Adaptive modal phase matching in waveguides for increased nonlinear conversion efficiency

Abstract

To solve the problem in which, localized thickness variations can change the phase matching condition needed to propagate light in a waveguide, thereby reducing efficiency of the waveguide.SOLUTION: To fabricate a waveguide with improved light coupling efficiency utilizing second order nonlinear optical coupling processes, localized thickness variations of at least one waveguide layer are first measured instead of assuming a constant thickness. The width of the waveguide is then fabricated based on the localized thickness variations in order to achieve a desired modal phase matching condition, for example, by finite element modeling. By doing so, the waveguide can improve light coupling efficiency by compensating for localized thickness variations during the fabrication process.SELECTED DRAWING: Figure 5

Description

[Technical Field]

[0001] (Statement regarding federally sponsored research and development) This invention was made with government support. The government has certain rights in this invention. [Background technology]

[0002] Mixing of second-order nonlinear waves in a waveguide is an important process for generating light of desired wavelengths that cannot be directly produced by lasers, as well as for generating entangled photons. Efficient power conversion in a waveguide for these processes depends on satisfying the phase-matching condition associated with the desired waveguide mode. In lithium niobate waveguides, (quasi-)phase matching can be achieved by periodic poling of the waveguide through a periodic polarization gradient. However, implementing periodic poling can be difficult and costly when fabricating lithium niobate waveguides.

[0003] During the manufacturing process, the thickness and width of a waveguide are assumed to be constant throughout the waveguide (unless it is intentionally tapered to allow for desired mode conversion). However, this assumption is not strictly valid because conventional manufacturing processes introduce localized, small-scale thickness variations within the waveguide. The spatial dimensions of the waveguide affect the phase-matching conditions associated with the waveguide. Thus, a waveguide with random thickness variations will introduce local variations in the phase-matching conditions required to generate the desired mode, causing the true local phase-matching conditions to deviate from the assumed constant phase-matching conditions. As a result, these thickness variations can reduce the power conversion efficiency for the desired mode and amplify the conversion of undesired “noisy” modes within the waveguide. In some situations, manufacturing defects can prevent devices implementing these waveguides from functioning properly. This problem is particularly pronounced for longer waveguides. Summary of the Invention

[0004] Details of one or more embodiments are set forth in the description below. Features shown or described in connection with one exemplary embodiment may be combined with the features of other embodiments. Accordingly, any of the various embodiments described herein can be combined to provide further embodiments. Aspects of the embodiments can be modified, as necessary, to employ concepts from any of the various patents, applications, and publications identified herein to provide still further embodiments.

[0005] In one embodiment, a method for fabricating a waveguide is disclosed. The method includes measuring local thickness variations of at least one waveguide layer. The at least one waveguide layer includes a second-order nonlinear optical medium. The method includes determining a correlation function for a given phase matching condition. The correlation function accounts for the measured local thickness variations, and the given phase matching condition is based on modal phase matching between two or more modes of light propagating in the waveguide. The method includes determining local widths of the waveguide. The local widths are determined from the correlation function and correspond to the measured local thickness variations. The method includes fabricating a width of the waveguide based on each of the local widths.

[0006] In another embodiment, a method for fabricating an optical system is disclosed. The method includes fabricating a waveguide by measuring local thickness variations of at least one waveguide layer. The at least one waveguide layer includes a second-order nonlinear optical medium. The waveguide is fabricated by determining a correlation function for a given phase matching condition. The correlation function accounts for the measured local thickness variations, and the given phase matching condition is based on modal phase matching between two or more modes of light propagating in the waveguide. The waveguide is fabricated by determining local widths of the waveguide. The local widths are determined from the correlation function and correspond to the measured local thickness variations. The waveguide is fabricated by fabricating a width of the waveguide based on each of the local widths. The method includes coupling the waveguide to a light source. The waveguide is configured to receive light from the light source. The method includes coupling the waveguide to an output coupler. The waveguide is configured to output light to the output coupler.

[0007] In yet another embodiment, a program product is disclosed. The program product includes a non-transitory processor-readable medium having program instructions embodied thereon configured to be executed by at least one processor. The at least one processor is configured to execute the program instructions to receive measurements of local thickness variations of at least one waveguide layer of a waveguide. The at least one waveguide layer includes a second-order nonlinear optical medium. The at least one processor is configured to determine a correlation function of a given phase matching condition. The correlation function takes into account the measured local thickness variations, and the given phase matching condition is based on modal phase matching between two or more modes of light propagating within the waveguide. The at least one processor is configured to determine a local width of the waveguide. The local width is determined from the correlation function and corresponds to the measured local thickness variations.

[0008] Other embodiments are also disclosed, as described below. [Brief explanation of the drawings]

[0009] Example embodiments are described with additional specificity and detail through the use of the accompanying drawings, as described below and in conjunction with the detailed description, with the understanding that the drawings depict example embodiments only and therefore should not be considered limiting in scope. [Figure 1] 1 illustrates an isometric view of an exemplary waveguide as described in one or more embodiments. [Figure 2] 1 illustrates a side view of a local thickness variation of a waveguide, as described in one or more embodiments. [Figure 3] 10 shows a graphical representation of the variation in measured thickness and the variation in the adaptive width of a waveguide as a function of position. [Figure 4] 3 illustrates a block diagram of a system configured to generate and output light according to the waveguides of FIGS. 1-2, as described in one or more embodiments. [Figure 5] 1 illustrates a flow diagram of a method for compensating for variations in measured local thickness of a waveguide, as described in one or more embodiments.

[0010] In accordance with common practice, the various features described are not drawn to scale but rather to emphasize particular features relevant to the exemplary embodiments. DETAILED DESCRIPTION OF THE INVENTION

[0011] In the following detailed description, reference is made to the accompanying drawings that form a part hereof, and in which are shown by way of illustration specific exemplary embodiments. It is to be understood, however, that other embodiments may be utilized and that logical, mechanical, and electrical changes may be made. Furthermore, the methods presented in the drawings and specification should not be construed as limiting the order in which individual steps may be performed. Therefore, the following detailed description is not to be construed in a limiting sense.

[0012] FIG. 1 depicts an isometric view of an exemplary waveguide 100 to which the techniques described in this disclosure may be applied. The waveguide 100 acts as a light transport medium, with light entering one end of the waveguide 100 and exiting at another end. A segment of the waveguide 100 is explicitly shown in FIG. 1 , and this segment can extend in three dimensions along its length, both into and out of the page. For educational purposes, the waveguide 100 is shown as a rectangular waveguide.

[0013] In some embodiments, as explicitly shown in FIG. 1 , the waveguide 100 comprises multiple layers 102, 104, and 106. Each layer 102, 104, and 106 may be made of a different material and perform a different function for the waveguide 100. Layer 106 is a substrate layer on which the base of the waveguide 100 is formed. The substrate layer 106 may be made of silicon or a silicon-based material. Above the substrate layer 106 is an intermediate layer 104. The intermediate layer may be made of a silicon-based material such as silicon dioxide and, depending on the embodiment, may propagate light entering either side of the waveguide 100 in different modes. Above the intermediate layer 104 is a top layer 102. Layer 102 is made of a second-order nonlinear optical medium such as lithium niobate. Depending on the embodiment, layer 102 converts light entering from either side of waveguide 100 from one mode to another so that the light propagates through intermediate layer 104 and is transmitted to top layer 102. Various nonlinear processes (also referred to as wave-mixing processes) can occur within waveguide 102, including optical frequency conversion, optical parametric amplification, optical parametric oscillation, and spontaneous parametric down-conversion.

[0014] To generate significant power output within waveguide 100 through a nonlinear process, an input optical mode interacts with the nonlinear medium of layer 102 through a nonlinear optical process to generate an output optical mode. It is advantageous to arrange for the optical phases of the input and output optical modes propagating within waveguide 100 to be phase-matched. While periodic poling can be used to create quasi-phase matching within waveguide 100, the optimal phase-matching condition is preferably true phase matching, which is created using modal phase matching. Modal phase matching offers distinct advantages by reducing the cost and complexity of fabricating waveguide 100 with the properties for generating a desired output wavelength from a given input wavelength during the manufacturing process.

[0015] The spatial parameters of the waveguide 100 are characterized by its length, width, and thickness in three dimensions. In FIG. 1 , the width w is defined as the space occupied by the waveguide 100 in the horizontal axis. Then, its thickness t is the space occupied in the vertical axis. Finally, the length l is the space occupied by the waveguide 100 in the third spatial axis (into and out of the page). For educational purposes, the width w, thickness t, and length l are defined relative to the top layer 102, but they can also be defined for the entire waveguide 100, including all of its layers 102, 104, and 106. During the manufacturing process, the top layer 102 is constructed after the fabrication of the other layers 104 and 106, and the thickness t of the top layer 102 is created before completing the width w.

[0016] Although FIG. 1 depicts the waveguide 100 as a perfect rectangle, in reality, inherent imperfections exist in the thickness t due to manufacturing imperfections in the thin-film material comprising the top layer 102 (see FIG. 2 ). That is, although not readily discernible, small variations exist on the inner and / or outer surfaces of the top layer 102 that describe horizontal lines defining the thickness t that are not “straight” as depicted in FIG. 1 . These variations or fluctuations distort the local thickness of the waveguide 100 from the average thickness of the source film from which the waveguide is fabricated. Furthermore, these variations are localized throughout the inner and / or outer surfaces of the top layer 102 such that the true thickness of the waveguide 100 is no longer constant but, in fact, varies spatially as a function of position (e.g., along the length l). As noted above, if not accounted for, these local thickness variations can adversely affect the quality of phase matching achieved within the waveguide 100.

[0017] To accommodate inherent variations in thickness t of waveguide 100, width w is optimally adjusted based on the spatially varying thickness of second-order nonlinear material layer 102. As a result, as depicted in FIG. 1 , width w of fabricated waveguide 100 is not perfectly straight or constant, but varies spatially along length l of waveguide 100 according to the correlated local thickness variations. The resulting waveguide 100 retains improved power conversion efficiency for desired modes while reducing the adverse effects of noisy modes being enhanced by uncompensated thickness variations.

[0018] FIG. 2 depicts a side view of local thickness variations in the waveguide 100. During fabrication of the thin film containing layer 102, these local thickness variations are introduced into the top layer 102 such that the thickness t is not constant but is actually a spatially dependent variable. As shown in FIG. 2, four different thicknesses are depicted along different locations of the waveguide layer 102. The first thickness is identified as t1 at local point l1. Further along the length, the thickness increases to t2 at local point l2, then decreases slightly to t3 at point l3. At l4, the thickness increases slightly again to t4. While the four thicknesses are depicted in FIG. 2 simply, the variations are not necessarily drawn to scale and are intended to visualize the spatial variations in the thickness of the waveguide layer 102. The thickness of the waveguide layer 102 may deviate in other respects from the simplified depiction shown in FIG. 2. The thickness can also be evaluated in a pseudo-microscopic manner at additional points along the waveguide layer 102 .

[0019] To determine the thickness at each local point along the waveguide layer 102, the thickness is empirically measured via reflectometry or other distance measurement techniques. Once the local thicknesses along the waveguide layer 102 have been determined, they are input into a numerical model to determine the electromagnetic properties of the waveguide 100 to satisfy the phase matching conditions of the desired modes. As a result of the numerical analysis, a corresponding width associated with each local thickness within the waveguide layer 102 that satisfies the applicable phase matching conditions is determined. Instead of maintaining a constant width based on a constant assumed thickness, the width of the waveguide layer 102 also varies locally, with each local width variation depending on the corresponding local thickness.

[0020] 3 shows a graphical representation of the variation in measured thickness and the variation in the adaptive width of a waveguide as a function of position. In particular, two correlation graphs 300A, 300B are illustrated in FIG. 3. Graph 300A illustrates the measured thickness (vertical axis) of the waveguide 100 as a function of the position / length (horizontal axis) of the waveguide 100. Graph 300B illustrates the determined local width (vertical axis) of the waveguide 100 at each position / length (horizontal axis).

[0021] Referring to graph 300A, the thickness is measured along the length of waveguide 100, thereby obtaining the local thickness variation. In graph 300A, the thickness varies between values ​​of approximately 29.9 microns and 30.1 microns, or a spatially dependent perturbation of approximately 0.2 microns relative to the assumed thickness of waveguide 100. As illustrated in graph 300A, the measured thickness varies over a length of substantially 1 centimeter. Particularly for longer waveguides, the thickness variation illustrated in graph 300A can significantly degrade the total power conversion efficiency of the desired mode throughout the waveguide.

[0022] Referring now to graph 300B, the width of the fabricated waveguide is varied to compensate for the measured thickness variations. In some embodiments, a numerical model executed by one or more processors is used to approximate a solution to Maxwell's equations based on the spatial dimensions and other characteristics of the waveguide 100, including the measured thickness variations. For example, the width can be generated from finite element modeling, finite difference modeling, and other numerical schemes. Since the desired modes to be supported by the waveguide 100 are known, an output can be generated and adjusted to determine a width that achieves the desired phase-matching condition.

[0023] As a result, as shown in graph 300B, the width of the waveguide also includes local width variations associated with the measured thickness variations. For example, referring to the correlation between graphs 300A and 300B, as the local thickness of the waveguide 100 decreases, the corresponding width of the waveguide 100 generally increases, and vice versa. However, depending on the characteristics of the waveguide and the desired mode, the width may otherwise vary relative to the measured local thickness variations.

[0024] 4 illustrates a block diagram of an exemplary photonics circuit 400 configured to generate and output light. The photonics circuit 400 may be implemented partially or entirely on a photonics chip. The photonics circuit 400 further includes a signal source 410 and an output coupler 412, which may be optically coupled by a waveguide and / or free-space optics.

[0025] Signal source 410 may include a signal-generating device, such as a laser, configured to transmit light through photonics circuit 400. The light generated by signal source 410 is received by waveguide 100, as described in conjunction with Figures 1-3 and which may include multiple waveguide layers. Waveguide 100 converts the light to a selected mode that is phase-matched via modal phase-matching techniques.

[0026] The light is then transmitted to output coupler 412. Output coupler 412 is configured to transmit the light through or out of photonics circuit 400. In some embodiments, output coupler 412 transmits the light into free space to be received by another detector, such as a satellite or photonics system located remotely from signal output coupler 412. In some embodiments, output coupler 412 can be signal emission optics, such as one or more lenses (e.g., ball lenses, gradient index (GRIN) lenses, etc.), polarizers, splitters, or other optical components. In some embodiments, the light output from output coupler 412 is utilized in conjunction with other optical functions, such as spectral filtering or mode conversion.

[0027] 5 depicts a flow diagram of a method 500 for compensating for variations in measured local thickness of a waveguide. Method 500 may be implemented via the techniques described with respect to FIGS. 1-4, but may also be implemented via other techniques. The blocks of the flow diagram are arranged generally sequentially for ease of explanation. However, it should be understood that this organization is merely exemplary, and that the processing associated with the methods described herein (and the blocks shown in the figures) may occur in a different order (e.g., at least some of the processing associated with the blocks may be performed in a parallel and / or event-driven manner).

[0028] The method 500 includes measuring the local thickness of the waveguide at block 502. In one example, the top layer 102, a second-order nonlinear optical medium, is deposited on an optical substrate at a relatively constant thickness. However, even with the best manufacturing techniques, local thickness variations exist in the top layer 102. Therefore, high-precision reflectometry or other distance measurement techniques are used to observe the local thickness variations of the waveguide layer.

[0029] Method 500 proceeds to block 504, where it calculates a correlation function for a given phase-matching condition. In some embodiments, the correlation function is a transfer function determined by finite element modeling or other numerical approximation techniques to determine the electromagnetic field distribution within the waveguide. Once the correlation function is determined, method 500 then proceeds to block 506, where it determines a local width of the waveguide corresponding to the measured local thickness variation. For example, the variation in the waveguide width can be determined by correlating the local thickness variation for a given modal phase-matching condition from the transfer function. Blocks 502-506 can be performed by one or more processors. When performing method 500, the degree of thickness variation can be compensated for during manufacturing to maintain the desired phase-matching condition.

[0030] Additionally, optionally, method 500 includes, at block 508, fabricating the width of the waveguide based on each local width determined by block 506. This step can be performed utilizing a suitable fabrication technique, such as waveguide etching, that is sensitive enough to realize the width variations determined in block 506. Block 508 is identified as optional because fabrication of the waveguide can be performed independently of, and by a separate entity, the processing and modeling that includes characterizing the waveguide.

[0031] The methods and techniques described herein may be implemented in part in digital electronic circuitry, or in a programmable processor (e.g., a special-purpose processor or a general-purpose processor such as a computer), firmware, software, or various combinations of each. Apparatus embodying these techniques may include suitable input and output devices, a programmable processor, and a storage medium tangibly embodying program instructions for execution by the programmable processor. Processes embodying these techniques may be performed by the programmable processor executing a program of instructions to perform the desired functions by operating on input data and generating appropriate output. The techniques may advantageously be implemented in one or more programs executable on a programmable system including at least one programmable processor coupled to receive data and instructions from, and transmit data and instructions to, a data storage system, at least one input device, and at least one output device. Generally, the processor receives instructions and data from a read-only memory and / or a random-access memory. Storage devices suitable for tangibly embodying computer program instructions and data include all forms of non-volatile memory, including, by way of example, semiconductor memory devices such as erasable programmable read-only memory (EPROM), electrically-erasable programmable read-only memory (EEPROM), and flash memory devices, magnetic disks (internal hard disk or removable disk), magneto-optical disks, etc. Any of the foregoing may be supplemented by, or incorporated in, specially-designed application-specific integrated circuits (ASICs). [Example]

[0032] Example 1 includes a method for fabricating a waveguide, the method including: measuring local thickness variations of at least one waveguide layer, at least one waveguide layer comprising a second-order nonlinear optical medium; determining a correlation function of a given phasematching condition, the correlation function taking into account the measured local thickness variations, the given phasematching condition being based on modal phasematching between two or more modes of light propagating in the waveguide; determining local widths of the waveguide, the local widths determined from the correlation function and corresponding to the measured local thickness variations; and fabricating a width of the waveguide based on each of the local widths.

[0033] Example 2 includes a method according to Example 1, in which the fabricated waveguide achieves a given phase-matching condition.

[0034] Example 3 includes the method of example 1 or 2, wherein the local width of the waveguide includes a local width variation.

[0035] Example 4 includes the method of any one of Examples 1-3, wherein as the measured local thickness variation decreases in thickness, the corresponding local width increases, and as the measured local thickness variation increases in thickness, the corresponding local width decreases.

[0036] Example 5 includes the method of any one of Examples 1-4, wherein the width of the waveguide is fabricated according to the measured local thickness variation to maintain a given phase matching condition satisfied along the length of the waveguide.

[0037] Example 6 includes the method of any one of examples 1-5, wherein the correlation function is a transfer function between a local thickness variation of at least one waveguide layer and a determined local width of the waveguide.

[0038] Example 7 includes the method of example 6, wherein the transfer function is generated from a finite element model.

[0039] Example 8 includes a method for manufacturing an optical system, the method including: measuring local thickness variations of at least one waveguide layer, at least one waveguide layer comprising a second-order nonlinear optical medium; determining a correlation function of a given phasematching condition, the correlation function taking into account the measured local thickness variations, the given phasematching condition being based on modal phasematching between two or more modes of light propagating in the waveguide; determining local widths of the waveguide, the local widths determined from the correlation function and corresponding to the measured local thickness variations; fabricating a width of the waveguide based on each of the local widths; coupling the waveguide to a light source, the waveguide configured to receive light from the light source; and coupling the waveguide to an output coupler, the waveguide configured to output light to the output coupler.

[0040] Example 9 includes the method of example 8, wherein the light source is configured to generate light in a first mode in the waveguide, and the waveguide is configured to convert the light in the first mode to a second mode and output the light in the second mode to the output coupler.

[0041] Example 10 includes the method of example 8 or 9, wherein the waveguide, the light source, and the output coupler are implemented in a photonics circuit.

[0042] Example 11 includes the method of any one of Examples 8-10, wherein as the measured local thickness variation decreases in thickness, the corresponding local width increases, and as the measured local thickness variation increases in thickness, the corresponding local width decreases.

[0043] Example 12 includes the method of any one of examples 8-11, wherein the width of the waveguide is fabricated according to the measured local thickness variation to maintain a given phase-matching condition satisfied along the length of the waveguide.

[0044] Example 13 includes the method of any one of examples 8-12, wherein the correlation function is a transfer function between a local thickness variation of at least one waveguide layer and a determined local width of the waveguide.

[0045] Example 14 includes the method of example 13, wherein the transfer function is generated from a finite element model.

[0046] Example 15 includes a program product including a non-transitory processor-readable medium having program instructions embodied thereon configured to be executed by at least one processor, wherein by executing the program instructions, the at least one processor is configured to: receive measurements of local thickness variations of at least one waveguide layer of a waveguide, the at least one waveguide layer including a second-order nonlinear optical medium; determine a correlation function of a given phasematching condition, the correlation function taking into account the measured local thickness variations, the given phasematching condition being based on modal phase matching between two or more modes of light propagating in the waveguide; and determine a local width of the waveguide, the local width being determined from the correlation function and corresponding to the measured local thickness variations.

[0047] Example 16 includes the program product of Example 15, wherein as the measured local thickness variation decreases in thickness, the corresponding local width increases, and as the measured local thickness variation increases in thickness, the corresponding local width decreases.

[0048] Example 17 includes the program product of any one of Examples 15-16, wherein the correlation function is a transfer function between the local thickness variation of at least one waveguide layer and the determined local width of the waveguide.

[0049] Example 18 includes the program product of example 17, wherein the transfer function is generated from a finite element model.

[0050] Example 19 includes the program product of any one of Examples 15-18, wherein the received local thickness variation measurements correspond to measurements received from a reflectometer.

[0051] Example 20 includes the program product of any one of Examples 15-19, wherein at least one processor provides a local width-based control signal to a manufacturing system for manufacturing the waveguide.

[0052] Although specific embodiments have been illustrated and described herein, those skilled in the art will recognize that any configuration which is expected to achieve the same purpose may be substituted for the specific embodiments shown. Therefore, it is manifestly intended that this invention be limited only by the claims and the equivalents thereof.

Claims

1. 1. A method for fabricating a waveguide, comprising: measuring local thickness variations of at least one waveguide layer, wherein the at least one waveguide layer comprises a second-order nonlinear optical medium; determining a correlation function for a given phase matching condition, the correlation function taking into account the measured local thickness variations, the given phase matching condition being based on modal phase matching between two or more modes of light propagating in the waveguide; determining a local width of the waveguide, the local width being determined from the correlation function and corresponding to the measured local thickness variation; and fabricating a width of the waveguide based on each of the local widths.

2. 2. The method of claim 1, wherein as the measured local thickness variation decreases in thickness, the corresponding local width increases, and as the measured local thickness variation increases in thickness, the corresponding local width decreases.

3. 2. The method of claim 1, wherein the width of the waveguide is fabricated according to the measured local thickness variations to maintain the given phase-matching condition satisfied along the length of the waveguide.

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