TECHNICAL FIELD

[0001] Embodiments of the present invention relate to the field of optical communication, and more specifically, to an optical fiber and a related design method.

BACKGROUND

[0002] The sharp increase of data traffic has led to the emergence of advanced multiplexing schemes for enhancing the capacity of optical fiber communication systems. In particular, multimode fibers (MMFs) can play an important role in that regard. However, dispersion phenomena (e.g., intermodal dispersion) seriously limits the transmission capacity of an optical communication system relying on the mode-division multiplexing technique. To alleviate this problem, various methods for mitigating the dispersive effects are proposed. Among these methods, optimizing a refractive index profile of an optical fiber is the most fruitful one. Thus, how to design the refractive index profile of the optical fiber is an urgent problem to be solved.

SUMMARY

[0003] Embodiments of the present application provide an optical fiber and a related design method. According to the technology, an optical fiber possessing desired properties can be obtained.

[0004] According to a first aspect, an embodiment of the present application provides an optical fiber. The optical fiber includes: a core and a cladding, where the cladding surrounds the core, a refractive index profile of the core is a first oscillating function, and a shape of the first oscillating function can be adjusted.

[0005] According to this embodiment, the oscillating function can provide rich geometry, therefore, by adjusting the geometry flexibly, a fiber with desired properties can be obtained easily.

[0006] In a possible design, where the first oscillating function includes: a Fourier series with at least one harmonic.

[0007] According to this embodiment, one of the components of the first oscillating function is the Fourier series with at least one harmonic. Due to the at least one harmonic may transform the shape of the first oscillating function, the fiber with desired properties can be obtained by optimizing the at least one harmonic of the Fourier series.

[0008] In a possible design, where the first oscillating function is a superposition of a bellshaped function and a second oscillating function, and a shape of the second oscillating function can be adjusted.

[0009] According to this embodiment, the second oscillating function can influence the bell- shaped function (which is often used to represent the refractive index profile of a GRIN fiber core), and give rise to local deviations of the bell-shaped function, thus fitting a spatial distribution of an electromagnetic field of the eigenmodes and affecting their properties with maximal efficiency. Tailoring the second oscillating function according to the targets enables a flexible control over the fiber mode and the mode group, and makes it possible to design an optical fiber profile possessing desired properties.

[0010] In a possible design, where the second oscillating function is a Fourier series with at least one harmonic.

[0011] According to this embodiment, the second oscillating function may be the Fourier series with at least one harmonic. Due to the at least one harmonic can transform the shape of the first oscillating function, the fiber with desired properties can be obtained by optimizing the at least one harmonic of the Fourier series. Notably, the Fourier series in the present application can also be replaced by other oscillating functions, such as Bessel functions, Chebyshev polynomials, etc.

[0012] In a possible design, where the Fourier series includes a first parameter, the first parameter is associated with the shape of the first oscillating function.

[0013] According to this embodiment, by optimizing the first parameter, the shape of the second oscillating function can be optimized, so that the first oscillating function with a desired shape can be obtained. [0014] Notably, the first parameter can include one parameter, or can include multiple parameters, which is not limited in the present application. Or it can be understood that the first parameter can be considered as one parameter or multiple parameters. As an example, the number of parameters included in the first parameter is 2. That is to say, the present application provides an opportunity to implement efficient few-parameter optimization routines that can influence the eigenmodes of an optical fiber, which enables a desired target function to converge rapidly to its global minimum in both narrowband and broadband.

[0015] In a possible design, where the first parameter is obtained by minimizing a group- velocity dispersion.

[0016] For instance, the target is to design an optical fiber with low group-velocity dispersion, then the first parameter can be obtained as a result of an optimization procedure aimed to minimize the group-velocity dispersion. In this manner, the optical fiber with low group-velocity dispersion can be obtained. As a result, the intermodal dispersion of the optical fiber is reduced.

[0017] In a possible design, where the second oscillating function includes at least one local extremum.

[0018] On one hand, the second oscillating function includes at least one local extremum, so that the refractive index profile of the optical fiber can be designed to align with the spatial distribution of a plurality of signal-carrying modes. On the other hand, the at least one local extremum can be designed to support propagation of the plurality of signal-carrying modes over a predetermined frequency band.

[0019] In a possible design, where the bell-shaped function is a parabolic function, and a maximum value of the parabolic function corresponds to a center of the core.

[0020] The maximum value of the parabolic function corresponds to the center of the core, which can be understood as follows: when the refractive index profile of the core is a parabolic function, the refractive index of the center of the core is the largest.

[0021] In a possible design, where the refractive index profile of the optical fiber includes at least one trench, the at least one trench is located between the core and the cladding, or is located in an area of the cladding.

[0022] According to a second aspect, an embodiment of this application provides a method for designing an optical fiber, where the method includes: obtaining a core, where a refractive index profile of the core is determined by adjusting a shape of a first oscillating function; and obtaining the optical fiber by combining a cladding and the core.

[0023] In a possible design, where the first oscillating function includes: a Fourier series with at least one harmonic.

[0024] In a possible design, where the first oscillating function is a superposition of a bellshaped function and a second oscillating function, and a shape of the second oscillating function can be adjusted.

[0025] In a possible design, where the second oscillating function is a Fourier series with at least one harmonic.

[0026] In a possible design, where the Fourier series includes a first parameter, and the first parameter is associated with the shape of the first oscillating function.

[0027] In a possible design, where the first parameter is obtained by minimizing a group- velocity dispersion.

[0028] In a possible design, where the second oscillating function includes at least one local extremum.

[0029] In a possible design, where the bell-shaped function is a parabolic function, and a maximum value of the parabolic function corresponds to a center of the core.

[0030] In a possible design, where the refractive index profile of the optical fiber includes at least one trench, the at least one trench is located between the core and the cladding, or is located in an area of the cladding.

[0031] According to a third aspect, an embodiment of this application provides a communication device. The communication device includes: an optical transmitter for transmitting an optical signal; an optical receiver for receiving the optical signal; and the optical fiber according to the first aspect or any possible implementation of the first aspect.

[0032] In a possible design, the communication device is a communication system.

DESCRIPTION OF DRAWINGS

[0033] FIG. 1 shows an example refractive index profile of a GRIN multimode optical fiber. [0034] FIG. 2 shows another example refractive index profile of a GRIN multimode optical fiber.

[0035] FIG. 3 shows an example cross-section of an optical fiber of the present application.

[0036] FIG. 4 shows an example refractive index profile of an optical fiber of the present application.

[0037] FIG. 5 shows another example refractive index profile of the optical fiber of the present application.

[0038] FIG. 6 shows another example refractive index profile of the optical fiber of the present application.

[0039] FIG. 7 shows an example refractive index profile of an h-GRIN fiber and a refractive index profile of an GRIN fiber.

[0040] FIG. 8 shows another example refractive index profile of the h-GRIN fiber and another refractive index profile of the GRIN fiber.

[0041] FIG. 9 shows an rms group delay in ps per km for the optical fibers described in FIG.

7.

[0042] FIG. 10 shows an rms group delay in ps per km for the optical fibers described in FIG. 8.

[0043] FIG. 11 shows an rms group delay in ps per km at a wavelength of 1550 nm for the optical fibers described in FIG. 7.

[0044] FIG. 12 shows an optical fiber communication device applicable to the embodiment of the present application.

DESCRIPTION OF EMBODIMENTS

[0045] The following describes the technical solutions in the present application with reference to the accompanying drawings.

[0046] An optical fiber is a fiber made of glass or transparent polymer that can be used as a means of transmitting light. Optical fiber transmission has the advantages of high speed and strong anti- interference ability. A thin optical fiber is encased in a plastic sheath that allows it to bend without breaking. Generally, an optical fiber includes a core that transmits an optical signal and a cladding that confines the optical signal within the core.

[0047] The embodiment of the present application mainly focuses on a multimode fiber (also known as a multimode optical fiber), and the following implementations are all described based on the multimode fiber.

[0048] The sharp increase of data traffic has led to the emergence of advanced multiplexing schemes for enhancing the capacity of optical fiber communication systems. In particular, multimode fibers (MMFs) may play an important role in that regard.

[0049] However, due to the group- velocity dispersion phenomenon (e.g., intermodal dispersion and chromatic dispersion), signal pulses spread in time while propagating through a multimode optical fiber, which leads to intersymbol interference, i.e. the receiver fails to distinguish separate pulses if they overlap at the output. Intermodal dispersion is a principal factor that seriously limits the transmission capacity of an optical communication system relying on the mode-division multiplexing technique. The strength of the intermodal dispersion can be quantified by a differential mode group delay (DMGD) calculated as a root-mean square (rms) group delay.

[0050] There are various methods for mitigating the dispersive effects. Optimizing a refractive index profile of an optical fiber is one of the most fruitful one.

[0051] At present, the conventional multimode optical fibers mainly include step-index fibers (SIFs) and graded- index (GRIN) multimode optical fibers. SIFs consist of a cylindrical inner core with a constant refractive index n ₁ , and the core is surrounded by a cladding with a constant refractive index n _c , where n _c <n ₁ . To further suppress the intermodal dispersion, GRIN multimode optical fibers have been introduced as an alternative to SIFs. In contrast to a SIF with a uniform core, the refractive index profile of the core of a GRIN fiber is a bell-shaped function that decreases on an interval between the fiber center and the cladding. This modification of the refractive index profile causes reduction of the intermodal dispersion from 50000 ps/km for SIFs to 100-200 ps/km for GRIN fibers. Still, this improvement does not fulfill requirements for long-haul multimode signal transmission, whereas a further decrease in the intermodal dispersion is hardly feasible within the class of analytically -given monotonic functions due to their restricted optimization potential. [0052] FIG. 1 shows an example refractive index profile of a GRIN multimode optical fiber. As shown in FIG. 1, the characteristics of the optical fiber are described by the refractive index profile that correlates the refractive index n with a fiber radius R. The distance R relative to the center of the optical fiber is shown on the x-axis, and the refractive index n at the radius R is shown on the y-axis.

[0053] In FIG. 1, the radius of the core is represented as R _co , the radius of the cladding is represented as R _cl , the refractive index of the core center is represented as n _co , and the refractive index of the cladding is represented as n _cl .

[0054] Notably, the refractive index profile of the GRIN fiber may also have one or more depressed trenches. FIG. 2 shows another example refractive index profile of a GRIN multimode optical fiber, where the refractive index profile of the GRIN fiber possesses one trench.

[0055] In view of this, the present application provides an optical fiber, where a refractive index profile of the core is a first oscillating function, and a shape of the first oscillating function can be flexibly adjusted, which makes it possible to design an optical fiber possessing desired properties.

[0056] The following describes the optical fiber provided in this application.

[0057] FIG. 3 shows an example cross-section of an optical fiber of the present application. As shown in FIG. 3, the optical fiber includes: a core and a cladding. The core, that is, the central part of the cross-section of the optical fiber, with a radius of r _co , is a main light guiding area of the optical fiber. The core is usually made of quartz glass. The cladding, that is, the envelope surrounding the core, with a radius of r _cl . Exemplarily, the optical fiber in the present application can be made of one or more of the following optical materials: fused silica, quartz glass and polymeric materials.

[0058] FIG. 4 shows an example refractive index profile of the optical fiber of the present application. In FIG. 4, the refractive index profile of the core is an oscillating function (expressed as a first oscillating function), and a shape of the first oscillating function can be adjusted. Since the oscillating function can provide rich geometry, by adjusting the geometry flexibly, a fiber with desired properties can be obtained easily.

[0059] In one possible implementation, the first oscillating function includes: a Fourier series with at least one harmonic. In other words, one of the components of the first oscillating function is the Fourier series with at least one harmonic. Due to the at least one harmonic can transform the shape of the first oscillating function, a fiber with desired properties can be obtained by optimizing the at least one harmonic of the Fourier series.

[0060] Optionally, the first oscillating function is a superposition of a bell- shaped function and a second oscillating function, and a shape of the second oscillating function can be adjusted. In this manner, the second oscillating function can influence the bell-shaped function (which is often used to represent the refractive index profile of a GRIN fiber core), and give rise to local deviations of the bell-shaped function, thus fitting a spatial distribution of an electromagnetic field of the eigenmodes and affecting their properties with maximal efficiency. Tailoring the second oscillating function according to the targets enables a flexible control over the fiber mode and the mode group, and makes it possible to design an optical fiber profile possessing desired properties.

[0061] Exemplarily, the be 11- shaped function may be a parabolic function, and a maximum value of the parabolic function corresponds to a center of the core.

[0062] The maximum value of the parabolic function corresponds to the center of the core, which can be understood as follows: when the refractive index profile of the core is a parabolic function, the refractive index of the center of the core is the largest.

[0063] Exemplarily, the second oscillating function may be a Fourier series with at least one harmonic. Notably, the Fourier series in the present application can also be replaced by other oscillating functions, such as Bessel functions, Chebyshev polynomials, etc.

[0064] Optionally, the Fourier series includes a first parameter, the first parameter is associated with the shape of the first oscillating function. As an example, by optimizing the first parameters, the shape of the second oscillating function can be optimized, so that the first oscillating function with a desired shape can be obtained.

[0065] Notably, the first parameter can include one parameter, or can include multiple parameters, which is not limited in the present application. As an example, the number of parameters included in the first parameter is 2, that is to say, the Fourier series includes 2 parameters. In this manner, the present application provides an opportunity to implement efficient few-parameter optimization routines that can influence the eigenmodes of an optical fiber, which enables a desired target function to converge rapidly to its global minimum in both narrowband and broadband. In a possible design, the first parameter may be at least one amplitude coefficient of the Fourier series.

[0066] Optionally, the first parameter is obtained by minimizing a group-velocity dispersion. For instance, the target is to design an optical fiber with low group-velocity dispersion, then the first parameter can be obtained as a result of an optimization procedure aimed to minimize the group-velocity dispersion. In this manner, the optical fiber with low group-velocity dispersion can be obtained. As a result, the intermodal dispersion of the optical fiber is reduced.

[0067] Notably, the above method of calculating the first parameter is only exemplary. In fact, there are different ways to calculate the first parameter according to different targets, which is not limited in the present application.

[0068] To make it easier to clarify the embodiments of the present application, assume that the first oscillating function is expressed as n(r), the bell-shaped function is expressed as n ₁ (r) , and the second oscillating function is expressed as n ₂ (r) , where r represents the distance relative to the center of the optical fiber. In a possible design, the first oscillating function can be represented as follows:

[0069]

[0070] Exemplarily, n ₁ (r) can be defined by the following equation:

[0072] where, n _co is a maximum value of n ₁ (r ,) and α is a non-dimensional parameter that outlines the shape of the refractive index profile. Optionally, the value of α can belong to the interval [1.9, 2.1]. As an example, α =1.94. And A can be represented as follows:

[0073]

[0074] where, n _cl is the refractive index of the cladding. [0075] Exemplarily, n ₂ (r) can defined by the following Fourier series with Nh+1 harmonics:

[0076]

[0077] where, A _k and B _k are amplitude coefficients obtained as a result of an optimization procedure aimed to minimize the group- velocity dispersion. The target function S used in the optimization is given by:

[0078]

[0079] where, i is an index of a wavelength, of which there are a total of M+1. k is a mode index, of which there are a total of N+1. Where stands for a group velocity of the k-th mode at the wavelength λ _i , and is an average group velocity of the N+1 modes at the wavelength λ _i .

[0080] Table 1 shows a set of optimization results of A _k and B _k .

[0081] Table 1

[0082] where, the value of B ₀ can be arbitrary, this is due to the fact that a zero-harmonic sin(0*x) is zero everywhere.

[0083] Optionally, the second oscillating function includes at least one local extremum, so that the refractive index profile of the optical fiber can be designed to align with the spatial distribution of a plurality of signal-carrying modes. On the other hand, the at least one local extremum can be designed to support propagation of the plurality of signal-carrying modes over a predetermined frequency band.

[0084] In a possible design, the refractive index profile of the optical fiber includes at least one trench, the at least one trench is located between the core and the cladding, or is located in an area of the cladding.

[0085] FIG. 5 shows another example refractive index profile of the optical fiber of the present application. Where the refractive index profile possesses one trench between the core and the cladding, and an outer radius of the trench is represented as r _tr , the refractive index of the trench is represented as n _tr .

[0086] FIG. 6 shows another example refractive index profile of the optical fiber of the present application. Where the refractive index profile possesses tow trenches between the core and the cladding, and the refractive index of the second trench is greater than that of the first trench. In FIG. 6, the outer radius of the first trench is represented as r _tr,1 , the refractive index of the first trench is represented as n _tr,1 ; and the outer radius of the second trench is represented as r _tr,2 , the refractive index of the second trench is represented as n _tr,2 . It should be noted that the first trench refers to the trench adjacent to the core, and the second trench refers to the trench adjacent to the cladding.

[0087] Notably, the number and location of the trench in FIG. 5 and FIG. 6 are only illustrative and do not limit the scope of the present application. In addition, it is understandable that the refractive index profile has an azimuthal symmetry around the center of the core. In other words, the refractive index depends only on the radial distance from the core center and does not depend on the polar angle.

[0088] Accordingly, the application also provides a method for designing an optical fiber. The method includes the following steps:

[0089] 1) obtain a core by adjusting a shape of a first oscillating function, a refractive index profile of the core is a first oscillating function, and a shape of the first oscillating function can be adjusted; and

[0090] 2) obtain the optical fiber by combining a cladding and the core.

[0091] The introduction of the core and the cladding can be referred to the above description. To avoid duplication, it will not be repeated here.

[0092] The following gives some examples of the refractive index profile of the optical fiber of the present application. To make it easier to describe, the following assumes that the optical fiber of the present application is named h-GRIN fiber. [0093] FIG. 7 and FIG. 8 show two examples of the refractive index profile of the h-GRIN fiber, where the core radius r _co of the h-GRIN fiber is 13 microns. As shown in FIG 5 and FIG 6, the refractive index profile of the core can be an oscillating function (e.g., the first oscillating function mentioned above), which is a superposition of a bell-shaped function and a second oscillating function. In the examples of FIG. 7 and FIG. 8, the second oscillating function is a Fourier series includes the amplitude coefficients A _k and B _k , where k is from 0 to 5, and the optimized amplitude coefficients are given in Table 1.

[0094] Specifically, FIG. 7 shows an example refractive index profile of the h-GRIN fiber and a refractive index profile of the GRIN fiber, where the core radius of the h-GRIN fiber and the core radius of the GRIN fiber are both 13 microns. The refractive index profile of the h- GRIN fiber and the GRIN fiber possess the same trench with the outer radius r _tr , the width w, and the depth Δr _tr .

[0095] In the example of FIG. 7, the outer radius of the trench r _tr is 20.5 microns, the width of the trench w is 7.5 microns (which typically lies between 5 and 8 microns), and the depth of the trench Δr _tr is 3·10 ^-3 (which typically lies between 1·10 ^-3 and 15·10 ^-3 microns).

[0096] Notably, the depth of the trench Δr _tr can also represent the refractive index difference between the refractive index of the trench and the refractive index of the cladding.

[0097] Specifically, FIG. 8 shows another example refractive index profile of the h-GRIN fiber and another refractive index profile of the GRIN fiber, where the core radius of the h- GRIN fiber and the core radius of the GRIN fiber are both 13 microns. The refractive index profile of the h-GRIN fiber and the GRIN fiber possess the same two trenches. The first trench has the outer radius r _tr,1 , the width w _{1 ,} and the depth Δr _tr,1 (i.e., the refractive index difference between the refractive index of the first trench and the refractive index of the cladding). The second trench has the outer radius r _tr,2 , the width w ₂ , and the depth Δr _tr,2 (i.e., the refractive index difference between the refractive index of the second trench and the refractive index of the cladding). It should be noted that the first trench refers to the trench adjacent to the core, and the second trench refers to the trench adjacent to the cladding.

[0098] In the example of FIG. 8, the outer radius of the first trench r _tr,1 is 20.5 microns, the width of the first trench w ₁ is 7.5 microns (which typically lies between 5 and 8 microns), and the depth of the trench Δr _tr,1 is 3·10 ^-3 (which typically lies between 1·10 ^-3 and 15·10 ^-3 microns). In the example of FIG. 8, the outer radius of the second trench r _tr2 , is 25 microns, the width of the second trench w ₂ is 4.5 microns (which typically lies between 4 and 6 microns), and the depth of the trench Δr _tr,2 is 1 ·10 ^-3 (which typically lies between 1 ·10 ^-3 and 10·10 ^-3 microns).

[0099] FIG. 9 shows an rms group delay in ps per km (ps/km) for the optical fibers described in FIG. 7. For the h-GRIN fiber, the rms group delay of 15 LP modes is about 4 ps/km at the wavelength of 1550 nanometers, and the rms group delay of 15 LP modes lies in the range between 4 ps/km and 7 ps/km in the SC-band (1490-1560 nm). For the GRIN fiber, the rms group delay of 15 LP modes is about 125 ps/km at the wavelength of 1550 nanometers, and the rms group delay of 15 LP modes lies in the range between 70 ps/km and 140 ps/km in the SC- band (1490-1560 nm).

[00100] FIG. 10 shows an rms group delay in ps per km (ps/km) for the optical fibers described in FIG. 8. For the h-GRIN fiber, the rms group delay of 15 LP modes is about 4 ps/km at the wavelength of 1550 nanometers, and the rms group delay of 15 LP modes lies in the range between 4 ps/km and 13 ps/km in the SCL-band (1460-1580 nm). For the GRIN fiber, the rms group delay of 15 LP modes is about 125 ps/km at the wavelength of 1550 nanometers, and the rms group delay of 15 LP modes lies in the range between 65 ps/km and 173 ps/km in the SCL- band (1460-1580 nm).

[00101] FIG. 11 shows an rms group delay in ps per km (ps/km) at the wavelength of 1550 nm for the optical fibers described in FIG. 7, where the vertical axis represents the rms group delay in ps/km, and the horizontal axis represents the standard deviation o of an additive white Gaussian noise (AWGN).

[00102] In the example of FIG. 11, the influence of the potential manufacturing imperfections is investigated for both the GRIN fiber and the h-GRIN fiber. The imperfections are simulated with help of the AWGN. As shown in FIG. 11, the h-GRIN fiber is robust with respect to manufacturing imperfections and retains the rms group delay less than 10 ps/km when the standard deviation o of the AWGN is less than 10 ^-5 .

[00103] FIG. 12 is an optical fiber communication device 10 applicable to the embodiment of the present application. Optionally, the optical fiber communication device can be an optical fiber communication system.

[00104] As shown in FIG. 12, the device 10 includes an optical transmitter 11, an optical receiver 12, and a multimode optical fiber 13. Where the optical transmitter 11 is connected with one end of the multimode optical fiber 13, and the optical receiver 12 is connected with the other end of the multimode optical fiber 13. The multimode optical fiber 13 can be, for example, the optical fiber described in any embodiment of the present application.

[00105] Notably, the multimode optical fiber 13 shown in the figure can be composed of multiple segments of the multimode optical fiber, which is not limited in the present application. [00106] The communication principle of optical fiber is described as follows. At the transmitting end, first, the information to be transmitted needs to be changed into an electrical signal, and then the electrical signal is modulated to a laser beam sent by a laser, and the intensity of the light changes with the amplitude (frequency) of the electrical signal, and then the optical signal is sent out through the optical fiber. At the receiving end, the detector converts the optical signal into an electrical signal after receiving it. Then, the electrical signal is demodulated and the original information is restored. That is, the optical signal is transmitted from the optical transmitter to the optical receiver through the optical fiber.

[00107] It should be noted that the specific examples in the embodiments of the present application are only to help those skilled in the art better understand the technical scheme of the application. The above specific implementations can be considered as the optimal implementations of the application, rather than limiting the scope of the embodiments of the application.

[00108] It also should be noted that “first”, “second” and various numerical numbers involved in the text are merely for the convenience of description and distinction, and are not intended to limit the protection scope of the embodiments of the application.

[00109] The foregoing descriptions are merely specific implementations of the present application, but are not intended to limit the protection scope of the present application. Any variation or replacement readily figured out by a person skilled in the art within the technical scope disclosed in the present application shall fall within the protection scope of the present application. Therefore, the protection scope of the present application shall be subject to the protection scope of the claims.