A special optical fiber with rotationally symmetric super-Gaussian distributed mode field output and its fabrication method.

Abstract

This invention discloses a special optical fiber with rotationally symmetric super-Gaussian mode field output and its fabrication method. The optical fiber comprises a core and a cladding. The core cross-sectional boundary is a finite-weight or continuous rotationally symmetric boundary. The core refractive index distribution is a non-monotonic continuous distribution along the equivalent radial direction, comprising, from the inside out, a central flat region, a refractive index rising region, a refractive index falling region, and a transition region. This non-monotonic continuous distribution is obtained based on the inversion of a preset rotationally symmetric super-Gaussian target mode field, ensuring that the dominant mode supported by the fiber at the operating wavelength exhibits a rotationally symmetric super-Gaussian mode field distribution with a flat central region, rapid edge attenuation, and corresponding to the cross-sectional boundary. The special optical fiber designs its refractive index profile through target mode field inversion and is fabricated using preform preparation and drawing processes. This invention achieves flat-top mode field output without external beam shaping elements, making it suitable for high-power fiber lasers, beam shaping, precision machining, and fiber array splicing applications.

Description

Technical Field

[0001] This application relates to the field of special fiber waveguide structure design and manufacturing technology, specifically to a special optical fiber for beam shaping, which outputs a rotationally symmetric super-Gaussian mode field based on a radial non-monotonic refractive index profile, and its fabrication method. Background Technology

[0002] In recent years, with the rapid development of high-power fiber lasers, laser communication, and precision optical processing, higher requirements have been placed on the spatial mode field distribution of output beams. An ideal mode field distribution should not only have high energy utilization efficiency but also exhibit uniform intensity in the central region and smooth edge transitions in the transverse space to reduce the adverse effects of diffraction, mode coupling, and nonlinearity. Among these, the super-Gaussian distribution, due to its flat central region, steep edge attenuation, and tunable transition characteristics, has significant advantages in high-power beam shaping and mode control, and is considered a target mode field model that approximates an ideal flat-top beam.

[0003] However, existing specialty optical fibers still have significant limitations in directly achieving high-quality ultra-Gaussian mode field output. On the one hand, traditional step-index or graded-index optical fibers typically exhibit a monotonically changing refractive index profile. Due to this limitation, the eigenmodes they support are mostly Gaussian or Gaussian-like, resulting in high central energy density. This can easily lead to material inhomogeneity or damage to optical components in high-power applications. Although external beam shaping can be achieved using diffractive optical elements or multimode interferometers, these solutions generally suffer from complex system structures, high insertion losses, and sensitivity to mechanical disturbances and environmental temperature changes, making it difficult to meet the application requirements of high integration and long-term stable operation.

[0004] On the other hand, existing technologies typically employ homogenized fibers to achieve beam homogenization. These fibers rely primarily on mode coupling and structural perturbations during multimode transmission to cause random mixing of the input light field during propagation, thereby achieving a statistically relatively uniform output light intensity distribution. For example, commercially available homogenized fibers often employ non-circular symmetric core structures or introduce perturbation enhancement mechanisms to improve mode coupling efficiency.

[0005] However, this type of homogenization mechanism is essentially a stochastic process and still has the following shortcomings:

[0006] (1) The output light field depends on random mode coupling, and its uniformity is only a statistically uniform distribution, making it difficult to achieve deterministic control of the target mode field;

[0007] (2) The shape of the output light field is difficult to design precisely, and it usually still close to the Gaussian distribution or its distortion form;

[0008] (3) The output characteristics are sensitive to input conditions and structural disturbances, and the stability is poor;

[0009] (4) It is difficult to achieve a mode field distribution with specific spatial symmetry characteristics.

[0010] Furthermore, while some non-circular symmetric or microstructured optical fibers improve mode field distribution to some extent, they typically suffer from complex manufacturing processes, high costs, and difficulties in consistency control. At the same time, their mode field characteristics often rely on multi-parameter coupling adjustment, lacking a structural method that allows direct design starting from the target mode field.

[0011] Furthermore, in applications requiring high-density splicing of fiber arrays, such as hexagonal array structures, not only is a specific polygonal geometric envelope required for the output beam, but the internal intensity distribution must also possess intrinsic super-Gaussian flat-top characteristics to improve the fill factor and reduce the splicing dead zone. However, existing circularly symmetric fibers or simple irregularly shaped core homogenized fibers struggle to simultaneously achieve precise control of the wavefront by rotationally symmetric geometric constraints and non-monotonic refractive index distribution at the waveguide structure level.

[0012] In summary, current technologies lack a fiber structure that can balance manufacturing feasibility with high-precision intrinsic mode field control. In particular, without the need for external optical shaping components, how to achieve a fiber structure with n-fold rotationally symmetric geometric boundaries and a non-monotonic radial refractive index distribution through reverse engineering of the waveguide structure, thereby intrinsically supporting high-order super-Gaussian mode field output, has become a key technical problem restricting the development of high-performance laser systems.

[0013] Therefore, it is necessary to propose a novel special fiber structure to achieve stable output of a super-Gaussian distributed mode field with rotational symmetry characteristics, thereby meeting the application requirements of high-power optics and precision optical field control. Summary of the Invention

[0014] The technical problem to be solved by the present invention is to provide a special optical fiber with rotationally symmetric super-Gaussian distributed mode field output and its preparation method. The special optical fiber achieves intrinsic control of the mode field distribution by constructing a specific refractive index distribution structure and cross-sectional geometry. The preparation method designs the refractive index profile by inverting the target mode field and combines preform preparation and drawing process to make the optical fiber, thereby overcoming the problems of difficulty in directly obtaining flat-top mode fields, insufficient control capability of non-circular symmetric mode fields, and dependence on external optical devices in the prior art.

[0015] To address the aforementioned technical problems, this invention provides a special optical fiber comprising a core and a cladding:

[0016] The cross-sectional boundary of the fiber core is a rotationally symmetric boundary, which is either a finite-weight rotationally symmetric boundary or a continuous rotationally symmetric boundary.

[0017] The fiber core has a non-monotonic refractive index profile distributed along an equivalent radial direction. The equivalent radial direction is characterized by an equivalent radial parameter, which is the ratio of the distance from any point in the cross-section to the geometric center of the fiber core to the distance from the geometric center through that point to the rotationally symmetric boundary. The non-monotonic refractive index profile includes, from the inside to the outside, a central flat region, a refractive index rising region, a refractive index falling region, and a transition region.

[0018] The refractive index of the central flat region is higher than that of the cladding; the refractive index of the rising refractive index region increases from the refractive index of the central flat region along the equivalent radial direction to a local maximum; the refractive index of the falling refractive index region decreases along the equivalent radial direction to a local minimum; the refractive index of the transition region transitions from the local minimum to the refractive index of the cladding; the "local maximum" refers to the maximum value of the refractive index within a small region near the boundary between the rising and falling refractive index regions; the "local minimum" refers to the minimum value of the refractive index within a small region near the boundary between the falling and transition regions.

[0019] The non-monotonic refractive index profile matches the rotationally symmetric super-Gaussian target mode field at the preset target wavelength, so that the dominant mode supported by the special optical fiber at the preset target wavelength exhibits a rotationally symmetric super-Gaussian flat-top mode field distribution with a flat central region, rapid edge attenuation, and corresponding to the rotationally symmetric boundary.

[0020] When the rotational symmetry boundary is a finite-weight rotational symmetry boundary, the finite-weight rotational symmetry boundary coincides with the original boundary after rotating 360° / n around the geometric center of the fiber core, where n is an integer greater than or equal to 3; when the rotational symmetry boundary is a continuous rotational symmetry boundary, the continuous rotational symmetry boundary coincides with the original boundary after rotating arbitrarily around the geometric center of the fiber core.

[0021] The rotational symmetry boundary includes a regular polygonal boundary or a circular boundary; when the rotational symmetry boundary is a regular polygonal boundary, the rotationally symmetric super-Gaussian flat-top mode field distribution has angular symmetry corresponding to the regular polygonal boundary. Preferably, the rotational symmetry boundary is a regular hexagonal boundary. The "angular symmetry" means that the spatial shape of the mode field distribution is consistent with the shape of the rotational symmetry boundary of the fiber core cross-section. For example, when the rotational symmetry boundary is a regular hexagon, the iso-intensity profile of the output mode field also presents as a regular hexagon, and the angular orientation of the hexagon is consistent with the boundary.

[0022] The rotationally symmetric super-Gaussian target model field is determined by the central field strength, the characteristic scale parameter, and the super-Gaussian order. When the rotationally symmetric boundary is a regular polygonal boundary, the characteristic scale parameter corresponds to the center-to-side distance of the regular polygonal boundary. When the rotationally symmetric boundary is a circular boundary, the characteristic scale parameter corresponds to the radius of the circular boundary or the characteristic radius of the model field.

[0023] The non-monotonic refractive index profile is determined based on the vacuum wavenumber at the preset target wavelength and the rotationally symmetric super-Gaussian target mode field inversion; the preset target wavelength is any working wavelength selected according to application requirements, and the non-monotonic refractive index profile is reconfigured as the preset target wavelength changes.

[0024] The non-monotonic refractive index profile is composed of at least one constant function segment and at least one continuously varying function segment, with adjacent function segments satisfying functional continuity. The refractive index decreasing region forms a low-refractive-index equivalent annular region, used to constrain the edge attenuation of the dominant mode and reduce the intensity fluctuations in the central region. For example, the refractive index of the refractive index decreasing region is lower than that of the regions on both sides (the refractive index increasing region and the transition region), forming an equivalent annular low-refractive-index region in the fiber core. This low-refractive-index equivalent annular region constrains the optical field, causing rapid attenuation at the edge of the dominant mode field while reducing the intensity fluctuations in the central region, thereby improving the flatness of the mode field.

[0025] As one of the core structural features of this invention, the transverse refractive index square distribution of the fiber core The following spatial equality constraints must be satisfied:

[0026]

[0027] in, The effective refractive index of the fundamental mode, The vacuum wavenumber is the operating wavelength. For the transverse Laplace operator; The target field distribution function is preset.

[0028] Define dimensionless equivalent radial parameter for:

[0029]

[0030] in, For the actual polar diameter, Polar angle, This represents the distance from the structural boundary to the center in the corresponding direction. The equivalent radial parameter is used to characterize the equivalent distance from any point in a rotationally symmetric structure to the center, along one lap of the outer boundary of the target cross-section. Therefore, the equivalent radial parameter The value is set to a constant 1, thus making the non-circular boundary correspond to a constant radius (i.e., a circle with radius 1) in the equivalent radial coordinate system. For ease of engineering implementation, an equivalent radial distance with the dimension of length is defined. ,in The center distance of the polygonal side or the radius of the circle of the structure.

[0031] Preferably, the target mode field is a rotationally symmetric superGaussian distribution, and its expression is:

[0032]

[0033] in, The center-to-center distance of the polygonal edge or the radius of the circle of the target model field, preferably corresponding to the center-to-center distance of the polygonal edge or the radius of the circle of the structure. It is a super-Gaussian order. The center field strength.

[0034] By introducing the equivalent radial parameters mentioned above, the ideal radially symmetric mode field distribution is mapped to a non-circular symmetric cross-sectional structure with rotational symmetry characteristics, thereby realizing the structured expression of the target mode field.

[0035] The dominant modes supported by the optical fiber at the operating wavelength are distributed in a flat-top shape, with an approximately constant light intensity distribution in the central region, rapid attenuation along the equivalent radial direction in the edge region, and a symmetrical distribution characteristic corresponding to the rotational symmetry structure in the angular direction; in a preferred embodiment, the mode field is distributed in a six-fold symmetry.

[0036] On the other hand, the present invention also provides a method for preparing the above-mentioned special optical fiber, comprising:

[0037] The rotational symmetry boundary and equivalent radial parameters of the fiber core cross section are determined based on the preset target wavelength and rotational symmetric super-Gaussian target mode field.

[0038] Based on the preset target wavelength and the rotationally symmetric super-Gaussian target mode field, a non-monotonic refractive index profile along the equivalent radial direction is obtained by inversion.

[0039] The optical fiber preform is prepared using an optical fiber preform preparation method capable of forming the non-monotonic refractive index profile, so that the optical fiber preform has a refractive index distribution corresponding to the central flat region, the refractive index rising region, the refractive index falling region, and the transition region.

[0040] The optical fiber preform is drawn into fibers to obtain the special optical fiber.

[0041] Compared with the prior art, the present invention has the following beneficial effects:

[0042] (1) By constructing a non-monotonic refractive index distribution, deterministic intrinsic control of the fiber mode field is achieved, so that the output mode field is close to the ideal super-Gaussian distribution.

[0043] (2) By introducing a rotationally symmetric cross-section structure, the traditional circular symmetry constraint is broken, and the designability and controllability of the model field spatial distribution are improved;

[0044] (3) By coordinating the design of the central flat region and the peripheral refractive index modulation region, the flatness of the mode field and the steepness of the edge are taken into account, effectively reducing the diffraction effect and the influence of mode coupling.

[0045] (4) By performing finite truncation and engineering discretization on the theoretical refractive index distribution, the structure can be adapted to existing optical fiber fabrication processes, thereby improving manufacturing feasibility.

[0046] (5) The target mode field output can be achieved without relying on external optical shaping elements, which is conducive to improving system integration and long-term stable operation. Attached Figure Description

[0047] Figure 1 This is a schematic diagram of the refractive index distribution of the special optical fiber of the present invention.

[0048] Figure 2 This is a schematic diagram of the cross-sectional physical structure of the special optical fiber of the present invention.

[0049] Figure 3 This is a diagram showing the refractive index distribution along the horizontal cross section of the special optical fiber of this invention.

[0050] Figure 4 This is an energy distribution diagram of the regular hexagonal super-Gaussian flat-top output mode field generated by the optical fiber transmission of this invention. Detailed Implementation

[0051] To clearly demonstrate the purpose, technical solution, and advantages of the present invention, the specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples.

[0052] The refractive index distribution formulas in the following embodiments are obtained by numerical calculation and engineering approximation based on the above theoretical inversion relationship, for a specific target mode field with a regular hexagonal fiber core, a working wavelength of 1064 nm, and a super-Gaussian order of a certain value.

[0053] Example: Special optical fiber with 10 μm hexagonal side-to-center spacing and ultra-Gaussian distributed mode field for 1064 nm laser transmission.

[0054] This embodiment provides a special optical fiber with rotationally symmetric super-Gaussian distributed mode field output. The special optical fiber includes a core and a cladding covering the core. The core cross-section is a regular hexagon with rotationally symmetric boundaries, exhibiting six-fold rotational symmetry. A polar coordinate system is established within the cross-section with the geometric center of the core as the origin O. The actual polar radius of any point P is r, and the polar angle is θ. The distance extending from the origin O along the angle θ direction to the regular hexagonal boundary is denoted as r. .

[0055] To facilitate the mapping of the circularly symmetric super-Gaussian target mode field to the boundary of the regular hexagonal fiber core, this embodiment introduces an equivalent radial parameter. Let the center-to-side distance of the regular hexagon be *a*, preferably *a* = 10 μm, and the equivalent radial distance of any point P be... Defined as:

[0056]

[0057] in, This is the equivalent radial distance with dimensions of length. When P lies on the boundary of the regular hexagon, ,therefore Therefore, the hexagonal boundary is mapped to a constant radius *a* in the equivalent radial coordinates, allowing the refractive index profile to be uniformly described along the equivalent radial direction. Within each 60° angular period of the hexagon, *R*(θ) can be determined by the boundary equation within that angular sector.

[0058] In this embodiment, the operating wavelength λ = 1064 nm is selected, corresponding to the vacuum wavenumber as follows: Under the weak-conductivity approximation, the transverse mode field E(x,y) of the optical fiber satisfies the transverse scalar wave equation:

[0059]

[0060] in, For the transverse Laplace operator, Let be the target modulus field distribution function. The refractive index distribution to be designed within the cross-section, Let be the effective refractive index of the target dominant mode. From the above equation, the inversion relationship of the square distribution of refractive index can be obtained:

[0061]

[0062] This formula shows that as long as the target model field is given in advance... The refractive index distribution matching the target mode field can then be obtained through transverse Laplace inversion. In this embodiment, the target mode field is set along the equivalent radial distance. Distributed supergaussian mode field:

[0063]

[0064] in, The center field strength is normalized to 1 in this embodiment. Let m be the hexagonal center distance of the target mode field, and m be the super-Gaussian order. Substituting this formula into the above expression for the square distribution of refractive index, we get:

[0065]

[0066] This embodiment takes , , The above formula can be simplified to:

[0067]

[0068] This equation gives the equivalent radial refractive index distribution of the fiber core region obtained by inversion from the target super-Gaussian mode field. Since the refractive index correction term in the equation includes... Therefore, in The rate of change of refractive index is very small in the central region close to 0, thus forming a central flat region; as... As the refractive index increases, it gradually increases, and at the condition that... It reaches a local maximum near the location, which is approximately [location missing]. As we continue outward, the refractive index begins to decrease, thus forming a region of decreasing refractive index. Consequently, the refractive index profile of this embodiment naturally exhibits a central flat region, a region of increasing refractive index, and a region of decreasing refractive index from the inside out.

[0069] To ensure a smooth transition between the theoretical refractive index profile obtained from the above equation and the cladding refractive index, and to adapt to actual preform fabrication and wire drawing processes, this embodiment further introduces an engineered smooth transition function. Let the cladding refractive index be... The starting position of the transition zone is The transition zone ends at the following location: The second derivative of the continuous fifth-order smooth transition function used is... Defined as:

[0070]

[0071] in, , is a dimensionless transition variable. This function in and The first and second derivatives at the point are both 0. Therefore, this function can smoothly transition the theoretical refractive index profile to the cladding refractive index, reducing undesirable mode perturbations caused by abrupt changes in refractive index.

[0072] Combining the refractive index distribution and transition function in the fiber core region, this embodiment ultimately adopts the equivalent radial refractive index distribution. It can be represented as:

[0073]

[0074] in, The formula is given by the equivalent radial refractive index distribution in the fiber core region. When hour, The refractive index is mainly obtained by inversion of the target super-Gaussian mode field; when When, the refractive index changes from Smooth transition to ;when hour, The refractive index is equal to the cladding refractive index. .

[0075] The non-monotonic refractive index distribution in this embodiment is as follows: Figure 1 As shown, the cross-section, from the inside out, includes: a central flat region near the center, a refractive index rising region where the refractive index gradually increases, a refractive index falling region where the refractive index decreases from a local maximum outwards, a transition region connecting to the cladding refractive index, and the cladding region, corresponding to regions 1-5 respectively. The direction perpendicular from the center point to the edge, indicated by the arrow, is the radial direction, and the distance is the edge-to-center distance. The physical structure of the optical fiber cross-section in this embodiment is as follows: Figure 2 As shown, the refractive index decreasing region forms a low-refractive-index equivalent annular region, which is used to constrain the edge of the dominant mode field, so that the output mode field maintains a high flatness in the central region and decays rapidly in the region near the hexagonal boundary. The refractive index distribution function along the horizontal cross section in this embodiment is shown in Figure 3.

[0076] Under the above structural parameters, by numerically solving the wave equation, it can be found that the fundamental mode supported by this optical fiber at a wavelength of 1064 nm exhibits a super-Gaussian distribution. Its light intensity distribution is basically flat in the central region, rapidly attenuates near the hexagonal boundary, and exhibits hexagonal symmetry overall.

[0077] Preferably, the mode field can be approximated in the following form:

[0078] The light intensity in the central region is approximately constant, while the light intensity at the edges follows a higher-order exponential decay law.

[0079] In this embodiment, the energy distribution of the hexagonal super-Gaussian flat-top exiting mode field generated by optical fiber transmission is shown in Figure 4.

[0080] The preform corresponding to the optical fiber is preferably prepared by plasma chemical vapor deposition (PCVD). By controlling the dopant gas concentration distribution during the deposition process, the aforementioned non-monotonic refractive index profile is achieved.

[0081] Specifically:

[0082] The region of increased refractive index is achieved by adjusting the Ge doping;

[0083] A refractive index reduction region is achieved by introducing F doping;

[0084] The width of each radial region is controlled by segmented deposition.

[0085] After the preform is prepared, the optical fiber of the target size is obtained through a drawing process.

[0086] In other embodiments, the operating wavelength λ, the center-to-center distance a, and the mode field characteristic scale are... Super-Gaussian order m, effective refractive index of the dominant mode Equivalent radial distance Transition function The start and end points of the transition zone and the refractive index of the cladding These parameters can be reset according to application requirements. After resetting, the equivalent radial refractive index distribution can be recalculated using the method described above to obtain a rotationally symmetric super-Gaussian distribution mode field special optical fiber that matches the new target mode field.

[0087] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A special optical fiber with rotationally symmetric super-Gaussian distributed mode field output, comprising a fiber core and a cladding covering the fiber core, characterized in that: The cross-sectional boundary of the fiber core is a rotationally symmetric boundary, which is either a finite-weight rotationally symmetric boundary or a continuous rotationally symmetric boundary. The fiber core has a non-monotonic refractive index profile distributed along an equivalent radial direction. The equivalent radial direction is characterized by an equivalent radial parameter, which is the ratio of the distance from any point in the cross-section to the geometric center of the fiber core to the distance from the geometric center through that point to the rotationally symmetric boundary. The non-monotonic refractive index profile includes, from the inside to the outside, a central flat region, a refractive index rising region, a refractive index falling region, and a transition region. The refractive index of the rising refractive index region increases from the refractive index of the central flat region along the equivalent radial direction to a local maximum value, the refractive index of the falling refractive index region decreases along the equivalent radial direction to a local minimum value, and the refractive index of the transition region transitions from the local minimum value to the refractive index of the cladding; The non-monotonic refractive index profile matches the rotationally symmetric super-Gaussian target mode field at the preset target wavelength, so that the dominant mode supported by the special optical fiber at the preset target wavelength exhibits a rotationally symmetric super-Gaussian flat-top mode field distribution with a flat central region, rapid edge attenuation, and corresponding to the rotationally symmetric boundary.

2. The special optical fiber according to claim 1, characterized in that, When the rotational symmetry boundary is a finite-weight rotational symmetry boundary, the finite-weight rotational symmetry boundary coincides with the original boundary after rotating 360° / n around the geometric center of the fiber core, where n is an integer greater than or equal to 3; when the rotational symmetry boundary is a continuous rotational symmetry boundary, the continuous rotational symmetry boundary coincides with the original boundary after rotating arbitrarily around the geometric center of the fiber core.

3. The special optical fiber according to claim 1, characterized in that, The rotationally symmetric boundary includes a regular polygonal boundary or a circular boundary; when the rotationally symmetric boundary is a regular polygonal boundary, the rotationally symmetric super-Gaussian flat-top mode field distribution has angular symmetry corresponding to the regular polygonal boundary.

4. The special optical fiber according to claim 3, characterized in that, The boundary of the regular polygon is a regular hexagonal boundary.

5. The special optical fiber according to claim 1, characterized in that, The rotationally symmetric super-Gaussian target model field is determined by the central field strength, the characteristic scale parameter, and the super-Gaussian order. When the rotationally symmetric boundary is a regular polygonal boundary, the characteristic scale parameter corresponds to the center-to-side distance of the regular polygonal boundary. When the rotationally symmetric boundary is a circular boundary, the characteristic scale parameter corresponds to the radius of the circular boundary or the characteristic radius of the model field.

6. The special optical fiber according to claim 1, characterized in that, The non-monotonic refractive index profile is determined based on the vacuum wavenumber at the preset target wavelength and the rotationally symmetric super-Gaussian target mode field inversion; the preset target wavelength is any working wavelength selected according to application requirements, and the non-monotonic refractive index profile is reconfigured as the preset target wavelength changes.

7. The special optical fiber according to claim 1, characterized in that, The non-monotonic refractive index profile is composed of at least one constant function segment and at least one continuously varying function segment, with adjacent function segments satisfying functional continuity; the refractive index decreasing region forms a low refractive index equivalent annular region, which is used to constrain the edge attenuation of the dominant mode and reduce the light intensity fluctuation in the central region.

8. A method for preparing the special optical fiber according to any one of claims 1 to 7, characterized in that, include: The rotational symmetry boundary and equivalent radial parameters of the fiber core cross section are determined based on the preset target wavelength and rotational symmetric super-Gaussian target mode field. Based on the preset target wavelength and the rotationally symmetric super-Gaussian target mode field, a non-monotonic refractive index profile along the equivalent radial direction is obtained by inversion. The optical fiber preform is prepared using an optical fiber preform preparation method capable of forming the non-monotonic refractive index profile, so that the optical fiber preform has a refractive index distribution corresponding to the central flat region, the refractive index rising region, the refractive index falling region, and the transition region. The optical fiber preform is drawn into fibers to obtain the special optical fiber.

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