Polarization-independent orbital angularmomentum generator based ona chiral fiber gratingYAN ZHANG, ZHIYONG BAI,* CAILING FU, SHEN LIU, JIAN TANG, JIAN YU, CHANGRUI LIAO,YING WANG, JUN HE, AND YIPING WANG
Key Laboratory of Optoelectronic Devices and Systems of Ministry of Education and Guangdong Province, College of Optoelectronic Engineering,Shenzhen University, Shenzhen 518060, China*Corresponding author: [email protected]
Received 19 October 2018; revised 14 November 2018; accepted 19 November 2018; posted 26 November 2018 (Doc. ID 348593);published 20 December 2018
The orbital angular momentum (OAM) of light has been ex-tensively studied during the past several decades, since Allenet al. first identified that light beams with helical phase frontscarry OAM [1]. This helical phase front can be described by atransverse phase structure represented as exp�ilφ�. This expres-sion indicates that every photon carries OAM equivalent to lℏ,where l is the topological charge, and φ is the azimuthal angle.OAM has been utilized in a variety of fields due to an unlimitedtopological charge number l and a unique phase singularity.A light beam carrying OAM has a vaster foreground in manyfields, such as optical tweezers [2], optical trapping [3], nano-scale microscopy [4], and advances in communication [5,6].
The generation of OAM has been investigated in multiplestudies, with various spatial methods proposed to induce OAMby utilizing the azimuthal phase structure. For example, spiral
phase plates [7] produce an angle-dependent phase delay atvarying azimuthal positions by using a precisely fabricatedplate. Mode converters constructed of cylindrical lenses [8]can transform Hermite–Gaussian beams into Laguerre–Gaussian laser modes. Q-plates [9] can excite OAM modes us-ing a non-homogeneous birefringent wave plate with a specifiedgeometry along the local optical axis. Photonic integratedcircuits provide a more compact version of an OAM generator[10–12]. Spatial light modulators (SLMs) based on computer-controlled holographic patterns [13] can be tuned to exciteOAM through the rearrangement of liquid crystal molecules.This approach is currently the most commonly used methodfor OAM generation. However, SLMs are polarization-sensitive, which includes certain limitations during practicalapplication. As such, the development of a polarization-insensitive SLM is of significant interest in the field [14].
Meanwhile, all-fiber OAM mode generators, with the ad-vantages of easy integration with existing devices, compatibilitywith fiber systems, robustness, cost-effectiveness, and lowinsertion loss, have received increased attention in recent yearsand have produced promising experimental results. For exam-ple, Li et al. [15] demonstrated selective conversion from LP11core modes to the LP-OAM�1 mode in a two-mode fiber(2MF) by utilizing mechanical long-period gratings and a par-allel metal slab. Zhao et al. [16] generated OAM�1 modescomposed of HEe
21 � iHEo21 in a 2MF based on a CO2 laser-
induced titled long-period fiber grating. Zhang et al. [17]generated OAM�2 modes composed of HEe
31 � iHEo31 in a
four-mode fiber using an acoustically induced fiber grating.The authors have previously reported all-fiber OAM generatorsbased on helical fiber gratings [18,19].
Unfortunately, these all-fiber generators either exhibitedunclear polarization characteristics or a sensitivity requiringspecialized polarization states for the input light beam.These polarization-dependent characteristics can limit theuse of OAM for micro-manipulation, communication, andother applications. As such, a novel technique is needed to
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In this Letter, we propose a novel polarization-insensitiveOAM generator utilizing a chiral fiber grating (CFG). TheCFG exhibited a coupling efficiency of more than 99% andwas produced by twisting a fused few-mode fiber (FMF) duringhydrogen-oxygen flame heating. The purity of the �1-orderOAM modes, excited by a left-handed CFG (LCFG) orright-handed CFG (RCFG), was higher than 93% due to hel-ical index modulation. This helical phase can be preserved forinput light of varying polarization states, indicating polarizationindependence. No coupling was observed between the −1- and�1-order OAM modes in this experiment, suggesting OAMchirality was determined only by the helicity of the CFG.Additionally, the polarization state of these excited OAMmodes was the same as that of the input light. The resultinghigh-purity OAM generator is stable, polarization-indepen-dent, and a viable candidate for future applications of OAM.
The experimental configuration shown in Fig. 1(a) was de-signed and constructed to fabricate CFGs in FMFs with a corediameter of 19 μm and a cladding diameter of 125 μm [20].One end included a FMF that was fixed on translation stage 2using a clamp. The other end was installed along the central axisof the rotator fixed on translation stage 1. A hydrogen-oxygenflame was used to locally heat the FMF to its melting point[21]. The FMF was twisted during the heating processwith varying rotational speeds (Ω), while simultaneouslybeing translated along the two stages at velocities of V 1 �1.60 mm∕s and V 2 � 1.57 mm∕s. This difference in speedproduced a constant stress along the fiber during hydrogen-oxygen flame heating; therefore, the efficiency and quality ofthe fabricated process can be improved by this method. Thelength L of the twisted FMF was determined by the equationL � V 1 × T (where T represents time), with a helical pitch ofΛ � V 1∕Ω and a twist rate of α � 2πΩ∕�V 1�. The RCFGand LCFG were produced by clockwise and counterclockwiserotations of the fused fiber, respectively, as shown in Figs. 1(b1)and 1(b2). The schematics in Figs. 1(b1) and 1(b2) of the CFGsillustrated helical grating modulations formed during the fab-rication processing. This type of grating modulation processeda radial and azimuthal distribution of refractive index changein the transverse cross section of the fiber. When the light
propagated through the CFG, each period directly added ahelical phase delay to the coupled modes. As such, a resonantenhancement of the helical phase can be formed in the coupledmodes, that is, OAM modes. Moreover, the grating pitch andmodulation strength, respectively, determined the resonantwavelength and mode coupling efficiency of the OAM modesin CFG. The grating pitch was jointly determined by thevelocities of the translation stages and rotator, and the gratingmodulation can be controlled by the speed difference betweenthe two translation stages and the fabrication time.
To achieve a resonant wavelength of the CFGs at around1550 nm, the fabrication parameters were set as follows. Therotation speed is Ω � 79 rpm. The corresponding twist rate,grating pitch, and grating length were α � 5.17 rad∕mm,Λ � 1192 μm, T � 30 s, and L � 48 mm, respectively.
The transmission spectra of the resulting CFGs wererecorded by an optical spectrum analyzer, combined with anamplified spontaneous emission broadband light source witha wavelength ranging from 1250 to 1650 nm. The resonantwavelength and attenuation were 1550.9 nm and 22.5 dBfor the RCFG and 1554.5 nm and 24.6 dB for the LCFG,as shown in Figs. 2(a) and 2(b). There is an evident differencein the resonant wavelengths of the RCFG and LCFG, whichmay have resulted from an imprecise rotation in the twoopposing directions. The dip loss and resonant wavelength, re-spectively, represented the strongest coupling strength and thebest operating wavelength of the proposed OAM mode gener-ators. Additionally, the bandwidth at −10 dB is about 25 nm,which can be regarded as the operating wavelength range of theproposed OAM mode generators.
A measurement system was constructed to characterize thepolarization, intensity distribution, and purity of OAM modesexcited in the CFGs, as shown in Fig. 3. Light from a tunablelaser (Model 81940A) with a wavelength ranging from 1520 to1630 nm was collimated by a 10× objective lens and then di-vided into two components, one of which was coupled intoCFG samples to generate OAM modes. The other componentwas used as a reference beam. A beam splitter was placed at theintersection point where these two beams interfered. As seen inFig. 3, polarizer 1 (P1) and a quarter-wave plate (QWP) werejointly used to generate arbitrary polarization states for the in-put light. Polarizer 2 (P2) was used to analyze the polarizationstates of the output light from the sampled CFGs. A half-waveplate (HWP) was then used to rotate the linear polarizationdirection of the reference beam. The resulting intensitydistribution and interference patterns were observed usingan infrared camera.
Using this described setup, we first investigated the intensitydistribution, helical phase, and polarization characteristics ofthe coupled high-order modes in the CFGs. The results are
Fig. 1. (a) Schematic diagram of the CFG fabrication setup usinga hydrogen-oxygen flame. Schematic diagram of periodic helicalstructures in the (b1) RCFG and (b2) LCFG. Fig. 2. Transmission spectra of (a) the RCFG and (b) LCFG.
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presented for the RCFG in Fig. 4(a) and for the LCFG inFig. 4(b). The polarization direction of P1 is parallel to thatof the input light from the polarized beam splitter (PBS).The terms of LP∥ and LP⊥ represent polarization directionsfor the linear polarization which are parallel and perpendicularto that of P1, respectively. Left-handed circularly polarized(LCP), and right-handed circularly polarized (RCP) input lightwere produced by adjusting the angle between the transparentaxis of P1 and the fast axis of the QWP. Intensity distributionsof coupled modes in the RCFG and LCFG are shown for LP∥input light in Figs. 4(a11) and 4(b11), respectively. The intensitydistribution periodically alternated between bright and darkfringes, while the angle between the polarization directionsof P1 and P2 was adjusting from 0° to 270°, with an intervalof 90°. This indicated that higher-order modes in the CFGswere linearly polarized and that the polarization directionwas the same as that of the input light. Excited phases inthe RCFG and LCFG were also demodulated using an inter-ference method. These spiral interference patterns are clearlyevident in Figs. 4(a12) and 4(b12), where P2 was oriented at0° and 180°. Sampled light from the CFGs faded as P2 wasoriented at 90° and 270°, where only the reference light wascaptured.
The LP∥ light could be rotated to LP⊥ by inserting an HWPbetween the QWP and the 10× objective lens. A similar evo-lution was observed in LP⊥, but with a phase delay of π∕2. Thisbehavior is shown in Figs. 4(a21) and 4(a22) for the RCFG, andFigs. 4(b21) and 4(b22) for the LCFG. The evolution of theseintensity profiles was obtained with rotations of P2 for RCP andLCP input light. The annular intensity of the coupled modesremained constant, as shown in Figs. 4(a31), 4(a41), 4(b31), and4(b41). This suggests that the coupled modes were circularlypolarized. The corresponding spiral interference patterns dis-played in Figs. 4(a32), 4(a42), 4(b32), and 4(b42) remained mostlyconstant. The polarization of coupled high-order modes inFig. 4 was the same as that of the input fundamental mode.The helical wavefronts were independent of the polarizationstates of the input light. In addition, the clockwise spiral inter-ference patterns occurring between coupled modes in theRCFG and the reference beam were independent of the polari-zation state, as shown in Fig. 4(a). The RCFG can only excite−1-order OAM. Similarly, the counterclockwise spiral interfer-ence patterns representing �1-order OAM only occurred inthe LCFG. As such, a definite chirality of the helical phasewas determined by the helicity of the CFG, independent ofthe polarization of the input light.
The purity of the generated OAM modes was measured forvarious input light polarization states using the mode decom-position method. Sampled light from the CFGs was incidenton a series of forked-grating holograms generated by a reflectivephase-only liquid crystal SLM, as shown in Fig. 5. These holo-grams were used to excite helical phases with l � −2, −1, 0,�1, and �2. As a result, the generated OAM modes in theCFGs could be converted to Gaussian beams when conjugatehelical phases were applied. The contribution of each compo-nent to the OAM modes was measured by recording the powerin the center of the converted optical field. The purity of theOAM modes was then determined by calculating the powerratio for each component of these OAM modes. Purity wasmeasured for input light with LP, RCP, and LCP polarizationstates, the results of which are plotted in Fig. 6.
As shown in Fig. 6(a1), the addition of a helical phase withl � �1 to sampled light from the RCFG resulted in the con-version of the recorded pattern center to a Gaussian-like beam,regardless of the polarization of the input light. This result con-firms the generation of −1-order OAM modes in the RCFG.The histograms corresponding to Fig. 6(a2) indicate that aprimary component of OAM modes in the RCF included−1-order modes with purities of 93.2%, 94%, and 93.4%for LP, RCP, and LCP polarization states, respectively. Theprimary components of OAM modes in the LCFG were of�1-order, with purities of 93.4%, 92.5%, and 92.7%.
Fig. 3. Schematic diagram of the experimental setup used fordetecting OAM modes generated by the CFG. PBS, polarized beamsplitter; BS, beam splitter; QWP, quarter-wave plate; HWP, half-waveplate; P1, polarizer 1; and P2, polarizer 2.
Fig. 4. Beam profiles and interference patterns for the �1-orderOAM modes generated by CFGs while rotating P2 from 0° to270° with a step size of 90°. The leftmost column shows varying polari-zation states of the input light. Also shown are (a) the�1-order OAMmode generated by the RCFG at a resonant wavelength of 1550.9 nmand (b) the −1-order OAMmode generated by the LCFG at a resonantwavelength of 1554.5 nm.
Fig. 5. Experimental setup used to measure the purity of the OAMmode excited by the inscribed CFG.
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The purity of the coupled OAM modes can be further im-proved by using a mode stripper before the CFGs to suppressthe input high-order modes. In addition, the coupled OAMmodes can be predicted a good stability. On one hand,OAM modes can be transmitted in a FMF for a long distance[11]. On the other hand, the coupled high-order modes werestill constrained in the fiber core, which will limit the interac-tion between light and external parameters.
We have proposed and demonstrated a polarization-independent OAM generator based on CFGs. The resultingRCFG and LCFG successfully excited −1- and �1-orderOAM modes, respectively, regardless of the input light polari-zation state. The high-order OAM modes can be excited by thesame method, except for adjusting the grating parameters. Thepurity of the produced OAMmodes was as high as 93%, with aslight fluctuation of 2%. The experimental results showed thatthese OAM modes could be generated with any desired polari-zation. As such, the proposed OAM generator could be ben-eficial in the study of the interaction between light and matterwhen the effects of polarization and phase must be investigatedindependently.
Funding. National Natural Science Foundation ofChina (NSFC) (61425007, 61605129, 61635007,61875134); Natural Science Foundation of Guangdong
Province (2014A030308007, 2015B010105007); ShenzhenScience and Technology Innovation Commission(JCYJ20170302143105991, JCYJ20170302152718747,JCYJ20170412105604705); China Postdoctoral ScienceFoundation (2016M600669, 2018M633115); Developmentand Reform Commission of Shenzhen MunicipalityFoundation.
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Fig. 6. Mode profiles occurring as a series of helical phases withl � −2, −1, 0, �1, and �2, added to the generated OAM modesfor the (a1) RCFG and (b1) LCFG for LP, RCP, and LCP input lightpolarization states. Also shown are the power ratios for each compo-nent in the OAM modes generated in the (a2) RCFG and (b2) LCFG.
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