Laser direct writing for non-linear waveguides

A waveguide includes multiple segments having different bend radii with substantially consistent cure profiles and related methods and systems for making and using the same. The waveguide is formed by modifying a laser beam used to write the waveguide to provide the consistent cure profile in the multiple segments. A marker characteristic of laser writing may be present in the waveguide. A method or system modifies an intensity profile or a shape profile of a laser beam to proactively compensate for exposure convolution based on the geometry of each waveguide segment. A convolution compensator is positioned in the path of the laser beam to modify the beam spot profile during writing to form the multiple segments of the waveguide in a photo-curable layer.

The disclosure herein relates to optical waveguides and their fabrication to reduce optical losses in an optical waveguide on a printed circuit board.

SUMMARY

The present disclosure relates to a waveguide formed by modifying a laser beam to fabricate a consistent refractive index profile between segments having different bend radii of an optical polymer waveguide formed by laser direct writing (LDW). The disclosure also relates to a method and system for modifying the laser beam spot profile used to trace and cure the waveguide to provide an accurate and consistent cure profile in the waveguide.

In at least one embodiment, a method includes tracing a non-linear waveguide segment in a photo-curable layer with a laser beam. The laser beam defines a spot profile. The laser beam is passed through a convolution compensator to modify at least a portion of the laser beam in response to at least one geometric property of the non-linear waveguide segment to define a modified beam portion of the laser beam and a modified spot profile different than the spot profile. A photo-curable layer is cured along the non-linear waveguide segment with the modified beam portion of the laser beam having the modified spot profile.

In another embodiment, a system includes an electromagnetic radiation source to cure a waveguide by directing a laser beam. The laser beam defines a spot profile. The system further includes a convolution compensator positioned to modify at least one of an intensity profile and a shape of the spot profile to compensate for exposure convolution in a photo-curable layer when the laser beam is directed at the photo-curable layer and translated along a non-linear path in a plane parallel to the photo-curable layer.

In a further embodiment, an apparatus includes a first waveguide segment, a second waveguide segment in series with the first waveguide segment, and a height profile. The first waveguide segment defines a first bend radius and a first cure profile. The second waveguide segment defines a second bend radius different than the first bend radius and a second cure profile substantially matching the first cure profile. The height profile defines a non-uniform height portion adjacent a side of at least one of the first and second waveguide segments.

The above summary is not intended to describe each embodiment or every implementation of the present disclosure. A more complete understanding will become apparent and appreciated by referring to the following detailed description and claims taken in conjunction with the accompanying drawings. In other words, these and various other features and advantages will be apparent from a reading of the following detailed description.

DETAILED DESCRIPTION

Polymer based optical waveguides provide numerous desirable properties for use in a multitude of electronic devices, including in some embodiments, data storage devices, network components, network appliances, routers, hubs and other similar devices. These waveguides can be formed on printed circuit boards (PCB), which, in turn, would be referred to as optical PCBs, or more generally, as optical boards. These waveguides and optical PCBs can function as a component or building block of a larger structure or apparatus. Alternatively the waveguides and optical PCBs can function on their own without any other related devices or structures. The waveguides and optical PCBs can be integrated and connected to other structures and different components as well as in order to provide an assembly.

The disclosure herein relates to optical waveguide fabrication to reduce optical losses in an optical waveguide on a printed circuit board. The present disclosure relates to a waveguide formed by modifying a laser beam to fabricate a consistent refractive index profile between segments having different bend radii of an optical polymer waveguide formed by laser direct writing (LDW). The disclosure also relates to a method and system for modifying the laser beam spot profile used to trace and cure the waveguide to provide an accurate and consistent cure profile in the waveguide.

An illustrative waveguide LDW method modifies an intensity profile, a shape profile, or both of a laser beam spot profile to proactively compensate for exposure convolution based on the characteristics of the waveguide segment to be written. In many embodiments, the method utilizes a convolution compensator positioned in the path of a laser beam to modify the laser beam spot profile during tracing and curing steps to form a waveguide segment in a photo-curable layer. The convolution compensator is operable to modify the intensity profile, the shape, or both of the spot profile based on the geometric properties of the waveguide segment being traced and cured. In some embodiments, the convolution compensator includes a reconfigurable density filter, an adaptive lens, or any number of both. It is to be understood that the convolution compensator configurations described herein are merely exemplary, and other convolution compensator configurations having additional or fewer compensation elements in any similar (e.g., equivalent) arrangement are considered by the present disclosure. While the present disclosure is not so limited, an appreciation of various aspects of the disclosure will be gained through a discussion provided below.

The methods described herein form a waveguide that more closely matches a desired or target cure profile along one or more waveguide segments. In some embodiments, the waveguide cure profile is more consistent along multiple waveguide segments. For example, the waveguide cure profile of a non-linear waveguide segment may be more consistent with, or substantially match, the waveguide cure profile of a proceeding or preceding linear segment in the same waveguide. In additional or alternative embodiments, the waveguide cure profile more closely matches a desired or target cure profile for all waveguide segments by compensating for exposure convolution. For example, a non-linear waveguide segment has a desirable symmetric waveguide profile instead of an undesirable asymmetric profile. Although in other examples, an asymmetric waveguide profile may be desirable.

Recognizing that the cure profile of a waveguide influences the refractive index profile, that mismatches in refractive index profiles between consecutive segments can contribute to optical losses, and that the actual waveguide refractive index profile may differ from the target refractive index profile due to exposure convolution, the methods described herein facilitate the formation of consistent and more accurate cure profiles for a waveguide for linear waveguide segments, non-linear segments, and combinations thereof. This may result in an exemplary waveguide with less optical loss in use than a waveguide formed by other methods, systems, or apparatuses.

Examples to be described include a system with reference toFIGS. 1, 3A, 3B, 8A, 8B, 9A and 9B, exemplary apparatus with reference toFIGS. 5 and 6, exemplary methods with reference toFIGS. 2, 4, 7, and 10, and exemplary spot profiles with reference toFIGS. 11A, 11B, 11C, and 11D. It will be apparent to one skilled in the art that elements from one embodiment may be used in combination with elements of the other embodiments, and that the possible embodiments of such method, system, or apparatus using combinations of features set forth herein is not limited to the specific embodiments shown in the figures and/or described herein. Further, it will be recognized that the size and shape of various elements herein may be modified but still fall within the scope of the present disclosure, although one or more shapes and/or sizes, or types of elements, may be advantageous over others.

Any channel, member, or other physical structure operable to guide electromagnetic radiation and useful to carry an optical signal can be a waveguide. In some cases, a waveguide is formed of glass or a polymer. Glass waveguides can exhibit a practically limited bend radius and be difficult to integrate into dense opto-electrical circuit boards. On the other hand, polymer waveguides may be integrated into high-density opto-electrical printed circuit boards (e.g., PCBs). A polymer waveguide can include a waveguide core layer that is optically transparent surrounded by a cladding layer typically having a lower refractive index than the waveguide core layer. As used herein, the term “waveguide” may refer only to the structure corresponding to the waveguide core layer, which may be formed from a photo-curable material layer.

Any useful polymeric material can be utilized to form the polymeric waveguide. In many embodiments the polymer waveguide is formed of a polyacrylate, polynorbornene or polysiloxane material.

Waveguides may be designed as multimode or singlemode. A multimode waveguide is a low cost option for integrating and coupling to embedded optical PCB channels. Singlemode waveguides enable ultra-low cost photonic integrated circuits, including silicon photonics, devices assembled directly onto small form factor boards.

Singlemode waveguides typically have a smaller core size, or lateral width, than multimode waveguides and typically exhibit less modal dispersion over a distance. Illustrative waveguides have a lateral width range of about 1-100 micrometers. The cross-sectional shape may be square, rectangular, half-dome, Gaussian-like, or another similar shape. In many embodiments, singlemode waveguides have a lateral width range of about 5-15 micrometers. In some embodiments, multimode waveguides have a lateral width range of about 35-100 micrometers.

The photo-curable layer may define a surface, such as a planar surface of a PCB. In many cases, the PCB surface is not perfectly “flat” and may include other features or variations without altering the general planar character of the PCB or the generally planar path of any waveguide formed thereon.

In some cases, waveguides formed on a planar surface may include a linear segment, a non-linear segment, or any number thereof. For each waveguide, the segments may be arranged in series (e.g., adjacent to, contiguous with, or essentially continuous end-to-end). In some embodiments, the waveguide segments are formed according to a bend radius. A non-linear segment may be defined by one or more bend radii, as well as an arc angle (e.g., a right-angle turn being 90 degrees) and a length of the segment (including one or more arc lengths), to form an overall shape of the non-linear segment on the planar surface. An illustrative non-linear segment defined by one bend radius forms a portion of a circle along an arc angle, such as a quarter circle that guides electromagnetic radiation around an arc angle of 90 degree bend. A linear segment may be considered to define a bend radius that is infinite. Non-limiting examples of smaller bend radii include about 15 mm, about 10 mm, about 5 mm, or about 1 mm. Accordingly, larger bend radii may range anywhere from the smaller bend radii to less than infinity.

Although some embodiments of a non-linear segment are single bend radius segments defined by a single bend radius along the length of the segment to achieve an arc angle, many other embodiments are graded bend segments defined by multiple incremental waveguide segments, each defining a bend radius incrementally changed from the bend radius of the previous incremental segment, to achieve the arc angle. In many embodiments, the graded bend segment defines gradually increasing bend radii. Due to having multiple bend radii, a graded bend segment defines a non-circular curve along its length. Non-limiting examples of graded bend segments include an oval section, an ellipse section, a parabola section, a hyperbola section, a sinusoidal section, an S-shape section, among others. In various embodiments, a non-linear segment is defined by multiple bend radii to form a convex segment, a concave segment, or combinations of both (e.g., an S shape).

Using a graded bend segment in a waveguide can improve optical losses versus a single bend radius segment, because the maximum bend mismatch from segment-to-segment can be reduced. In one example, a single bend radius segment defines a single bend radius X to achieve an arc angle and maintains the bend radius along its length wherein ΔX is the change from the preceding segment's bend radius to X. On the other hand, in another example, a graded bend segment defines the bend radius of the first incremental segment as Y1and defines an incremental arc angle from the preceding segment's bend radius to Y as ΔY1, which is less than ΔX. In addition, ΔY2, ΔY3, . . . and ΔYn represent the bend radius changes between subsequent incremental segments, which are each less than ΔX. Due to the slower change in bend radius along the arc angle, in some embodiments, the graded bend segment has a longer length than the arc length of a single bend radius segment achieving the same arc angle.

In many embodiments, the arc length of each of the plurality of incremental waveguide segments is a fraction of the total length of the graded bend segment, which may be less than about 50%, less than about 33.3%, less than about 25%, less than about 20%, less than about 10%, less than about 5%, or less than about 1%. The arc length of each incremental segment may be the same or different. In one embodiment, the number of incremental segments, the arc length of each, the change in bend radius from segment-to-segment, or a combination thereof is selected to improve optical loss in the waveguide.

Polymer waveguides may be formed at least by photolithography or laser direct writing (LDW). The photolithography process can form high-quality waveguides. However, the process requires high-resolution masks and can be prohibitively expensive and time-intensive. On the other hand, an LDW process does not require masks and can be substantially faster than photolithography for producing waveguides depending on the design of the waveguide layout. An illustrative LDW process for writing a waveguide includes moving or translating an electromagnetic radiation source along a path to trace and to cure selective portions of a photo-curable polymer layer to form the waveguide core structure in the polymer core layer.

Any energy source, with sufficient optical power and intensity for the appropriate wavelength(s) to cure the photo-curable polymer core layer, can be an electromagnetic radiation source for LDW. In many embodiments the electromagnetic radiation source provides a laser beam of concentrated or focused radiation. In some embodiments, the laser beam is an ultraviolet (UV) laser beam.

A laser beam may have a cross-sectional profile, which defines the spot profile of the laser beam. The spot profile is defined as one or more characteristics of a cross-section of the laser beam incidence on a surface, such as that of the photo-curable layer or another object (e.g., convolution compensator). In some embodiments, the cross-sectional profile may be the same or similar as the spot profile (e.g., flat surface and perpendicular incidence). In many embodiments, the spot profile defines an intensity profile, a shape profile, or both, for example. In many embodiments, the shape profile of the laser beam is a circular and the intensity profile is uniform. The uniform intensity profile of the spot profile may be achieved by directing a laser beam, which has a Gaussian intensity beam cross-sectional profile, through a spatial filter (e.g., a pin hole), which allows only the relatively uniform center portion of the Gaussian intensity profile to pass through (i.e., forming a “top hat” profile). In other embodiments, the intensity profile is Gaussian in response to a Gaussian intensity beam cross-sectional profile.

In some applications, a translator directs the beam from the electromagnetic radiation source to trace and to cure the photo-curable layer along a trace. In many embodiments, the translator moves the source in a plane offset and parallel to the planar surface defined by a photo-curable layer of a PCB to trace the waveguide geometry.

The translator may move the laser beam in one dimension parallel to the plane of the PCB to trace a linear waveguide segment (e.g., a waveguide segment with an infinite bend radius). The translator may also move the electromagnetic radiation source in two dimensions parallel to the plane of the PCB to trace a linear or non-linear waveguide segment. In many embodiments, the translator rotates the laser beam in response to the direction of translation to align the laser beam spot profile to the waveguide segment being traced. For example, the laser beam may be rotated continuously while tracing a continuous non-linear waveguide segment. A non-limiting example of aligning the laser beam spot profile to the waveguide segment is rotating the laser beam to align the respective widths of the laser beam spot profile and the waveguide segment as the orientation of the waveguide segment may rotate during a trace (e.g., a non-linear waveguide segment, a change in bend radius, or a change in translation direction in the plane).

The LDW process can provide comparable performance to photolithography for some waveguide segments depending on the waveguide geometry. However, a waveguide segment fabricated with an LDW process and including a finite bend radius can exhibit significantly decreased performance when compared to fabrication by photolithography due to exposure convolution inherent in the LDW process.

Optical losses depend at least partially on the geometry of the waveguide. For example, a waveguide having a bend radius at or near the critical bend radius may experience substantial optical losses. The critical bend radius relates to the critical angle for an optical ray of a signal transmitted through the waveguide along a propagation direction. The critical bend radius for an optical ray describes a radius at or above which the conditions for total internal reflection are satisfied and below which the waveguide may lose at least some signal energy, resulting in optical losses. The bend radius of a waveguide segment influences the angle of incidence for at least some optical rays of the signal. Depending on the critical angle, defined by the difference in the index of refractions of the core and cladding at the waveguide boundary, optical rays with an angle of incidence at or below the critical angle may satisfy the conditions for total internal reflection within the waveguide. On the other hand, angles above the critical angle may expel the optical ray out of the waveguide boundary. Thus, the critical bend radius for a waveguide depends on the particular geometry of the waveguide, such as the segment bend radius or the core width, which can affect optical losses.

Used herein, “convolution” expresses how the shape of one optical function is modified by the other optical function by integration. In one embodiment, a convolution expresses how the intensity distribution of a laser beam spot profile as applied to a photo-curable layer (the first optical function) is modified by the path of tracing a waveguide in the photo-curable layer over time (the second optical function) by integration. In other words, the convolution of these functions expresses the total sum of energy that the waveguide in the photo-curable layer is exposed to from the laser beam spot profile for each point of the waveguide, along its width and length, as the laser beam passes over the photo-curable layer to trace and cure the waveguide. This particular convolution is an example of “exposure convolution,” as used herein.

In some cases, exposure convolution can cause a waveguide with a linear and a non-linear segment to have uneven curing between the segments when written by an LDW process. For example, when tracing the non-linear waveguide segment having a finite bend radius, the photo-curable layer along the trace receives uneven total amounts of energy from the laser beam across its width. For example, an inner portion of the waveguide segment receives more total energy than a central portion, which receives more total energy than an outer portion of the waveguide. This is because the laser beam passes more quickly over the outer portion than the central portion, which passes more quickly over the central portion than the inner portion. The total energy received across the waveguide width will be different for the linear waveguide segment and the non-linear waveguide segment, and thus the curing profiles will also be different.

The total energy can be determined by integrating the distribution of the laser beam, directed onto the photo-curable layer during the trace, along the curved path of the laser beam over the time required to write the waveguide.

In various cases, exposure convolution can also cause a waveguide having only a linear waveguide segment or only a non-linear waveguide segment to have non-uniform curing when written by an LDW process. In many embodiments, a laser beam has a spot profile that is symmetric but varies in width along the shape profile of the spot profile (e.g., a circle has a variable width shape profile), varies in intensity across the waveguide width (e.g., a Gaussian beam spot has a variable intensity profile across the width), or both. In such embodiments, a linear waveguide segment being written will receive more total energy in the inner part of the waveguide width (e.g., central portion along the waveguide width) than the outer part of the waveguide width (e.g., side portions near the edges that flank the central portion). The result is a symmetric but uneven cure profile across the width of the waveguide segment corresponding to the variable shape profile of the laser beam spot profile across the spot profile width. This effect would also apply to writing a non-linear waveguide segment, which may be further compounded by the uneven total energy between the inner portion and the outer portion relative to the bend of the non-linear waveguide segment, as described in the foregoing.

Uneven and non-uniform curing may result in uneven refractive index profiles, uneven waveguide cross-sections, or both, which may contribute to optical losses, particularly as the bend radius for a waveguide segment approaches the critical bend radius. In some cases, the decrease in performance is exponentially proportional to the decrease in bend radius. A convolution compensator addresses the effect of exposure convolution by modifying the laser beam used to form the waveguide segment, which can improve cure profile accuracy and improve optical losses.

FIG. 1is a schematic diagram of an exemplary waveguide laser direct writing (LDW) system10capable of compensating for exposure convolution. The LDW system10includes an electromagnetic radiation source12, which is traced along a path14relative to a photo-curable layer16, to provide energy to cure a portion of the photo-curable layer to form a waveguide. In the illustrated embodiment, the photo-curable layer16has a planar surface for receiving energy from the source12. The photo-curable layer16may be one layer of an optical PCB, which also has other layers, such as a lower and upper waveguide cladding layer (e.g.,FIGS. 5-6).

A convolution compensator18is positioned in the path of a laser beam20emitted from the source12and optionally modifies the laser beam to compensate for exposure convolution. For example, the laser beam20defines a spot profile22, and when the laser beam20passes through the convolution compensator18, at least a portion of the laser beam is modified to define a modified beam portion23of the laser beam and to define a modified spot profile24different than the spot profile22.

The spot profiles22,24are two-dimensional cross-sections of the laser beam20parallel to the surface of the photo-curable layer16in the area wherein the photo-curable layer receives laser beam energy. In the illustrated embodiment, the spot profiles22,24are also orthogonal to the direction of beam propagation.

In various embodiments, the laser beam spot profile22is uniform in intensity distribution. In other embodiments, the laser beam spot profile22of the electromagnetic radiation source12is not uniform in intensity. Non-limiting examples of intensity profiles include a Gaussian distribution, a donut-shaped distribution, a half-dome or semi-circular distribution, or any of these passed through a spatial step filter, among others.

Used herein, “uniform intensity distribution” means less than 2% variation in intensity measured from the maximum intensity throughout the spot profile as received by the photo-curable layer16.

A translator (not shown) may be coupled to the source12to direct the source along the path14to trace a waveguide26(e.g., the waveguide core) in the photo-curable layer16with the laser beam20. In some embodiments, the translator moves the source12in a plane parallel to the surface of the photo-curable layer16. In many embodiments, the translator is a two-dimensional translator capable of tracing linear and non-linear paths to enable the formation of linear and non-linear segments of the waveguide26. In one embodiment, the translator is capable of rotating the laser beam20to align the laser beam spot profile22,24to the waveguide being traced.

In various embodiments, the convolution compensator18modifies an intensity profile, a shape of the spot profile22, or both. In some embodiments, the convolution compensator18modifies at least a portion of the laser beam20based on at least one geometric property of a waveguide26desired to be written. As described herein in more detail, when the photo-curable layer16is cured by the laser beam20, the LDW system10is capable of directing a consistent total amount of energy onto the photo-curable layer16while tracing and curing the waveguide26, in other words compensating for exposure convolution.

In at least one embodiment, the resulting waveguide26formed by LDW system10has a consistent waveguide cure profile along a length of the waveguide having multiple waveguide segments, even for segments in series having different bend radii. In at least some embodiments, the resulting waveguide26formed by LDW system10has a uniform waveguide cure profile along the length of each waveguide segment, whether linear or non-linear.

FIG. 2is a schematic time-lapse representation of a process30to form a waveguide126with a waveguide LDW system, such as system10(FIG. 1). In the illustrated embodiment, the process30begins with tracing a path14,14′ with a laser beam spot profile22at a constant speed over a surface of a photo-curable layer to selectively cure waveguide126. The laser beam cures a first segment28and then a second segment35with the same spot profile22for both segments. As shown, the spot profile22is not modified by the convolution compensator18(FIG. 1) between the first segment28and the second segment35to compensate for differences in geometry. As a result, the second segment35has a weighted, asymmetric cure profile and cross-sectional height profile (e.g., similar to cross-sectional shape indicated by top surface530ofFIG. 6) different than the first segment28.

The first segment28is a linear waveguide segment defining a lateral width50. The second segment35is a non-linear waveguide segment defining a lateral width55. As shown, the non-linear second segment35forms a bend. The non-linear second segment35defines an outer edge40and an inner edge45separated by the width55. The inner edge45is on the inner side of the bend opposite the outer edge40on the outer side.

As illustrated, the widths50,55are the same and consistent throughout the length of each respective segment. In other embodiments (not shown), the widths may be different between the segments, throughout a segment, or both.

The first segment28and the second segment35each have a different bend radius. As shown, the bend radius for the first segment28is infinite, which forms a linear segment. On the other hand, the non-linear second segment35has at least one bend radius that is finite.

In the illustrated embodiment, the non-linear portion of the path14′ comprises a single bend radius segment. However, the non-linear portion of the path14′ may have a plurality of bend radii, such as a graded bend segment described herein elsewhere.

Bend radii for a segment are defined between an origin point outside of the segment and a corresponding line parallel to the non-linear portion of the path14′. Because each segment has a width55, a segment will define more than one bend radius and will comprise a range of bend radii bounded by the bend radius R1and the bend radius R3. As illustrated, the first radius R1is defined from an origin point to a line along the inner edge45, the second radius R2is defined from the same origin point to a line following the path14′ along the center of the width55, and the third radius R3is defined from the same origin point to a line along the outer edge40. In the illustrated embodiment, radii R1and R3are offset by half of the width55of the segment35from R2. As used herein, bend radius60refers to the radius R2along the path14′ at the center of the width.

The process30forms the first and second segments28,35in a series arrangement. As shown, the laser beam with spot profile22traces and cures the linear first segment28and thereafter traces and cures the non-linear second segment35. In other words the segments28,35are arranged adjacent to, contiguous with, or essentially continuous end-to-end to each other. In other embodiments (not shown), the segments may not be adjacent, may be formed in different order, or both.

The spot profile22may be of any suitable shape described herein in more detail with respect toFIG. 11. In the illustrated embodiment, the laser beam spot profile22defines a circular shape and a uniform intensity profile. In other embodiments, the spot profile22defines a non-circular shape, a non-uniform intensity profile, or both.

When the writing process30translates the laser beam with this spot profile22at a constant speed along the linear and non-linear portions of the path14,14′, a consistent total energy amount is delivered via exposure convolution along the path14,14′ over the first segment28. As a result, the linear first segment28has a symmetric first cure profile throughout the length of the segment along the waveguide propagation direction and throughout the width of the segment transverse to the waveguide propagation direction.

On the other hand, the non-linear second segment35has an asymmetric second cure profile different than the first cure profile. As shown, the cure profile for the second segment35defines an increasing cure gradient along the width55from the outer edge40to the inner edge45. In other words, the second cure profile is weight-shifted, or has a center of gravity that is shifted, closer to the inner edge45, because different portions of the laser beam travel at different angular speeds65depending on the distance to the origin point (e.g., bend radius). As shown, a portion of the laser beam directed nearer the outer edge40moves more quickly than a portion of the laser beam directed nearer the inner edge45. Thus, an uneven total energy amount is delivered via exposure convolution to the non-linear second segment35, at least along the width55.

The cure profile of the first segment28is different than the cure profile of the second segment35, which has bend radius60different than the bend radius of the first segment28. In many cases, the inconsistency between cure profiles may contribute to optical losses due to refractive index mismatching during propagation, particularly between segments having different bend radii and in segments having a bend radii less than the critical bend radius.

FIGS. 3A and 3Bare schematic diagrams of an exemplary laser beam120with a uniform spot profile22and an exemplary convolution compensator118in position to modify the beam of corresponding cross-sectional profiles22,182,124. As illustrated, the laser beam120includes a first portion21having spot profile22, which is directed into the convolution compensator118. The laser beam120is passed through the convolution compensator118and at least a portion123of the laser beam is modified into modified spot profile124.

A user may determine desired or target curing profiles for the waveguide for fabrication with the dynamically reconfigurable convolution compensator118. In response, the intensity profile can be selectively modified. As illustrated, the spot profile22has a circular shape profile and a uniform intensity profile, although other shape or intensity profiles may be used (e.g., rounded rectangle). The convolution compensator118modifies the laser beam120to address any undesired effects of exposure convolution in response to a geometric characteristic, a laser beam spot profile characteristic, or both, for example. In many embodiments, the laser beam120is modified in response to at least one geometric property of the waveguide segment to be written, such as the bend radius of the segment, the width of the segment, the trace speed, the intensity of the laser beam, and the shape of the spot profile, among others. In some embodiments, the laser beam120is modified in response to at least one characteristic of the laser beam spot profile, such as a width of the spot profile, a shape profile along the width, and an intensity profile along the width, among others.

At trace speed, the convolution compensator118is operable to modify the laser beam120as needed in “real time” during a waveguide writing process, for example from the bend radius of the first segment28to the bend radius60of the second segment35. In many embodiments, the convolution compensator118is operable to modify the laser beam120in “real time” for graded bend segments having multiple incremental waveguide segments that are each a fraction of the total length of the graded bend segment and require a different beam modification for each incremental segment. As used herein, “real time” relates to the operable speed and responsiveness of the LDW system being sufficient to compensate for exposure convolution at trace speed.

The speed of translation in the waveguide writing process depends on many factors to fabricate a desirable waveguide. In an exemplary embodiment, the trace speed of the beam spot is about 8 mm/s to about 12 mm/s. In other embodiments, the trace speed is less than about 8 mm/s or, alternatively, greater than about 12 mm/s. The trace speed may also vary during the waveguide writing process depending on the desired characteristics of the waveguide.

In many embodiments, the convolution compensator118is further operable to dynamically modify the laser beam120to write segments having different bend radii for a continuous waveguide. In various embodiments, the laser beam120with the modified intensity profile124is directed onto a photo-curable layer to write a non-linear waveguide segment based on at least the bend radius of the segment.

In some cases, the resulting non-linear waveguide segment has a symmetric cure profile. In various cases, the non-linear waveguide has a cure profile that substantially matches the cure profile of the linear waveguide segment written with the laser beam120having the spot profile22. In many embodiments, when cure profiles have been substantially matched, the resulting waveguide segments exhibit substantially matching heights, refractive index profiles, or other waveguide segment characteristics.

Used herein, “substantially matching cure profiles” means less than about 2% variation in the amount of curing energy delivered to a corresponding point along the cross-sectional width of each waveguide segment being written.

In the illustrated embodiment, the modified intensity spot profile124is a simple linear gradient from an outer side140to an opposing inner side145suited for writing a single-bend radius, non-linear waveguide segment wherein the outer side140passes more quickly over a photo-curable layer than the inner side145while tracing. In other words, the convolution compensator118applies a decreasing intensity gradient from the outer side140to the inner side145to the intensity profile to modify spot profile22into modified spot profile124.

The exemplary convolution compensator118includes a reconfigurable filter180operable to modify the intensity profile of the laser beam spot profile22. The filter180may be configured by a user to be responsive to transitions between segments having different geometric properties, such as different bend radii, during an LDW writing process.

Various embodiments comprise a reconfigurable filter180capable of transitioning gradually from one graded density profile182. In an example embodiment, the reconfigurable filter180comprises a liquid crystal array capable of being reconfigured continuously from profile-to-profile. In other various embodiments, the reconfigurable filter180is capable of being reconfigured discretely from profile-to-profile marked by more abrupt transitions between profiles. However, it is to be understood that in some cases a plurality of intermediate profiles may be used such that each individual discrete transition is small enough to be considered continuous for purposes of the laser direct writing particular application.

In some embodiments, the reconfigurable filter180is a neutral density filter. In various embodiments, the neutral density filter has a graded density profile182from one end to an opposite end to modify the laser beam120from a uniform spot profile22to the graded intensity profile124. However, any suitable gradient profile capable of compensating for exposure convolution may be used. In one embodiment, the graded density profile180decreases in the direction that the intensity gradient of the modified intensity profile124increases.

In another example embodiment, the reconfigurable filter180is reconfigured by swapping neutral density filters with different density gradients corresponding to different bend radii. In one embodiment, the reconfigurable filter180swaps out all neutral density filters enabling the convolution compensator118to selectively modify or not modify the laser beam120.

In some embodiments, as the writing process transitions between writing a first waveguide segment and writing a second waveguide segment having different bend radii, the convolution compensator118concurrently transitions from one configuration to another configuration while the laser beam120continues to move at a constant speed. In some cases, the convolution compensator118gradually modifies the laser beam120between the bend radii in a continuous manner, for example, utilizing a reconfigurable filter180capable of transitioning gradually from profile-to-profile.

In other cases, wherein the convolution compensator118uses discrete states (e.g., not continuous, such as physically swapping filters), the waveguide may include a transition waveguide segment125(FIG. 4) between the first and second waveguide segments described herein in more detail.

FIG. 4is a schematic time-lapse representation of an exemplary process130to form a consistent waveguide226with a symmetric cure profile for use with a convolution compensator (e.g.,118ofFIG. 3A) and a uniform laser beam spot profile22. Many elements shown inFIG. 4are the same elements shown inFIG. 2and are numbered the same.

In the illustrated embodiment, the process130begins with tracing the path with a laser beam spot profile22at a constant speed over a surface of a photo-curable layer to selectively cure waveguide226. The laser beam with spot profile22cures a first segment28having width50. Then, the laser beam with modified spot profiles124,124′,124″ different than spot profile22cures a second segment135having outer edge40and inner edge45separated by width55.

As illustrated, the modified spot profiles124,124′,124″ have the same intensity and shape profiles. In many embodiments, the profiles are the same when the second segment135has a single bend radius. In other embodiments, the modified spot profiles124,124′,124″ are each different, for example, when the second segment135is a graded bend segment defined by multiple incremental segments and corresponding bend radii. Each spot profile depends on the corresponding bend radius.

The second segment135has a different bend radius than the first segment28. As shown, the second segment135is non-linear in the form of a bend defined by bend radius60, so portions of the laser beam travel at different speeds65(e.g., more quickly over the outer edge segment portions than the inner edge segment portions).

The modified spot profile124compensates for exposure convolution while tracing based on at least one geometric property of the second segment135, such as the bend radius60. As shown, the modified spot profile124includes a non-uniform intensity profile that increases from one side directed at inner edge segment portions to an opposing side directed at outer edge segment portions. The shape of the modified spot profile124retains a circular shape.

As a result of the process130, the second segment135has a cure profile that is desired and substantially matches the cure profile of the first segment28, which is symmetric and may improve optical losses in the waveguide226relative to waveguide126(FIG. 2). In some embodiments, the waveguide226may include a transition waveguide segment125between the first and second segments28,135.

In various embodiments, the transition waveguide segment125is formed by a non-continuous or discrete modification of the laser beam used to cure the waveguide. Generally, the longer the transition time or distance between configurations of the convolution compensator, the longer the transition waveguide segment125will be.

In many embodiments, the transition waveguide segment125has a linear length or arc length that is less than 10%, less than 5%, less than 1%, less than 0.5%, or less than 0.1% of the length of the first or second waveguide segment.

In some embodiments, the characteristics of the transition waveguide segment125, including physical dimensions, do not substantially impact the performance of the waveguide between the first and second waveguide segments. For example, the transition waveguide segment125may have a sufficiently short length or sufficiently small variation from the first and second segments28,135.

A waveguide, such as exemplary waveguide500having a convolution-compensated cure profile as shown inFIGS. 5-6, may be formed at least partly by process130, or any other process described herein. The waveguide500may be utilized in an optical board, such as exemplary optical board600inFIG. 5. In turn, the optical board may be utilized to form optical circuits or assemblies for various applications. In particular,FIG. 5shows a plan view of the optical board600showing the waveguide500extending from one edge to another edge of the board in a schematic representation. Alternatively,FIG. 5can be described as a partial view of an optical portion of a board600showing only a portion of a waveguide500, and the board600may include other waveguides or even non-optical components (e.g., electrical or electronic). From an elevation viewpoint,FIG. 6shows the waveguide500along a cross-section502.

In the illustrated embodiment, the waveguide500extends through the optical board600and includes a first segment having a first bend radius to a second segment having a second bend radius, similar to the waveguide226shown in FIG.4. In many embodiments, the cross-sectional profiles of the first and second segments may substantially match cross-section502shown inFIG. 6.

As shown along cross-section502, the waveguide500includes a waveguide core505, lower waveguide cladding510, and upper waveguide cladding515. In an exemplary LDW process, a photo-curable layer may be disposed on the lower cladding510and selectively cured via writing to form the waveguide core505. The uncured portion of the photo-curable layer may be removed. Then, the upper cladding515may be formed over the waveguide core505to surround the core with cladding. The waveguide core505defines a waveguide top or top surface520(e.g., upper surface) and one or more waveguide sides525, both being adjacent to the upper waveguide cladding515. The waveguide500may be described as a written waveguide.

In many embodiments, the waveguide core505has a different refractive index than the cladding510,515. As shown, the waveguide core505has a uniform refractive index profile across its width.

In the embodiment shown, the top surface520of the core505may not be substantially uniform in height. The top surface520may be described as non-planar. Thus, the height may vary along the top surface520in an amount greater than or equal to about 0.1%, to about 1%, to about 10%, to about 25%, or to about 50% of the maximum height of the core505. In various embodiments, the height varies along the top surface520in an amount preferably less than about 1%, less than about 5%, less than about 10%, or less than about 25% of the maximum height of the core505.

In many illustrative embodiments, a written waveguide500may exhibit characteristic markers of laser writing, which may distinguish the written waveguide from a waveguide formed by photolithography. Non-limiting examples include markers related to cross-sectional shape, for example, some of which are described herein. In at least some illustrative embodiments, the top surface520may include a non-uniform height portion and an optional uniform height portion. The non-uniform height portion may be adjacent to a uniform height portion. The non-uniform height portion may be adjacent to a side of the core505of the waveguide (e.g., waveguide side(s)525).

In the illustrated embodiment, the top surface520includes a substantially uniform height center portion and two non-uniform height outer portions, for example. The top surface520may define a maximum height. In at least some illustrative embodiments, the top surface520defines a maximum height toward the center of the cross-section, and the top surface520reduces in height proximal, or adjacent, to the one or more sides525. The reduction in height may define a rounded edge, for example. In other words, the top surface520may define a height profile, for the waveguide500or any segment of the waveguide, which may be described as extending along a width of the waveguide500or any segment of the waveguide.

A convolution compensator, such as any described herein, may be utilized to influence the cross-sectional shape of the waveguide500. For example, the non-uniform portion, or reduction in height, may be the result of curing with a laser beam having an intensity profile with higher intensity toward the center of the profile and a lower intensity toward the periphery. In at least one embodiment, the waveguide core layer may have been cured with a laser beam spot profile having a rounded rectangular shape profile (e.g., spot profile650ofFIG. 11B) or a circular shape with modified intensity profile (e.g., spot profile600ofFIG. 11A). In alternative embodiments (not shown), the waveguide core505has another non-linear shape, such as a half-dome or a Gaussian-like curve, for example, which may be caused by curing with a circular laser beam spot profile (e.g., spot profile22ofFIG. 3B).

In many illustrative embodiments, the waveguide sides525may indicate a written waveguide versus a photolithography-formed waveguide. For example, the waveguide sides525may define a width. The width may define a width profile, which may be described as extending along a height of the waveguide500or any segment of the waveguide. In many embodiments, the width profile may be substantially uniform. In other words, the sides525may be substantially parallel. The parallel sides may be formed due to the collimated nature of the electromagnetic radiation from a laser beam. This may differ from a waveguide formed by photolithography, which may include sloped sides due to diffraction effects of light passing a photolithography mask before being absorbed into the photo-curable layer.

Used herein, “substantially parallel” means the variation in distance between the sides505along the height is less than about 0.1%, less than about 1%, or less than about 5% of a maximum width between the sides. In some cases, the maximum width is located at the base of the waveguide core505adjacent to the lower cladding510.

In some illustrative embodiments, a transition waveguide segment may indicate a written waveguide, as described with respect toFIG. 4, for example. The transition waveguide segment may be disposed between two main segments (e.g., first segment28and second segment135ofFIG. 4). Perhaps as best shown inFIG. 5, a transition waveguide segment may be located in the waveguide500along a cross-section504. The transition waveguide segment may include a non-uniform top or non-uniform top surface530(e.g., upper surface) different than the uniform top surface520of corresponding main segments. In other words, the cross-sectional profile of the transition waveguide segment may differ from the cross-sectional profile of the main segments, such as the first segment or the second segment described herein elsewhere. This may differ from a waveguide formed by photolithography, which may utilize a substantially stationary, uniform, and consistent light-source to cure the photo-curable layer.

In the illustrated embodiment, the top surface530of the transition waveguide segment may resemble the top surface520modified by exposure convolution or resemble an artifact of transitioning the convolution compensator, transitioning the path of the laser beam, or both, for example. In many embodiments, the variation between the top surface of the transition waveguide segment and the top surfaces of the main segments is less than the variation would be between main segments having different bend radii formed by LDW without convolution compensation, which may be beneficial to improve optical loss.

An exemplary waveguide may be formed utilizing process230. As shown inFIG. 7, a schematic time-lapse representation of an exemplary process230may form a consistent waveguide326with a non-uniform cure profile using the exemplary convolution compensator (e.g.,118ofFIG. 3A) and a non-uniform laser beam spot profile222. Many elements shown are the same elements shown inFIG. 4and are numbered the same. However,FIG. 7differs in that the spot profile222used to cure the first segment228of the waveguide326has a non-uniform intensity profile, which is then modified by a convolution compensator to cure the second segment235. Although the spot profile222is not uniform, the convolution compensation steps are the same as used in process130.

As shown, the spot profile222is circular and has a Gaussian intensity profile decreasing in intensity from the center of the circle toward the perimeter. In some cases, the Gaussian intensity profile may be beneficial in forming a graded index polymer waveguide by LDW, such as in a photoaddressing process or others, which may improve modal dispersion and improve confinement of signal energy.

Exemplary process230begins with tracing the path with a laser beam spot profile222at a constant speed over a surface of a photo-curable layer to selectively cure waveguide326. The laser beam with spot profile222cures a first segment228having width50. Then, the laser beam with modified spot profile224different than spot profile222cures a second segment235having outer edge40and inner edge45separated by width55.

The second segment235has a different bend radius than the first segment228. As shown, the second segment235is non-linear in the form of a bend defined by bend radius60, so portions of the laser beam travel at different speeds65(e.g., more quickly over the outer edge segment portions than the inner edge segment portions).

The modified spot profile224compensates for exposure convolution while tracing based on at least one geometric property of the second segment235, such as the bend radius60. As shown, the modified spot profile224includes a non-uniform intensity profile that resembles a graded intensity profile that increases from one side directed at inner edge segment portions to an opposing side directed at outer edge segment portions, which is applied to the Gaussian intensity profile of spot profile222. The shape of the modified spot profile224retains a circular shape.

As a result of the process230, the second segment235has a cure profile that is desired and substantially matches the cure profile of the first segment228, which has a Gaussian distribution along the width55and may improve optical losses in the waveguide326relative to waveguide126(FIG. 2). In some embodiments, the waveguide326may include a transition waveguide segment between the first and second segments228,235similar to the transition waveguide segment125described with respect toFIG. 4.

FIGS. 8A and 8Bare schematic diagrams of an exemplary uniform laser beam320and another exemplary convolution compensator318in position to modify the beam and of corresponding cross-sectional profiles22,192,324. Convolution compensator318is similar to convolution compensator118. However, the convolution compensator318is configured to modify the shape of the spot profile22, whereas the convolution compensator118ofFIG. 3is configured to modify the intensity profile of the spot profile22.

In a manner similar to that described with respect to convolution compensator118, a laser beam320includes a first portion21having spot profile22, which is directed into the convolution compensator318and at least a portion323of the laser beam is modified to have a modified spot profile324. However, the spot profile22may be modified from a circular shape into a different, non-circular shape, shown as modified spot profile324. In the illustrated embodiment, the modified shape of the spot profile324resembles a gradual taper that narrows from an outer side340to an opposing inner side345, which is applied to the circular shape of the spot profile22. In other words, the convolution compensator318as illustrated applies a taper to the shape of the spot profile22.

The exemplary convolution compensator318includes an adaptive lens190having a cross-sectional area192larger than the spot profile22and operable to modify the shape of the laser beam spot profile22. The lens190may be configured by a user to be responsive to transitions between segments having different geometric properties, such as different bend radii, during an LDW writing process. In some embodiments, the adaptive lens190is an optofluidic lens. However, any suitable beamforming lens capable of compensating for exposure convolution may be used.

In various embodiments, the adaptive lens190is adaptable to various waveguide segment geometries by applying any number of electrical signals to the lens. The electrical signals may be continuously variable or discrete, for example. In one embodiment, the adaptive lens190is adaptable to pass a laser beam without reshaping the spot profile22, enabling the convolution compensator318to selectively modify or not modify the laser beam320.

In some embodiments, the transition of the convolution compensator318is discrete and not continuous from state-to-state and may result in the formation of a transition waveguide segment similar to transition waveguide segment125(FIG. 4).

FIGS. 9A and 9Bare a schematic diagrams of an exemplary uniform laser beam420and a further exemplary convolution compensator418in position to modify the beam and of corresponding cross-sectional profiles22,482,492,424. Similar toFIGS. 3A and 3B and 8A and 8B, a laser beam420includes a first portion21having spot profile22, which is directed into the convolution compensator418and at least a portion423of the laser beam is modified to have a modified spot profile424. However, the convolution compensator418is capable of modifying the intensity profile, the shape, or both of the spot profile22in a manner similar to those described with respect to convolution compensators118and318.

In the illustrated embodiment, the shape profile of the modified spot profile424resembles a gradual taper that narrows from an outer side440to an opposing inner side445, which is applied to the circular shape of the spot profile22being modified to have a graded intensity profile. In other words, the convolution compensator418applies a taper and an intensity gradient to spot profile22.

In various embodiments, the convolution compensator418provides a modified spot profile424that is narrower at the inner side445than outer side440but does not resemble the shape profile of spot profile22. In one example, the convolution compensator418modifies a circular shape to a rounded trapezoid shape. In another example, the convolution compensator418modifies a rounded rectangle to a rotated, rounded rectangle.

In some embodiments, the convolution compensator418includes a reconfigurable filter480having a graded density profile482(similar to reconfigurable filter180and profile182) and an adaptive lens490having a cross-sectional area492(similar to adaptive lens190and area192). Utilizing both the filter480and the lens490can increase the flexibility and performance of the convolution compensator418. In one example, the convolution compensator418is capable of compensating for even smaller bend radii or more rapid changes in bend radii (e.g., quicker transitions) than a convolution compensator having only one of the filter480and the lens490.

The convolution compensator418can selectively modify the intensity profile, the shape, or a combination thereof. Such modifications can also be concurrent, staggered, or a combination thereof. In one embodiment, the convolution compensator418cooperatively applies filter480to modify the intensity profile and applies the lens490to modify the shape of the spot profile22.

In one example, the transition of the filter480, the lens490, or both is discrete and not continuous from state-to-state and may result in the formation of a transition waveguide segment similar to transition waveguide segment125(FIG. 4). However, the convolution compensator418may transition more gradually between segments by staggering the transition of the filter480and the lens490for example.

In another example, the graded density profile482can be less accentuated than the graded density profile182(FIG. 3B) to achieve the same exposure convolution compensation by concurrently applying a taper with lens490to the spot profile22, which itself can be less accentuated than the taper provided by the adaptive lens190(FIG. 8A) to achieve the equivalent convolution compensation.

An exemplary waveguide may also be formed utilizing process430. As shown inFIG. 10, a schematic time-lapse representation of an exemplary process430may form a consistent waveguide426with a uniform cure profile using a convolution compensator (e.g.,418) and a uniform laser beam spot profile22′ having a rounded rectangular shape. Many elements shown are the same elements shown inFIGS. 4 and 7and are numbered the same.

In the illustrated embodiment, the process430begins with tracing the path with a laser beam spot profile22′ at a constant speed over a surface of a photo-curable layer to selectively cure waveguide426. The laser beam with spot profile22′ cures a first segment28having width50. Then, the laser beam with a modified spot profile424,424′,424″ different than spot profile22′ cures a second segment135having outer edge40and inner edge45separated by width55. Both the first segment28and the second segment135have substantially uniform cure profiles.

As can be seen, the spot profile22′ has a rounded-rectangular shape profile, which may have been modified by a convolution compensator from a circular shape profile to compensate for exposure convolution during tracing based on the shape or intensity of the laser beam spot profile. In the illustrated embodiment, the initial modified spot profile424is rotated one or more times as illustrated by modified spot profiles424′ and424″ while tracing the second segment135. In many embodiments, the modified spot profile424is rotated by a translator. In other embodiments, the modified spot profile424is apparently rotated by a convolution compensator by modifying the shape profile to simulate rotation by the translator.

As shown, the second segment135has a different bend radius than the first segment28. As shown, the second segment135is non-linear in the form of a bend defined by bend radius60, so portions of the laser beam travel at different speeds65(e.g., more quickly over the outer edge segment portions than the inner edge segment portions).

The modified spot profile424compensates for exposure convolution while tracing based on at least one geometric property of the second segment135, such as the bend radius60. As shown, the modified spot profile424defines a non-uniform intensity profile that decreases from the first side to the opposing second side and has a modified shape profile that resembles a gradual taper applied to the rounded-rectangular spot profile22′ that narrows from the first side to the opposing second side.

As a result of the process430, the second segment135has a cure profile that is desired and substantially matches the cure profile of the first segment28, which is uniform and may improve optical losses in the waveguide426relative to waveguide126(FIG. 2). In some embodiments, the waveguide426may include a transition waveguide segment between the first and second segments28,135similar to the transition waveguide segment125described with respect toFIG. 4, which may have more gradual transitions than transition waveguide segment125.

FIGS. 11A, 11B, 11C, and 11Dare schematic representations of exemplary laser beam spot profiles. In some embodiments, the spot profiles600,650,655,660represent spot profiles of a laser beam modified by a convolution compensator capable of modifying the intensity profile, the shape profile, or both to achieve a substantially uniform cure profile when writing a waveguide. In other embodiments, the spot profiles600,650,655,660represent the beam cross-sectional profile prior to modification by a convolution compensator. In yet further embodiments, each of the spot profiles600,650,655,660may be further modified by a convolution compensator, for example, to move from writing a linear waveguide segment to a non-linear waveguide segment or vice versa.

As used herein, “substantially uniform cure profile” means less than about 2% variation in the amount of curing energy delivered along the cross-sectional width of the waveguide segment being written.

Intensity profiles may be uniform or uneven, such as a gradient. Non-limiting examples of spot profile shapes include: a closed conic section, an oval, a polygon, any rounded corner versions thereof, any symmetric versions thereof, any asymmetric versions thereof, any combination of linear or non-linear lines to form an outer perimeter, any tapered versions thereof, any rotations thereof, or any combinations thereof. A polygon may be a triangle, a quadrilateral, a pentagon, a hexagon, and so forth. A symmetric version of a quadrilateral may be a square or a rectangle, for example, whereas an asymmetric version may be a trapezoid. An example of a symmetric version of a closed conic section may be a circle or an ellipse.

As illustrated, spot profile600includes a width605extending from a first side or outer side610to a second or inner side615opposite the first side, and a central portion620between a first outer portion625and a second outer portion630opposite the first outer portion. The shape profile is variable along the width (e.g., uneven or non-uniform), and the intensity profile is a variable gradient across the width. For example, the circular shape has less area in each outer portion per unit width than in the central portion (e.g., uneven across the width in area), which would result in an uneven cure profile due to the shape alone. However, the intensity of the central portion620is less than the intensity of the outer portions625,630, which compensates for the effects of the variable shape profile. Thus, in some cases, the spot profile600is useful to trace a linear waveguide segment, wherein the variable shape and intensity profiles balance along the width605to address the effects of exposure convolution and produce a substantially uniform cure profile.

Turning to spot profile650, the shape profile is a rounded rectangle, similar to spot profile22′ (FIG. 10). The shape profile of a rectangle is more uniform or even along the width (e.g., less variable) than the other spot profile600and may be substantially uniform. In addition, the intensity gradient is more uniform than the other spot profile600and may be substantially uniform. Similar to spot profile600, the spot profile650may be useful to trace a linear waveguide segment wherein the substantially uniform shape and intensity profiles balance along the width to address the effects of exposure convolution and produce a substantially uniform cure profile.

Referring now to spot profile655, the shape profile is a rounded rectangle, similar to the other spot profile650, which would result in an uneven cure profile for a non-linear waveguide segment. However, the intensity gradient is more uneven than spot profile650. As shown, the intensity gradient is higher in a first outer portion than the central portion and higher in the central portion than a second outer portion opposite the first outer portion. In contrast to the other spot profiles600,650, the spot profile655may be useful to trace a non-linear waveguide segment, wherein the substantially uniform shape profile and variable intensity profile balance along the width to address the effects of exposure convolution and produce a substantially uniform cure profile.

With regard to spot profile660, the intensity gradient is substantially uniform along the width similar to spot profile650. However, the shape profile is variable. As shown, the shape profile is a tapered, rounded rectangle (e.g., a rounded trapezoid) resembling a taper applied to spot profile650narrowing from an outer side to an inner side opposite the inner side. Similar to the spot profile655, the spot profile660may be useful to trace a non-linear waveguide segment, wherein the variable uniform shape profile and substantially uniform intensity profile balance along the width to address the effects of exposure convolution and produce a substantially uniform cure profile.

In many embodiments, a convolution compensator is capable of modifying the shape or intensity of any laser beam spot profile into another laser beam spot profile according to a characteristic of the cross-sectional profile (e.g., width, shape profile, or intensity profile), a characteristic of a waveguide segment (e.g., waveguide width or a bend radius of the current, previous, or subsequent waveguide segment to be written), or any combination thereof. In one example, a convolution compensator modifies a slightly Gaussian, circular laser beam cross-sectional profile (e.g., variable shape profile and slightly variable intensity profile) into spot profile650to trace a linear waveguide segment. To trace a subsequent non-linear waveguide segment, the convolution compensator modifies the spot profile650into spot profile660to compensate for exposure convolution caused by differing ben radii between the linear and non-linear waveguide segments.

It is noted that terms such as “top”, “bottom”, “above, “below”, etc. may be used in this disclosure. These terms should not be construed as limiting the position or orientation of a structure, but should be used as providing spatial relationship between the structures.

Embodiments of the a method, system, and apparatus for modifying the laser beam spot profile used to trace and cure the waveguide having segments with different bend radii to provide a consistent cure profile in the waveguide are disclosed. The implementations described above and other implementations are within the scope of the following claims. One skilled in the art will appreciate that the present disclosure can be practiced with embodiments other than those disclosed. The disclosed embodiments are presented for purposes of illustration and not limitation, and the present invention is limited only by the claims that follow.