1006 IEEE PHOTONICS TECHNOLOGY LETTERS,VOL.27.NO.9.MAY 1,2015 Temperature-Insensitive Mode Converters With CO2-Laser Written Long-Period Fiber Gratings Jiangli Dong and Kin Seng Chiang,Member;IEEE Abstract-We fabricate mode converters by directly writing alignment problem [8]-101,but the fabrication processes long-period gratings in a two-mode fiber with a CO2 laser. required are complicated and expensive.All-fiber mode These mode converters allow the fundamental LPoi mode to converters compatible with optical fiber links have been be converted to any of the four higher order cylindrical vector modes or the LPj1 modes.The transmission characteristics of demonstrated with the effect of multimode interference in these devices are insensitive to temperature variations and the a multimode fiber (simulation only)[11],the principle of mode conversion efficiency is insensitive to the polarization state adiabatic transition in a photonic-crystal fiber [4].[12],and of the input light.One of our typical gratings,which contains long-period fiber gratings (LPFGs)[3],[13]-[17].Among 15 grating periods,can provide a conversion efficiency >99% these all-fiber devices,LPFGs offer many distinct advantages, over a bandwidth of 34.0 nm in the C-band.These robust mode converters could find applications in mode-division-multiplexing such as low reflection,low loss,and high fabrication and systems and other applications that require cylindrical vector design flexibility.An LPFG mode converter can be formed in modes. a fiber by mechanical means [3],[13],[14]or by exposing the Index Terms-Long-period fiber grating,mode converter, fiber to an ultra-violet (UV)laser [15].a heat source [161,or mode-division multiplexing,cylindrical vector modes. a CO2 laser [17].The early CO2-laser writing method for the fabrication of mode converters [17]involves two steps:the I.INTRODUCTION surface of the fiber is first ablated periodically by a CO2 laser beam and the ablated fiber is next annealed with an electric arc HE transmission capacity of single-mode fibers (SMFs) to form a grating.The resultant grating has a very large index is rapidly approaching the limit and new technologies are being developed to sustain the network traffic growth.Mode- change(~0.1)and suffers from a relatively high insertion loss. In the present study,we employ a direct CO2-laser writing division multiplexing(MDM)is a promising technology for method to fabricate LPFG mode converters in a two-mode increasing the transmission capacity of optical fibers [1],[2] In MDM transmission systems,mode converters are important fiber (TMF),where the CO2 laser can be computer- devices,which can be used,for example,at the sending and programmed to generate the grating profile.This CO2-laser writing method has been applied to the fabrication of sophisti- receiving ends to couple the fundamental mode to selected cated LPFG filters in different types of SMFs (see [18],[19]). high-order modes and vice versa.Mode converters can also be used as elements to generate cylindrical vector beams [3],[4] By properly controlling the amount of radiation on the fiber,the laser beam can induce an index change in the fiber for applications in electron acceleration [5],high-resolution without causing any visible damage to the fiber.Our CO2-laser metrology [6]and material processing [7].In this letter,we written LPFG mode converters are insensitive to temperature demonstrate robust all-fiber mode converters for the conversion variations and the mode conversion efficiency is insensitive between the fundamental mode and the higher-order modes to the polarization state of the input light.One of our typical with potential applications in the aforementioned areas. Mode conversion has been realized for long-haul MDM LPFGs,which contains 15 grating periods,shows a conversion transmission with bulk-optic components,such as phase efficiency higher than 99%over a bandwidth of 34.0 nm plates [1]and spatial light modulators [2].Such mode from 1529.1 to 1563.1 nm.We can obtain the four orthogonal converters can be implemented with readily available discrete LPI modes or the four cylindrical vector modes (the TEoI, TMo.HESY and HE modes)by adjusting the polarization components,but the complication in optical alignment makes it difficult to build compact,low-loss systems with these state of the LPor mode launched into the mode converter. devices.Integrated-optics mode converters based on various II.GRATING FABRICATION mode coupling mechanisms have been proposed to ease the The TMF used in our study was a commercial fiber (Two-Mode Step-Index Fiber,OFS).To determine the pitch Manuscript received December 1,2014;revised January 21,2015:accepted February 16,2015.Date of publication February 24,2015;date of current of the LPFG mode converter,we first wrote a fiber Bragg version April 10,2015.This work was supported by the Research Grants grating (FBG)in the TMF with an excimer laser,which Council through the Hong Kong Special Administrative Region,China, under Project CityU 112113. emitted at the UV wavelength 248 nm.The FBG had a length The authors are with the Department of Electronic Engineering.City of ~20 mm and a pitch of 536 nm.Prior to writing the FBG. University of Hong Kong,Hong Kong (e-mail:jldong2-c@my.cityu.edu.hk; we loaded the TMF with hydrogen at 100 bars and 70 C eeksc@cityu.edu.hk) for 7 days. Color versions of one or more of the figures in this letter are available online at http://ieeexplore.ieee.org. The transmission spectrum of the FBG with both the Digital Object Identifier 10.1109/LPT.2015.2405092 LPor and LP11 modes launched into the fiber is shown 1041-11352015 IEEE.Personal use is permitted,but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information
1006 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 27, NO. 9, MAY 1, 2015 Temperature-Insensitive Mode Converters With CO2-Laser Written Long-Period Fiber Gratings Jiangli Dong and Kin Seng Chiang, Member, IEEE Abstract— We fabricate mode converters by directly writing long-period gratings in a two-mode fiber with a CO2 laser. These mode converters allow the fundamental LP01 mode to be converted to any of the four higher order cylindrical vector modes or the LP11 modes. The transmission characteristics of these devices are insensitive to temperature variations and the mode conversion efficiency is insensitive to the polarization state of the input light. One of our typical gratings, which contains 15 grating periods, can provide a conversion efficiency >99% over a bandwidth of 34.0 nm in the C-band. These robust mode converters could find applications in mode-division-multiplexing systems and other applications that require cylindrical vector modes. Index Terms— Long-period fiber grating, mode converter, mode-division multiplexing, cylindrical vector modes. I. INTRODUCTION THE transmission capacity of single-mode fibers (SMFs) is rapidly approaching the limit and new technologies are being developed to sustain the network traffic growth. Modedivision multiplexing (MDM) is a promising technology for increasing the transmission capacity of optical fibers [1], [2]. In MDM transmission systems, mode converters are important devices, which can be used, for example, at the sending and receiving ends to couple the fundamental mode to selected high-order modes and vice versa. Mode converters can also be used as elements to generate cylindrical vector beams [3], [4] for applications in electron acceleration [5], high-resolution metrology [6] and material processing [7]. In this letter, we demonstrate robust all-fiber mode converters for the conversion between the fundamental mode and the higher-order modes with potential applications in the aforementioned areas. Mode conversion has been realized for long-haul MDM transmission with bulk-optic components, such as phase plates [1] and spatial light modulators [2]. Such mode converters can be implemented with readily available discrete components, but the complication in optical alignment makes it difficult to build compact, low-loss systems with these devices. Integrated-optics mode converters based on various mode coupling mechanisms have been proposed to ease the Manuscript received December 1, 2014; revised January 21, 2015; accepted February 16, 2015. Date of publication February 24, 2015; date of current version April 10, 2015. This work was supported by the Research Grants Council through the Hong Kong Special Administrative Region, China, under Project CityU 112113. The authors are with the Department of Electronic Engineering, City University of Hong Kong, Hong Kong (e-mail: jldong2-c@my.cityu.edu.hk; eeksc@cityu.edu.hk). Color versions of one or more of the figures in this letter are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/LPT.2015.2405092 alignment problem [8]–[10], but the fabrication processes required are complicated and expensive. All-fiber mode converters compatible with optical fiber links have been demonstrated with the effect of multimode interference in a multimode fiber (simulation only) [11], the principle of adiabatic transition in a photonic-crystal fiber [4], [12], and long-period fiber gratings (LPFGs) [3], [13]–[17]. Among these all-fiber devices, LPFGs offer many distinct advantages, such as low reflection, low loss, and high fabrication and design flexibility. An LPFG mode converter can be formed in a fiber by mechanical means [3], [13], [14] or by exposing the fiber to an ultra-violet (UV) laser [15], a heat source [16], or a CO2 laser [17]. The early CO2-laser writing method for the fabrication of mode converters [17] involves two steps: the surface of the fiber is first ablated periodically by a CO2 laser beam and the ablated fiber is next annealed with an electric arc to form a grating. The resultant grating has a very large index change (∼0.1) and suffers from a relatively high insertion loss. In the present study, we employ a direct CO2-laser writing method to fabricate LPFG mode converters in a two-mode fiber (TMF), where the CO2 laser can be computerprogrammed to generate the grating profile. This CO2-laser writing method has been applied to the fabrication of sophisticated LPFG filters in different types of SMFs (see [18], [19]). By properly controlling the amount of radiation on the fiber, the laser beam can induce an index change in the fiber without causing any visible damage to the fiber. Our CO2-laser written LPFG mode converters are insensitive to temperature variations and the mode conversion efficiency is insensitive to the polarization state of the input light. One of our typical LPFGs, which contains 15 grating periods, shows a conversion efficiency higher than 99% over a bandwidth of 34.0 nm from 1529.1 to 1563.1 nm. We can obtain the four orthogonal LP11 modes or the four cylindrical vector modes (the TE01, TM01, HEeven 21 , and HEodd 21 modes) by adjusting the polarization state of the LP01 mode launched into the mode converter. II. GRATING FABRICATION The TMF used in our study was a commercial fiber (Two-Mode Step-Index Fiber, OFS). To determine the pitch of the LPFG mode converter, we first wrote a fiber Bragg grating (FBG) in the TMF with an excimer laser, which emitted at the UV wavelength 248 nm. The FBG had a length of ∼20 mm and a pitch of 536 nm. Prior to writing the FBG, we loaded the TMF with hydrogen at 100 bars and 70 °C for 7 days. The transmission spectrum of the FBG with both the LP01 and LP11 modes launched into the fiber is shown 1041-1135 © 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information
DONG AND CHIANG:TEMPERATURE-INSENSITIVE MODE CONVERTERS WITH CO2-LASER WRITTEN LPFGs 1007 30 0 -5 wgp) 40 -10 50 -15 -20 -60 -25 3 51.0 13501400145015001550160016501700 1551.51552.01552.51553.0 Wavelength(nm) Wavelength(nm) (a) Fig.1. Measured transmission spectrum of an FBG written in the TMF. 0 ▣ 巴 10 In Mode Stripper 1 Mode Stripper 2 Out Broadband Optical -15 Source SMF PC OH Mode Converter SMF Analyzer 20 Fig.2.Experimental setup for monitoring the transmission spectrum of the 25 LPFG mode converter. -3 1450 1500155016001650 in Fig.1,where the insets are the mode patterns obtained at the Wavelength(nm) transmission end of the FBG for different transmission (b) dips [20].As shown in Fig.1,the Bragg wavelengths of the 0 LPoI and LP modes are 1552.7 and 1551.4 nm,respectively, from which we can determine the effective indices of the 马 two modes and then calculate the pitch of the LPFG for -10 the coupling between the two modes.The calculated pitch is 1.278 mm.The actual pitch used in our experiments -15 was somewhat shorter.The discrepancy could be caused by -20 the change in the refractive-index profile of the fiber after UV exposure. - We wrote the LPFG in the TMF(without hydrogen loading) 1450 150015501600 1650 by irradiating the fiber from one side with a CO2 laser Wavelength(nm) (c) (CO2-H10,Han's Laser).The CO2 laser had a maximum Fig.3.Normalized transmission spectra of the (a)15-period,(b)20-period, average output power of 10 W and the frequency of the laser and (c)30-period gratings,measured for the LPo mode. pulses was 5 kHz.The laser beam was focused onto the TMF (with its jacket removed)to a spot of ~90 um and controlled by a computer to scan point-wisely across the fiber in the strippers on the two sides of the LPFG along the TMF to transverse direction at a speed of 0.91 mm/s.The CO2-laser strip off any LPu mode to ensure that only the LPoi was beam was advanced along the fiber at steps to repeat the launched into the LPFG and detected at the output.We also transverse scanning process with each step equal to the grating placed a polarization controller(PC)along the input SMF for period.A scanning cycle was completed when the number the adjustment of the polarization state of the input light.The of periods required was reached.The scanning cycle could LPFG was naturally bent when released from the fabrication be repeated as many times as needed [18],[19].The energy setup.We kept it straight with minimum tension in our density of the CO2 laser used was 11 J/mm2.Because the experiments. TMF was exposed to the CO2-laser beam on one side,the Here we present the results for three typical samples: laser beam induced an asymmetric refractive-index distribution a 15-period grating with a pitch of 1.205 mm,a 20-period across the core,which made possible the coupling between the grating with a pitch of 1.200 mm,and a 30-period grating LPoI mode and the LPi1 mode. with a pitch of 1.200 mm,for which the numbers of CO2-laser scanning cycles used were 90,81 and 65,respec- tively.The transmission spectra of the three gratings are shown III.EXPERIMENTAL RESULTS AND DISCUSSION in Fig.3(a),(b),and(c),respectively.The 15-period grating To monitor the transmission spectrum of the LPFG during shows a conversion efficiency higher than 20 dB(99%)over a the writing process,we launched light from a broadband bandwidth of 34.0 nm from 1529.1 to 1563.1 nm with a peak source into the LPFG through an SMF and detected the output value of 26.0 dB at ~1533 nm.The 20-period grating shows light from the LPFG with an optical spectrum analyzer through a peak conversion efficiency of 27.4 dB at ~1562 nm with another SMF,as shown in Fig.2.We placed two mode a 20-dB bandwidth of 21.0 nm,while the 30-period grating
DONG AND CHIANG: TEMPERATURE-INSENSITIVE MODE CONVERTERS WITH CO2-LASER WRITTEN LPFGs 1007 Fig. 1. Measured transmission spectrum of an FBG written in the TMF. Fig. 2. Experimental setup for monitoring the transmission spectrum of the LPFG mode converter. in Fig. 1, where the insets are the mode patterns obtained at the transmission end of the FBG for different transmission dips [20]. As shown in Fig. 1, the Bragg wavelengths of the LP01 and LP11 modes are 1552.7 and 1551.4 nm, respectively, from which we can determine the effective indices of the two modes and then calculate the pitch of the LPFG for the coupling between the two modes. The calculated pitch is 1.278 mm. The actual pitch used in our experiments was somewhat shorter. The discrepancy could be caused by the change in the refractive-index profile of the fiber after UV exposure. We wrote the LPFG in the TMF (without hydrogen loading) by irradiating the fiber from one side with a CO2 laser (CO2-H10, Han’s Laser). The CO2 laser had a maximum average output power of 10 W and the frequency of the laser pulses was 5 kHz. The laser beam was focused onto the TMF (with its jacket removed) to a spot of ∼90 µm and controlled by a computer to scan point-wisely across the fiber in the transverse direction at a speed of 0.91 mm/s. The CO2-laser beam was advanced along the fiber at steps to repeat the transverse scanning process with each step equal to the grating period. A scanning cycle was completed when the number of periods required was reached. The scanning cycle could be repeated as many times as needed [18], [19]. The energy density of the CO2 laser used was 11 J/mm2. Because the TMF was exposed to the CO2-laser beam on one side, the laser beam induced an asymmetric refractive-index distribution across the core, which made possible the coupling between the LP01 mode and the LP11 mode. III. EXPERIMENTAL RESULTS AND DISCUSSION To monitor the transmission spectrum of the LPFG during the writing process, we launched light from a broadband source into the LPFG through an SMF and detected the output light from the LPFG with an optical spectrum analyzer through another SMF, as shown in Fig. 2. We placed two mode Fig. 3. Normalized transmission spectra of the (a) 15-period, (b) 20-period, and (c) 30-period gratings, measured for the LP01 mode. strippers on the two sides of the LPFG along the TMF to strip off any LP11 mode to ensure that only the LP01 was launched into the LPFG and detected at the output. We also placed a polarization controller (PC) along the input SMF for the adjustment of the polarization state of the input light. The LPFG was naturally bent when released from the fabrication setup. We kept it straight with minimum tension in our experiments. Here we present the results for three typical samples: a 15-period grating with a pitch of 1.205 mm, a 20-period grating with a pitch of 1.200 mm, and a 30-period grating with a pitch of 1.200 mm, for which the numbers of CO2-laser scanning cycles used were 90, 81 and 65, respectively. The transmission spectra of the three gratings are shown in Fig. 3(a), (b), and (c), respectively. The 15-period grating shows a conversion efficiency higher than 20 dB (99%) over a bandwidth of 34.0 nm from 1529.1 to 1563.1 nm with a peak value of 26.0 dB at ∼1533 nm. The 20-period grating shows a peak conversion efficiency of 27.4 dB at ∼1562 nm with a 20-dB bandwidth of 21.0 nm, while the 30-period grating
1008 IEEE PHOTONICS TECHNOLOGY LETTERS,VOL.27.NO.9.MAY 1,2015 可O D TEo1 Fig.4.Near-field output patters from the TMF taken for the 15-period grating at five wavelengths,which correspond to Points A,B,C.D,and E marked in the transmission spectrum in Fig.3(a). TMoi shows a peak conversion efficiency of 22.0 dB at ~1551 nm with a 20-dB bandwidth of 4.4 nm.As expected,the bandwidth of the grating decreases with an increase in the period number. The 15-period grating has a 20-dB bandwidth that covers most of the C-band.The resonance wavelengths of the three gratings are slightly different,which can be attributed to the use of different numbers of CO2-laser scanning cycles in the writing process.The transmission spectra shown in Fig.3 are insensitive to the polarization state of the input light. Fig.5.Near-field output patterns from the TMF through the output polarizer obtained for the 15-period grating operating at 1550 nm for each of the To confirm that the rejection dips shown in Fig.3 cylindrical vector modes generated,where the arrows specify the orientations are caused by the coupling from the LPoi mode to the of the transmission axis of the output polarizer. LPI mode,we launched the LPor mode into each grating with a tunable laser (which had a tuning range from 1.446759 (HESyen and HEdd)at the wavelength 1550 nm. 1454 to 1641 nm)and inspected the output near-field The corresponding resonance-wavelength separation between patterns from the TMF with an infrared camera(with the the TEor and HE21 (even or odd)modes is ~3.6 nm and that mode stripper on the output side of the fiber removed). between the TMoi and HE21 modes is ~1.2 nm.The resonance We selected five wavelengths to cover different parts of the wavelengths for these modes are so close to each other that rejection band,which are labelled in the transmission spectrum their rejection bands overlap with each other.Therefore,the in Fig.3(a)as A (1467.9 nm),B(1509.1 nm),C(1533.4 nm),rejection bands shown in Fig.3 are actually due to the coupling D (1604.2 nm),and E(1640.9 nm).Typical near-field output to any of these cylindrical vector modes or a mix of them, patterns captured for the 15-period grating at these five wave-depending on the polarization state of the LPo mode launched lengths are shown in Fig.4.As the wavelength moves into into the grating.The mode coupling effect can be explained the rejection band,the output pattern starts to show the by the coupled-mode theory,where the coupling strength is contribution from the LPu mode (Point A)and,near the determined by the spatial overlap between the LPol mode resonance wavelength,the output pattern shows primarily and any of the cylindrical vector modes over the area of the LPu mode (Points B and C).When the wavelength the refractive-index distribution induced by the CO2 laser. moves away from the rejection dip (Points D and E),the An asymmetrically induced index distribution in the fiber core LPuI mode component diminishes.The spatial interference gives rise to a finite spatial overlap between the two modes between the LPoI and LPu modes leads to asymmetric field and thus makes possible their coupling. patterns,as shown by the patterns at Points A,D,and E By carefully adjusting the polarization state of the input in Fig.4.No cladding modes appear in the output patterns LPor mode,we could generate various cylindrical vector across the rejection band,which indicates that the grating does modes,which showed similar donut-shaped mode patterns. not cause any observable coupling from the LPor mode or To identify these vector modes,we placed a polarizer at the LP]mode to any cladding modes.These results confirm the TMF output and inspected the near-field output pattern the function of the LPFG as an LPoI-LPu mode converter from the fiber through the polarizer with the infrared camera. in the rejection band.We obtained similar results for the By rotating the output polarizer,we could obtain clean 20-period and 30-period gratings. LP mode patterns and identify each of the cylindrical vector The near-field output pattern near the resonance wavelength modes by analyzing the orientations and the polarizations of in Fig.4 shows a donut-shaped pattern,which indicates a mix the LP1 mode patterns [21],as shown in Fig.5 for the of the LPu modes.We were able to obtain clean LPI mode 15-period grating operating at the wavelength 1550 nm,where patterns with various orientations by adjusting the polariza- the arrows specify the orientations of the transmission axis of tion state of the input light.The exact higher-order modes the output polarizer in relation to the orientations of the mode supported by the TMF are the four cylindrical vector modes,patterns.These results confirm the operation of the grating as namely,the TEo.TMo.HESYen,and HEdd modes,where an LPoI-LP mode converter or a cylindrical vector mode the HESyen and HEdd modes are strictly degenerate.For our generator. TMF,which has a numerical aperture of 0.12,a core diameter The variations of the resonance wavelengths of the of 19 um,a cladding diameter of 125 um,and a cladding three gratings with the temperature are shown in Fig.6(a) index of 1.444,the effective indices of the four vector modes For a temperature change of 57 C(from 21 to 78 C),the are calculated to be 1.446762 (TEo1),1.446758 (TMo1),and shifts in the resonance wavelength for the 15-period
1008 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 27, NO. 9, MAY 1, 2015 Fig. 4. Near-field output patterns from the TMF taken for the 15-period grating at five wavelengths, which correspond to Points A, B, C, D, and E marked in the transmission spectrum in Fig. 3(a). shows a peak conversion efficiency of 22.0 dB at ∼1551 nm with a 20-dB bandwidth of 4.4 nm. As expected, the bandwidth of the grating decreases with an increase in the period number. The 15-period grating has a 20-dB bandwidth that covers most of the C-band. The resonance wavelengths of the three gratings are slightly different, which can be attributed to the use of different numbers of CO2-laser scanning cycles in the writing process. The transmission spectra shown in Fig. 3 are insensitive to the polarization state of the input light. To confirm that the rejection dips shown in Fig. 3 are caused by the coupling from the LP01 mode to the LP11 mode, we launched the LP01 mode into each grating with a tunable laser (which had a tuning range from 1454 to 1641 nm) and inspected the output near-field patterns from the TMF with an infrared camera (with the mode stripper on the output side of the fiber removed). We selected five wavelengths to cover different parts of the rejection band, which are labelled in the transmission spectrum in Fig. 3(a) as A (1467.9 nm), B (1509.1 nm), C (1533.4 nm), D (1604.2 nm), and E (1640.9 nm). Typical near-field output patterns captured for the 15-period grating at these five wavelengths are shown in Fig. 4. As the wavelength moves into the rejection band, the output pattern starts to show the contribution from the LP11 mode (Point A) and, near the resonance wavelength, the output pattern shows primarily the LP11 mode (Points B and C). When the wavelength moves away from the rejection dip (Points D and E), the LP11 mode component diminishes. The spatial interference between the LP01 and LP11 modes leads to asymmetric field patterns, as shown by the patterns at Points A, D, and E in Fig. 4. No cladding modes appear in the output patterns across the rejection band, which indicates that the grating does not cause any observable coupling from the LP01 mode or the LP11 mode to any cladding modes. These results confirm the function of the LPFG as an LP01–LP11 mode converter in the rejection band. We obtained similar results for the 20-period and 30-period gratings. The near-field output pattern near the resonance wavelength in Fig. 4 shows a donut-shaped pattern, which indicates a mix of the LP11 modes. We were able to obtain clean LP11 mode patterns with various orientations by adjusting the polarization state of the input light. The exact higher-order modes supported by the TMF are the four cylindrical vector modes, namely, the TE01, TM01, HEeven 21 , and HEodd 21 modes, where the HEeven 21 and HEodd 21 modes are strictly degenerate. For our TMF, which has a numerical aperture of 0.12, a core diameter of 19 µm, a cladding diameter of 125 µm, and a cladding index of 1.444, the effective indices of the four vector modes are calculated to be 1.446762 (TE01), 1.446758 (TM01), and Fig. 5. Near-field output patterns from the TMF through the output polarizer obtained for the 15-period grating operating at 1550 nm for each of the cylindrical vector modes generated, where the arrows specify the orientations of the transmission axis of the output polarizer. 1.446759 (HEeven 21 and HEodd 21 ) at the wavelength 1550 nm. The corresponding resonance-wavelength separation between the TE01 and HE21 (even or odd) modes is ∼3.6 nm and that between the TM01 and HE21 modes is ∼1.2 nm. The resonance wavelengths for these modes are so close to each other that their rejection bands overlap with each other. Therefore, the rejection bands shown in Fig. 3 are actually due to the coupling to any of these cylindrical vector modes or a mix of them, depending on the polarization state of the LP01 mode launched into the grating. The mode coupling effect can be explained by the coupled-mode theory, where the coupling strength is determined by the spatial overlap between the LP01 mode and any of the cylindrical vector modes over the area of the refractive-index distribution induced by the CO2 laser. An asymmetrically induced index distribution in the fiber core gives rise to a finite spatial overlap between the two modes and thus makes possible their coupling. By carefully adjusting the polarization state of the input LP01 mode, we could generate various cylindrical vector modes, which showed similar donut-shaped mode patterns. To identify these vector modes, we placed a polarizer at the TMF output and inspected the near-field output pattern from the fiber through the polarizer with the infrared camera. By rotating the output polarizer, we could obtain clean LP11 mode patterns and identify each of the cylindrical vector modes by analyzing the orientations and the polarizations of the LP11 mode patterns [21], as shown in Fig. 5 for the 15-period grating operating at the wavelength 1550 nm, where the arrows specify the orientations of the transmission axis of the output polarizer in relation to the orientations of the mode patterns. These results confirm the operation of the grating as an LP01-LP11 mode converter or a cylindrical vector mode generator. The variations of the resonance wavelengths of the three gratings with the temperature are shown in Fig. 6(a). For a temperature change of 57 °C (from 21 to 78 °C), the shifts in the resonance wavelength for the 15-period
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(b) [9]D.Dai,Y.Tang,and J.E.Bowers,"Mode conversion in tapered Fig.6.Variations of (a)the resonance wavelengths and (b)the contrasts of submicron silicon ridge optical waveguides."Opi.Exp..vol.20,no.12. the 15-period,20-period,and 30-period gratings with the temperature. [10] vang in andK.$Chang."Mode converter with polymer long-period waveguide grating,"in Proc.Asia Commun. 20-period,and 30-period gratings are only 2.5 Photon.Conf:.Nov.2014,pp.1-3,paper AW4C.4. 1.4,and 1.0 nm,respectively.The temperature sensitivity [11]C.P.Tsekrekos and D.Syvridis,"All-fiber broadband LPo2 mode of the mode converter is much lower than that of a typical converter for future wavelength and mode division multiplexing systems,"IEEE Photon.Technol.Lett.,vol.24.no.18.pp.1638-1641. conventional cladding-mode LPFG.The very low temperature Sep.15,2012. sensitivities of the LPFG mode converters suggest that the [12]K.Lai,S.G.Leon-Saval,A.Witkowska,W.J.Wadsworth,and effective indices of the LPor and LP modes of the fiber are T.A.Birks,"Wavelength-independent all-fiber mode converters," 0pt.Let,vol.32,no.4,pp.328-330,Feb.2007. similarly influenced by the temperature.The slight differences [13]A.Li,X.Chen,A.Al Amin,J.Ye,and W.Shieh,"Space-division in the temperature sensitivities of the three gratings can multiplexed high-speed superchannel transmission over few-mode fiber,' be attributed to the use of different CO2-laser doses in the J.Lightw.Technol.,vol.30,no.24,pp.3953-3964.Dec.15,2012. [14]H.Sakata.H.Sano,and T.Harada,"Tunable mode converter using writing of the gratings,since different CO2-laser doses can electromagnet-induced long-period grating in two-mode fiber"Opt. modify the properties of the fiber glass differently [22]. Fiber Technol.,vol.20,no.3.pp.224-227.Jun.2014. The variations of the contrasts of the three gratings [15]S.Ramachandran,Z.Wang,and M.Yan,"Bandwidth control of long- period grating-based mode converters in few-mode fibers,"Opt.Lett., (i.e.,the depths of the rejection bands shown in Fig.3) vol.27,no.9.Pp.698-700,May2002. with the temperature are shown in Fig.6(b),which indicates [16]L.Gruiner-Nielsen and J.W.Nicholson,"Stable mode converter for conversion between LPo and LP using a thermally induced long that the grating contrast is also insensitive to temperature period grating,"in Proc.IEEE Photon.Soc.Summer Topical Meeting, variations. jul.2012,pp.214-215.paper WC1.2 [17]C.D.Poole,H.M.Presby,and J.P.Meester,"Two-mode fibre spatial- IV.CONCLUSION mode converter using periodic core deformation,"Electron.Lett.,vol.30. no.17,Pp.1437-1438,Aug.1994. We have experimentally demonstrated CO2-laser written [18]H.W.Lee,Y.Liu,and K.S.Chiang."Writing of long-period grat- LPFGs in a TMF for achieving conversion between ings in conventional and photonic-crystal polarization-maintaining fibers by CO2-laser pulses,"IEEE Photon.Technol.Lett.,vol.20.no.2. the fundamental mode and the higher-order modes.The Pp.132-134,Jan.15,2008. CO2-laser writing process can be computer-programmed and [19]Y.Gu,K.S.Chiang,and Y.J.Rao,"Writing of apodized phase. the growth of the grating can be monitored in real time.The shifted long-period fiber gratings with a computer-controlled CO2 laser," IEEE Photon.Technol.Lett.,vol.21,no.10,pp.657-659,May 15,2009 transmission characteristics of the gratings are insensitive to [20]J.Dong and K.S.Chiang,"Mode-locked fiber laser with transverse- temperature variations and the mode conversion efficiency is mode selection based on a two-mode FBG."IEEE Photon.Technol. polarization-insensitive.By control of the polarization state of Le,vol.26,no.17,Pp.1766-1769,Sep.1,2014. the input LPor mode,these gratings can function as effective [21]G.Volpe and D.Petrov,"Generation of cylindrical vector beams with few-mode fibers excited by Laguerre-Gaussian beams,"Opt.Commun., LPoI-LPu mode converters or cylindrical vector vol.237,no.1-3,pp.89-95,Jul.2004. mode generators.One of our typical gratings,which contains [22]Y.Liu,H.W.Lee,K.S.Chiang,T.Zhu,and Y.J.Rao,"Glass 15 grating periods,can provide a conversion efficiency higher structure changes in CO-laser writing of long-period fiber gratings in boron-doped single-mode fibers,"J.Lightw.Technol..vol.27.no.7. than 99%over a bandwidth of 34.0 nm in the C-band. Pp.857-863,Apr.1,2009
DONG AND CHIANG: TEMPERATURE-INSENSITIVE MODE CONVERTERS WITH CO2-LASER WRITTEN LPFGs 1009 Fig. 6. Variations of (a) the resonance wavelengths and (b) the contrasts of the 15-period, 20-period, and 30-period gratings with the temperature. 20-period, and 30-period gratings are only 2.5, 1.4, and 1.0 nm, respectively. The temperature sensitivity of the mode converter is much lower than that of a typical conventional cladding-mode LPFG. The very low temperature sensitivities of the LPFG mode converters suggest that the effective indices of the LP01 and LP11 modes of the fiber are similarly influenced by the temperature. The slight differences in the temperature sensitivities of the three gratings can be attributed to the use of different CO2-laser doses in the writing of the gratings, since different CO2-laser doses can modify the properties of the fiber glass differently [22]. The variations of the contrasts of the three gratings (i.e., the depths of the rejection bands shown in Fig. 3) with the temperature are shown in Fig. 6(b), which indicates that the grating contrast is also insensitive to temperature variations. IV. CONCLUSION We have experimentally demonstrated CO2-laser written LPFGs in a TMF for achieving conversion between the fundamental mode and the higher-order modes. The CO2-laser writing process can be computer-programmed and the growth of the grating can be monitored in real time. The transmission characteristics of the gratings are insensitive to temperature variations and the mode conversion efficiency is polarization-insensitive. By control of the polarization state of the input LP01 mode, these gratings can function as effective LP01−LP11 mode converters or cylindrical vector mode generators. 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