High-density integrated optical waveguide

Abstract

A high-density integrated optical waveguide. The optical waveguide is provided on a waveguide substrate, and comprises a plurality of curved waveguides; a rectangular coordinate system is established

Description

[0001] This application claims the priority to the Chinese Application No. 202010690095.X, filed with the Chinese Patent Office on July 17, 2020 and entitled "HIGH-DENSITY INTEGRATED OPTICAL WAVEGUIDE", which is incorporated herein by reference in its 5 entirety. FIELD OF THE INVENTION

[0002] The present disclosure relates to a field of integrated photonics, and in particular, to a high-density integrated optical waveguide. BACKGROUND OF THE INVENTION 10

[0003] As the modem Internet of Things, big data, and the like rise, demand of the human society for information processing with a higher speed, a larger broadband network capacity, stronger confidentiality, and the like has increased dramatically, and electrical chips have obviously reached a bottleneck stage. Similar to the development idea of integrated circuits, an integrated optical chip system may be formed to achieve a certain function by integrating two or 5 more discrete optical elements on a small substrate (below centimeter scale). The integrated optical chip system is expected to be a promising development direction for large-capacity and high-rate information systems due to advantages of high speed, low power consumption, and high-density integration.

[0004] Moreover, silicon on insulator (SOI) has become one of the most widely used platforms 20 in integrated photonics. On this basis, many photonic devices with a wide range of applications have been developed, such as waveguides and directional couplers. However, in a high-density integrated chip, existence of diffraction limit aggravates crosstalk between the elements, thereby limiting further improvement of chip integration. On the other hand, these integrated photonic devices generally are sensitive to structure and wavelength. Therefore, it is an urgent problem to 25 be resolved in the current industry of chips how to realize crosstalk-free transmission and broadband coupling of signals within a broadband in a high-density integrated chip.

[0005] Regarding low-crosstalk transmission, there are mainly two means at present. The first 18 02 25 means is to regulate a waveguide width to increase mode mismatch, thereby reducing crosstalk. For this means, the waveguide width needs to be designed. The second means is to insert several auxiliary small waveguides between waveguides, to reduce crosstalk by reducing a waveguide mode width. As the auxiliary waveguide is usually small in size, this means is also a challenge 5 for large-scale fabrication. Regarding broadband coupling, there are two mainstream schemes at present. One scheme is to introduce a compensation process of a Mach-Zehnder interferometer, where phases on one arm of the interferometer may be adjusted through thermal effects, electrooptic effects, and the like, to achieve dynamic modulation of a coupling distance; however, for large-scale integration, power is consumed more, a technical difficulty is greater, and size is larger. 10 The other scheme is to adopt a heat insulation design. Similarly, by using this scheme, it is also larger in size. In addition, there are several other schemes, such as a design of using surface Plasmon. Through this scheme, a size of a device may be reduced, but greater metal losses may be generated. A design of asymmetric waveguides may also be adopted. Regarding this scheme, losses are not large, the size is also small, but improvement of the bandwidth is limited. Recently, 5 it is reported that an erasable directional coupler may be achieved based on the use of a localized laser annealing process, which does provide a solution for on-demand fabrication. However, more losses are inevitably generated and the whole process is made more complicated. In view of the foregoing demand background and state of the art, it can be seen that integrated chips at present stay in a design paradigm dominated by straight waveguides. In terms of important performance 20 indicators such as high-density integration, low crosstalk, high efficiency, robustness, and broadband, satisfaction of some performances inevitably results in loss in some of other performances. As a result, existing integrated chips mainly based on straight waveguides cannot get rid of sensitivity to and dependence on parameters such as waveguide gap and wavelength under high-density integration. It is a long-standing goal pursued by researchers in the field of 25 integrated optics technologies how to achieve an integrated device with all of high-density integration, low crosstalk, high efficiency, robustness, and broadband. SUMMARY OF THE INVENTION

[0006] An objective of the present disclosure is to provide a high-density integrated optical waveguide, to resolve a problem that existing integrated chips mainly based on straight 30 waveguides cannot get rid of sensitivity to and dependence on parameters such as waveguide gap 18 02 25 and wavelength under high-density integration.

[0007] To achieve the foregoing objective, the present disclosure provides the following solutions.

[0008] A high-density integrated optical waveguide, where the optical waveguide is disposed 5 on a waveguide substrate and includes a plurality of curved waveguides;

[0009] where on the basis of a rectangular coordinate system established by taking a curve direction of the curved waveguide as a y axis and taking a propagation direction of light as an x axis, the curved waveguide is periodically curved in the curve direction along the propagation direction; and 10

[0010] the plurality of curved waveguides are arranged in parallel along the y-axis direction and are perpendicular to the y-axis direction to form a curved-waveguide array, where an optical-waveguide signal transmission function or an optical-waveguide directional coupling function of the optical waveguide is realized by providing a coupling coefficient between the curved waveguides. 5

[0011] The coupling coefficient between the curved waveguides is provided based on a curve amplitude and a curve period of the curved waveguide, an incident wavelength of incident light, a refractive index of the waveguide substrate, and a periodic interval of the curved waveguide.

[0012] The coupling coefficient between the curved waveguides has an expression: c^o / o^u^no^ / PA), where 20

[0013] c represents the coupling coefficient between the curved waveguides; co represents a coupling coefficient between the first straight waveguide array or a coupling coefficient between the second straight waveguide array with co>O; A represents the curve amplitude; P represents the curve period; drepresents the periodic interval at which the waveguides are arranged, and satisfies d=w+gap; ir represents a waveguide width; gap represents a gap between the waveguides; A 25 represents the incident wavelength; and no represents a refractive index of the substrate.

[0014] Jo{^An^JPP) is made less than 0, and the coupling coefficient is less than 0, and the optical waveguide further includes a first straight waveguide array and a second straight waveguide array;

[0015] the first straight waveguide array includes a plurality of first straight waveguides 30 arranged in parallel along the y axis; the second straight waveguide array includes a plurality of 18 02 25 second straight waveguides arranged in parallel along the y axis; and a coupling coefficient between the first straight waveguides is equal to that between the second straight waveguides, and both the coupling coefficient between the first straight waveguides and the coupling coefficient between the second straight waveguides are greater than 0; 5

[0016] an output end of the first straight waveguide array is connected to an input end of the curved-waveguide array; an output end of the curved-waveguide array is connected to an input end of the second straight waveguide array; the first straight waveguide array, the curved-waveguide array and the second straight waveguide array form a three-stage cascade structure; the incident light enters the three-stage cascade structure from an input end of the first straight 10 waveguide array, the incident light is dispersed in the first straight waveguide array by coupling, the curved-waveguide array re-converges dispersed light to the second straight waveguide array by negative coupling; and by match between positive coupling strength and the negative coupling strength in the three-stage cascade structure, the optical-waveguide signal transmission function with low crosstalk for broadband is realized. 5

[0017] Optionally, the optical waveguide includes a plurality of three-stage cascade structures, and the plurality of three-stage cascade structures are arranged in parallel along an x-axis direction.

[0018] Optionally, Jo(4ti2Anod / PP) is made equal to 0, the coupling coefficient is equal to 0, and the incident light is transmitted in the curved-waveguide array, to realize the optical-waveguide signal transmission function with low crosstalk for broadband. 20

[0019] Optionally, Jo(4Tt2AnodlPX) is made less than 0 and the coupling coefficient is less than 0; the curved-waveguide array specifically includes two curved waveguides, and the two curved waveguides are arranged in parallel along the y-axis direction, to realize the optical-waveguide directional coupling function for broadband.

[0020] Optionally, periodic curve of the curved waveguide is expressed by: 25 y(x)=Azos(2wdP+(i)), where

[0021] y(x) represents a periodic curve function for the curved waveguide, A representing the curve amplitude, P representing the curve period, and (p representing a curve initial phase.

[0022] According to the specific embodiments provided in the present disclosure, the present disclosure discloses following technical effects. The present disclosure provides a high-density 30 integrated optical waveguide, where a plurality of curved waveguides are disposed on the 18 02 25 waveguide substrate, to form a curved-waveguide array. The optical-waveguide signal transmission function or the optical-waveguide directional coupling function of the optical waveguide is realized by adjusting the coupling coefficient between the curved waveguides.

[0023] According to the present disclosure, low-crosstalk transmission and robust coupling of 5 broadband under high-density integration is realized by using regulation and control of the curved waveguide for coupling, quite good robustness to structural deviation and wavelength variation are exhibited, and tolerance for fault tolerance in processing is improved. In this way, processing costs are saved.

[0024] Meanwhile, the optical waveguide provided in the present disclosure does not need to 10 be further adjusted and corrected after processing, thereby avoiding extra energy consumption and losses; is fully compatible with the current manufacturing process, without bringing in additional processing difficulties; and is easy for large-scale production with low requirements on production accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] To describe the technical solutions of the embodiments of the present disclosure or technical solutions in the prior art to be more clear, the accompanying drawings used for the embodiments are briefly described below. Apparently, the accompanying drawings stated below are merely some examples for the present disclosure, and other accompanying drawings may also be derived by one of ordinary skills in the art according to these accompanying drawings without 20 an effective effort.

[0026] FIG. 1 is a schematic diagram illustrating a positive-coupling straight-waveguide array and a negative-coupling curved-waveguide array that are cascaded for realizing broadband optical waveguide transmission with low crosstalk;

[0027] FIG. 2 is a schematic diagram illustrating a zero-coupling curved-waveguide array for 25 realizing broadband optical waveguide transmission with low crosstalk;

[0028] FIG 3 is a schematic diagram illustrating a negative-coupling curved waveguide for realizing optical-waveguide directional coupling with robustness and broadband;

[0029] FIG. 4 is a schematic diagram illustrating a straight-waveguide array with 7V waveguides and a curved-waveguide array with N waveguides; 30

[0030] FIG 5 is a schematic diagram illustrating a three-stage cascade structure with two 18 02 25 straight-waveguide arrays and a curved-waveguide array being cascaded together;

[0031] FIG 6 is a schematic diagram illustrating connection of a curved waveguide, at a respective initial phase <p=Q and (p=n, with a straight waveguide;

[0032] FIG. 7 is a diagram illustrating a relation of a coupling coefficient c between waveguides 5 varying with wavelength for a cascade structure at different curve amplitudes A=Q pm and J=0.74 pm;

[0033] FIG. 8 is a diagram illustrating a relation of transmission efficiencies of a transmission port and a crosstalk port varying with wavelength for a cascade structure with N=2\

[0034] FIG. 9 is a schematic diagram illustrating an optical field in a waveguide propagated for 10 100 pm and 200 pm under corresponding different wavelengths in a cascade structure;

[0035] FIG. 10 is a diagram illustrating a relation of transmission efficiencies of a transmission port and a crosstalk port varying with wavelength for a cascade structure with A-7;

[0036] FIG 11 is a schematic diagram illustrating a corresponding optical field propagated for 100 pm under different wavelengths in a cascade structure; 5

[0037] FIG. 12 is a diagram illustrating a relation of a coupling coefficient c between waveguides varying with wavelength for a zero-coupling curved waveguide with a curve amplitude of A=0.51 pm;

[0038] FIG. 13 is a diagram illustrating a relation of transmission efficiencies of a transmission port and a crosstalk port varying with wavelength for zero-coupling curved waveguides with N=2\ 20

[0039] FIG. 14 is a schematic diagram illustrating an optical field in a waveguide propagated for 100 pm under corresponding different wavelengths for a zero-coupling curved waveguide;

[0040] FIG. 15 is a diagram illustrating a relation of transmission efficiencies of a transmission port and a crosstalk port varying with wavelength for zero-coupling curved waveguides with N=T;

[0041] FIG. 16 is a schematic diagram illustrating a corresponding optical field propagated for 25 100 pm under different wavelengths for a zero-coupling curved waveguide;

[0042] FIG 17 is a diagram illustrating a relation of a coupling coefficient c between waveguides varying with wavelength at different curve amplitudes A;

[0043] FIG. 18 is a diagram illustrating a relation of coupling degree varying with wavelength;

[0044] FIG. 19 is a diagram illustrating a relation of isolation degree varying with wavelength; 30

[0045] FIG. 20 is a diagram illustrating a relation of directivity varying with wavelength; 18 02 25

[0046] FIG. 21 is a schematic diagram illustrating propagation of an optical field in a waveguide under different wavelengths for a straight waveguide;

[0047] FIG. 22 is a schematic diagram illustrating propagation of an optical field in a waveguide under different wavelengths for a curved waveguide; 5

[0048] FIG. 23 is a diagram illustrating a relation of a coupling coefficient c between waveguides varying with waveguide gap at different curve amplitudes A\

[0049] FIG. 24 is a diagram illustrating a relation of coupling degree varying with waveguide gap;

[0050] FIG. 25 is a diagram illustrating a relation of isolation degree varying with waveguide 10 gap;

[0051] FIG. 26 is a diagram illustrating a relation of directivity varying with waveguide gap;

[0052] FIG. 27 is a diagram illustrating propagation of an optical field in a waveguide under different waveguide gaps for a curved waveguide; and

[0053] FIG. 28 is a diagram illustrating propagation of an optical field in a waveguide under 5 different waveguide gaps for a curved waveguide.

[0054] Explanation of reference signs: 1 indicating a cascade structure of a straight waveguide and a curved waveguide (including multiple cascades); 2 indicating a zero-coupling curved-waveguide array; and 3 indicating two curved waveguides. DETAILED DESCRIPTION OF THE EMBODIMENTS 20

[0055] The technical solutions in the embodiments of the present disclosure are described to be clear and achieve with reference to the accompanying drawings in the embodiments of the present disclosure. Obviously, the described embodiments are merely some, not all, of embodiments of the present disclosure. According to the embodiments in the present disclosure, all other embodiments derived by one of ordinary skills in the art without an effective effort fall into the 25 protection scope of the present disclosure.

[0056] The present disclosure has an objective of providing a high-density integrated optical waveguide, in which broadband optical waveguide transmission with low crosstalk is realized by using positive-and-negative coupling cascade generated by cascading straight waveguides and curved waveguides; and broadband optical waveguide transmission with low crosstalk is realized 30 for wavelength stability by using zero coupling generated by curved waveguides, for example, 18 02 25 FIG. 2 is a schematic diagram illustrating a zero-coupling curved-waveguide array for realizing broadband optical waveguide transmission with low crosstalk. Optical-waveguide directional coupling with robustness and broadband is realized for structural and wavelength stabilities by using negative coupling generated by curved waveguides, for example, FIG. 3 is a schematic 5 diagram illustrating a negative-coupling curved waveguide for realizing optical-waveguide directional coupling with robustness and broadband.

[0057] To make the foregoing objectives, features, and advantages of the present disclosure more obvious and easier to be understood, the present disclosure is further described in detail below with reference to the accompanying drawings and specific implementations. 10

[0058] A high-density integrated optical waveguide is provided, where the optical waveguide is disposed on a waveguide substrate and includes a plurality of curved waveguides; a rectangular coordinate system is established by taking a curve direction of the curved waveguide as a y axis and taking a propagation direction of light as an x axis, where on the basis of the rectangular coordinate system, the curved waveguide is periodically curved in the curve direction along the 5 propagation direction; and the plurality of curved waveguides are arranged in parallel along a y-axis direction, and the curved waveguides are perpendicular to the y-axis direction to form a curved-waveguide array, where an optical-waveguide signal transmission function or an optical-waveguide directional coupling function of the optical waveguide is realized by adjusting a coupling coefficient between the curved waveguides. 20

[0059] The curved waveguide is periodically curved in an x direction along the propagation direction j, for example, is curved in a shape of a trigonometric function: y(x)=Acos(27tx / P+cp), where A represents a curve amplitude; P represents a curve period; and (p represents a curve initial phase representing an initial state of the curved waveguide. As shown in FIG. 6, FIG. 6 shows a schematic diagram illustrating connection of a curved waveguide, at a respective initial phase ^=0 25 and ^=7t, with a straight waveguide. A represents a total number of waveguides in the waveguide array, indicating a number of channels of signals that need to be transmitted; M represents a number of stages in cascades and may be an integer greater than 1, where M=3 for a three-stage cascade structure; d represents a periodic interval at which the waveguides are arranged, ir represents a waveguide width, and gap represents a gap between the waveguides, where d-w^ 30 A represents an incident wavelength, n represents a refractive index of the waveguide, no 18 02 25 represents a refractive index of the substrate, c represents a coupling coefficient between the curved waveguides, and is dependent on parameters such as A, no, d, P and X.

[0060] The coupling coefficient is adjusted based on the curve amplitude and the curve period of the curved waveguide, an incident wavelength of the incident light, the refractive index of the 5 waveguide substrate, and the periodic interval of the curved waveguides.

[0061] The coupling coefficient is expressed as: c=coJo(A7?AnodlPP), where c represents the coupling coefficient between the curved waveguides; and co represents a coupling coefficient between straight waveguides, co>O, and the straight waveguide is a first straight waveguide or a second straight waveguide; A represents the curve amplitude; P represents the curve period; d 10 represents the periodic interval at which the waveguides are arranged, satisfying d=\v+gap, where w represents the waveguide width, and gap represents the gap between the waveguides; A represents the incident wavelength; and no represents the refractive index of the substrate.

[0062] As an optional implementation, the optical waveguide further includes a first straight waveguide array and a second straight waveguide array, where the first straight waveguide array 5 includes a plurality of first straight waveguides arranged in parallel along the y axis; and the second straight waveguide array includes a plurality of second straight waveguides arranged in parallel along the y axis. A coupling coefficient between the first straight waveguides is equal to that between the second straight waveguides, and both the coupling coefficient between the first straight waveguides and the coupling coefficient between the second straight waveguides are 20 greater than 0. An output end of the first straight waveguide array is connected to an input end of the curved-waveguide array. An output end of the curved-waveguide array is connected to an input end of the second straight waveguide array. The first straight waveguide array, the curved-waveguide array, and the second straight waveguide array form a three-stage cascade structure. The incident light enters the three-stage cascade structure from the input end of the first straight 25 waveguide array. The incident light is dispersed in the first straight waveguide array by coupling. The curved-waveguide array re-converges dispersed light to the second straight waveguide array by negative coupling. By match between positive coupling strength and the negative coupling strength in the three-stage cascade structure, the optical-waveguide signal transmission function with low crosstalk for broadband is realized. 30

[0063] The optical waveguide includes a plurality of three-stage cascade structures, and the 18 02 25 plurality of three-stage cascade structures are arranged in parallel along an x-axis direction.

[0064] Formation of this structure is described in detail below by taking a three-stage structure as an example: first, N straight waveguides are arranged in parallel along a y direction to form a structure of straight-waveguide array, as shown in FIG. 4; subsequently, the straight waveguides 5 in the straight-waveguide array are curved to form a structure of curved-waveguide array; and then two straight-waveguide arrays and one curved-waveguide array are interconnected along the x direction, so that the three-stage cascade structure shown in FIG. 5 may be formed. Other multistage cascade structures may be achieved by interconnecting a plurality of straight-waveguide arrays and curved-waveguide arrays. Each waveguide in the waveguide array is a channel for 10 optical signal transmission. In an ideal situation, an optical signal entering a certain waveguide may be output from the waveguide at an output end, and a waveguide without input of the optical signal would not output the optical signal at the output end. However, due to evanescent wave coupling effect between the waveguides, signals may affect each other. Sometimes for the waveguide without signal input, a signal may also occur at the output end, which is a crosstalk 5 signal. Moreover, intervals are smaller in the waveguide array, crosstalk may be more serious, especially in a case of high-density integration (d-Miy Herein, crosstalk generated in a straightwaveguide structure may be eliminated through introduction of the curved waveguide. Meanwhile, because this effect is for broadband, low or no crosstalk transmission under high-density integration may be realized within a wavelength range of the broadband. 20

[0065] Coupling between the waveguides may be effectively reduced by curving the waveguides. If a waveguide system satisfies a "weak-guide, weak-coupling" condition, a relation of the coupling coefficient c between the curved waveguides with other parameters may be approximately expressed as: c=coJo(4n2AwPPP), where co represents the coupling coefficient between the straight waveguides, and generally it is satisfied that co>O; and Jo represents a first 25 type of lowest order Bessel function. Therefore, when appropriate parameters are taken for A, P, d. 2, and wo, the function may be made satisfy that Jo(47t2JnoJ / P2)<O, and thus the coupling coefficient c between the waveguides may be a negative value. It should be noted that under a condition of high-density integration, the "weak-guide, weak-coupling" condition may not be satisfied. Therefore, the coupling coefficient between the curved waveguides may not strictly 30 satisfy the expression c=coJo(47t2JnoJ / P2), but is more complex. However, negative coupling 18 02 25 effects generated by the curved waveguide still exist, and a relation graph representing that the coupling coefficient between the curved waveguides under a condition of high-density integration varies with some parameters may be obtained by means of simulation, as shown in FIG. 7.

[0066] To realize transmission of a plurality of channels of signals, it is first considered to 5 arrange N straight waveguides in parallel along the y direction to form a straight-waveguide array. If a width of the waveguide is w and a gap between the waveguide is gap, a period of the waveguide array is d=w+gap. As shown in FIG. 1, the coupling coefficient co between straight waveguides is greater than zero. Another waveguide array is considered, having parameters completely consistent with those of the straight-waveguide array, in which all waveguides are just 10 curved so that a curved-waveguide array may be obtained, with a coupling coefficient being negative. Then, several curved-waveguide arrays and straight-waveguide arrays form a multistage cascade structure by waveguide-to-waveguide connection in the propagation direction (the x direction), as shown in FIG. 1. Light is dispersed in a straight waveguide by coupling and is converged in a curved waveguide by negative coupling. Therefore, the light may be re-converged, 5 at a specific propagation distance, to a waveguide where an incident port is located, so as to achieve a signal transmission function. Meanwhile, since the match between positive and negative couplings strengths is kept within a very long wavelength range, a broadband transmission function with low crosstalk may be realized.

[0067] A general case is considered. To be specific, M waveguide arrays are cascaded in M 20 stages in the propagation direction x, where an z* waveguide array has a length and a coupling coefficient represented by Lt and c,, respectively. Generally, c, may be expressed as a function c / (A, x) about a wavelength A and a propagation distance x. A device has a total length of L=L]+L2+.. +Li+..., and if x=0 is taken as the input end, x=L is taken as the output end, where N waveguides at the input end may are arbitrarily inputted with A different signals. 25

[0068] If the following expression is satisfied: L J ^(2,x)dx + J c2(X,x)dx +...+ J cf(2,x)tfc-i-... = 0, (I) x=0 x=Ll x=Li_i

[0069] the N signals may be perfectly obtained from light at the output end of x=L . “Perfectly” means that the signals at the output end of x=L have strength and phase distribution that are completely consistent with those of the signals at the input end of x=0. In this case, the signal 18 02 25 transmission function is achieved. For convenience, let the coupling coefficient not varying with the propagation direction x, and the foregoing expression may be simplified as: ci(A)Zi+c2(A)Z2+ ... +Ci(X)Li+... =0, (2)

[0070] Generally, a coupling coefficient between straight waveguides of a dielectric is a 5 positive value, with coupling magnitude varying with wavelength. Therefore, to satisfy expression (2), one way is that there are both positive coupling and negative coupling in the cascade structure; and the other way is that all coupling coefficients are equal to zero. In addition, to realize the broadband transmission function, expression (2) still must be satisfied or approximately satisfied within a certain band. 10

[0071] To obtain zero coupling and negative coupling, the curved waveguide is analytically modeled as below:

[0072] The curved waveguide is periodically curved in the y direction along the propagation direction x, for example, is curved in a shape of a trigonometric function: y(y)=Acos(2Tix / P+(p) (3) 5

[0073] where A represents the curve amplitude; P represents the curve period; and (p represents the curve initial phase. Value of (p has little effect on result, and (p is made equal to rr (or 0), as shown in FIG 6. Because slope of bend is zero in this case, light may enter a curved waveguide system without losses.

[0074] By curving the waveguides, the coupling between the waveguides may be effectively 20 reduced, and even may be zero or a negative value. In this case, positive-coupling straight waveguides and negative-coupling curved waveguides are cascaded to form a cascade structure. Light is dispersed in the straight waveguide by coupling and is converged in the curved waveguide by negative coupling, and thus the transmission function is realized. Alternatively, the transmission function may also be realized by using zero coupling. 25

[0075] When appropriate parameters are taken for A, P, d, 2, and no, expression (2) may be satisfied in a certain band. Regarding either a scheme in which positive and negative couplings are cascaded or a zero coupling scheme, an optical waveguide transmission function for broadband can be realized.

[0076] As an optional implementation, the incident light is transmitted in the curved-waveguide 30 array, to realize the broadband optical-waveguide signal transmission function with low crosstalk. 18 02 25

[0077] N curved waveguides are arranged in parallel along the y direction. Coupling effects between the waveguides may be eliminated by curving the waveguides, where an optical signal entering a certain waveguide may not be coupled to an adjacent waveguide, and thus crosstalk is eliminated, thereby achieving low-crosstalk transmission. Meanwhile, the effects are for 5 broadband, a low-crosstalk transmission function may be realized within a wavelength range of the broadband.

[0078] Coupling between the waveguides may be effectively reduced by curving the waveguides. If a waveguide system satisfies the "weak-guide, weak-coupling" condition, the relation between the coupling coefficient c between the curved waveguides and other parameters 10 may be approximately expressed as: c=coJo(47t2Anod / PP), where co represents the coupling coefficient between the straight waveguides; and Jo represents a first type of lowest order Bessel function. Therefore, when appropriate parameters are taken for A, P, d, A, and no, the function may be made satisfy that Jo(47i2Anod / PX)=O, and thus the coupling coefficient c between the waveguides may be zero. It should be noted that under a condition of high-density integration, 5 the "weak-guide, weak-coupling" condition may not be satisfied. Therefore, the coupling coefficient between the curved waveguides may not strictly satisfy the expression c=coJo(4ti2Anod / P^, but is more complex. However, zero coupling effects generated by the curved waveguide still exist, and a relation graph representing that the coupling coefficient between the curved waveguides under a condition of high-density integration varies with some parameters 20 may be obtained by means of simulation, as shown in FIG. 12.

[0079] To realize transmission of a plurality of channels of signals, it is first considered to arrange N curved waveguides in parallel along the y direction to form a single curved-waveguide array. A coupling coefficient in this array is zero, and may be approximately equal to zero within a certain band range. Light entering such a waveguide array with a coupling coefficient of zero 25 would not be coupled into an adj acent waveguide. Therefore, the broadband transmission function with low crosstalk may also be realized through a structure of single curved-waveguide array.

[0080] As an optional implementation, Jo(4n2Anod / PA) is made less than 0, the coupling coefficient is less than 0; the curved-waveguide array specifically includes two curved waveguides; and the two curved waveguides are arranged in parallel along the y-axis direction, 30 to realize the optical-waveguide directional coupling function in a broadband. 18 02 25

[0081] This structure is formed by arranging two curved waveguides in parallel along the y-direction, where broadband coupling effects between the waveguides may be achieved by curving the waveguides. In other words, an optical signal entering a certain waveguide can be stably coupled to an adjacent waveguide within the wavelength range of the broadband, so as to realize 5 a broadband directional coupling function.

[0082] Coupling between the waveguides may be effectively reduced by curving the waveguides. If a waveguide system satisfies the "weak-guide, weak-coupling" condition, the relation between the coupling coefficient c between the curved waveguides and other parameters may be approximately expressed as: c=coJo(4ii2Anod / PX), where co represents the coupling 10 coefficient between the straight waveguides; and Jo represents a first type of lowest order Bessel function. Therefore, when appropriate parameters are taken for A, P, d, A, and no, the function may be made satisfy that Jo(4n2Anod / PX)<O, and thus the coupling coefficient c between the waveguides may be a negative value. It should be noted that under a condition of high-density integration, the "weak-guide, weak-coupling" condition may not be satisfied. Therefore, the 5 coupling coefficient between the curved waveguides may not strictly satisfy the expression c=coJo(4i?AnodlPP), but is more complex. However, zero coupling effects generated by the curved waveguide still exist, and a relation graph representing that the coupling coefficient between the curved waveguides under a condition of high-density integration varies with some parameters may be obtained by means of simulation, as shown in FIG. 17. Different from sensitivity of the 20 positive coupling between the straight waveguides to wavelength and structural parameters, the negative coupling slightly varies within a much large wavelength range and a much large waveguide gap variation range. Therefore, a structure of two curved waveguides is formed by arranging two curved waveguides in parallel along the y-direction. A waveguide directional coupling function may be realized through coupling effects of light between two curved 25 waveguides, and the directional coupling function may be maintained within a much long wavelength band and a much large waveguide gap variation range.

[0083] After the negative coupling is realized by curving the waveguides, when it is found that appropriate parameters are taken for A, P, d, z. and no, the coupling between the waveguides slightly varies within a much large wavelength range and a much large waveguide gap variation 30 range, that is: c(A+AA)~c(A), c(gap+^gap)~c(gap), (4) (5) 18 02 25

[0084] where, AA and i^gap represent variations in wavelength and waveguide gap, respectively.

[0085] Generally, under the condition of high-density integration, a negative value is taken for 5 the coupling in expressions (4) and (5). To be specific, stable negative coupling properties can be maintained in a large waveband or a large structural parameter variation range. In this case, a broadband optical-waveguide directional coupling function with structural robustness may be realized.

[0086] It should be noted that, previously, a zero-coupling scheme of realizing optical 10 transmission is obtained by expression (2). However, actually the zero-coupling scheme may be considered as a special case for expressions (4) and (5). To be specific, when appropriate parameters are taken for A, P, d, A, and no, it may be made that c(A+AA)~c(A)=0, (6) (7) 5

[0087] Stable zero coupling properties can be maintained in a large waveband or a large structural parameter variation range. In this case, a broadband optical-waveguide transmission function with structural robustness may be realized.

[0088] In view of the above, the coupling effects between the waveguides may be flexibly regulated by curving the waveguides, and various functions such as broadband low-crosstalk 20 transmission and broadband directional coupling may be realized by controlling curve parameters.

[0089] To better understand the present disclosure, further explanations are given below with reference to the embodiments.

[0090] Generally, this embodiment is directed to a near-infrared band. In an air environment, curved waveguides are designed for silicon waveguides on an alumina substrate. The present 25 disclosure is also applicable for other wavelength bands and material systems. As shown in FIG. 1, the optical waveguide transmission technology is based on two schemes: (1) a cascade structure of straight waveguides and curved waveguides (including multiple cascades), herein a three-stage cascade structure is taken as an example, in which a straight-waveguide array is connected to a curved-waveguide array, and the curved-waveguide array is connected to another straight- 30 waveguide array; and (2) a structure of single curved-waveguide array. The optical waveguide 18 02 25 directional coupling technology is based on (3) two curved waveguides. A width w of a silicon waveguide is 400 nm, and a curve modulation period is P=10 pm. In this embodiment, a simulation test is performed on device performance by using COMSOL Multiphysics.

[0091] FIG. 7 to FIG. 11 illustrate simulation results of realizing broadband low-crosstalk 5 transmission by cascaded straight waveguides and curved waveguides. During simulation, a fundamental mode TE mode supported by the waveguide is used for being incident. Coupling under different curve amplitudes A and different wavelengths 2 is simulated in a case of J=760 nm. With 4=0, a curved waveguide degenerates to a straight waveguide. It may be seen that in the case of straight waveguides, as the wavelength increases, a coupling coefficient between two 10 waveguides gradually increases. When A gradually increases from 0 to 0.74 pm, that is, the straight waveguide becomes a curved waveguide, it is found that a coupling coefficient between two waveguides becomes a negative value; and in this case, an absolute value of the coupling coefficient is approximately equal to a coupling coefficient between straight waveguides. Moreover, this equality may be maintained in a much long band, that is, cA °(z)~-cA °'74,im(z). The 5 straight waveguide and the curved waveguide can be cascaded because they have the same widths both with w=400 nm. Considering the three-stage cascade structure of straight-waveguide-to-curved-waveguide-to-straight-waveguide, when a total length is L, each of two straight waveguides has a length selected to be L / 4, and the middle curved waveguide has a length selected to be / . / 2. In this case, expression (2) can be satisfied. FIG. 8 calculates variations of transmission 20 and crosstalk with wavelength in cases of different lengths L (£=100 pm and 200 pm) for two waveguides, i.e., N=2. It may be learned that the device (where £=100 pm) may maintain high transmission efficiency (>-0.1 dB) and low crosstalk (<-20 dB) in a much large wavelength range (>200 nm). If the length is increased to 200 pm, although the crosstalk increases, relatively high transmission efficiency (>-0.19 dB) may still be kept in a much large wavelength band (>200 nm). 25 FIG. 9 illustrates an optical field propagated for 100 pm and 200 pm in a waveguide structure under different wavelengths. It may be learned that the optical field can maintain high transmission efficiency and low crosstalk in a much long wavelength band. FIG. 10 and FIG. 11 illustrate simulation results of transmitting a plurality of channels of signals by using an array where N=7. Multi-channel signal transmission is performed by using seven waveguides, for 30 example, "1011010", as an example, where "1" represents presence of signal transmission exists, 18 02 25 and "0" represents absence of signal transmission. FIG. 10 calculates variations of transmission efficiencies and crosstalk with wavelength for different channels when a length satisfies Z=100 pm. It may be learned that the device may maintain high transmission efficiency (-0.46-0.27 dB) and low crosstalk (<-20.3 dB) in a much large wavelength range (1300-1450 nm). FIG. 11 5 illustrates an optical field propagated for 100 pm in a waveguide structure under different wavelengths. It may be learned that the optical field can maintain high transmission efficiency and low crosstalk in a much long wavelength band.

[0092] FIG. 12 to FIG. 16 illustrate simulation results of realizing broadband low-crosstalk transmission by using zero-coupling curved waveguides. In the case of 6 / =760 nm, when it is 10 found that A=Q.51 pm, the coupling coefficient between two waveguides is approximately zero, and may be kept zero in a very long wavelength band. In other words, expression (6) may be satisfied. FIG. 13 calculates variations of transmission and crosstalk with wavelength for propagation of 100 pm in cases of N=2. It may be learned that the device may maintain high transmission efficiency (>-0.138 dB) and low crosstalk (<-15 dB) in a much large wavelength 5 range (> 100 nm). FIG. 14 illustrates propagation of an optical field in a waveguide structure under different wavelengths. It may be learned that the optical field can maintain high transmission efficiency and low crosstalk in a much long wavelength band. FIG. 15 and FIG. 16 illustrate simulation results of transmitting a plurality of channels of signals by using an array where N=7. Multi-channel signal transmission is performed by using seven waveguides, for example, 20 "lonoio", as an example, where "1" represents presence of signal transmission, and "0" represents absence of signal transmission. FIG. 15 calculates variations of transmission efficiencies and crosstalk with wavelength for different channels when a length satisfies / .= 100 pm. It may be learned that the device may maintain high transmission efficiency (-0.85-0.63 dB) and low crosstalk (<-9.8 dB) in a much large wavelength range (1300-1450 nm). FIG. 16 25 illustrates an optical field propagated for 100 pm in a waveguide structure under different wavelengths. It may be learned that the optical field can maintain high transmission efficiency and relatively low crosstalk in a much long wavelength band.

[0093] FIG. 17 to FIG. 22 illustrate simulation results of realizing broadband coupling by using curved waveguides. Coupling under different curve amplitudes A and different wavelengths 2 is 30 simulated in a case of gap=200 nm, that is, ¢7=760 nm. With .4=0. coupling of a conventional 18 02 25 straight waveguide is illustrated; and it may be learned that in this case, coupling amplitude varies as the wavelength varies. After the length is fixed, energy distribution of an output port may also vary. When curved waveguides, i.e., A>0, are considered, it is found that the coupling coefficient between two waveguides gradually becomes a negative value, and the coupling gradually slows 5 down with varying of wavelength. Particularly, with A=0.9 pm, the coupling coefficient in this case nearly does not vary as the wavelength varies, that is, expression (4) may be satisfied. FIG. 18 to FIG. 20 respectively calculate coupling degree, isolation degree, and directivity at different wavelengths in cases of straight waveguides ¢4=0) and curved waveguides ¢4=0.9 pm). Regarding the straight waveguide, a length of the device is selected to be 15.6 pm; and a length 10 of the curved waveguide is 34.8 pm. It may be learned that a curved-waveguide coupler has lower coupling degree and has a much large bandwidth as compared with a conventional straightwaveguide coupler, where the bandwidth reaches nearly 200 nm when the coupling degree is 1 dB. In addition, the curved-waveguide coupler is superior to a conventional straight-waveguide directional coupler in indicators of isolation degree and directivity. FIG. 21 and FIG. 22 intuitively 5 illustrate propagation of an optical field in a straight-waveguide coupler and a curved-waveguide coupler. It may be learned that the optical field can be well coupled to another waveguide within a band of 1350-1550 nm. Moreover, performance of the conventional straight-waveguide coupler drastically varies with varying of the wavelength.

[0094] FIG. 23 to FIG. 28 illustrate simulation results of realizing coupling with structural 20 robustness by using curved waveguides. Coupling under different curve amplitudes A and different waveguide gaps gap is simulated in a case of 2=1550 nm. With A=0, coupling of a conventional straight waveguide is illustrated; and it may be learned that in this case, coupling amplitude varies as the waveguide gap varies. After the length is fixed, energy distribution of an output port may also vary. When curved waveguides, i.e., A>0, are considered, it is found that the 25 coupling coefficient between two waveguides gradually becomes a negative value, and the coupling gradually slows down with varying of waveguide gap. Particularly, with / 4=0.9 pm, the coupling coefficient in this case nearly does not varying with varying of waveguide gap, that is, expression (5) may be satisfied. FIG. 24 to FIG. 26 respectively calculate coupling degree, isolation degree, and directivity at different wavelengths in cases of straight waveguides ( / 4=0) 30 and curved waveguides ( / 4=0.9 pm). Regarding the straight waveguide, a length of the device is 18 02 25 selected to be 23 pm; and a length of the curved waveguide is 34.5 pm. It may be learned that a curved-waveguide coupler has lower coupling degree as compared with a conventional straightwaveguide coupler, and coupling degree less than 1 dB can still be maintained under the vary of a waveguide gap of nearly 200 nm. In addition, the curved-waveguide coupler is superior to the 5 conventional straight-waveguide coupler in indicators of isolation degree and directivity. FIG. 27 and FIG. 28 intuitively illustrate propagation of an optical field in a straight-waveguide coupler and a curved-waveguide coupler. It may be learned that although gap varies within a large range of 200-400 nm, the optical field still can be well coupled to another waveguide. Moreover, performance of the conventional straight-waveguide coupler drastically varies with varying of the 10 waveguide gap.

[0095] On-chip optical waveguide transmission and coupling realized based on curved waveguides are shown below:

[0096] 1) For an optical signal input from a port of a certain waveguide, a broadband signal transmission function with low crosstalk may be realized through a cascade structure of a positive-5 coupling straight waveguide and a negative-coupling curved waveguide.

[0097] 2) For an optical signal input from a port of a certain waveguide, a broadband signal transmission function with low crosstalk may be realized through a zero-coupling curved waveguide.

[0098] 3) A broadband optical-waveguide directional coupling function may be realized 20 through negative coupling achieved by a curved waveguide.

[0099] In view of the above, according to the present disclosure, broadband optical waveguide transmission with low crosstalk is realized by using positive-and-negative coupling cascade generated by cascading straight waveguides and curved waveguides; broadband optical waveguide transmission with low crosstalk is realized for wavelength stability by using zero 25 coupling generated by curved waveguides; and optical-waveguide directional coupling with robustness and broadband is realized for structural and wavelength stabilities by using negative coupling generated by curved waveguides.

[00100] The present disclosure is completely compatible with the current manufacturing process, without bringing in additional processing difficulties; is easy for large-scale production with low 30 requirements on production accuracy.

[00101] The various embodiments in this specification are described in a progressive way, and each embodiment focuses on a difference from other embodiments. For same or similar parts among the various embodiments, reference may be made to each other.

[00102] The principle and implementations of the present disclosure are described in this 5 specification by applying specific examples, and the description of the foregoing embodiments is merely for helping to understand the method and the core idea of the present disclosure. Meanwhile, for a person skilled in the art, according to the idea of the present disclosure, changes may be made to the specific implementations and application scope. In view of the above, the contents of this specification should not be construed as limitation to the present disclosure. LD CM 18 02 25

Claims

1. A high-density integrated optical waveguide, disposed on a waveguide substrate, comprising a plurality of curved waveguides,wherein on the basis of a rectangular coordinate system established by taking a curve 5 direction of the curved waveguide as a y axis and taking a propagation direction of light as an x axis, the curved waveguide is periodically curved in the curve direction along the propagation direction; andthe plurality of curved waveguides are arranged in parallel along a y-axis direction and are perpendicular to the y-axis direction to form a curved-waveguide array, wherein an optical-10 waveguide signal transmission function or an optical-waveguide directional coupling function of the optical waveguide is realized by providing a coupling coefficient between the curved waveguides,wherein the coupling coefficient between the curved waveguides is provided based on a curve amplitude and a curve period of the curved waveguide, an incident wavelength of incident light, a refractive index of the waveguide substrate, and a periodic interval of the curved waveguide,and the optical waveguide further comprises a first straight waveguide array and a second straight waveguide array;wherein the coupling coefficient between the curved waveguides has an expression: c=c^^idAn^dlP}^^ wherein c represents the coupling coefficient between the curved waveguides;20 co represents a coupling coefficient between the first straight waveguide array or a coupling coefficient between the second straight waveguide array, with co>O; A represents the curve amplitude; P represents the curve period; d represents the periodic interval at which the waveguides are arranged, with d w w representing a waveguide width, and gap representing a gap between the waveguides; A represents the incident wavelength; and wo represents a refractive25 index of the substrate,wherein JA^An^dlPX') is made less than 0 and the coupling coefficient between the curved waveguides is less than 0,wherein the first straight waveguide array comprises a plurality of first straight waveguides18 02 25arranged in parallel along the y axis; the second straight waveguide array comprises a plurality of second straight waveguides arranged in parallel along the y axis; and the coupling coefficient between the first straight waveguides is equal to that between the second straight waveguides, and both the coupling coefficient between the first straight waveguides and the coupling coefficient 5 between the second straight waveguides are greater than 0;an output end of the first straight waveguide array is connected to an input end of the curved-waveguide array; an output end of the curved-waveguide array is connected to an input end of the second straight waveguide array; the first straight waveguide array, the curved-waveguide array and the second straight waveguide array form a three-stage cascade structure; the incident light 10 enters the three-stage cascade structure from an input end of the first straight waveguide array; the incident light is dispersed in the first straight waveguide array by coupling; the curved-waveguide array re-converges dispersed light to the second straight waveguide array by negative coupling; and by match between positive coupling strength and the negative coupling strength in the three-stage cascade structure, the optical-waveguide signal transmission function with low crosstalk for broadband is realized.

2. The high-density integrated optical waveguide according to claim 1, wherein the optical waveguide comprises a plurality of three-stage cascade structures, and the plurality of three-stage cascade structures are arranged in parallel along an x-axis direction.

3. The high-density integrated optical waveguide according to claim 1, wherein 20 Jo(47i2Anod / PX) is made equal to 0 and the coupling coefficient between the curved waveguides is equal to 0, and the incident light is transmitted in the curved-waveguide array, to realize the optical-waveguide signal transmission function with low crosstalk for broadband.

4. The high-density integrated optical waveguide according to claim 1, wherein Jo(4n2Anod / PP) is made less than 0 and the coupling coefficient between the curved waveguides is 25 less than 0; the curved-waveguide array specifically comprises two curved waveguides, and the two curved waveguides are arranged in parallel along the y-axis direction, to realize the optical-waveguide directional coupling function for broadband.LD5. The high-density integrated optical waveguide according to any one of claims 1 to 4, wherein a periodic curve of the curved waveguide is expressed by: y(x)=Acos(2wclP+(p),wherein y(x) represents a periodic curve function for the curved waveguide, A representing the curve amplitude; P representing the curve period; and (p representing a curve initial phase.

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