3/7/2011 RKK EC831EC831 1Power Launching and Coupling Unit‐5 3/7/2011 RKK EC831EC831 2 Power Launching Considerations Numerical Aperture Core Size Refractive Index Profile Core Cladding index difference of the fiber Radiance Angular Power Distribution of the optical source 3/7/2011 RKK EC831EC831 3 Coupling Efficiency s F P P = = sourse the from emitted power fiber the into coupled power η Source Optical Fiber s P F P 3/7/2011 RKK EC831EC831 4 Lambertian Source Lambert's cosine law in optics says that the radiant intensity observed from a "Lambertian" surface is directly proportional to the cosine of the angle θ between the observer's line of sight and the surface normal. The law is also known as the cosine emission law or Lambert's emission law. It is named after Johann Heinrich Lambert, from his Photometria, published in 1760 3/7/2011 RKK EC831EC831 5 Source‐to‐Fiber Power Launching Radiance (or brightness) B at a given diode drive current is the optical power radiated into a unit solid angle per unit emitting surface area and is generally specified in terms of W/cm 2 .sr. Consider Fig. which shows a spherical coordinate system characterized by R, θ, and φ, with the normal to the emitting surface being the polar axis. 3/7/2011 RKK EC831EC831 6 Source‐to‐Fiber Power Launching The radiance may be a function of both θ and φ, and can also vary from point to point on the emitting surface. Surface‐emitting LEDs are characterized by their Lambertian output pattern. The power delivered at an angle θ, measured relative to a normal to the emitting surface, varies as cosθ because the projected area of the emitting surface varies as cosθ with viewing direction. The emission pattern for a Lambertian source follows the relationship B(θ, φ) = B o cosθ where B o is the radiance along the normal to the radiating surface. The radiance pattern for this source is shown in Fig. 3/7/2011 RKK EC831EC831 7 Source‐to‐Fiber Power Launching Edge‐emitting LEDs and laser diodes have different radiances B(θ, 0 o ) and B(θ, 90 o ) in the planes parallel and normal, respectively, to the emitting‐junction plane of the device. The radiances can be approximated by The integers T and L are the transverse and lateral power distribution coefficients, respectively. For edge emitters, L=1 (a Lambertian distribution with a 120 o half‐ power beam width) and T is significantly larger. For laser diodes, L can take on values over 100. θ ϕ θ ϕ ϕ θ L T B B B cos cos cos sin ) , ( 1 0 2 0 2 + = 3/7/2011 RKK EC831EC831 8 Source‐to‐Fiber Power Launching Example : A lambertian pattern with a laser diode has a lateral (φ = 0 o ) half‐ power beam width of 2θ = 10 o . we have B(θ=5 o , φ = 0 o ) = B o (cos5 o ) L = (1/2)B o Solving for L, we have L = [log 0.5 / log(cos5 o )] = [log 0.5/log 0.9962] = 182 The narrower output beam from a laser diode allows more light to be coupled into an optical fiber 3/7/2011 RKK EC831EC831 9 Power‐Coupling Calculation Consider the case shown in Fig. for a symmetric source of brightness B(A s , Ω s ), where A s and Ω s are the area and solid emission angle of the source, respectively. The coupled power can be found using the relationship 3/7/2011 RKK EC831EC831 10 Power‐Coupling Calculation The total coupled power is determined by summing up the contributions from each individual emitting‐point source of incremental area dθ s rdr; that is, integrating over the emitting area. If the source radius r s is less than the fiber‐core radius a, then the upper integration limit r m = r s ; for source areas larger than the fiber‐core area, r m = a Assume a surface‐emitting LED of r s < a. This is a Lambertian emitter, For step‐index fibers the NA is independent of θ s and r, so that (for r s < a) P LED,step = (πr s ) 2 B 0 (NA) 2 = 2(πr s ) 2 B 0 n 1 2 Δ 3/7/2011 RKK EC831EC831 11 Power‐Coupling Calculation Assume Total optical power P s emitted from the source area A s into a hemisphere (2π sr) is given by Hence P LED,step = P s (NA) 2 for r s < a When the radius of the emitting area is larger than the radius a of the fiber‐core area, Therefore P LED,step = (a/r s ) 2 P s (NA) 2 for r s > a 3/7/2011 RKK EC831EC831 12 Power‐Coupling Calculation Example : Consider an LED that has a circular emitting area of radius 35‐mm and a Lambertian emission pattern with 150 W/(cm2.sr) axial radiance. Let us compare the optical powers coupled into two step‐index fibers, one of which has a core radius of 25‐mm with NA = 0.20 and the other has a core radius of 50‐mm with NA = 0.20. For the larger core fiber, we get P LED,step = P s (NA) 2 = π 2 r s 2 B 0 (NA) 2 = π 2 (0.0035cm) 2 [150W/(cm 2 .sr)](0.20) 2 = 0.725 mW When the fiber end‐face area is smaller than the emitting surface area, the coupled power is less than the above case by the ratio of the radii squared: P LED,step = (a/r s ) 2 P s (NA) 2 = (25μm/35μm) 2 (0.725mW) = 0.37 mW 3/7/2011 RKK EC831EC831 13 Power‐Coupling Calculation The power coupled from a surface‐emitting LED into a graded‐index fiber becomes (for r s < a) 3/7/2011 RKK EC831EC831 14 Power‐Coupling Calculation If the refractive index n of the medium is different from n 1 , then the power coupled into the fiber reduces by the factor R = (n 1 ‐n) 2 /(n 1 +n) 2 where R is the Fresnel reflection or the reflectivity at the fiber‐core end face. The reflection coefficient r = (n 1 ‐n)/(n 1 +n) relates the amplitudes of the reflected and the incident wave. 3/7/2011 RKK EC831EC831 15 Power‐Coupling Calculation Example : A GaAs optical source with a refractive index of 3.6 is coupled to a silica fiber that has a refractive index of 1.48. If the fiber end and the source are in close physical contact, then the Fresnel reflection at the interface is R = [(n 1 ‐n)/(n 1 +n)] 2 = [(3.60‐1.48)/(3.60+1.48)] 2 = 0.174 This value of R corresponds to a reflection of 17.4% of the emitted optical power back into the source. Given that P coupled = (1‐R)P emitted the power loss L in decibels is found from L = ‐10.log[P coupled /P emitted ] = ‐10.log(1‐R) = ‐10log(0.826) = 0.83 dB This number can be reduced by having an index‐matching material between the source and the fiber end. . 3/7/2011 RKK EC831EC831 16 Power Launching versus Wavelength The number of modes that can propagate in a graded‐index fiber of core size a and index profile α is M = [α/(α+2)].[2πan 1 /λ] 2 Δ Twice as many modes propagate in a given fiber at 900‐nm than at 1300‐ nm. The radiated power per mode, P s /M, from a source at a particular wavelength is given by the radiance multiplied by the square of the nominal source wavelength, P s /M = B o λ 2 Twice as much power is launched into a given mode at 1300‐nm than at 900‐nm. Two identically sized sources operating at different wavelengths but having identical radiances will launch equal amounts of optical power into the same fiber. 3/7/2011 RKK EC831EC831 17 Equilibrium Numerical Aperture An example of the excess power loss is shown in Fig. in terms of the fiber NA. At the input end of the fiber, the light acceptance is described in terms of the launch numerical aperture NA in . 3/7/2011 RKK EC831EC831 18 Equilibrium Numerical Aperture If the light‐emitting area of the LED is less than the cross‐sectional area of the fiber core, then the power coupled into the fiber is given by P LED = P s (NA in ) 2 In long fiber lengths after the launched modes have come to equilibrium (which is often taken to occur at 50‐m), the effect of the equilibrium numerical aperture NA eq becomes apparent. The optical power in the fiber scales as P eq = P 50 (NA eq / NA in ) 2 where P 50 is the power expected in the fiber at the 50‐m point based on the launch NA. 3/7/2011 RKK EC831EC831 19 LENSING FOR COUPLING IMPROVEMENT Possible Lensing Schemes are shown in Fig. : A rounded‐end fiber; A small glass sphere (nonimaging microsphere) in contact with both the fiber and the source; A larger spherical lens used to image the source on the core area of the fiber end: A cylindrical lens generally formed from a short section of fiber; A system consisting of a spherical‐ surfaced LED and a spherical‐ ended fiber; and A taper‐ended fiber. 3/7/2011 RKK EC831EC831 20 FIBER‐TO‐FIBER JOINTS For a graded‐index fiber with a core radius a and a cladding index r 2 , and with k = 2π/λ, the total number of modes is where n(r) defines the refractive‐index variation of the core. The total number of modes can relate to a local numerical aperture NA(r) through The fraction of energy coupled from one fiber to another is proportional to the common mode volume M comm . The fiber‐to‐fiber coupling efficiency is given by η F = (M comm /M E ) where M E is the number of modes in the emitting fiber. 3/7/2011 RKK EC831EC831 21 FIBER‐TO‐FIBER JOINTS The fiber‐to‐fiber coupling loss L F is given in terms of η F as L F = ‐10 log η F Consider all fiber modes being equally excited, then the output beam fills the entire output NA; as shown in Fig. (a) If steady‐state modal equilibrium has been established in the emitting fiber, the optical power is concentrated near the center of the fiber core, as shown in Fig. (b). The optical power emerging from the fiber then fills only the equilibrium NA. 3/7/2011 RKK EC831EC831 22 Fiber Cable an Fiber Joints Joints in fiber are needed for a number of reasons: Fiber is available and can only be installed in lengths up to about 2km, for longer spans a joint is needed For the repair of damaged fiber For test purposes at terminal equipment There are three basic types of joint: Optical fiber connector, demountable connection Fusion splice, permanent connection Mechanical splice 3/7/2011 RKK EC831EC831 23 Fiber Cable an Fiber Joints 3/7/2011 RKK EC831EC831 24 Loss in Fiber Joints There are several sources of loss in a fiber joint: 3/7/2011 RKK EC831EC831 25 Fresnel Loss at an Interface Loss is associated with interfaces between two media where there is a step change in the refractive index Loss occurs because of reflection at the interface. Fraction of light reflected at the interface given by Fresnel Formula, The loss in decibel due to Fresnel reflection is given by 2 ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + − = b a b a n n n n r ( ) r Loss Fres − − = 1 log 10 10 3/7/2011 RKK EC831EC831 26 Fresnel Loss at an Interface Typically Fresnel loss or reflection occurs at joints with an air gap For a fiber joint loss occurs twice, once at each fiber‐air interface. Hence total loss in decibel due to Fresnel reflection is given by Problem: Show that for a fiber with an n 1 = 1.5 a small air gap results in a total Fresnel loss of .36 dB ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + − − − = 2 0 1 0 1 10 1 log 20 n n n n Loss Fres 3/7/2011 RKK EC831EC831 27 FIBER‐TO‐FIBER JOINTS Mechanical misalignment losses Lateral (axial) misalignment loss is a dominant Mechanical loss. 2 / 1 2 2 step , 2 1 2 arccos 2 ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − − = = a d a d a d a A comm F π π π η 3/7/2011 RKK EC831EC831 28 FIBER‐TO‐FIBER JOINTS Longitudinal offset effect 3/7/2011 RKK EC831EC831 29 Fiber Optic Connectors Invariably used to connect fiber to terminal equipment, such as lasers or photodiodes. Each fiber cladding is located exactly within a precision ferrule, using adhesive. Joint is formed by precisely aligning both ferrules within an adaptor. Wide variety of connectors have evolved, to suit different applications, Mostly based on ferrule design 3/7/2011 RKK EC831EC831 30 Optical Fiber Connectors Some of the principal requirements of a good connector design are as follows: 1- low coupling losses 2- Interchangeability 3- Ease of assembly 4- Low environmental sensitivity 5- Low-cost and reliable construction 6- Ease of connection 3/7/2011 RKK EC831EC831 31 Connector loss Connector loss is random, not only between different connectors of the same type but also between each mating (repeatability). Attenuation (Insertion Loss): Return Loss : Reflections are the optical power directed back toward the source. Most common source of reflection is a fiber joint. Magnitude of reflection is defined by the "Return Loss" 3/7/2011 RKK EC831EC831 32 Optical Fiber Couplers Couplers are one of the most common devices in optical fiber systems. Used to split, combine and route signals within systems. 3/7/2011 RKK EC831EC831 33 Classification of Fiber Couplers 3/7/2011 RKK EC831EC831 34 Coupler Split Ratio 3/7/2011 RKK EC831EC831 35 Coupler Insertion Loss 3/7/2011 RKK EC831EC831 36 Coupler Excess Loss 3/7/2011 RKK EC831EC831 37 Coupler Crosstalk or Directivity 3/7/2011 RKK EC831EC831 38 Exercise A four port multimode FBT coupler has 60 μW of optical power launched into port 1.The measured powers at the other ports are: Port 2: 0.004 μW Port 3: 26.0 μW Port 4: 27.5 μW Determine the excess loss, insertion loss, directivity, and split ratio for this coupler.