304 JOURNAL OF LIGHTWAVE TECHNOLOGY,VOL.30,NO.3,FEBRUARY 1,2012 Single-,Few-,and Multimode Y-Junctions John D.Love and Nicolas Riesen Abstract-The theory of modal propagation through symmetric and asymmetric 2-D weakly guiding Y-junctions is extended to cover few-mode,multimode,and multiarm Y-junctions.A concep- B A B tual approach based on the evolution of modal effective indexes and composite supermodes is used to determine the qualifative func- First-Even First Even +Odd tionality of these devices,with quantification being determined nu- Supermode Supermodes merically using the beam propagation method. Index Terms-Asymmetric Y-junctions,mode-division multi- plexing,mode separation,power splitting,symmetric Y-junctions. 3dB Attenuation Fundamental Mode I.INTRODUCTION Fundamental Mode HE majority of fiber-or waveguide-based light-manip- (a). (b) ulating devices that are used to modify the amplitude or Fig.1.(a)Forward and (b)backward modal propagation through a symmetric, phase of the fundamental mode(FM)rely on the basic optical single-mode Y-junction. phenomena of interference,coupling,or reflection for their functionality.These devices include,for example,a wide va- riety of couplers,interferometers,and wavelength multiplexers past [2]-[6].Asymmetric Y-junctions where the arms have and demultiplexers.In addition to these devices,there is another differing cross sections (or differing refractive indexes)have class of devices whose functionality is based solely on their received far less attention.Nonetheless they are sometimes geometrical design.This class includes,for example,tapered used as polarization splitters,mode combiners,and mode single-mode fibers or waveguides that modify their transverse splitters in optical switches [7]-[9].They can also be used as modal field distribution via cross-sectional variations along wavelength multiplexers [10],and as variable power splitters their length.Provided that such a change is undertaken suffi- when designed with an adjustable gap region [11].The use ciently slowly,i.e.,approximately adiabatically,there will be a of asymmetric Y-junctions for mode-division multiplexing of negligible loss of modal power through radiation or coupling few-mode waveguides for high-capacity data transmission has to other modes [1]. also been suggested [12]. A second category of devices that rely solely on geomet- The beam propagation method(BPM)has been used to an- rical design for their functionality are Y-junctions.The basic alyze numerically the behavior of weakly guiding 2-D Y-junc- Y-junction has a stem and two diverging arms,and its light split- tions.In the case of weak guidance,where the core-cladding ting and light combining properties can be generalized to mul-index difference is small,the TE and TM modes are degenerate tiarm Y-junctions.Like tapers,the cross-sectional evolution of and,hence,exhibit similar behavior [13]. Y-junctions,needs to occur sufficiently slowly with axial dis- The simulations in this paper assume typical parameters such tance to ensure approximate adiabatic propagation of modes as a pure silica cladding,small index contrast,and a 1.55 um through the device.This ensures that minimal power is trans- source wavelength.The simple Y-junction structures simulated ferred between the modes or to the radiation field.In practice, in general have stem widths equal to the sum of the output arm this is readily achieved by making the divergence/taper angle widths.It should,however,be noted that the behavior of the between the two arms sufficiently small. Y-junction is largely insensitive to the specific geometry of the These approximately adiabatic devices can be subdivided taper,provided a sharp junction vertex is maintained [1]. into two categories:symmetric and asymmetric.Symmetric single-mode Y-junctions are wavelength-independent,equal II.TWO-ARM Y-JUNCTIONS 3 dB splitters and have been studied to some extent in the A.Single-Mode Symmetric Y-Junctions The working mechanism of single-mode symmetric Y-junc- Manuscript received August 16,2011;revised December 04,2011;accepted tions can be described by considering normal local even and odd December 09,2011.Date of publication December 15,2011;date of current version January 25,2012. supermodes covering the two output arms A and B as shown in The authors are with the Physics Education Centre,The Australian National Fig.1[4]. University,Canberra,A.C.T.0200,Australia(e-mail:john.love@anu.edu.au; This description is possible when the branching angle,0 is nicolas.riesen@anu.edu.au). Color versions of one or more of the figures in this paper are available online approximately adiabatic (1).The power of the FM in the at http://ieeexplore.ieee.org. stem of the Y-junction will split equally into FMs in the output Digital Object Identifier 10.1109/JLT.2011.2179976 arms as shown in Fig.1(a)just by symmetry.This can also be 0733-8724/$26.00C20111EEE304 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 30, NO. 3, FEBRUARY 1, 2012 Single-, Few-, and Multimode Y-Junctions John D. Love and Nicolas Riesen Abstract—The theory of modal propagation through symmetric and asymmetric 2-D weakly guiding Y-junctions is extended to cover few-mode, multimode, and multiarm Y-junctions. A concep￾tual approach based on the evolution of modal effective indexes and composite supermodes is used to determine the qualitative func￾tionality of these devices, with quantification being determined nu￾merically using the beam propagation method. Index Terms—Asymmetric Y-junctions, mode-division multi￾plexing, mode separation, power splitting, symmetric Y-junctions. I. INTRODUCTION T HE majority of fiber- or waveguide-based light-manip￾ulating devices that are used to modify the amplitude or phase of the fundamental mode (FM) rely on the basic optical phenomena of interference, coupling, or reflection for their functionality. These devices include, for example, a wide va￾riety of couplers, interferometers, and wavelength multiplexers and demultiplexers. In addition to these devices, there is another class of devices whose functionality is based solely on their geometrical design. This class includes, for example, tapered single-mode fibers or waveguides that modify their transverse modal field distribution via cross-sectional variations along their length. Provided that such a change is undertaken suffi- ciently slowly, i.e., approximately adiabatically, there will be a negligible loss of modal power through radiation or coupling to other modes [1]. A second category of devices that rely solely on geomet￾rical design for their functionality are Y-junctions. The basic Y-junction has a stem and two diverging arms, and its light split￾ting and light combining properties can be generalized to mul￾tiarm Y-junctions. Like tapers, the cross-sectional evolution of Y-junctions, needs to occur sufficiently slowly with axial dis￾tance to ensure approximate adiabatic propagation of modes through the device. This ensures that minimal power is trans￾ferred between the modes or to the radiation field. In practice, this is readily achieved by making the divergence/taper angle between the two arms sufficiently small. These approximately adiabatic devices can be subdivided into two categories: symmetric and asymmetric. Symmetric single-mode Y-junctions are wavelength-independent, equal 3 dB splitters and have been studied to some extent in the Manuscript received August 16, 2011; revised December 04, 2011; accepted December 09, 2011. Date of publication December 15, 2011; date of current version January 25, 2012. The authors are with the Physics Education Centre, The Australian National University, Canberra, A.C.T. 0200, Australia (e-mail: john.love@anu.edu.au; nicolas.riesen@anu.edu.au). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JLT.2011.2179976 Fig. 1. (a) Forward and (b) backward modal propagation through a symmetric, single-mode Y-junction. past [2]–[6]. Asymmetric Y-junctions where the arms have differing cross sections (or differing refractive indexes) have received far less attention. Nonetheless they are sometimes used as polarization splitters, mode combiners, and mode splitters in optical switches [7]–[9]. They can also be used as wavelength multiplexers [10], and as variable power splitters when designed with an adjustable gap region [11]. The use of asymmetric Y-junctions for mode-division multiplexing of few-mode waveguides for high-capacity data transmission has also been suggested [12]. The beam propagation method (BPM) has been used to an￾alyze numerically the behavior of weakly guiding 2-D Y-junc￾tions. In the case of weak guidance, where the core-cladding index difference is small, the TE and TM modes are degenerate and, hence, exhibit similar behavior [13]. The simulations in this paper assume typical parameters such as a pure silica cladding, small index contrast, and a 1.55 m source wavelength. The simple Y-junction structures simulated in general have stem widths equal to the sum of the output arm widths. It should, however, be noted that the behavior of the Y-junction is largely insensitive to the specific geometry of the taper, provided a sharp junction vertex is maintained [1]. II. TWO-ARM Y-JUNCTIONS A. Single-Mode Symmetric Y-Junctions The working mechanism of single-mode symmetric Y-junc￾tions can be described by considering normal local even and odd supermodes covering the two output arms A and B as shown in Fig. 1 [4]. This description is possible when the branching angle, is approximately adiabatic . The power of the FM in the stem of the Y-junction will split equally into FMs in the output arms as shown in Fig. 1(a) just by symmetry. This can also be 0733-8724/$26.00 © 2011 IEEE