Waveguide for low-loss, high-speed electro-optic modulator

Abstract

A waveguide device includes a substrate including an electro-optic material, a waveguide formed in the electro-optic material, and a plurality of electrodes formed proximate to the waveguide. The electro-optic material has a first refractive index. The waveguide includes a plurality of tracks. The tracks include a second refractive index that is less than the first refractive index, are parallel to one another in a common direction that is perpendicular to a direction of the waveguide, and form an arrangement in a plane that is perpendicular to the direction of the waveguide. The arrangement includes at least 40 equilateral triangles of equal side length, wherein all three corners of each of the equilateral triangles individually coincide with a different track of the plurality of tracks in the plane that is perpendicular to the direction of the waveguide.

Description

TECHNICAL FIELD

[0001] The present disclosure relates to an optical waveguide device, in particular a recessed cladding waveguide device, and in particular to an optical waveguide device with electrodes suitable for providing an electro-optic modulator. BACKGROUND

[0002] Low voltage, low insertion loss electro-optic modulators (EOMs) are key elements for high speed optical switching. From a quantitative point of view, an ideal insertion loss is 3 dB or less. For switching of electro-optic modulators in the GHz frequency range, a control voltage of less than 20 V is beneficial, since it becomes increasingly challenging to provide larger control voltages at such high frequencies. In order to achieve a control voltage of 20 V or less using known electro-optic materials, while requiring an optical path in the electro-optic material of several centimeters and a distance between the electrodes of the EOM and the optical path of several tens of micrometers. These can be achieved using waveguide architectures for electro-optic modulators. Planar waveguides fabricated in LiNb03thin films are the typical building blocks in high speed modulators. However, such waveguides have a high propagation loss, typically exceeding 3 dB / cm. Waveguides fabricated in electro-optic crystals (or crystalline films) with a propagation loss of less than 0.5 dB / cm can provide key elements for optical switching operation in the GHz frequency range. SUMMARY

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

[0004] This object is achieved by a waveguide device according to the present disclosure. The present disclosure provides an electro-optic modulator comprising a waveguide device. The present disclosure relates to a method of fabricating a waveguide device suitable for providing the above-mentioned key parameters. The dependent claims relate to preferred embodiments.

[0005] In a first aspect, a waveguide device comprises a substrate comprising an electro-optic material, a waveguide formed in the electro-optic material, and a plurality of electrodes formed proximate to the waveguide. The electro-optic material has a first refractive index. The waveguide comprises a plurality of tracks. The tracks comprise a second refractive index that is less than the first refractive index, are parallel to each other in a common direction that defines a direction of the waveguide, and form an arrangement in a plane that is perpendicular to the direction of the waveguide. The arrangement comprises at least 40 equilateral triangles of equal side length, wherein all three angles of each of the equilateral triangles individually coincide with a different track of the plurality of tracks in the plane that is perpendicular to the direction of the waveguide.

[0006] In the context of the present disclosure, equilateral triangles can serve as a reference for the track arrangement, but do not add any physical structure to the waveguide device.

[0007] Corresponding waveguides can provide a propagation loss as low as 0.15 dB / cm, or 0.45 dB for a waveguide length of 30 mm, which corresponds to a length typically applied in electro-optical modulators suitable for providing a p phase shifter. The low propagation loss is a result of the waveguide track arrangement and the track manufacturing method. In combination with the low refractive index of the tracks, this arrangement provides the waveguide with an embedded cladding. The waveguide geometry supports a low control voltage, which can be lower than 20 V depending on the implementation. Particularly beneficial electrode arrangements can further reduce the control voltage.

[0008] At least 30, particularly at least 40 or, particularly at least 50 or all equilateral triangles can form a lattice, wherein at least one angle of each equilateral triangle in the lattice coincides with an angle of another equilateral triangle in the lattice. Any triangle in the lattice can be interconnected to any other triangle in the lattice via a triangle in the lattice, particularly via an edge of a triangle in the lattice. An edge of a triangle in the lattice can connect an angle of a triangle in the lattice. The lattice can be hexagonal and / or constitute a part of a hexagonal lattice. Particularly, at least two angles of each equilateral triangle in the lattice can each coincide with an angle of a different equilateral triangle in the lattice. Particularly, all three angles of each equilateral triangle in the lattice can each coincide with an angle of a different equilateral triangle in the lattice.

[0009] Any pair of two different equilateral triangles can share at most one same track. Any pair of two different angles of equilateral triangles can share at most one same track. According to embodiments, when an angle of a first equilateral triangle coincides with a first track, a second track and a third track, no more than one angle of any other equilateral triangle coincides with the first track, the second track or the third track.

[0010] The arrangement can comprise at least 50 or at least 60 equilateral triangles of the same side length.

[0011] The same side length can be at least 2 pm or at least 3 pm.

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

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

[0014] According to embodiments, each of the equilateral triangles in the arrangement can be interpreted as a shifted image of any other equilateral triangle in the arrangement, wherein the shift can be a translation in a plane perpendicular to the waveguide direction. The shifted image can be a non-rotated image that is linearly translated in the plane perpendicular to the waveguide direction.

[0015] The center of the arrangement in a plane perpendicular to the waveguide direction can refer to the center of the cross-section of the track in a plane perpendicular to the waveguide direction.

[0016] The arrangement can comprise an outer boundary that is substantially hexagonal.

[0017] The arrangement can comprise at least 30, in particular at least 35 or at least 40 tracks, preferably each track being located at the center of an equilateral hexagon formed by other tracks in a plane perpendicular to the waveguide direction, wherein each equilateral hexagon has the same side length.

[0018] According to embodiments, the waveguide device can have translational symmetry along the waveguide direction.

[0019] According to embodiments, a plurality of planes perpendicular to the waveguide direction, in particular all planes perpendicular to the waveguide direction, form an arrangement having some or all of the features described above or further below.

[0020] The tracks can form an arrangement in any plane perpendicular to the waveguide direction along the length of the waveguide device.

[0021] The electro-optical material can comprise or be a nonlinear optical material and / or a crystalline material that does not have inversion symmetry, such as RbTiOPO4 or KTiOPO4.

[0022] Such electro-optical material can provide a high electro-optical coefficient, which can be beneficial for establishing electro-optical modulators with short optical path lengths, such as pi phase shifters, in the electro-optical material. The short optical path length of the electro-optical material can reduce propagation losses and reduce the capacitance of the waveguide device, which can increase the switching speed.

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

[0024] The first refractive index can be the refractive index of the electro-optical material for light having a polarization perpendicular to the waveguide direction. The first refractive index can be the refractive index of the electro-optical material for electromagnetic waves having an electrical telecommunication wavelength, such as electromagnetic waves having a wavelength of 1.55 pm or 1.3 pm in vacuum.

[0025] Thus, the electro-optical modulator applying the waveguide device can be adapted to operate at telecommunication wavelengths, which is beneficial for communication applications.

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

[0027] The second refractive index can be the refractive index for electromagnetic waves having telecommunication wavelengths for the orbitals.

[0028] The second refractive index can be the refractive index for light having a polarization perpendicular to the waveguide direction for the orbitals.

[0029] The extension of each of the plurality of orbitals in a plane perpendicular to the waveguide direction along at least one direction can be less than 5 pm, in particular less than 2 pm or less than 1 pm. The extension of each of the plurality of orbitals in the plane perpendicular to the waveguide direction along a second direction can be at least 5 pm (in particular, at least 6 pm or at least more than 7 pm), wherein the second direction in the plane perpendicular to the waveguide direction is perpendicular to the at least one direction in the plane perpendicular to the waveguide direction. The extension of each of the plurality of orbitals in the plane perpendicular to the waveguide direction along the second direction can be at most 10 pm, in particular at most 9 pm or at least 8 pm.

[0030] The plurality of orbitals can form at least a portion of an outer boundary of the waveguide.

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

[0032] At least one of the plurality of electrodes or all of the plurality of electrodes can comprise or consist of a noble metal, such as copper or gold.

[0033] The waveguide can comprise a core. The core can be defined by a first interruption of the arrangement of orbitals, the arrangement comprising an equilateral triangle in a plane perpendicular to a direction of the waveguide.

[0034] The minimum distance between the center of the core and the nearest electrode of the plurality of electrodes can be at most 60 pm, in particular at most 40 pm, in particular at most 30 pm or at most 20 pm.

[0035] The minimum distance between the center of the core and the nearest electrode can reduce a control voltage required for establishing an electro-optical modulator with the waveguide device, such as a phase shifter, e.g., a p-phase shifter. The reduced control voltage can increase a switching speed of the electro-optical modulator.

[0036] The first interruption can comprise electro-optical material free of orbitals.

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

[0038] The nearest electrode can be the electrode of the plurality of electrodes that is closest to the center of the core in a plane perpendicular to the waveguide direction.

[0039] The core can be surrounded by the arrangement in a plane perpendicular to the waveguide direction on at least two sides, in particular on at least three sides. The sides can correspond to directions, wherein an angle between any two directions can be an integer multiple of 90°.

[0040] The track arrangement surrounding the core can be adapted to confine electromagnetic waves at the core and to reduce propagation losses related to electromagnetic wave leakage to loss-increasing regions, such as absorbing and / or metallic regions.

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

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

[0043] The cladding thickness can be asymmetric such that a portion of the track arrangement having a smallest cladding thickness in a plane perpendicular to the waveguide direction is arranged between the core and one of the plurality of electrodes, in particular between the core and the nearest electrode. The smallest cladding thickness can correspond to one track. The portion of the arrangement having the smallest cladding thickness can include or be a break of the hexagonal symmetry of the track arrangement.

[0044] The track arrangement having a smallest thickness between the waveguide and / or the core and the electrodes can reduce a distance between the two. The reduced distance can help to form a large electric field and thus to facilitate operation of the waveguide device, e.g. as a phase shifter such as a p-phase shifter, while applying moderate control voltages at the electrodes. The moderate control voltages can increase the switching speed of the waveguide device.

[0045] The smallest cladding thickness can be less than 30 pm, in particular less than 25 pm or less than 20 pm.

[0046] According to embodiments, the smallest cladding thickness can be at least 10 pm, in particular at least 12 pm or at least 15 pm.

[0047] This thickness range can allow for a short distance between the waveguide and / or its core and the nearest electrode, while at the same time providing sufficient electromagnetic wave confinement to the waveguide and / or its core to avoid losses related to electromagnetic wave leakage towards the electrodes.

[0048] The minimum cladding thickness can be zero, and / or there can be no track arrangement in the portion of the arrangement having the minimum cladding thickness.

[0049] In a plane perpendicular to the waveguide direction, the track arrangement and the plurality of electrodes can collectively enclose the core. In particular, in a plane perpendicular to the waveguide direction, the track arrangement and the nearest electrode can collectively enclose the core. For example, any half-line in a plane perpendicular to the waveguide direction starting from the center of the core can intersect the track arrangement or one of the plurality of electrodes, in particular the nearest electrode.

[0050] The absence of a waveguide cladding and / or the track arrangement in the portion having the minimum thickness can further reduce the distance between the waveguide and / or its core and the nearest electrode, thereby reducing the control voltage. However, in such embodiments, the propagation loss can increase due to electromagnetic wave leakage from the waveguide and / or its core to the electrode(s).

[0051] At least one of the plurality of electrodes can be arranged on a first surface, wherein the first surface is a surface of the substrate and / or a surface of the electro-optical material.

[0052] Arranging the electrodes on a surface of the substrate and / or the electro-optical material can provide a device design that can be easily and economically realized using available technology.

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

[0054] A first electrode of the plurality of electrodes and a second electrode of the plurality of electrodes can be arranged on opposite sides of the waveguide.

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

[0056] Embedding the at least one electrode into the substrate and / or the electro-optical material can bring the electrodes closer to the waveguide or its core and, thus, can further reduce the control voltage, however, can come at the expense of increasing the complexity and cost of electrode manufacturing.

[0057] The minimum distance between the center of the core and the first surface can be at most 60 pm, in particular at most 40 pm, in particular at most 30 pm, in particular at most 20 pm, or at most 15 pm.

[0058] In embodiments having a waveguide portion with a minimum thickness, the waveguide portion with the minimum thickness can be arranged partly or completely between the waveguide core and the first surface.

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

[0060] The corresponding extension can facilitate the use of the waveguide device as an electro-optical modulator, e.g. as a phase shifter such as a p-shift.

[0061] The at least one electrode can 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-optical modulator in which the waveguide device is applied.

[0063] The at least one electrode can comprise the nearest electrode.

[0064] The plurality of electrodes can further comprise at least one counter electrode different from the at least one electrode, wherein the at least one counter electrode is arranged on the first surface.

[0065] Arranging a counter electrode on the first surface as well can provide a device design that can be easily and economically realized using known techniques.

[0066] The at least one counter electrode can be in direct contact with the electro-optical material.

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

[0068] The at least one counter electrode can be arranged parallel to the at least one electrode.

[0069] In some embodiments, the minimum distance between the at least one counter electrode and the at least one electrode can not exceed 300 pm, in particular not exceed 150 pm, in particular not exceed 100 pm or 80 pm.

[0070] The at least one counter electrode can comprise at least two counter electrodes.

[0071] The at least two counter electrodes can be arranged on opposite sides of the at least one electrode on the first surface. Alternatively or in addition, the at least two counter electrodes can be symmetrically arranged in the vicinity of the at least one electrode on the first surface, in particular with respect to a mirror plane intersecting the at least one electrode and / or the core of the waveguide.

[0072] The at least two counter electrodes can be arranged parallel to each other.

[0073] The at least two counter electrodes can be arranged parallel to the at least one electrode.

[0074] A minimum distance between any of the at least two counter electrodes and the at least one electrode can not exceed 300 pm, in particular not exceed 150 pm, in particular not exceed 100 pm or 80 pm.

[0075] The first surface can be planar. Surfaces of the at least one electrode and at least one counter electrode can be coplanar to each other, and in particular also to the first surface.

[0076] In a second aspect, an electro-optical modulator comprises a waveguide device as outlined above. In particular, the electro-optical modulator can be a phase shifter, in particular a pi 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 to operate at a control voltage of at most 20 V between the at least one electrode and the at least one counter electrode.

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

[0080] In a third aspect, a method for manufacturing a waveguide device comprises providing a substrate comprising an electro-optical material having a first refractive index; and forming a waveguide in the electro-optical material. Forming the waveguide comprises forming a plurality of waveguide tracks such that the tracks are parallel to each other and have a uniform direction defining a waveguide direction, and such that the tracks comprise an arrangement in a plane perpendicular to the waveguide direction. The arrangement comprises at least 40 equilateral triangles of equal side length. All three angles of each of the equilateral triangles individually coincide with a different track of the plurality of tracks in the plane perpendicular to the waveguide direction. Forming each track of the plurality of tracks comprises focusing a laser beam into the electro-optical material to permanently reduce the refractive index in a focal point of the laser beam from the first refractive index to a second refractive index smaller than the first refractive index; and propagating the focal point of the laser beam along the waveguide direction to form the track having the second refractive index in the electro-optical material.

[0081] The method of the present disclosure can provide a technique for laser writing a waveguide having reduced refractive index tracks, which is sometimes also referred to as an embedded cladding waveguide. The embedded cladding waveguide can provide low propagation loss. The arrangement of tracks having equilateral triangles can further reduce the propagation loss.

[0082] The method can further comprise generating the laser beam using a laser. The laser can be a pulsed laser, in particular a pulsed laser providing a laser beam with a pulse duration below 1 ps, in particular below 0.5 ps. The laser can be an infrared laser, providing a laser beam with a wavelength of at most 11 pm, in particular at most 1100 nm.

[0083] The repetition rate of the pulsed laser can be at least 1 kHz. The repetition rate of the pulsed laser can be at most 200 kHz.

[0084] The propagating of the laser beam focus can comprise translating the substrate, in particular while keeping the position of the laser fixed. The translating of the substrate can use a translation stage, in particular an at least partially automated translation stage. Alternatively or additionally, the propagating of the laser beam focus can comprise translating the position of the laser beam.

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

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

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

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

[0089] Focusing the laser beam into the electro-optical material can comprise generating a longitudinal width of the laser beam at the focus along the waveguide direction and perpendicular to the direction of the laser beam, and generating a transversal width of the laser beam at the focus perpendicular to the waveguide direction and perpendicular to the direction of the laser, and wherein the longitudinal width is larger than the transversal width.

[0090] The longitudinal width and the transversal width can refer to the laser beam width perpendicular to the direction of the laser beam, respectively.

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

[0092] The longitudinal width can refer to the laser beam width along the waveguide direction. The transversal width can refer to the laser beam width perpendicular to the waveguide direction. 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 long axis of the elliptical cross-section can be parallel to the direction of the waveguide. The short axis of the elliptical cross-section can be perpendicular to the direction of the waveguide.

[0094] The non-circular or asymmetric cross-section of the laser beam at the focal point can cause the track roughness to be reduced and result in further reduction of the propagation loss of the waveguide.

[0095] The longitudinal width and / or the lateral width can refer to the extension of the laser beam at the focal point and perpendicular to the direction of the laser beam, respectively.

[0096] The method can further comprise, prior to focusing, providing 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 the direction of the waveguide and to the direction of the laser beam, wherein 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 the focal point having a longitudinal width exceeding a lateral width by focusing.

[0098] Alternatively or in addition, the method can comprise 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 produce a longitudinal width that is greater than a lateral width. In such embodiments, the method can comprise producing a second focal point in addition to the focal point.

[0099] In such embodiments, the laser beam can have a second longitudinal width at the second focal point along the direction of the waveguide and a second lateral width at the second focal point along a direction perpendicular to the direction of the waveguide and to the direction of the laser beam, wherein the second lateral width is greater than the second longitudinal width.

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

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

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

[0103] The collimator, such as the slit collimator, can have a width of at least 0.2 mm. The collimator, such as the slit collimator, can have a width of at most 1.5 mm.

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

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

[0106] Focusing the laser beam into the electro-optical material can include transmitting the laser beam through a first surface, wherein the first surface is a surface of the substrate and / or a surface of the electro-optical material.

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

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

[0109] Forming the plurality of waveguide tracks can include forming one track of the plurality of tracks at a greater distance from the first surface before forming one track of the plurality of tracks at a lesser distance from the first surface.

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

[0111] Forming the plurality of waveguide tracks can include forming a track of the plurality of tracks at a greater distance from a center of the waveguide in a plane parallel to the first surface before forming a track of the plurality of tracks at a lesser distance from the center of the waveguide in the plane parallel to the first surface.

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

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

[0114] The at least one pair of electrodes can be characterized by features corresponding to features described above in the context of waveguide devices. BRIEF DESCRIPTION OF DRAWINGS

[0115] The techniques of the present disclosure, as well as the advantages thereof, will be best understood by reference to the following description of exemplary embodiments in conjunction with the accompanying drawings, in which:

[0116] Figure 1aA waveguide with a racetrack arrangement in an electro-optical material is shown;

[0117] Figure 1b A waveguide with a racetrack arrangement in an electro-optical material is shown; Figure 1a

[0118] Figure 1c A waveguide with a racetrack arrangement in an electro-optical material is shown; Figure 1a Figure 1b

[0119] Figure 2a A device for manufacturing a waveguide with a racetrack arrangement in an electro-optical material according to an embodiment is shown as seen along a translation direction;

[0120] Figure 2b A device for manufacturing a waveguide with a racetrack arrangement in an electro-optical material according to an embodiment is shown as seen from a direction perpendicular to the translation direction;

[0121] Figure 2c A device for manufacturing a waveguide with a racetrack arrangement in an electro-optical material according to another embodiment is shown as seen along a translation direction;

[0122] Figure 2d A device for manufacturing a waveguide with a racetrack arrangement in an electro-optical material according to another embodiment is shown as seen from a direction perpendicular to the translation direction; Figure 2c

[0123] Figure 2e A cross-sectional view of a device for manufacturing a waveguide along a plane 216e of Figure 2a Figure 2b Figure 2c and Figure 2d is shown;

[0124] Figure 2f A cross-sectional view of a device for manufacturing a waveguide along a plane 216f of Figure 2a Figure 2b Figure 2c and Figure 2d is shown;

[0125] Figure 2g A cross-sectional view of a device for manufacturing a waveguide along a plane 216g of Figure 2a Figure 2b Figure 2c and Figure 2d is shown;

[0126] Figure 2h A cross-sectional view of a device for manufacturing a waveguide along a plane 216h of Figure 2c and Figure 2d is shown; ​​​​​​​​​​

[0127] Figure 2i A method for manufacturing a waveguide according to an embodiment is illustrated;

[0128] Figure 3 A method for manufacturing a waveguide according to a different embodiment is illustrated;

[0129] Figure 4 A waveguide device according to an embodiment is shown;

[0130] Figure 5a An electric field induced in a waveguide device by applying a control voltage is illustrated;

[0131] Figure 5b A minimum electric field and a maximum electric field induced in a waveguide device by applying a control voltage are illustrated;

[0132] Figure 6 Modulation of the refractive index produced in the core of a waveguide device by applying a control voltage is illustrated;

[0133] Figure 7 The length of a waveguide device suitable for operating as a p phase shifter is depicted;

[0134] Figure 8a A waveguide device according to another embodiment is shown;

[0135] Figure 8b An electric field of an electromagnetic wave propagating in the core of a waveguide device is illustrated; Figure 8a

[0136] Figure 9a A waveguide device according to another embodiment is shown;

[0137] Figure 9b An electric field of an electromagnetic wave propagating in the core of a waveguide device is illustrated; Figure 9a

[0138] Propagation loss in a waveguide device is illustrated; Figure 10

[0139] A waveguide device according to another embodiment is shown; and Figure 11

[0140] A waveguide device according to yet another embodiment is shown. Figure 12 DETAILED DESCRIPTION

[0141] Figure 1a ​​is a schematic illustration of a waveguide device 120. The waveguide device 120 is formed on and in a substrate 102. The waveguide device 120 comprises 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), included in the substrate 102.

[0142] The substrate 102 can be entirely composed of the RTP 104, or it can include additional structures, for example for optical or plasmonic wave guiding, or for establishing electronic functionality. To this end, the additional structures can include portions composed of linear dielectric, semiconducting, and / or metallic structures. Alternatively or in addition to the RTP, other electro-optic materials 104, such as potassium titanyl phosphate (KTP, KTiOPO4), can be applied in the substrate 102.

[0143] Applying a control voltage between an electrode 302 and a counter electrode 304 of the plurality 300 of electrodes modulates the refractive index of the core 110 of the waveguide 100 and allows the waveguide device 120 to operate as an electro-optic modulator. The waveguide 100 and the electrodes 302, 304 overlap along a distance L defining a length L of the waveguide device 120. By coupling optical fibers (not shown) to a first end 100a and a second end 100b of the waveguide device 120, light can be coupled into and out of the waveguide device 120.

[0144] Figure 1a A detailed view illustrates a cross-section of the waveguide 100 of the waveguide device 120 in a plane perpendicular to the waveguide 100. The waveguide 100 can have a similar cross-section in any plane perpendicular to the waveguide 100. In particular, the waveguide 100 can have a similar cross-section in any plane perpendicular to the waveguide along the length L of the waveguide device 120. For example, if the waveguide device 120 is curved, or if additional structures of the substrate 102 are formed in the vicinity of the waveguide device 120, the cross-section can deviate slightly along the length L of the waveguide device 120.

[0145] The waveguide 100 is formed by an arrangement 108 of tracks 106 in the electro-optic material 104. The tracks 106 contain a modified RTP having a refractive index lower than that of the RTP 104. Its arrangement 108 can be characterized by adjacent tracks 106 intersecting at the corners of an equilateral triangle having the same size and orientation. Thus, the arrangement 108 and / or the tracks 106 can form part of a hexagonal lattice, but in some embodiments they deviate from a perfect hexagonal lattice. In a central region 110 of the waveguide, the arrangement 108 of tracks has an interruption 112 in which no tracks 116 are present, and the central region 110 is composed of substantially unmodified RTP 104.

[0146] Because the central region 110 has a higher refractive index than the tracks 106, the waveguide 100 is adapted to confine electromagnetic waves to the central region 110 in the x-y plane 114. Thus, the central region acts as a core 110 of the waveguide 100. The waveguide 100 can be referred to as an embedded cladding waveguide 100. The embedded cladding waveguide 100 guides electromagnetic waves along a direction z of the waveguide 100 that is perpendicular to the x-y plane 114. Along the direction z of the waveguide 100, the waveguide 100 has translational symmetry along its length, and a constant cross-sectional structure, possibly except for minor changes due to, for example, waveguide 100 bending or kinks.

[0147] Embedded cladding waveguide materials have previously been implemented in materials with a garnet-type structure, such as cubic YAG:Nd (propagation loss at 1064 nm of 0.7 dB / cm) and orthorhombic YAP:Nd (propagation loss at 1064 nm of 0.52 dB / cm), as in Y. Jia, C. Cheng, J. R. Vázquez 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 Vázquez 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 loss. However, for waveguide devices such as electro-optic modulators, waveguides with a significant electro-optic coefficient in the electro-optic material, and thus a crystalline material without inversion symmetry, such as RTP or KTP, are desirable.

[0148] Figure 1b and Figure 1cThe arrangement 108 of the tracks 106 is illustrated in more detail. The arrangement 108 can have a significant influence on the propagation loss of electromagnetic waves propagating in the direction z along the waveguide in the core 110. The waveguide 100 according to the present specification has a minimum propagation loss, which is achieved using the depicted arrangement 108 of the tracks 106. The arrangement 108 can be illustrated with equilateral triangles 116 of the same size or edge length, respectively. The introduction of these equilateral triangles 116 is for illustration and reference purposes and does not add any physical structure to the waveguide 100 according to the present specification. Figure 1a

[0149] Any equilateral triangle 116 is constituted in such a way that each of its corners lies in a 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 116 shares at most one cross-section of the same track 106. In other words, if one corner of a first equilateral triangle 116 and one corner of a second equilateral triangle 116 lie in the same cross-section of the same track 106, the other two corners of the first equilateral triangle 116 lie in cross-sections of tracks different from the cross-sections of the tracks in which the other two corners of the second equilateral triangle lie.

[0150] Figure 1b Figure 1c A representative alternative to the arrangement 108 using a lattice 118a, 118b, 118c, 118d of equilateral triangles 106 is also illustrated. In contrast to the individual equilateral triangles 116 described above, the equilateral triangles can each be identified at arbitrary positions of the arrangement 108 (except for the above-mentioned limitation), the lattice 118a, 118b, 118c, 118d comprising a plurality of related equilateral triangles 116.

[0151] According to a first definition, any equilateral triangle 116 of the lattice 118a, 118b, 118c, 118d shares at least one corner with a neighboring triangle 116 of the lattice 118a, 118b, 118c, 118d. For example, the lattice 118a, 118b, 118c, 118d comprises 3, 6, 52 and 11 such equilateral triangles 116.

[0152] The lattice 118a, 118b, 118c, 118d can alternatively be defined such that any equilateral triangle 116 of the lattice 118a, 118b, 118c, 118d shares at least two corners with a neighboring triangle of the lattice 118a, 118b, 118c, 118d. According to this definition, for example, the lattice 118a, 118b, 118c, 118d comprises 1, 4, 52 and 9 equilateral triangles 116.

[0153] ​​The lattices 118a, 118b, 118c, 118d can also be defined such that any equilateral triangle 116 of the lattice 118a, 118b, 118c, 118d shares all its corners with neighboring triangles of the lattice 118a, 118b, 118c, 118d. According to this definition, for example, the lattices 118c, 118d comprise 35 and 3 equilateral triangles 116, respectively. Figure 1b The portions 118a, 118b of the arrangement 108 that do not contain any such equilateral triangles 116 do not qualify as lattices according to this definition.

[0154] The arrangement 108 with equilateral triangles 116 corresponds to an arrangement that is at least locally hexagonal and / or approximately hexagonal. In other words, the arrangement 108 exhibits at least locally and / or approximately hexagonal symmetry. In particular, any group of equilateral triangles 116 that can be described as a lattice 118a, 118b, 118c, 118d constitutes a portion of a hexagonal lattice and exhibits exact local hexagonal symmetry. Thus, each lattice 118a, 118b, 118c, 118d that is composed of equilateral triangles 116 corresponds to a portion of a hexagonal lattice and has local hexagonal symmetry. However, this does not necessarily hold for the orbits 106 that correspond to the lattices 118a, 118b, 118c, 118d. The orbits 106 can have a reduced symmetry shape and / or the center of the orbits 106 can be offset from the corners of the equilateral triangles 116, as long as the corners of the equilateral triangles 116 lie within the cross-section of the orbits 106.

[0155] The arrangement 108 with 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 cladding waveguide 100, because the relative difference between the modified RTP of the orbits 106 and the refractive index of the unmodified RTP 104 is only 0.006 to 0.009. Since the arrangement 118 with equilateral triangles 116 is at least locally hexagonal and / or approximately hexagonal, it provides a more optimal (approximately closest) orbit 106 packing density. Thus, the arrangement 108 makes the best possible use of the limited refractive index difference to achieve the strongest possible confinement and the lowest possible propagation loss.

[0156] Figure 2a , Figure 2b , Figure 2c , Figure 2d , Figure 2e , Figure 2f , Figure 2g , Figure 2h and Figure 2iAn apparatus and a method for manufacturing a waveguide 100 are illustrated. The apparatus comprises a laser system 200 with a laser. The laser apparatus 200 emits a substantially parallel laser beam 202 with a wavelength of 1030 nm, a pulse duration of 180 fs, a repetition rate of 5 kHz, a pulse energy in the range of 250 nJ to 400 nJ, and a diameter of 4.5 mm. The laser beam 202 is focused into the KTP 104 substrate 102 through a surface 208 using a microscope objective 204 with a numerical aperture of 0.65. Under these conditions, a modified RTP region of Figure 1a , Figure 1b and Figure 1c and the final track 106 along the direction y has an extension in the range of 8 pm to 12 pm as well.

[0157] The substrate 102 is positioned on a translation stage 210 with a translation direction 212 being z to propagate the focal point 206 in the electro-optical material 104 to write the track 106. Figure 2a and Figure 2c shows the apparatus as seen along the translation direction 212 (z), whereas Figure 2b and Figure 2d shows the apparatus as seen 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 waveguide 100 to be produced.

[0158] The polarization of the laser beam 202 is perpendicular to the translation direction 212 (z) as it has been found that this geometry minimizes the refractive index of the modified RTP.

[0159] As depicted in Figure 2a and Figure 2c the laser beam 202 is focused to the focal point 206 along a direction x perpendicular to the direction 212 (z) of the translation stage 210 with a lateral width w2.

[0160] As depicted in Figure 2b and Figure 2d the laser beam 202 is focused to the focal point 206 along a direction z parallel to the direction 212 (z) of the translation stage 210 with a longitudinal width wl. The longitudinal width wl and the lateral width w2 refer to the width of the laser beam 202 in the focal point 206 along the direction 212 of the translation stage and the waveguide and perpendicular to the direction 212, respectively, and are both perpendicular (lateral) to the direction of the laser beam 202. The longitudinal width wl is greater than the lateral width w2.

[0161] As depicted in Figure 2a andFigure 2b As shown, a spectral slit 214 with a width of 1 mm can be introduced into the substantially parallel laser beam 202 emitted by the laser system 200 to achieve a greater longitudinal width wl. The spectral slit 214 causes the extension of the substantially parallel laser beam 202 along one direction 212(z) perpendicular to the direction y of the laser beam 202 to be reduced. Thus, focusing the laser beam 202 using the microscope objective 204 results in a greater longitudinal width wl along this direction 212(z).

[0162] 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, in particular into the substantially parallel laser beam 202, to produce a longitudinal width wl along the direction 212(z) that exceeds the transverse width w2 along the perpendicular direction y.

[0163] Figure 2c and Figure 2d A corresponding embodiment is illustrated in Fig. 2. In this embodiment, the focal point 206 refers to a plane 216g perpendicular to the direction of the laser beam 202 at a position along the direction of the laser beam 202 at which the width w2 of the laser beam 202 along the transverse direction (with respect to the translation direction 212 or the direction of the waveguide 100, respectively) is minimal. Thus, in the focal point, the laser beam 202 exhibits a beam waist w2 along the transverse direction x. In addition, a second focal point 206’ is formed at the beam waist position of the laser beam 202 along the translation direction 212, corresponding to a plane 216h perpendicular to the direction of the laser beam 202. In the second focal point 206’, the order of the beam width is reversed compared to the focal point 206, i.e. the transverse width of the laser beam 202 exceeds the longitudinal width. The greater longitudinal width in the focal point compared to the transverse width results in a smoother formed track and a reduced propagation loss of the formed waveguide, which is therefore desirable. Thus, the focal point 206, but not the second focal point 206’, is used for forming the waveguide. For details on focusing using anisotropic focusing elements such as cylindrical lenses, see, for example, A. G. Okhrimchuk “Femtosecond Fabrication of Waveguides in Ion-Doped Laser Crystals”, DOI: 10.5772 / 12885 “Coherence and Ultrashort Pulse Laser Emission”, November 2010.

[0164] SSFedotov and AGOkhrimchuk's paper, "Smooth Writing In YAG Single Crystal with Beam Waist of an Elliptical Cross-Section," Frontiers in Optics / Laser Science, p. JTh4B.40 (OSA, 2020), has demonstrated the use of a laser beam with an elliptical cross-section to write orbitals into YAG:Nd. However, the question of whether this technique can be applied to electro-optic materials and / or to generate triangular arrangements remains unresolved.

[0165] Figure 2e The apparatus for manufacturing waveguide 100 is shown along... Figure 2a , Figure 2b , Figure 2c and Figure 2d The cross-section of plane 216e. In plane 216e, the laser beam 202 has a substantially circular cross-section 218.

[0166] Figure 2f The apparatus for manufacturing waveguide 100 is shown along... Figure 2a , Figure 2b , Figure 2c and Figure 2d The cross section of plane 216f. In plane 216f, laser beam 202 has a cross section 220 corresponding to an ellipse. The extension e2 along the direction x perpendicular to the translation direction 212(z) exceeds the extension e1 along the translation direction 212(z).

[0167] Figure 2g The apparatus for manufacturing waveguide 100 is shown along... Figure 2a , Figure 2b , Figure 2c and Figure 2d The cross-section of plane 216g. This plane 216g corresponds to the focal point 206 of the laser beam. In this plane 216g, 206, the laser beam 202 has a longitudinal width w1 along the direction 212(z) of the translation stage 210 and a transverse width w2 along the 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.

[0168] Figure 2h The apparatus for manufacturing waveguide 100 is shown along... Figure 2c and Figure 2dThe cross-section of plane 216h corresponds to the second focal point of the laser beam. Within plane 216h, 206', the laser beam 202 has a longitudinal width along direction 212(z) of the translation stage 210 and a transverse width along direction x perpendicular to direction 212(z) of the translation stage 210. The longitudinal width along direction 212(z) of the translation stage 210 is smaller than the transverse width along direction x perpendicular to direction 212(z) of the translation stage 210.

[0169] Figure 2i The flowchart summarizes the basic process steps of method 230 for forming a waveguide device. The method begins by providing 232 a substrate 102 comprising an electro-optic material 104 having a first refractive index, and continues by forming 234 waveguides 100 in the electro-optic material 104. Forming 234 waveguides 100 includes forming a plurality of tracks 106 of waveguide 100. Forming any track 106 236 includes focusing 238 a laser beam 202 into the electro-optic material 104 to reduce the refractive index in the focal point 206. Forming any track 106 236 further includes propagating 240 of the focal point 206 of the laser beam 202 along the direction z of the waveguide 100 to form the track 106.

[0170] Figure 3 A preferred embodiment of a method for manufacturing a waveguide is illustrated. Figure 3 Number 106' in the sequence gives the order, according to which the following is used in Figure 2a to Figure 2i The method described in the context is used to write track 106. Tracks with smaller numbers 106' are written first, followed by tracks with larger numbers 106'. Tracks farther from surface 208 are written before those closer to surface 208. In this way, the reflection and scattering of the laser beam 202 by the tracks 106 already written in the substrate 102 are minimized. When a set of tracks 106, 106' are at the same distance from surface 208, the tracks 106, 106' closer to the waveguide center 110 in that set are written first.

[0171] Figure 4 A waveguide device having a waveguide 100 in an electro-optic material 104 on a substrate 102 is shown. The waveguide 100 can be similar to... Figure 1a , Figure 1b , Figure 1c , Figure 2a to Figure 2i and / or Figure 3The waveguide described in the context of FIG. 1. In addition, a plurality of 300 electrodes 302, 304 are formed on the 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 of width w. Two counter electrodes 304 are symmetrically arranged at a distance g near the electrodes 302 on the surface 208. Along the direction z of the waveguide 100, the waveguide 100 and the plurality of 300 electrodes 302, 304 have translational symmetry along their respective lengths, and have the same cross-section, except for minor changes due to, for example, waveguide device bending or kinks.

[0172] A control voltage is applied between the electrodes 302 and the counter electrodes 304 to operate the waveguide device. The application of the control voltage induces an electric field at the location of the core 110, which changes the refractive index of the core 110. Thus, the waveguide device acts as an electro-optic modulator to modulate an electromagnetic wave confined within the core 110 and propagating along the waveguide direction z.

[0173] The degree of modulation depends on the magnitude of the electric field induced at the location of the core 100 by the application of the control voltage to the electrodes 302, 304. A greater degree of modulation is desirable because it allows the use of a shorter length waveguide device to achieve a preselected modification of the electromagnetic wave, such as a π phase shift. When a preselected modification is made, a shorter length waveguide device will reduce the propagation loss suffered by the electromagnetic wave as it propagates in the waveguide 100.

[0174] Generally, providing a waveguide device with a shorter distance h between the core 110 and the nearest electrode 300 will enhance the electric field at the location of the core 100 and the degree of modulation. In the embodiment of FIG. 1, the shortest 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 and the radius of the core 110. Figure 4 In the embodiment of FIG. 1, where the thickness t of the waveguide 100 formed by the arrangement 108 of the tracks 106 is substantially the same in each direction (isotropic), the minimum distance h between the center 402 of the core 110 and the nearest electrode 300 depends on the thickness t of the waveguide 100. According to the depicted embodiment, the minimum minimum distance h is the sum of the thickness t and the radius of the core 110.

[0175] Figure 5a The electric field 500 induced by the application of the control voltage between the electrodes 302 and the counter electrodes 304 is illustrated. At the location 110 of the core, the electric field 500 is oriented approximately perpendicular to the surface 208 and / or the interface between the electrodes 208 and the substrate 102 (or electro-optic material 104), respectively. Thus, the electric field 500 at the location 110 of the core can be characterized by its y-component Ey. The y-component Ey is maximum at the interface between the electrodes 302 and the substrate 102, and decreases with increasing distance d to the electrodes 302.

[0176] Figure 5bThe maximum y-component max(Ey) and the minimum y-component min(Ey) of the electric field in the region 110 of the core are shown 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 promote a uniform modulation of the confined electromagnetic wave in the core 110. Figure 5b It is demonstrated that for waveguide devices the deviation is usually small and can be further minimized using a width w of the electrode 302 of about 60 pm to 100 pm.

[0177] Figure 6 The final change of the refractive index An of the light having a polarization along the direction y perpendicular to the surface 208 is shown which is achieved by applying a control voltage of 37 V between the electrode 302 and the counter electrode 304 yy For a waveguide device with a width w of the electrode 302 of 50 pm and a distance g between the electrode 302 and the counter electrode 304 of 10 pm, the change of the refractive index An of the waveguide device has been determined yy .

[0178] Using the change of the refractive index, the length L of the waveguide device is calculated which is suitable to operate the waveguide device as a p phase shifter. Figure 7 Corresponding lengths L of the electrode 302 are given for different widths w of the electrode 302 when the distance g between the electrode 302 and the counter electrode 304 is equal to 30 pm and the distance h between the center 402 of the core 110 and the nearest electrode 302 is equal to 50 pm. For an optimized electrode width w of about 50 pm to 100 pm, like 70 pm, a waveguide device length L of 30 mm is sufficient to establish a p phase shifter. When a p phase shift of the electromagnetic wave is performed, the length L reduces the optical path length of the electromagnetic wave propagating in the core 110 and thus minimizes the propagation loss of the electro-optical modulator.

[0179] The length L of the waveguide device of the electro-optical modulator, like the p phase shifter, can be further reduced by enhancing the electric field 500 at the core 110, respectively, by increasing the overlap between the electric field 500 and the confined electromagnetic wave in the core.

[0180] Figure 8a An embodiment of the waveguide device is shown in which the distance h between the center 402 of the waveguide 100 and the nearest electrode 302 is reduced. The reduction of the distance h is achieved by forming the arrangement 108 of tracks 106 with an anisotropic thickness, i.e. different thicknesses t, t’ along different directions. In the region between the core 110 and the nearest electrode 302, the thicknesses t, t’ are minimal. Thus, the minimal thickness t’ of the waveguide 100, instead of the thickness t of the waveguide 100, determines the minimal distance h between the center 402 of the core 110 and the nearest electrode 302. Figure 4 The anisotropic thickness t in the embodiment determines the minimal distance h between the center 402 of the core 110 and the nearest electrode 302. The minimal thickness t’ of the waveguide 100 is smaller than the thickness t of the waveguide 100.Figure 4 The isotropic thickness t of the embodiment. This enhances the electric field induced at the location of the core 110 by applying a control voltage between the electrode 302 and the counter electrode 304. Thus, an electro-optical modulator such as a pi-phase shifter can be implemented with a reduced length L of the waveguide device and / or a reduced control voltage. Consequently, the propagation loss of the electro-optical modulator is reduced and / or the switching frequency of the electro-optical modulator is increased. For example, when according to Figure 8a The waveguide device of the embodiment of Figure 8a The waveguide device of the embodiment of

[0181] Figure 8b The equal electric field lines 600 of an electromagnetic wave propagating in the waveguide 100 are depicted for a waveguide device of the embodiment of Figure 8a The waveguide device of the embodiment of Figure 8a , Figure 8b The arrangement 108 of the tracks 106 of the embodiment of

[0182] Figure 9a and Figure 9b An embodiment is shown in which the minimum thickness t' of the waveguide 100 is further reduced, and thus the minimum distance h between the core 110 and the nearest electrode 302 is also further reduced. In this embodiment, the minimum thickness t' is essentially zero, and there are no tracks in the region between the core 110 and the nearest electrode 302. The distance between the center 402 of the core 110 and the electrode 302 is minimized and essentially corresponds to the radius of the core 402. Thus, the electric field 500 induced at the location of the core 110 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 along the core 110 is also enhanced.

[0183] However, the lack of tracks 106 in the region between the core 110 and the nearest electrode 302 will result in leakage of the electromagnetic wave from the core 110 to the electrode 302. This is illustrated in Figure 9b The equal electric field lines 600 of an electromagnetic wave are depicted for such an embodiment. The overlap between the electromagnetic wave and the electrode 302 results in absorption of the electromagnetic wave in the electrode 302 and an increased propagation loss.

[0184] In summary, Figure 9a and Figure 9bEmbodiments of the application can provide enhanced electric field 500 and refractive index modulation at the location of the core 110, however this can come at the cost of more severe electromagnetic field distortion and greater propagation loss.

[0185] Figure 10 The graphs of FIGS. 7A, 7B, 8A, 8B, 9A, 9B illustrate the propagation loss 700a, 700b, 702a, 702b, 704a, 704b of waveguide devices having a minimum thickness t' of one track 116 (700a, 702a, 704a), and having a minimum thickness t' of substantially zero (700b, 702b, 704b), respectively. Figure 8a Figure 8b Embodiments of the application), and having a minimum thickness t' of substantially zero (700b, 702b, 704b, respectively). Figure 9a Figure 9b Embodiments of the application).

[0186] In detail, the various data sets 700a, 700b, 702a, 702b, 704a, 704 represent the propagation loss of devices having the following characteristics:

[0187] 700a: minimum thickness t' of one track 116, copper electrodes, control voltage of 37 V;

[0188] 700b: minimum thickness t' of one track 116, copper electrodes, control voltage of 0 V;

[0189] 702a: minimum thickness t' of one track 116, gold electrodes, control voltage of 37 V;

[0190] 702b: minimum thickness t' of one track 116, gold electrodes, control voltage of 0 V;

[0191] 704a: minimum thickness t' of zero, copper electrodes, control voltage of 37 V;

[0192] 704b: minimum thickness t' of zero, copper electrodes, control voltage of 0 V.

[0193] Figure 10 It is demonstrated that, at an optimal distance h between the center 402 of the core and the nearest electrode 302 of 14 pm, devices having a minimum thickness t' of one track 116 (700a, 702a, 704a, respectively) provide a propagation loss as low as 0.15 dB / cm (copper electrodes) or 0.2 dB / cm (gold electrodes). Thus, a corresponding waveguide device having a length L of 3 cm has a total propagation loss of 0.45 dB (copper electrodes) or 0.6 dB (gold electrodes). In contrast, for devices having a minimum thickness t' of substantially zero (700b, 702b, 704b, respectively), the propagation loss is about 0.65 dB / cm. Figure 8a Figure 8b Figure 9a Figure 9b

[0194] Figure 11 and​​​​​​Figure 12 A waveguide device according to an alternative embodiment is depicted. Figure 11 and Figure 12 The waveguide 100 of the embodiment depicted in Figure 1a , Figure 1b and Figure 1c embodiments described in the context of Figure 2a to Figure 2i and Figure 3 Each waveguide device also comprises a plurality of 300 electrodes 302, 304.

[0195] However, the waveguide devices according to the embodiments of Figure 11 and Figure 12 differ from each other and from the embodiments described above in the geometrical arrangement of the electrodes 300, 302, 304. In particular, Figure 11 and Figure 12 The electrodes 302 and counter electrodes 304 of the embodiments of

[0196] In the embodiments of Figure 11 The electrodes 300, 302, 304 are substantially flat in a plane y, z parallel to the waveguide 100 and perpendicular to the surface 208. As described in the context of Figure 2a to Figure 2i and Figure 3 Such electrodes are manufactured by first forming the waveguide 100 in the electro-optical material 104 of the substrate 102. Thereafter, an etching or laser cutting step is performed to selectively remove a portion of the substrate 102 and to create a void structure having the shape of the electrodes 300, 302, 304 to be formed. The etching or laser cutting step can use a photolithographic etching step, in particular an anisotropic etching step, or a maskless laser cutting step or a combination of both. Thereafter, the void structure is filled with an electrically conductive material, such as titanium, tantalum, gold or copper or a combination thereof, deposited from the gas phase, for example in a vacuum chamber.

[0197] Figure 12 The embodiments of Figure 11embodiments, but with 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 in the core 110. The curved electrodes 300, 302, 304 are manufactured using at least one photolithography etching step, in particular using a combination of anisotropic and isotropic etching steps, and / or a maskless laser cutting step. In comparison to the electrodes 300, 302, 304 described above, Figure 12 The more complex shape of the electrodes 300, 302, 304 of the embodiments of the waveguide device of Figure 12 The more complex shape of the electrodes 300, 302, 304 of the embodiments of the waveguide device of

[0198] The description and drawings are only intended to illustrate the present disclosure and its associated numerous advantages, and should not be construed as implying any limitation. The scope of the present disclosure will be determined solely by the appended claims.

[0199] List of reference signs

[0200] 100 waveguide

[0201] 100a, 100b first end of the waveguide, second end of the waveguide

[0202] 102 substrate

[0203] 104 electro-optical material

[0204] 106, 106’ track

[0205] 108 arrangement in a plane perpendicular to the direction of the waveguide

[0206] 110 central region of the waveguide, core

[0207] 112 first interruption of the track arrangement

[0208] 114 plane (xy-plane) perpendicular to the direction of the waveguide

[0209] 116 equilateral triangle

[0210] 118a-d lattice consisting of equilateral triangles

[0211] 120 waveguide device

[0212] z direction of the waveguide

[0213] t, t’ thickness of the waveguide

[0214] 200 laser device with a laser

[0215] 202 laser beam

[0216] 204 microscope objective

[0217] 206 focal point

[0218] 206' second focal point

[0219] 208 first surface

[0220] 210 translation stage

[0221] 212 translation direction

[0222] 214 slit

[0223] 216e, 216f, 216g, 216h reference surface

[0224] 218 substantially circular cross-section

[0225] 220 cross-section corresponding to an ellipse

[0226] 222 anisotropic focusing element, cylindrical lens

[0227] e1 first extension

[0228] e2 second extension

[0229] 230 method for manufacturing a waveguide device

[0230] 232 providing a substrate

[0231] 234 forming a waveguide

[0232] 236 forming a plurality of tracks

[0233] 238 focusing a laser beam into an electro-optical material

[0234] 240 propagating a focal point of the laser beam

[0235] w1 longitudinal width of the laser beam in the focal point (relative to the translation direction of the translation stage)

[0236] w2 transversal width of the laser beam in the focal point (relative to the translation direction of the translation stage)

[0237] 300 plurality of electrodes

[0238] 302 electrode

[0239] 304 (plurality of) counter-electrodes

[0240] 402 center of the core

[0241] g distance between the electrode and the counter-electrode

[0242] h distance between the center of the core and the nearest electrode

[0243] w electrode width

[0244] 500 electric field

[0245] d distance from first surface

[0246] L extension of electrode in direction of waveguide

[0247] 600 equal electric field lines

[0248] 700a, 700b propagation loss

[0249] 702a, 702b propagation loss

[0250] 704a, 704b propagation loss

Claims

1. A waveguide device (120) comprising: a substrate (102) comprising an electro-optical material (104) having a first refractive index; a waveguide (100) formed in the electro-optical material (104), the waveguide (100) comprising a plurality of tracks (106); and a plurality (300) of electrodes (302, 304) formed in the vicinity of the waveguide (100); wherein the tracks (106) comprise a second refractive index smaller than the first refractive index, are parallel to each other in a common direction (z) defining a direction (z) of the waveguide (100), and form an arrangement (108) in a plane (114) perpendicular to the direction (z) of the waveguide (100); and wherein the arrangement (108) comprises at least 40 equilateral triangles (116) of equal side length, wherein all three angles of each of the equilateral triangles (116) individually coincide with a different track (106) of the plurality of tracks (106) in the plane (114) perpendicular to the direction (z) of the waveguide (100); wherein the waveguide (100) comprises a core (110); and wherein the waveguide (100) comprises an asymmetric cladding thickness (t, t’), such that a portion of the waveguide (100) having a smallest thickness (t’) is arranged between the core (110) and one electrode (302) of the plurality of electrodes (302, 304).

2. The waveguide device (120) according to claim 1, wherein the core (110) is defined by a first interruption (112) of the arrangement (108) of the tracks (106), the arrangement comprising the equilateral triangles (116) in a plane (114) perpendicular to the direction (z) of the waveguide (100), and wherein the minimum distance (h) between the center (402) of the core (110) and the nearest electrode (302) of the plurality (300) of electrodes (302, 304) is at most 40 .

3. The waveguide device (120) according to claim 1 or 2, wherein the portion of the waveguide (100) having the smallest thickness (t’) is arranged between the core (110) and a nearest electrode of the plurality of electrodes.

4. The waveguide device (120) according to any one of the preceding claims, wherein, at least one electrode (302) of the plurality (300) of electrodes (302, 304) is arranged on a first surface (208), wherein the first surface (208) is a surface (208) of the substrate (102) and / or a surface (208) of the electro-optical material (104).

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

6. The waveguide device (120) of claim 4, wherein, the plurality (300) of electrodes (302, 304) further comprises at least one counter electrode (304) different from the at least one electrode (302), wherein the at least one counter electrode (304) is arranged on the first surface (208).

7. The waveguide device (120) according to any one of the preceding claims, wherein the electro-optical material (104) comprises a nonlinear optical material and / or a crystalline material without inversion symmetry, or the electro-optical material (104) is a nonlinear optical material and / or a crystalline material without inversion symmetry.

8. An electro-optical modulator comprising a waveguide device (120) according to any of the preceding claims, wherein, The electro-optical modulator is Phase shifter.

9. A method (230) for manufacturing a waveguide device, the method comprising: providing (232) a substrate (102) comprising an electro-optical material (104) having a first refractive index; and forming (234) a waveguide (100) in the electro-optical material (104); wherein forming (234) the waveguide (100) comprises: forming (236) a plurality of tracks (106) of the waveguide (100) such that the tracks (106) are parallel to each other in a common direction (z) defining a direction (z) of the waveguide (100), and such that the tracks (106) comprise an arrangement (108) in a plane (114) perpendicular to the direction (z) of the waveguide (100), wherein the arrangement (108) comprises at least 40 equilateral triangles (116) of equal side length, wherein all three angles of each of the equilateral triangles (116) each coincide with a different track (106) of the plurality of tracks (106) in the plane (114) perpendicular to the direction (z) of the waveguide (100); wherein the forming (236) each track (106) of the plurality of tracks (106) comprises: focusing (238) a laser beam (202) into the electro-optical material (104) to reduce a refractive index in a focal point (206) of the laser beam from the first refractive index to a second refractive index smaller than the first refractive index; and propagating (240) the focal point (206) of the laser beam (202) along the direction (z) of the waveguide (100) to form a track (106) having the second refractive index in the electro-optical material (104), wherein focusing (238) the laser beam (202) into the electro-optical material (104) comprises producing a longitudinal width (wl) of the laser beam in the focal point (206) along the direction (z) of the waveguide (100) and perpendicular to a direction of the laser beam, and producing a transversal width (w2) of the laser beam in the focal point (206) perpendicular to the direction (z) of the waveguide (100) and perpendicular to the direction of the laser beam, wherein the longitudinal width (wl) is larger than the transversal width (w2).

10. The method (230) of claim 9, further comprising: introducing an anisotropic focusing element (222) into the laser beam (202) to produce the longitudinal width (wl) larger than the transversal width (w2).

11. The method (230) of claim 9, further comprising: providing the laser beam (202) as a substantially parallel beam (220) before the focusing (238), the beam having a first extension (el) along the direction (z) of the waveguide (100) and a second extension (e2) along a direction (x) perpendicular to the direction (z) of the waveguide (100) and to a direction (y) of the laser beam, wherein the second extension (e2) exceeds the first extension (el).

12. The method (230) of claim 11, further comprising: before providing the laser beam (202) as a substantially parallel beam (220) having the first extension (el) and the second extension (e2): providing the laser beam (202) as a substantially parallel beam having a substantially circular cross-section (218); and forming the substantially parallel light beam having the substantially circular cross-section (218) into a substantially parallel light beam having the first extension (el) and the second extension (e2).

13. The method (230) of any of claims 9 to 12, further comprising: forming a plurality (300) of electrodes (302, 304) in the vicinity of the waveguide (100).

14. The method (230) of claim 13, wherein the focusing (238) the laser beam (202) into the electro-optical material (104) includes transmitting the laser beam (202) through a first surface (208), wherein, The first surface (208) is a surface (208) of the substrate (102) and / or of the electro-optical material (104), and wherein forming the plurality (300) of electrodes (302, 304) further comprises forming at least one electrode (302) of the plurality (300) of electrodes (302, 304) on the first surface (208).

15. The method (230) of claim 14, wherein, forming the plurality (300) of electrodes (302, 304) further comprises forming at least one counter electrode (304) of the plurality (300) of electrodes (302, 304) on the first surface (208), wherein the at least one counter electrode (304) is different from the at least one electrode (302).

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