Microrod-assisted elliptical core few-mode optical fiber with high refractive index

Abstract

The utility model provides an elliptical core few-mode optical fiber assisted by a high-refractive-index microrod. The optical fiber is composed of a pure silicon dioxide elliptical fiber core, air holes, high-refractive-index microrods and a cladding, wherein the fiber core has step refractive index distribution; by the aid of the structure of the pure silicon dioxide elliptical fiber core and the air hole, low-crosstalk, low-intrinsic-loss and low-bending-loss seven-ermius-Gaussian mode operation is realized, mode degeneracy is broken through by the elliptical fiber core and microrod structure, light field regulation and control and mode maintaining functions are realized, complex MIMO-DSP processing is eliminated, and the optical fiber is high in performance and high in stability. And the good performance of the MIMO-FREE application is realized.

Description

Technical Field

[0001] This patent application involves a new type of optical fiber, and proposes a high-refractive-index micron-rod-assisted elliptical-core few-mode optical fiber, which can be applied to new-generation information technology fields such as mode division multiplexing. Background Art

[0002] With the rapid development of various communication services, traditional single-mode optical fiber can no longer meet the needs of more communication services due to the limitation of nonlinear Shannon limit. Mode division multiplexing technology based on few-mode optical fiber has doubled the transmission capacity and spectrum efficiency of single-mode optical fiber, becoming a hot topic in the current field of optical fiber communication. As the transmission carrier of information in optical fiber communication system, how to improve the transmission performance of optical fiber and reduce the loss and crosstalk of few-mode optical fiber is an urgent problem to be solved in optical transmission technology.

[0003] In view of the limited capacity of single-mode optical fiber, the traditional round-core few-mode optical fiber currently proposed is constantly breaking through the transmission capacity or spectrum efficiency of optical fiber [Zhang Q, Han W, Xiong Z, et al. 3×34Gb / s PDM-QPSK signalmode division multiplexing experiment based on fewmode fiber[J].Optical Communication Technology, 2022, 46(1): 77-80; RADEMACHER G, PUTTNAM BJ, RS, et al.10.66Peta-Bit / s Transmission over a 38-Core-Three-Mode Fiber.In OpticalFiber Communication Conference(OFC), OSA Technical Digest(Optical Society of America), 2020, Paper Th3H.1; BEPPU S, SOMA D, SUMITA S, et al.402.7-Tb / s MDM-WDMTransmission over Weakly Coupled 10-Mode Fiber Using Rate-Adaptive PS-16QAMSignals[J].Journal of Lightwave Technology, 2020, 38: 2835-2841; WAKAYAMA Y, SOMAD, BEPPU S.266.1-Tbit / s Transmission over 90.4-km 6-Mode Fiber with InlineDual C+L-Band 6-Mode EDFA[J].Journal of Lightwave Technology, 2019, 37: 404-410; SOMA D, BEPPU S, WAKAYAMA Y, et al. 257-Tbit / s Weakly Coupled 10-Mode C+L-Band WDM Transmission [J]. Journal of Lightwave Technology, 2018, 36: 1375-1381; WEERDENBURG J, RYF R, ALVARADO-ZACARIAS J, et al. 138-Tb / s Mode-and Wavelength-Multiplexed Transmission over Six-Mode Graded-Index Fiber [J]. Journal of Lightwave Technology, 2018, 36: 1369-1374; ], but the crosstalk and loss between the modes of these round-core few-mode fibers still exist. The crosstalk between the modes requires the use of multiple-input multiple-output digital signal processing. The loss of the optical fiber will affect the transmission distance or relay distance of the optical communication system. The loss of the optical fiber is the most important parameter that determines the capacity of the optical fiber communication system.In order to solve the crosstalk and loss in optical fiber, ring-core few-mode fiber [Shuo C, Yue T, Huiping T.Eight-mode ring-core few-mode fiber using cross-arranged different-material-filling side holes.[J].Applied optics,2020,59(15); BRUNET C, UNG L, WANG L, et al.Design of a Familyof Ring-Core Fibers for OAM Transmission Studies[J].Optics Express,2015,23(8):10553-10563; RAMACHANDRAN S, KRISTENSEN P, YAN M F.Generation and Propagation of Radially Polarized Beams in Optical Fibers[J].Optics Letters, 2009, 34(16): 2525-2527.], elliptical core few-mode fiber [Corsi, A.; Chang, JH; Rusch, LA; LaRochelle, S. 2018; PARMIGIANI F,JUNG Y,. L, et al. Elliptical Core Few Mode Fibers for Multiple-Input Multiple Output-Free Space Division Multiplexing Transmission[J]. IEEE Photonics Technology Letters, 2017, 29(21): 1764 - 1767; IP E, MILIONE G, LI M, et al. SDM Transmission of Real-Time 10GbE Traffic using Commercial SFP+ Transceivers over 0.5km Elliptical-Core Few-Mode Fiber[J]. Optics Express, 2015, 23(13): 17120 - 17126], Elliptical Ring Core Few-Mode Fiber[Xiaoqiang Z, Yong J, Yong X, et al. Polarization-maintaining fiber composed of an elliptical ring core and two circular air holes.[J]. Applied optics, 2019, 58(32); ZHAO J, TANG M, OH K, et al. Polarization-maintaining few mode fiber composed of a central circular-hole and an elliptical-ring core[J]. Photonics Research, 2017, 5(03): 261 - 266; WANG L, NEJAD R M, CORSI A, et al. Linearly Polarized Vector Modes: Enabling MIMO-Free Mode-Division multiplexing[J]. Optics Express, 2017, 25(10): 11736 - 11748; WANG L, LAROCHELLE S.Design of Eight-Mode Polarization-Maintaining Few-Mode Fiber for Multiple-Input Multiple-Output-Free Spatial Division Multiplexing[J]. Optics Letters,2015,40(24):5846-5849], panda-type few-mode fiber [Zhang, J.; Chen, YK.; Wu, ZC.; Feng, SJ.; Shum, P.; Huang, TY. Panda type separated-circles-formed elliptical ring core few-mode fiber. Opt. Fiber Technol. 2022, 73, 103067; Du, ZY; Wang, CC.; Li, PX.; Li, P; Zheng, JJ.; Ning, TG. Fully degeneracy-lifted PANDA few-mode fiber based on the segmented ring-core. Optik 2022, 255, 168710; YAN H, LI S, XIE Z, et al. Design of PAND Ring-Core Fiber with 10 Polarization-Maintaining Modes[J]. Photonics Research, 2017, 5(1): 1-5; CAO Y, ZHAO Y, YU X, et al. Design and Characterization of 16-Mode PANDA Polarization-Maintaining Few-Mode Ring-Core Fiber for Spatial Division Multiplexing[J]. Optical Engineering, 2017, 56: 116102] and bow-tie-type few-mode fiber [Ci Y, Ren F, Lei X, et al. A Weakly-Coupled Double Bow-Tie Multi-Ring Elliptical Core Multi-Mode Fiber for Mode Division Multiplexing across C+L+U Band[J]. Applied Sciences, 2023, 13(10); Zhang, J.; Ren, F.; Niu, J.; Lei, X.; Zhang, Y.; Cui, F.; Wang, J.Design of weakly coupled 20-eigenmode bow-tie rectangular dual-step fiber for short-haul communication in Oband.Opt.Eng.2021, 60, 126107; Yang, TX; Zhang, H.; Xi, LX; Yang, JX; Chen, Z.; Wang, XQ; Zhang, XGDesign of a novel bow-tie polarization ring-core few-modefiber for MIMO-free MDM system.In Proceedings of the 26th Optoelectronics andCommunications Conference, Hong Kong, China, 3-7July 2021.] was proposed and demonstrated to have the ability to separate spatial modes and reduce mode coupling. Compared with traditional circular few-mode fibers, ring-core few-mode fibers (RC-FMF) have a larger effective mode area to achieve low nonlinearity, low transmission loss and microbend loss. For example, the eight-mode ring-core few-mode fiber mentioned in the article [Shuo C, Yue T, Huiping T.Eight-mode ring-core few-mode fiber using cross-arranged different-material-filling side holes. [J]. Applied optics, 2020, 59 (15);] uses a ring-core few-mode fiber (RC-FMF) with cross-arranged different materials filling the side holes. On the basis of having a larger effective area, it can better break the degeneracy between modes. Both elliptical core and elliptical ring core fibers have the characteristic that the core is elliptical. Due to the influence of the elliptical shape characteristics, it is conducive to breaking the degeneracy between modes, improving the utilization rate of the channel, and has greater design freedom. For elliptical ring core fibers, the power of the guided mode is strongly restricted along the ring core, and the loss is significantly reduced. The introduction of panda-type few-mode fiber and bow-tie-type few-mode fiber is also to better improve the effective refractive index difference between modes, break through the limitations of traditional single-mode fiber, reduce the crosstalk caused by mode coupling, and try to eliminate the need for multiple-input and multiple-output digital signal processing, thereby increasing the potential for transmission capacity and spectrum efficiency.

[0004] All of the above few-mode fibers are polarization-maintaining few-mode fibers. The x-component and y-component in the mode are separated, and the relative refractive index difference between the modes is greater than 10. -4 The magnitude of the crosstalk between the xy components of the mode can be reduced to a certain extent; if the receiving end compensates through digital signal processing, it will still increase the complexity, calculation amount, cost, etc. of the short-distance transmission system. In order to further reduce the crosstalk of the optical fiber and break the degeneracy of the spatial mode, the application of multi-input multi-output operation is a preferred solution for future short-distance data transmission. In summary, taking effective measures to break the degeneracy of the spatial mode, eliminate complex multi-input multi-output digital signal processing (MIMO-DSP), and realize MIMO-free (MIMO-FREE) applications has important academic and application value, and the research is of great significance and has broad application prospects. Utility Model Content

[0005] This patent application proposes a high-refractive-index micron-rod-assisted elliptical-core few-mode optical fiber, which combines the advantages of a pure silica elliptical core, a step-index distribution, high-refractive-index micron-rods, and an air-hole-assisted region, breaks the degeneracy of spatial modes, realizes light field control and mode preservation functions, eliminates complex MIMO-DSP processing, and realizes low-loss, low-crosstalk MIMO-FREE applications, providing important support for in-depth research in the fields of fiber optics, fiber communications, fiber wireless access, optical information processing, and new generation information technology.

[0006] The technical solution adopted by this patent application to solve its technical problem is:

[0007] A high refractive index micron rod assisted elliptical core few-mode optical fiber; characterized in that: the optical fiber is composed of a pure silica elliptical core, an air hole, a high refractive index micron rod and a cladding, wherein the core has a step refractive index distribution; the horizontal radius of the elliptical core is a x =7.2μm, vertical radius is a y =4.8μm, ellipticity ρ = a x / a y=1.5; the four circular structures in the core are high refractive index microrods, the refractive index of the two microrods on the X axis is the same, the refractive index of the two microrods on the Y axis is the same, and the radius of these four microrods is exactly the same, radius R1 = 0.6μm; the four circular structures on the XY axis outside the core are air holes, the two holes on the X axis are exactly the same, radius R3 = 7μm; the two holes on the Y axis are also exactly the same, radius R2 = 7.6μm; except for the elliptical core, high refractive index microrods and air holes, the rest is cladding, and the outer cladding radius value is R = 62.5μm; the center coordinates of the core are (0, 0); the center coordinates of the high refractive index microrods on the X axis inside the core are (-3.5E-6 , 0) and (3.5E-6, 0), the center coordinates of the high refractive index microrod on the Y axis inside the fiber core are (0, 4.2E-6) and (0, -4.2E-6) respectively; the center coordinates of the two air holes on the X axis outside the fiber core are (-1.95E-5, 0) and (1.95E-5, 0) respectively, and the center coordinates of the two air holes on the Y axis outside the fiber core are (0, 1.77E-5) and (0, -1.77E-5) respectively; the refractive indexes of the pure silica core, the high refractive index microrod on the X axis, the high refractive index microrod on the Y axis, the air hole region and the cladding are n1 = 1.4440, n2 = 1.4590, n3 = 1.4670, n4 = 1, and n = 1.4292 respectively. The mode field characteristics of the spatial mode in the optical fiber can be changed by changing the refractive index distribution, size and position of the core and cladding.

[0008] The beneficial effects of this patent application are as follows:

[0009] 1. The elliptical core and high refractive index microrods break the degeneracy of spatial modes, realize the light field control and mode preservation functions, effectively improve the effective refractive index difference between modes, facilitate low crosstalk transmission between modes, eliminate complex MIMO-DSP processing, realize good transmission of MIMO-FREE applications, and further improve the fiber transmission performance;

[0010] 2. The optical fiber adopts air hole auxiliary area, which can effectively reduce bending loss;

[0011] 3. The optical fiber integrates a pure silica core to achieve low loss, providing important support for in-depth research in the fields of fiber optics, fiber optic communications, fiber optic wireless access, optical information processing, and next-generation information technology.

[0012] 4. The Hermite-Gaussian mode field characteristics in the optical fiber can be changed by changing the size, position and refractive index distribution of the core, cladding, high refractive index microrods and air holes. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1This is a schematic diagram of the cross section of a high refractive index micron rod assisted elliptical core few-mode optical fiber applied for in this patent; the optical fiber consists of a pure silica elliptical core with a step refractive index distribution (the oblique shaded part), air holes (the four dot shaded circular holes on the XY axis), high refractive index micron rods (the horizontal and vertical shaded parts) and a cladding (the white part).

[0014] Figure 2 The x-polarized electric field distribution of HG30, HG02, HG11, HG20, HG01, HG10 and HG00 modes at 1.55 μm is given. The equipotential lines in the figure represent the strength of the incident light electric field. The greater the density, the stronger the electric field.

[0015] Figure 3 The effective refractive index of seven modes varies with input wavelength. The solid lines with squares, asterisks, diamonds, circles, triangles, pentagrams, and hexagons are the variations of the HG00, HG10, HG01, HG20, HG11, HG02, and HG30 modes, respectively.

[0016] Figure 4 The changes of DMGD of HG30, HG02, HG11, HG20, HG01 and HG10 modes with incident wavelength are shown. The solid lines with five-pointed stars, six-pointed stars, triangles, circles, diamonds and asterisks in the figure represent the changes of DMGD of HG30, HG02, HG11, HG20, HG01 and HG10 modes respectively.

[0017] Figure 5 The graph shows how the intrinsic loss of the seven Hermite-Gaussian modes varies with the input wavelength. The solid lines with hexagonal stars, pentagonal stars, triangles, circles, diamonds, asterisks and squares are the changes in the intrinsic loss of the HG30, HG02, HG11, HG20, HG01, HG10 and HG00 modes, respectively.

[0018] Figure 6 The dispersion of the Hermite-Gaussian modes of HG30, HG02, HG11, HG20, HG01, HG10 and HG00 varies with the incident wavelength. The solid lines with circles, asterisks and triangles in the figure represent the variation of the material dispersion, waveguide dispersion and total dispersion of each Hermite-Gaussian mode, respectively.

[0019] Figure 7 The figure shows the variation of the bending loss of the HG30 Hermite-Gaussian mode with the bending radius when the air hole does not rotate with the fiber core. The solid lines with asterisks, circles, squares, triangles and hexagonal stars in the figure respectively represent the variation of the bending loss with the bending radius when the angle θ between the major axis of the ellipse and the X-axis is 0°, 30°, 45°, 60° and 90°.

[0020] Figure 8 The figure shows the variation of the bending loss of the HG30 Hermite-Gaussian mode with the bending radius when the air hole rotates with the fiber core. The solid lines with asterisks, circles, squares, triangles and hexagonal stars in the figure respectively represent the variation of the bending loss with the bending radius when the angle θ between the major axis of the ellipse and the X-axis is 0°, 30°, 45°, 60° and 90°. DETAILED DESCRIPTION

[0021] The technical solution of the present patent application is described in detail below in conjunction with the embodiments and drawings, but the protection scope is not limited thereto.

[0022] Example 1 Figure 1 This is a schematic diagram of a high refractive index micron rod assisted elliptical core few-mode optical fiber in this patent application. The optical fiber is composed of a pure silica elliptical core, an air hole, a high refractive index micron rod and a cladding, wherein the core has a step refractive index distribution; the horizontal radius of the elliptical core is a x =7.2μm, vertical radius is a y =4.8μm, ellipticity ρ = a x / a y =1.5; the four circular structures in the core are high refractive index microrods, the refractive index of the two microrods on the X axis is the same, the refractive index of the two microrods on the Y axis is the same, and the radius of these four microrods is exactly the same, radius R1 = 0.6μm; the four circular structures on the XY axis outside the core are air holes, the two holes on the X axis are exactly the same, radius R3 = 7μm; the two holes on the Y axis are also exactly the same, radius R2 = 7.6μm; except for the elliptical core, high refractive index microrods and air holes, the rest is cladding, and the outer cladding radius value is R = 62.5μm; the center coordinates of the core are (0, 0); the center coordinates of the high refractive index microrods on the X axis inside the core are (-3.5E-6, 0) and (3.5E-6, 0), the center coordinates of the high refractive index microrod on the Y axis inside the fiber core are (0, 4.2E-6) and (0, -4.2E-6) respectively; the center coordinates of the two air holes on the X axis outside the fiber core are (-1.95E-5, 0) and (1.95E-5, 0) respectively, and the center coordinates of the two air holes on the Y axis outside the fiber core are (0, 1.77E-5) and (0, -1.77E-5) respectively; the refractive indexes of the pure silica core, the high refractive index microrod on the X axis, the high refractive index microrod on the Y axis, the air hole refractive index region and the cladding are n1 = 1.4440, n2 = 1.4590, n3 = 1.4670, n4 = 1, and n = 1.4292 respectively. The mode field characteristics of the spatial mode in the optical fiber can be changed by changing the refractive index distribution, size and position of the core and cladding.

[0023] Figure 2The electric field distribution of x polarization of HG30, HG02, HG11, HG20, HG01, HG10 and HG00 modes at 1.55μm wavelength is given. The equipotential lines in the figure represent the strength of the incident light electric field. The greater the density, the stronger the electric field. HG30, HG02, HG11, HG20, HG01, HG10 and HG00 represent the seven modes corresponding to the optical fiber. The optical fiber we proposed has a clear mode-preserving function, and realizes the mode-preserving operation of seven Hermite-Gaussian modes: HG30, HG02, HG11, HG20, HG01, HG10 and HG00. The large effective refractive index difference between the Hermite-Gaussian modes, the pure silica elliptical core and the air hole structure realize low crosstalk, low intrinsic loss and low bending loss operation. The elliptical core and microrod structure break the mode degeneracy, realize the light field control and mode-preserving functions, eliminate the complex MIMO-DSP processing, and achieve good performance of MIMO-FREE applications.

[0024] Figure 3 The effective refractive index of the seven modes of the few-mode fiber varies with the wavelength of the incident light. The solid lines with squares, asterisks, diamonds, circles, triangles, five-pointed stars, and six-pointed stars represent the changes of the HG00, HG10, HG01, HG20, HG11, HG02, and HG30 modes, respectively. Figure 3 It can be seen that the effective refractive index of the seven modes decreases with the increase of the wavelength of the incident light, and the change of the effective refractive index is slow; for a given incident wavelength, the effective refractive index of the HG00 mode is the largest, the effective refractive index of the HG30 mode is the smallest, and the effective refractive index of the HG00, HG10, HG01, HG20, HG11, HG02 and HG30 modes decreases in turn; when the wavelength of the incident light is 1.55μm, the effective refractive indexes of the HG00, HG10, HG01, HG20, HG11, HG02 and HG30 modes are 1.44229, 1.43962, 1.43796, 1.43562, 1.43308, 1.43159 and 1.43016 respectively. The large effective refractive index difference between the modes achieves low mode crosstalk.

[0025] Figure 4The changes of DMGD of HG30, HG02, HG11, HG20, HG01 and HG10 modes with incident wavelength are shown. The solid lines with five-pointed stars, six-pointed stars, triangles, circles, diamonds and asterisks in the figure represent the changes of DMGD of HG30, HG02, HG11, HG20, HG01 and HG10 modes respectively. In the wavelength range of 1.3μm to 1.5μm, the DMGD value of the HG02 mode is the largest, and the DMGD value of the HG10 mode is the smallest; when the wavelength is 1.55μm, the DMGD of the HG30, HG02, HG11, HG20, HG01 and HG10 modes are 9.44999ps / m, 14.5928ps / m, 8.51065ps / m, 15.8745ps / m, 10.2658ps / m and 7.72212ps / m, respectively, with a large differential mode group delay.

[0026] Figure 5 It can be obtained that the intrinsic loss of each Hermite-Gaussian mode in the few-mode fiber we proposed in the C-band is small. In addition, the upper left corner is the refractive index distribution diagram of the optical fiber along the X-axis and along the Y-axis.

[0027] Figure 6 The dispersion of the Hermite-Gaussian modes of HG30, HG02, HG11, HG20, HG01, HG10 and HG00 varies with the incident wavelength. The solid lines with circles, asterisks and triangles in the figure represent the changes in the material dispersion, waveguide dispersion and total dispersion of each Hermite-Gaussian mode, respectively. It can be seen from the figure that in the wavelength range of 1.3um to 1.6um, the waveguide dispersion of the HG10 mode varies relatively smoothly, the material dispersion and total dispersion of the HG10 mode increase with the increase of the incident wavelength, and the total dispersion of the HG10 mode gradually increases from 4.25675ps / (nm·km) to 30.5567ps / (nm·km). In the wavelength range of 1.3um to 1.6um, the waveguide dispersion of the HG30 mode varies greatly, and the total dispersion of the HG30 mode gradually decreases from 1.80465ps / (nm·km) to -17.6002ps / (nm·km).

[0028] Figure 7 The figure shows the change of bending loss of the HG30 Hermite-Gaussian mode with bending radius when the air hole does not rotate with the fiber core. The solid lines with asterisks, circles, squares, triangles and hexagonal stars in the figure respectively represent the change of bending loss with bending radius when the angle θ between the major axis of the ellipse and the X-axis is 0°, 30°, 45°, 60° and 90°. It can be seen from the figure that the bending loss of HG30 gradually decreases with the increase of bending radius at 0°, 30°, 45°, 60° and 90°. The bending loss of other Hermite-Gaussian modes is smaller.

[0029] Figure 8 The figure shows the change of bending loss of the HG30 Hermite-Gaussian mode with bending radius when the air hole rotates with the fiber core. The solid lines with asterisks, circles, squares, triangles and hexagonal stars in the figure respectively represent the change of bending loss with bending radius when the angle θ between the major axis of the ellipse and the X-axis is 0°, 30°, 45°, 60° and 90°. The bending loss fluctuates locally with the increase of bending radius, but generally decreases with the increase of bending radius.

[0030] In short, the proposed optical fiber breaks the spatial mode degeneracy, realizes the light field control and mode preservation functions, and has the advantages of low loss and low crosstalk. It should be pointed out that the specific implementation method is only a more representative example of this technology. Obviously, the technical solution of this technology is not limited to the above embodiment, and there can be many variations. Those of ordinary skill in the art who have obtained the technology clearly disclosed or obtained without objection based on the written description of the document should be considered to be within the scope of protection of this patent.

Claims

1. A high refractive index micro-rod assisted elliptical core few-mode optical fiber; characterized in that: The optical fiber is composed of a pure silica elliptical core, an air hole, a high refractive index microrod and a cladding, wherein the core has a step refractive index distribution; the horizontal radius of the elliptical core is a x =7.2μm, vertical radius is a y =4.8μm, ellipticity ρ = a x / a y =1.5; the four circular structures in the core are high refractive index microrods, the refractive index of the two microrods on the X axis is the same, the refractive index of the two microrods on the Y axis is the same, and the radius of these four microrods is exactly the same, radius R1 = 0.6μm; the four circular structures on the XY axis outside the core are air holes, the two holes on the X axis are exactly the same, radius R3 = 7μm; the two holes on the Y axis are also exactly the same, radius R2 = 7.6μm; except for the elliptical core, high refractive index microrods and air holes, the rest is cladding, and the outer cladding radius value is R = 62.5μm; the center coordinates of the core are (0, 0); the center coordinates of the high refractive index microrods on the X axis inside the core are (-3.5E-6 , 0) and (3.5E-6, 0), the center coordinates of the high refractive index microrod on the Y axis inside the fiber core are (0, 4.2E-6) and (0, -4.2E-6) respectively; the center coordinates of the two air holes on the X axis outside the fiber core are (-1.95E-5, 0) and (1.95E-5, 0) respectively, and the center coordinates of the two air holes on the Y axis outside the fiber core are (0, 1.77E-5) and (0, -1.77E-5) respectively; the refractive indices of the pure silica core, the high refractive index microrod on the X axis, the high refractive index microrod on the Y axis, the air hole region and the cladding are n1=1.4440, n2=1.4590, n3=1.4670, n4=1, and n=1.4292 respectively.

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