Chapter 10 WDM concepts and components

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1 Chapter 10 WDM concepts and components - Outline 10.1 Operational principle of WDM 10. Passive Components - The x Fiber Coupler - Scattering Matrix Representation - The x Waveguide Coupler - Mach-Zehnder Interferometer Multiplexers - Fiber Grating Filters 10.3 Tunable Sources 10.4 Tunable Filters - System considerations - Tunable filter types

2 10.1 Operational Principle of WDM What is WDM : The technology of combining a number of wavelengths onto the same fiber is known as wavelength-division-multiplexing or WDM DWDM : dense wavelength-division-multiplexing (channel spacing is dense)

3 10.1 Operational Principle of WDM ITU (International Telecommunication Union) specify channel spacing in terms of frequency - C band (conventional band) : nm - L band (longer wavelength band) : nm - frequency reference THz ( nm) - Channel spacing: 00 GHz, 100 GHz, 50 GHz, 5 GHz ITU GRID TABL (part of it) Channel # Frequency (GHz) Wavelength (nm)

4 10.1 Operational Principle of WDM Frequency spacing, wavelength spacing: c Δ ν = Δλ, (10 1) λ xample 10-1 If one takes a spectral band of 0.8 nm (or, equivalently, a mean frequency spacing of 100 GHz) within which narrow-linewidth lasers are transmitting, ask how many channels can be sent in the 155-to nm band on a single fiber. Advantages: - Capacity upgrade - Transparency: each optical channel can carry any transmission format (asynchronous and synchronous digital data; analog information) - Wavelength routing - Wavelength switching

5 10.1 Operational Principle of WDM Key feature of WDM is that the discrete wavelengths form an orthogonal set of carriers that can be separated, routed and switched without interfering each other The implementation of WDM networks requires a variety of passive and active devices to combine, distribute, isolate, and amplify optical power at different wavelength. Active devices: Tunable optical filters, tunable sources, optical amplifier, etc. Passive devices: Multiplexer / Demultiplexer, Add/drop filters couplers, grating, etc

6 10. Passive Components Passive devices operate completely in the optical domain to split or combine light stream Three fundamental technologies for making passive components are based on optical fibers, integrated optical waveguides, and bulk microoptics The x Fiber Coupler x coupler: Input P 0 Throughout power P 1, P Crosstalk: P 3, P 4

7 10. Passive Components The x Fiber Coupler For ideal coupler : = 0sin (κ ), (10 ) 1 = 0cos (κ ), (10 3) P P z P P z z : coupler drawing length κ : coupling coefficient describing the interaction between the fields in the two fibers Fused coupler can be used as a WDM (see next slide)

8 10..1 The x Fiber Coupler Principle : Multiplexer / Demultiplexer (MUX/DMUX) using fused coupler : Also called WDM : such as, WDM (980/1550 nm) WDM (1480/1550 nm) P P z = 0sin (κ ), (10 ) 1 = 0cos (κ ), (10 3) P P z z : coupler drawing length κ : coupling coefficient describing the interaction between the fields in the two fibers Question 10-3 consider the coupling ratios as a function of pull lengths as shown in fig p10-3 for a fused biconical tapered coupler. The performance are given for 1310 nm and 1540 nm operation. Discuss the behavior of the coupler for each wavelength if it pull length is stopped at the following points: A, B, C, D,, and each F.

9 10. Passive Components The x Fiber Coupler Parameters : - Coupling ratio (splitting ratio) - xcess loss - Insertion loss - Crosstalk P P1+ P Coupling ratio = 100%, (10 4) P P1+ P 0 xcess loss=10log, (10 5) P i Insertion loss=10log, (10 6) P i: input; j: output j 3 Crosstalk loss=10log, (10 7) P0 xample 10- A x biconical tapered fiber coupler has an input optical power level of P 0 =00μW. The output powers at the other three ports are P 1 =90μW P =85μW and P 3 =6.3nW. Find coupler ratio, excess loss, insertion loss, and crosstalk. P

10 10. Passive Components 10.. Scattering Matrix Representation One can analyze a x guided-wave coupler as a four terminal device that has inputs and outputs by using matrix method Scattering Matrix Input field: Output field: Coupler : S a b a 1 = a b 1 = b s s 11 1 = s1 s Assume coupler is lossless : I=bb+ bb = aa + aa * * * * and b = S a b1 s11 s1 a1 a1s11+ as1 b = s1 s a = a1s1 as + One can find the matrix for coupler : 1 ε j ε S = j ε 1 ε ε : coupling ratio from port a 1 to port b xample 10-3 Assume we have a 3-dB coupler, so that half of the input power gets coupled to the second fiber. Find coupling ratio of the coupler and coupler matrix.

11 10. Passive Components The x waveguide coupler Wavewguide devices have an intrinsic wavelength dependence in the coupling region (guide width w, gap s, and refractive index) Loss in semiconductor waveguide devices: 0.05 < α < 0.3 cm -1 P P z e α z = 0sin (κ ), (10 18) α ; optical loss coefficient z : coupler drawing length κ : coupling coefficient describing the interaction between the fields in the two fibers

12 10. Passive Components The x waveguide coupler P P z e α z = 0sin (κ ), (10 18) α ; optical loss coefficient z : coupler drawing length κ : coupling coefficient describing the interaction between the fields in the two fibers Complete power transfer to the nd guide occurs when the guide length L is : π L = ( m+ 1), with m = 0,1,... (10 1) κ xample 10-4 A symmetric waveguide coupler has a coupling coefficient κ = 0.6 mm -1. Find the coupling length for m=1

13 10. Passive Components Mach-Zehnder Interferometer Multiplexers Wavelength-dependent multiplexer/demultiplexer (WDM) can be made using Mach-Zehnder (MZ) interferometers. x MZ interferometer consists of 3 stages: 3-dB splitter, phase shift, 3-dB combiner. Due to the phase shift between the two arms, the recombined signals will interference constructively at one output and destructively at the other : Demultiplexer (Demux) : in,1 will separate at out,1, out, Multiplexer (Mux) : Both outputs out,1 and out, combine at in,1 λ 1, λ λ 1 λ

14 10..5 Mach-Zehnder Interferometer Multiplexers How to find output P1 and P by using matrix method? Write matrix for each stage: - phase shift : M Δφ - 3-dB splitting coupler : M coupler - 3-dB combining coupler : M coupler Obtain the total matrix for MZ interferometer : M=M M M coupler coupler Find output -field out,1 and out, : Δφ Find output power (or intensity) P out,1 and P out, : M M out,1 in, in,1 = M out, = in, M 1 M in, * out,1 = out,1 out,1 out,1 P = ; * out, = out, out, out, P =

15 10..5 Mach-Zehnder Interferometer Multiplexers Details for matrix of each component : 3-dB splitting coupler : M coupler Coupler matrix : s s cos κd jsin κd 11 1 M coupler =, (10 9) s1 s = jsinκd cos κd 3-dB coupler matrix (no loss) : 1 1 j M 3-dB coupler =, (10 30) j 1 phase shift : M Δφ Assuming same sources for the two arms, phase shift due to the arm length difference: π n π n φ L ( L L), (10 31) λ λ Assume: n 1 =n =n eff ; k =πn eff /λ, Δ = 1 +Δ Δ φ = kδl, (10 3) Matrix of the phase shift : Total matrix : M jkδl / e 0 M Δφ =, (10 33) jkδl / 0 e M M sin( kδl/ ) j cos( kδl/ ) 11 1 M=Mcoupler MΔφ M coupler = (10 35) M1 M = cos( kδl/ ) sin( kδl/ )

16 10..5 Mach-Zehnder Interferometer Multiplexers Find output -field out,1 and out, : out,1 in,1 M 11 M1 in,1 M = = M M out, in, 1 in, M M sin( kδl/ ) cos( kδl/ ) 11 1 M=Mcoupler MΔφ M coupler = j (10 35) M1 M = cos( kδl/ ) sin( kδl/ ) out,1 =j in,1 sin( kδ L/ ) + in, cos( kδl/ ) (10 36) out, =j in,1 cos( kδ L/ ) + in, sin( kδl/ ) (10 37) Assume that in, = 0, out,1 =j in,1 sin( kδl/ ) out, =j in,1 cos( kδl/ ) Find output power (or intensity) P out,1 and P out, : P = = P sin ( kδl/) * out,1 out,1 out,1 in,1 P = = P cos ( kδl/) * out, out, out, in,1

17 10..5 Mach-Zehnder Interferometer Multiplexers Spectrum or magnitude response of P out,1 and P out, : Ref: optical filter design and analysis p167 P = = P sin ( kδl/) * out,1 out,1 out,1 in,1 P = = P cos ( kδl/) * out, out, out, in,1 Maximum and minimum of P out,1 and P out, : When: kδ L/= mπ P out,1 = 0; P out, = 1 kδ L/= mπ Frequency spacing for bar or cross: Δ f = n eff c ΔL n eff : effective refractive index of a waveguide This gives rise to the frequency spacing for the two Mux/Demux frequency is Δf /, i.e., Δ c f =, (10 41) n eff ΔL (different approach with our books)

18 10. Passive Components Mach-Zehnder Interferometer Multiplexers xample 10-6 Assume that the input wavelengths of x silicon MZI are separated by 10 GHz (i.e., Δλ =0.08 nm at 1550 nm). With n eff =1.5 in a silicon waveguide, find the waveguide length difference ΔL. xample of 4x4 MZI: c Δ L1 = Δ L = (10-4) n (Δν) eff c Δ L = = ΔL (10-43) 3 1 neff ( Δν)

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