Optical property of Few-Mode Fiber with Non-uniform Refractive Index for Cylindrical Vector Beam Generation

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1 Optical prperty f Few-Mde Fiber with Nn-unifrm Refractive Index fr ylindrical Vectr Beam Generatin Hngye Li a, Hngdan Wan* a, Zuxing Zhang* a, b, Bing Sun a, Lin Zhang a, b a Nanjing University f Psts and Telecmmunicatins, Nanjing 213, hina b Astn Institute f Phtnic Technlgies, Astn University, Birmingham B4 7ET, UK ABSTRAT This paper investigates ptical prperties f few-mde fiber with nn-unifrm refractive index, namely: the few mde fiber with U-shape refractive index and the tw-mde and fur-mde few-mde fiber with bent radius. Finite element methd is used t analyze the mde distributins based n their nn-unifrm refractive index. Effective mde cntrl can be achieved thrugh these few mde fibers t achieve vectr beam generatin. Finally, reflectin spectra f a few-mde fiber Bragg grating are calculated theretically and then measured under different bending cnditins. Experimental results are in gd accrdance with the theretical nes. These few mde fibers shw ptential applicatins in generatin f cylindrical vectr beam bth fr ptical lasing and sensing systems. Keywrds: few-mde fiber, cylindrical vectr beam, nn-unifrm refractive index, few-mde fiber Bragg grating 1. INTRODUTION ylindrical vectr beams (VBs) have drawn cnsiderable attentin recently fr their symmetric intensity and plarizatin prperties. The symmetrical plarizatin results in many applicatins, such as ptical tweezers, surface plasmn resnance and material prcessing [1-3]. Hw t generate the VBs including radically (TM1) and azimuthally (TE1) plarized beams has becme a ht tpic. Tw methds are cmmnly used, namely the external-cavity ( passive ) and the internal-cavity ( psitive ) methd [4]. The frmer cnsist f spatial light mdulatr, wave plate and ther spatial light units fr generating spatial beams with symmetrical plarizatin [5, 6]. The latter cntains birefringence elements r few-mde fiber gratings (FMFG) as the mde selectr t achieve high-rder mdes inside a fiber device, [7, 8]. such as the few-mde fiber lng perid grating (FMF-LPG) and the few-mde fiber Bragg grating (FMF-BG) The FMF-LPG cnverts LP1 mde t LP11 mdes by mechanical stress frm special mechanical hlders [7], result in an increased dimensin and higher prbability f fiber damage. The FMF-BG is frmed by a peridic index mdulatin ver the phtsensitive fiber cre alng prpagatin length, having the advantages f high-efficiency, lw cst and all-fiber structure [8]. The frward prpagating mdes can be cupled t the phase-matched backward prpagating mdes, the fundamental mde inside the few-mde fiber is cnverted t the high-rder mdes, with mdal prperties determined by the index prfile ver the fiber cre. Hwever, UV-side-writing r fiber bending f actual used FMF brings birefringence and affects mdal cnversin due t the nn-unifrm refractive index prfile ver the fiber cre. Since the high-rder mde excitatin and cnversin efficiency decide the VBs generatin efficiency, there still need effrts t investigate the ptical prperty f a specially designed FMF with a nn-unifrm refractive index prfile and t effectively achieve VBs with higher mde purity. In this paper, we investigate the ptical prperties f the FMFs with U-shape refractive index and bent FMF Bragg Grating (FMFBG). The reflectin and transmissin spectra f the FMFG are studied theretically based n a 3- dimensinal nn-unifrm refractive index prfile. Then the reflectin spectra f the fur-mde FMFBG and the transmissin spectrum f the fur-mde FMFBG as well as its mdal prfile are measured experimentally, high rder mdes culd be excited and cntrlled. Finally, the reflectin spectra under special bending cnditin are als given experimentally t achieve effective mde cntrl. *hdwan@njupt.edu.cn; *zxzhang@njupt.edu.cn; phne ; fax Advanced Laser Manufacturing Technlgy, edited by Bingheng Lu, Huaming Wang, Prc. f SPIE Vl. 1153, 1153K 216 SPIE cde: X/16/$18 di: / Prc. f SPIE Vl K-1

$1 The U-shape refractive index FMF Figure 1 and Figure 2 illustrate the parameters f a U-shape refractive$ $The LP11 mde is cnfined in the high refractive index ring and the fundamental mde pwer is extremely weak.$ Thus, the U-shape index FMF can be used t suppress the fundamental mde and excite the LP11 mde.

Thus, the U-shape index FMF can be used t suppress the fundamental mde and excite the LP11 mde.

$Parameters and refractive index prfile f the U-shape refractive index FMF, Fig.$ $2 The bent FMF The refractive index f bent fibers can be calculated using the Marcuse frmula: n n(1 x / R),$ 1 demnstrates the mdal prfile f a tw-mde fiber (with nrmalized frequency V=6.4) with different bending radius.

1 demnstrates the mdal prfile f a tw-mde fiber (with nrmalized frequency V=6.4) with different bending radius.

Therefre, small bending results in suppressin f the high-rder mdes first, with the fundamental mde r lw-rder

Table 1 and 2 shw the calculated mdal prfile f the tw and fur mde fibers with different bending radius.

2 2. MODAL PROPERTIES OF THE FMFS WITH NON-UNIFORM REFRATIVE INDEX PROFILE 2.1 The U-shape refractive index FMF Figure 1 and Figure 2 illustrate the parameters f a U-shape refractive index FMF and its mde distributin prfile at 155nm, respectively. The LP11 mde is cnfined in the high refractive index ring and the fundamental mde pwer is extremely weak. Thus, the U-shape index FMF can be used t suppress the fundamental mde and excite the LP11 mde. With prper pumping methd, this kind f fiber culd be used fr fiber lasers t generate VBs. Fig1.Parameters and refractive index prfile f the U-shape refractive index FMF, Fig.2 Mde distributin prfile f U-shape refractive index FMF at 155nm 2.2 The bent FMF The refractive index f bent fibers can be calculated using the Marcuse frmula: n n(1 x / R), where n is refractive index f cre r cladding, R is the bending radius[4]. Table.1 demnstrates the mdal prfile f a tw-mde fiber (with nrmalized frequency V=6.4) with different bending radius. Obviusly, higher mdes dissipate prir t lwer mdes when the curvature radius cntinues t be decreased. Therefre, small bending results in suppressin f the high-rder mdes first, with the fundamental mde r lw-rder mdes retain, which is testified experimentally in the fllwing part f this paper. Table 1 and 2 shw the calculated mdal prfile f the tw and fur mde fibers with different bending radius. It can be seen that, a reduced bending radius results in decreased mdes number being cnfined inside the bent fiber cre. Table.1 Mdal prfile f the tw-mde FMF with different bending radius. Re: Reserve; BD: Begin Dissipating; D: Dissipate urvature Radius R/cm LP1 LP11 LP21 LP2 1 Re Re Re BD 5 Re Re BD D 4 Re Re D D 2 Re D D D 1 D D D D Prc. f SPIE Vl K-2

3 Table.2 Mdal prfile f the fur-mde FMF with different bending radius. When the curvature radius is 4cm, nly the fur lwest mdes (LP1, LP11, LP21, LP2) exist. Re: Reserve; BD: Begin Dissipating; D: Dissipate urvature radius R/cm LP1 LP11 LP21 LP2 LP31 LP12 1 Re Re Re Re Re BD 4 Re Re Re Re D D 3 Re Re Re D D D 2 Re Re D D D D 1 D D D D D D 3.1 Operatin principle 3. OPTIAL PROPERTIES OF THE FMFBG Mdal cupling prcess decides the reflectin spectra f a specific FMFBG. The cupling intensity is decided by the t verlap integral K kj z x, y, z ekt x, y e jt x, y dxdy 4, where e kt x, y and e jt x, y are the nrmalized electric cre field f mde k and mde j, respectively. The resnance wavelength is decided by the phase matching frmula: 2 k j, where k, j and are the prpagatin cnstant f mde k, prpagatin cnstant f mde j and perid f grating [5]. The cupling prcess ccurs when the frward mde and backward mde satisfy phase matching frmula in fiber Bragg grating. Fr self-cupling, the phase matching frmula can be simplified as B 2 n eff ( B and are the resnance wavelength and effective refractive index, respectively), the simplified frmula is n eff n n. B eff,1 eff, Reflectin spectra f the tw-mde FMFBG The grating perid f the tw-mde FMFBG is 533nm. Fig. 3(a) and (b) illustrates the fiber dispersin curve and reflectin spectra under different mde-rati (the mde intensity rati between LP1 mde and LP11 mde). Three reflectin peaks represent the self-cupling and mutual-cupling between the LP1 and LP11mdes.The reflectin peak intensity is decided by the mde-rati, increased intensity f single mde results in enhanced self-cupling. Prc. f SPIE Vl K-3

<a) dispersin curve E 5.91 x 16 : 5.9 O 5.89 O O 5.88 ( Q ñ 5.87 1542 1543 (b) reflectin spectra - LP1 - LP11 - - 7if 1544 1545 1546 1547 1548 wa elength/rrn O m 1.

4 <a) dispersin curve E 5.91 x 16 : 5.9 O 5.89 O O 5.88 ( Q ñ (b) reflectin spectra - LP1 - LP if wa elength/rrn O m 1.5 x x P1: LP11=1:1 x LP1: LP11=1:1 -LP1: LP11=1: wavelength /nm Fig.3 Optical dispersin curves and reflectin spectra f the tw-mde FMFBG with different mde-rati: Blue, LP1:LP11=1:1; Red, LP1:LP11=1:1; Green, LP1:LP11=1: Reflectin spectra f the fur-mde FMFBG The calculated dispersin curve and reflectin spectra f the fur-mde FMFBG (with nrmalized frequency V=6.8 and grating perid = 533nm) are presented in Fig.4. There are 1 peaks in the reflectin spectra (4 self-cupling peaks and 6 mutual-cupling peaks). (a)dispersin curve x m TA LP LP7 -LP 11 U c 5.89 rn áo 5.88 fl (b)reflectin spectra LP1 LP11 LP21, LP7-LP21 IIIIIÍIII - LP7-LP2 LP77-LP21 LP17-LP2 LP21-LP ó.2 c d wavelength /nm 3.2 Experimental results and discussin Fig.4 Optical dispersin curves and reflectin spectra f the fur-mde FMFBG Figure 5 illustrates the measured reflectin spectra f ur self-made three different FMFBGs: a step-index fur-mde FMFBG, a graded-index fur-mde FMFBG and a step-index tw-mde FMFBG, respectively. Prc. f SPIE Vl K-4

(a) (b) -2 E ß -4 m -6 w N -8 1538 -step index fur -mde FMFG 154 1542 1544 1546 1548-4 - Grade Index fur mde FMFG. E á -5 ti -6 1-7 1546 1548 155 1552 Fig.

5 (a) (b) -2 E ß -4 m -6 w N step index fur -mde FMFG Grade Index fur mde FMFG. E á -5 ti Fig.5 Reflectin spectra f: (a) the step-index fur-mde FMFBG; (b) the graded-index fur-mde FMFBG with 2.5µm ffset splicing t the SMF Figure 6 shws the measured transmissin spectra f the step-index tw-mde FMFBG and the mdal prfile (measured by a NIR-D) near three transmissin-dip wavelengths. Accrding t the theretical analysis, three kinds f mde-cupling prcess are invlved, namely the self-cupling f the LP1 mde ( nm); the mutual-cupling between the LP11 and LP1 mdes ( nm) and the self-cupling f the LP11 mde ( nm). In the inset picture (iii), the LP1 mde is reflected and the LP11 mde transmits thrugh the FBG and is detected by the D Hwever, because f the nn-unifrm refractive index prfile ver the fiber cre, mdal prfile f the LP11 mde takes n a tw-lbe shape, rather than a dughnut-shape, which is in gd accrdance with the simulatins. VB can be achieved using this tw-mde FMFBG near the self-cupling wavelength f the LP1 mde m ß ÿ -52- uei -54- c Ñ Wavelength(dBm) Fig. 6 The measured transmissin spectrum f the step-index tw-mde FMFBG, the inset picture shws the mdal prfile near three different transmissin-dip wavelengths Figure 7 shws different reflectin spectra f the bent step index fur-mde FBG with curvature radius increased frm R 1 t R 6. High rder mdes are excited thrugh ff-set splicing methd as shwn in tp f Fig.7 and several peaks in the FMFBG s reflectin spectra appear. The number f these resnant peaks is reduced with the bent radius reduced. When the curvature radius is R 1, nly fundamental mde can be excited, with mre than ne resnant peak appears in the reflectin spectra. Due t the nn-unifrm crss refractive index prfile, energy can be transferred frm ne mde t the ther mdes. These agree well with ur theretical analysis: higher mdes lse energy but lwer mdes retain within bent FMFs, which ffers an effective methd t excite and cntrl high rder mde fr generatin f the VBs. Prc. f SPIE Vl K-5

, - -24-48 -72 1535-24 -48-72 1535 m -24 73-48 -72 ó 1535 J ó -24 vi -48 Ç -72 1535 6 1,. 154 1545 155 5 3 Aw1/ 154 1545 155 154 1545 155 MM^ 154 1545 155, 1535 154 1545 155 1535 154 1545 155 Fig.

6 , m ó 1535 J ó -24 vi -48 Ç , Aw1/ MM^ , Fig.7 Reflectin spectra f the bent fur-mde FMFBG with different curvature radius. High rder mde is excited thrugh an 3µm ffset-splicing methd. 4. ONLUSION In cnclusin, we investigate the ptical prperties f FMF with nn-unifrm refractive index prfile theretically and experimentally. Fr the U-shape refactive index FMF, if applied in fiber laser, VBs are generated by adjusting pump pwer; Fr the bent FMFs, high ptical mdes in the FMF can be effectively suppressed thrugh decreasing curvature radius; Fr the FMFBGs, the number f reflectin peaks decreases with minimized curvature radius. Based n the FMFs with specially designed refractive index prfile, we can cntrl the mde distributin f FMFs effectively and realize required VBs in an all-fiber, flexible manner. These few-mde fibers shw ptential applicatins in generating cylindrical vectr beam bth fr ptical lasing and sensing systems. 5. AKNOWLEDGMENT This wrk is supprted by Natinal Science Fundatin f Jiangsu Prvince (N. BK215858), P. R. hina and NUPTSF (Grant N. NY21459 and NY21383). References [1] Y. Kzawa, S. Sat, etc Optical trapping f micrmeter-sized dielectric particles by cylindrical vectr beams Opt. Express, 18(1): (21). [2] W. hen, Q. Zhan, etc Realizatin f evanescent Bessel beam via surface plasmn interference excited by a radially plarized beam Opt. Letters, 34(6): (29). [3] M. Meier, etc Material prcessing with pulsed radially and azimuthally plarized laser radiatin Applied physics a- materials Science & Prcessing, 86: (27). [4] Y. Kzawa, S. Sat, etc Generatin f a radially plarized laser beams by use f a cnical Brewster prism, Opt. Letters 3(22): (25). [5] Y. Li, J. G. Hu, etc, haracteristic analysis f tw-mde fiber Bragg grating, App. Physics, 117(4), (214). Prc. f SPIE Vl K-6

7 [6] M. M. Ali, Y. Jung, K. Lim, etc haracterizatin f mde cupling in few-mde fiber Bragg gratings with selective mde excitatin. IEEE Phtn.Tech. Letters, 27(16): (215). [7] Y. H. Zha, Y. Q. Liu, L. Zhang, etc, Mde cnverter based n the lng-perid fiber gratings written in the twmde fiber, Opt. Express 24(6): (216) [8] B. Sun, A. T. Wang, etc Lw-threshld single-wavelength all-fiber laser generating cylindrical vectr beams using a few-mde fiber Bragg grating, Opt. Letters, 37(4), (212) Prc. f SPIE Vl K-7

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