Magnetically controllable wavelength-divisionmultiplexing fiber coupler Wei Lin,1 Hao Zhang,1,3 Binbin Song,1 Yinping Miao,2 Bo Liu,1,4 Donglin Yan,1 and Yange Liu1 1
Key Laboratory of Optical Information Science and Technology, Ministry of Education, Institute of Modern Optics, Nankai University, Tianjin 300071, China 2 Tianjin Key Laboratory of Film Electronic & Communication Devices, School of Electronics Information Engineering, Tianjin University of Technology, Tianjin, 300384 China 3 [email protected]
4 [email protected]
Abstract: In this paper, a magnetically controllable wavelength-divisionmultiplexing (WDM) fiber coupler has been proposed and experimentally demonstrated. A theoretical model has been established to analyze the influences of the weak as well as strong couplings to the wavelength tunability of this coupler. Experimental results show that the operation wavelength tunability of the proposed WDM coupler could be fulfilled for an applied magnetic field intensity range of 0 Oe to 500 Oe, and particularly it possesses high operation performances within the magnetic field intensity ranging from 25 Oe to 125 Oe when additional transmission loss and isolation are both considered. Within this range, the two selected channels show the wavelength tunability of 0.05 nm/Oe and 0.0744 nm/Oe, respectively, and the isolation between the two branches is higher than 24.089 dB. Owing to its high isolation, good splitting ratio stability, and high wavelength tunability, the proposed controllable WDM coupler is anticipated to find potential applications in such fields as fiber laser, fiber sensing and fiber-optic communications. Moreover, the fiber coupler integrated with the magnetic fluid would be valuable for the design of magnetically controllable mode-division-multiplexing devices. ©2015 Optical Society of America OCIS codes: (060.2310) Fiber optics; (060.2340) Fiber optics components; (160.3820) Magneto-optical materials; (230.3810) Magneto-optic systems.
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1. Introduction As one of the most efficient methods to expand the transmission spectral window, wavelength division multiplexing (WDM) is one of the key technologies for optical communications as well as optical sensing systems . Due to the great demands of data exchange applications in multi-channel optical networks, much efforts have been put on the development of multiplexing/demultiplexing components, including diffraction grating , dielectric film filter , fiber Bragg grating , long period fiber grating , and fiber coupler . Amongst these components, fiber coupler plays a particularly significant role in building up all-fiber
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optical systems and have attracted increasing research interests in the past few decades [7~12]. The wavelength tunability of fiber couplers provides convenient, fiber-compatible and hence low loss approaches for wavelength channel selection and add/drop in fiber-optic systems, and they have found various applications in such ever-growing fields as fiber laser, fiber sensor, and fiber-optic communications technologies. In the past few years, wavelength tunability of fiber couplers has been fulfilled by employing the micro-mechanical platform or thermo-optical medium [13–17]. Fiber-optic couplers could be generally classified into two categories: the mechanically tunable [13, 14] and evanescent-field-assisted ones [15–17]. The latter would be of special attraction as the evanescent field is highly sensitive to the environmental medium. This property makes it possible to achieve a tunable WDM coupler with high performances by integrating the fiber-optic coupler with various functional materials. As an attractive functional material, the magnetic fluid (MF) possesses many intriguing magneto-optical properties such as tunable refractive index , tunable transmission , tunable birefringence and dichroism , etc. By using these properties, a good variety of magneto-optical devices have been proposed, including magnetic field sensors [21–24], optical switches [25, 26], and optical modulators [27, 28], etc. The variation in refractive index of the MF could normally reach a magnitude of 10−2 when external magnetic field is applied . This property could be exploited to tune the coupling coefficient of fiber-optic couplers. Actually some works have been engaged on the design of MF-based tunable couplers [30, 31]. These works aim to theoretically design the magnetically controlled coupler operating at one particular wavelength. In the work presented in this paper, we have theoretically proposed and experimentally validated a magnetically controllable wavelength-selective fiber coupler for WDM applications. Its wavelength tunability is achieved by integrating the fiber coupler with the MF. A theoretical model has been set up to analyze the operation principle of the proposed WDM coupler, which is verified by our experimental observation on the transmission spectral evolution in response to the applied magnetic field intensity. Our proposed magnetically controllable WDM coupler has high channel wavelength tunability and splitting ratio with high isolation, which ensures its applicability for potential applications in fiber laser and fiber-optic communications systems, as well as fiber sensing occasions. Furthermore, our proposed schemes also support the magnetically controllable mode division multiplexing by using the MF-integrated fiber coupler. 2. Theory 2.1 Fundamental principle Several schemes have been proposed to analyze the coupling mathematically of tapered fiber couplers [10–12]. According to the fusion degree, the coupling region of the fiber coupler can be classified into weakly coupling and strong coupling regions, as shown in Fig. 1. Under weakly coupling condition, the two fibers are not fused together. When the light propagating through the two fibers is constrained inside the core area, the coupling between the two fibers is rather weak and could be actually neglected. As the fiber radius further reduces during the pulling process and the fiber core would no longer thoroughly constrain the light, and the fiber cladding would turn to serve as the waveguide core with ambient medium working as the waveguide cladding. In this case the coupling coefficient could be expressed as : 1/ 2
2 Δ ⋅ r 2π D
3 − U∞ λ 2 −V (2 D − 2) U V e = ∞ V 5/ 2 eV (2 D − 2) 2π r 2 n2 π D
where, Δ = (n22-n32)/2n22 and V = 2πr(n22-n32)1/2/λ refer to the relative refractive index difference and normalized propagation constant, respectively. Here n2 and n3 represent the
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refractive indices of the cladding and the external medium, respectively, and r is the fiber radius which depends on the fusion degree and length of the tapering region. The eigenvalue U∞, is 2.405 when the fundamental core mode is far from cut-off region. D is defined as D = d/2r to describe the fusion degree, where d is the inter-core distance.
Fig. 1. Schematic diagram of a symmetrical 2 × 2 tapered coupler.
For the strong coupling case, the fibers are fused together and Eq. (1) is no longer valid. Under this condition, the coupler could be considered as a hybrid waveguide and the coupling coefficient can be calculated by half of the propagation constant difference between the even and odd modes. In other words, the fiber fusion region is simplified as a rectangular waveguide and the coupling coefficient can be described as :
β 0 − β1
3πλ 1 ⋅ (2) 2 2 32n2 r (1 + 1/ V ) 2 Therefore, the phase difference between the light at the two output ports can be calculated by integrating the coupling efficient along z-axis over the coupling region, as expressed by the following equation : CSC =
ϕ (λ , n3 ) = CWC (λ , n3 , z)dz + CSC (λ , n3 , z)dz
(3) = ϕWC (λ , n3 ) + ϕ SC (λ , n3 ) Thus the normalized powers of the output ports could be acquired using PC (λ) = 1- sin2 φ (λ, n3) and PD (λ) = sin2 φ (λ, n3) . It should be noted that the transmission loss is neglected in the above calculation. However, with the reduction of fiber radius, stronger evanescent field would be excited and will be absorbed or scattered by ambient medium, causing considerable transmission loss when the light propagates though the fiber fusion region. Besides, the modal phase difference between the two fibers should be also taken into account as it is rather difficult to maintain identical fiber geometry during the pulling process. Considering these factors, the output powers normalized to the input power should be modified as: WC
PC (λ ) = 10−α (1 − F sin 2 ϕ (λ , n3 ))
PD (λ ) = 10−α F sin 2 ϕ (λ , n3 )
where, α = α0 + αext (H) is the transmission loss introduced during the pulling process and the ambient medium, and F≡|κ|2/φ2 (0≤F≤1) is the phase matching degree. Here, κ is the coupling coefficients between the two fibers. For an ideal fiber coupler, the phase is well matched and in practical applications it is reasonable to assume that F≈1. The performance of the coupler can be theoretically evaluated by the following parameters, including insertion loss L, additional loss Ladd, and splitting ratio SR, which could be expressed below: LX = −10 lg
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PX = −10 lg PX (λ ) ; X = C or D Pin
Received 11 Feb 2015; revised 13 Apr 2015; accepted 15 Apr 2015; published 21 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.011123 | OPTICS EXPRESS 11126
Ladd = −10 lg
Pout ,total Pin
= −10 lg( PC (λ ) + PD (λ ))
− L /10 = α = −10 lg 10( C ) + 10( − LD /10)
PX × 100% = 10− ( L − Ladd )/10 × 100% ; X = C or D Pout ,total
When sin2 φ (λ, n3) = 1, the minimum PC (λ) could be reached while the maximum could be acquired when sin2 φ (λ, n3) = 0. Thus, for port C, the band-pass or band-rejection operations can be achieved when the following conditions are respectively satisfied: π 2 + kπ ϕ (λ , n3 ) = kπ
band-rejection channel ; k is integer band-pass channel
(1 − F ) × 100% SRC − channel = 1
band-rejection channel band-pass channel
2.2 Theoretical analysis As the applied magnetic field intensity varies, the refractive index and transmission loss of the magnetic fluid would change accordingly [18, 19]. And therefore, the phase difference of the coupler φ (λ, n3), the phase matching degree F as well as the transmission loss α would change accordingly. Since the transmission loss increases with the increment of the magnetic field intensity, the additional loss would increase according to Eq. (7) . While, the insertion losses are affected by the transmission loss α, the phase difference φ (λ, n3) and the phase matching degree F. However, the channel splitting ratio SR only depends on the phase matching degree F. Additionally, the channel wavelength would also shift with the variation in the refractive index of the magnetic fluid, and the corresponding sensitivity can be expressed as: ∂ϕ ∂ϕ ∂ϕ − WC + SC ∂n3 ∂n3 ∂n ∂λ (11) =− 3 = ϕ ϕ ϕ ∂ ∂ ∂ ∂n3 WC + SC ∂λ ∂λ ∂λ According to Eqs. (1) and (2), it is easy to deduce that ∂φSC/∂n3 0 and ∂φWC/∂n3>0. And in order to ensure good light constraint ability, the eigenvalues V of the tapered fiber should be larger than 2.045, which means that ∂φSC/∂λ >0. Thus, if weak coupling is the major factor that account for the coupling mechanism, ∂λ/∂n30 and ∂φWC/∂n3>0. Under the strong coupling condition, in order to maintain good light constraint ability, the eigenvalue V of the tapered fiber should be larger than 2.045, and ∂φSC/∂λ is larger than 0. Hence according to Eqs. (11)-(15), the channel wavelength would shift toward longer wavelength region with the increment of ambient refractive index when -∂φSC/∂n3>∂φWC/∂n3, while it will turn out blue shift when -∂φSC/∂n3