 Electric field d Distance from the first surface L Extension of the electrode along the direction of the waveguide 600 Equipotential lines 700a, 700b Propagation losses 702a, 702b Propagation losses 704a, 704b Propagation losses

Claims

1. An optical waveguide device (120), comprising: a substrate (102) including an electro-optic material (104) having a first refractive index; an optical waveguide (100) formed in the electro-optic material (104), the optical waveguide (100) including a plurality of tracks (106); a plurality of electrodes (302, 304) formed in the vicinity of the optical waveguide (100); wherein the tracks (106) include a second refractive index smaller than the first refractive index, have a common direction (z) defining a direction (z) of the optical waveguide (100), are parallel to each other, and form a configuration (108) in a plane (114) perpendicular to the direction (z) of the optical waveguide (100); the configuration (108) includes at least 40 equilateral triangles (116) having the same side length, and all of the three corners of each of the equilateral triangles (116) respectively coincide with different tracks (106) of the plurality of tracks (106) in the plane (114) perpendicular to the direction (z) of the optical waveguide (100); the optical waveguide (100) includes a core (110); the optical waveguide (100) includes an asymmetric cladding thickness (t, t'), whereby a portion of the optical waveguide (100) having a minimum thickness (t') is configured between the core (110) and an electrode (302) of the plurality of electrodes (302, 304); an optical waveguide device (120).

2. The core (110) is defined by a first interruption portion (112) of the configuration (108) of the tracks (106) including the equilateral triangles (116) in the plane (114) perpendicular to the direction (z) of the optical waveguide (100); The optical waveguide device (120) according to claim 1, wherein a minimum distance (h) between a center (402) of the core (110) and the closest electrode (302) of the plurality of electrodes (302, 304) is at most 40 μm.

3. The optical waveguide device (120) according to claim 2, wherein a portion of the optical waveguide (100) having the minimum thickness (t') is configured between the core (110) and the closest electrode (302).

4. At least one of the plurality of electrodes (302, 304), i.e., the electrode (302), is formed on the first surface (208), and the first surface (208) is the surface (208) of the substrate (102) and / or the surface (208) of the electro-optic material (104). The waveguide device (120) according to any one of claims 1 to 3.

5. The waveguide device (120) according to claim 4, wherein the at least one electrode (302) is in direct contact with the electro-optic material (104).

6. The waveguide device (120) according to claim 4, wherein the plurality of electrodes (302, 304) further includes at least one counter electrode (304) different from the at least one electrode (302), and the at least one counter electrode (304) is formed on the first surface (208).

7. The electro-optic material (104) includes a nonlinear optical material and / or a crystal material without inversion symmetry, or is a nonlinear optical material and / or a crystal material without inversion symmetry. The waveguide device (120) according to any one of claims 1 to 3.

8. An electro-optic modulator comprising the waveguide device (120) according to any one of claims 1 to 3, wherein the electro-optic modulator is a π-phase shifter.

9. A method (230) for manufacturing a waveguide device, comprising: Providing (232) a substrate (102) including an electro-optic material (104) having a first refractive index; Forming (234) a waveguide (100) in the electro-optic material (104). Forming the waveguide (100) (234) includes: Forming a plurality of tracks (106) of the waveguide (100) (236), wherein the tracks (106) have a common direction (z) defining the direction (z) of the waveguide (100) and are parallel to each other, and the tracks (106) are included in a configuration (108) within a plane (114) perpendicular to the direction (z) of the waveguide (100), and the configuration (108) includes at least 40 equilateral triangles (116) of the same side length, and each of the three corners of the equilateral triangle (116) all coincides with a different track (106) of the plurality of tracks (106) within the plane (114) perpendicular to the direction (z) of the waveguide (100). Forming each track (106) of the plurality of tracks (106) (236) is Focusing a laser beam (202) in the electro-optic material (104) (238) to reduce the refractive index at the focus (206) of the laser beam from the first refractive index to a second refractive index smaller than the first refractive index. Propagating the focus (206) of the laser beam (202) along the direction (z) of the waveguide (100) to form the track (106) having the second refractive index in the electro-optic material (104) (240). Focusing the laser beam (202) on the electro-optic material (104) (238) includes generating a longitudinal width (w1) of the laser beam at the focus (206) along the direction (z) of the waveguide (100) and perpendicular to the direction of the laser beam, and generating a lateral width (w2) of the laser beam at the focus (206) perpendicular to the direction (z) of the waveguide (100) and perpendicular to the direction of the laser beam, and the longitudinal width (w1) is greater than the lateral width (w2). Method (230). **Claim 10** The method (230) according to claim 9, further comprising introducing an anisotropic focusing element (222) into the laser beam (202) to generate a longitudinal width (w1) greater than the lateral width (w2). **Claim 11** Before the said focusing (238), further comprising providing the laser beam (202) as a parallel beam (220) having a first extension (e1) along the said direction (z) of the said waveguide (100) and a second extension (e2) along a direction (x) perpendicular to both the said direction (z) of the said waveguide (100) and the direction (y) of the said laser beam, the said second extension (e2) exceeding the said first extension (e1), the method (230) according to claim 9.

12. Before providing the laser beam (202) as a parallel beam (220) having the said first extension (e1) and the said second extension (e2), providing the laser beam (202) as a parallel beam having a circular cross-section (218); further comprising shaping the parallel beam having the circular cross-section (218) into the parallel beam having the said first extension (e1) and the said second extension (e2), the method (230) according to claim 11.

13. The method (230) according to any one of claims 9 to 12, further comprising forming a plurality of electrodes (302, 304) in the vicinity of the said waveguide (100).

14. Focusing the laser beam (202) on the said electro-optical material (104) (238) includes transmitting the laser beam (202) through a first surface (208), the said first surface (208) being the surface (208) of the said substrate (102) and / or the surface (208) of the said electro-optical material (104), and forming the plurality of electrodes (302, 304) further includes forming at least one electrode (302) of the plurality of electrodes (302, 304) on the said first surface (208), the method (230) according to claim 13.

15. Forming the plurality of electrodes (302, 304) further includes forming at least one counter electrode (304) of the plurality of electrodes (302, 304) on the said first surface (208), the said at least one counter electrode (304) being different from the said at least one electrode (302), the method (230) according to claim 14.

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