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? CHAPTER 5 POWER LAUNCHING AND COUPLING

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Summary 5.1 SOURCE-TO-FIBER POWER LAUNCHING 5.1.1Source Output Pattern 5.1.2 Power-Coupling Calculation

5.l.3 Power Launching versus Wavelength

5.l.4 Eauilibrium Numerical Aperture

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5.2 LENSING SCHEMES FOR COUPLING IMPROVEMENT 5.2.1 Nonimaging Microsphere

5.2.2 Laser Diode-Fiber Coupling

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5.3 FIBER-TO-FIBER JOINTS 5.3.l Mechanical Misalignment 5.3.2 Fiber-Related Losses

5.3.3 Fiber End-Face Preparation

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5.4 LED COUPLING TO SINGLE-MODE FIBERS 5.5 FIBER SPLICING Istruction 5.5.l Splicing Techniques 5.5.2 Splicing Single-Mode Fibers 5.6 OPTICAL FIBER CONNECTORS Istruction 5.6.1 Connector Types 5.6.2 Single-Mode Fiber Connectors 5.6.3 Connector Return Loss

5.1.1Source Output Pattern To determine the optical power-accepting capability of a fiber, the spatial radiation pattern of the source must first be known. This pattern can be fairly complex consider Fig. 5-l, which shows a spherical coordinate system characterized by R, θ, and ф, with the normal to the emitting surface being the polar axis. The radiance may be a function of both θ and ф, and can also vary from point to point on the emitting surface. A reasonable assumption for simplicity of analysis is to take the emission to be uniform across the source area.

Surface-emitting LEDs are characterized by their lambertian output pattern, which means the source is equally bright when viewed from any direction. 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 thus follows the relationship B(θ, Ф) = B0cosθ (5-l) where B0 is the radiance along the normal to the radiating surface. The radiance pattern for this source is shown in Fig. 5-2. Edge-emitting LEDs and laser diodes have a more complex emission pat-tern. These devices have different radiances B(θ, 0") and B(θ, 90") in the planes parallel and normal, respectively, to the emitting junction plane of the device. These radiances can be approximated by the general form

The integers T and L are the transverse and lateral power distribution coefficients respectively. In general, for edge emitters, L = l (which is a lambertiandistribution with a l20" half power beam width) and T is significantly larger. For laser diodes, L can take on values over l00.

5.1.2 Power-Coupling Calculation To calculate the maximum optical power coupled into a fiber, consider first the case shown in Fig. 5-3 for a symmetric source of brightness B(As,Ωs), where As and Ωs are the area and solid emission angle of the source, respectively. Here, the fiber end face is centered over the emitting surface of the source and is positioned as close to it as possible. The coupled power can be found using the relationship

where the area and s0lid acceptance angle of the fiber define the limits of the integrals. In this expression, first the radiance B(θ,ф) from an individual radiating point source on the emitting surface is integrated over the solid acceptance angle of the fiber- This is shown by the expression in square brackets, where θ0,maxis the maximum acceptance angle of the fiber, which is related to the numerical aperture NA through Eq(2-23). The total c0uPled power is then determined by summing up the contributions from each individual endtting-p0int s0uree of incremental area dθs r dr; that is, integrating over the emitting area. F0r simplicity, here the emitting surface is taken as being circular. If the source radius rs is less than the fiber-core radius a, then the upper integration limit rm = rs; for source areas larger than the fiber-core area, rm = a.

As an example, assume a surface-emitting LED of radius rs less than the fiber-core radius a. Since this is a lambertian emitter, Eq. (5-l) applies and Eq.(5-3) becomes

where the numerical aperture NA is defined by Eq. (2-23). For step-index fibers the numerical aperture is independent of the positions os and r on the fiber end face, so that Eq. (5-4) becomes (for rs<a) Consider now the total optical power Ps that is emitted from the source of area A. into a hdrisphere (27πsr). This is given by

In the case of a graded-index fiber, the numerical aperture depends on the distance r from the fiber axis through the relationship defined by Eq (2-80). Thus, using Eqs. (2-8oa) and (2-8ob), the power coupled from a surface-emitting LED into a graded-index fiber becomes (for rs <a)

where the last expression was obtained from Eq (5-6)

For computer-based analyses, a Fourier technique can be used in place of a numerical integration of the above expressions to .rapidly calculate the optical power coupled from an LED into a large-core fiber.2 Furthermore, the foregoing analyses assumed perfect coupling conditions between the source and the fiber. This can be achieved only if the refractive index of the medium separating the source and the fiber end matches the index nl of the fiber core. If the refractive index n of this medium is different from nl, then, for perpendicular fiber end faces, the power coupled into the fiber reduces by the factor

where R is the Fresnel reflection or the reflectivity at the fiber-core end face. The ratio r = (nl n)/(nl + n), which is known as the reflection coefficient, relates the amplitude of the reflected wave to the amplitude of the incident wave. The calculation of power coupling for nonlambertian emitters following a cylindrical cosmθ distribution is left as an exercise. The power launched into a fiber from an edge-emitting LED that has a non-cylindrical distribution is rather complex. An example of this has been given by Marcuse , to which the reader is referred for details. Section 5.4 presents a simplified analysis of this in the discussion on coupling LEDs to single-mode fibers.

5.l.3 Power Launching versus Wavelength It is of interest to note that the optical power launched into a fiber does not depend on the wavelength of the source but only on its brightness; that is, its radiance. Let us explore this a little further. We saw in Eq. (2-8l) that the number of modes that can propagate in a graded-index fiber of core she a and index profile a is

Thus, for example, twice as many modes propagate in a given fiber at 900 nm than at 1300 nm. The radiated power per mode, Ps/M, from a source at a particular wavelength is given by the radiance multiplied by the square of the nominal source wavelength, Ps/M=B0/λ (5-12) Thus, twice as much power is launched into a given mode at l300 nm than at 900nm. Hence, two identically sized sources operating at different wavelengths but having identical radiances will launch equal amounts of optical power into the same fiber. 5.l.4 Namerical Ape As we noted earlier, a light source is often supplied with a short (l- to 2-mp fiber flylead attached to it in order to facilitate coupling the source to a system fiber. To achieve a low coupling loss, this flylead should be connected to a system fiber that has a nominally identical NA and core diameter. A certain amount of optical power (ranging from 0. l to l dB) is lost at this junction, the exact loss depending on the connecting mechanism; this is discussed in Sec. 5.3. In addition to the coupling loss, an excess power loss will occur in the first few tens of meters of the system fiber. This excess loss is a result of nonpropagating modes scattering out of the fiber as the launched modes come to an equilibrium condition (see Sec.3.4). This is of particular importance for surface-emitting LEDs, which tend to launch power into all modes of the fiber. Fiber-coupled lasers are less prone to this effect since they tend to excite fewer nonpropagating fiber modes.

The excess power loss must be analyzed carefully in any system design, since it can be significantly higher for some types of fibers than for others.5An example of the excess power loss is shown in Fig. 5-4 in terms of the fiber numerical aperture- At the input end of the fiber, the light acceptance is described in terms of the launch numerical aperture NAin. If the light-emitting area of the LED is less than the cross-sectional area of the fiber core, then, at this point, the power coupled into the fiber is given by Eq. (5-7), where NA = NAin. However, when the optical power is measured in long fiber lengths after the launched modes have come to equilibrium (which is often taken to occur at 50m), the effect of the equilibrium numerical aperture NA. becomes apparent' At this point, the optical power in the fiber scales as

where P50 is the power expected in the fiber at the 50-m point based on the launch NA. The degree of mode coupling occurring in a fiber is primarily a function of the core-cladding index differenceIt can thus vary significantly among different fiber types- Since most optical fibers attain 80-90 percent of their equilibrium NA after about 50 m, it is the value of NAeq that is important when calculating launched optical power in telecommunication systems.

5.2 LENSING SCHEMES FOR COUPLING IMPROVMENT The optical power-launching analysis given in Sec. 5.l is based on centering a flat fiber end face directly over the light source as close to it as possible. If the source-emitting area is larger than the fiber-core area, then the resulting optical power coupled into the fiber is the maximum that can be achieved. This is a result of fundamental energy and radiance conservation principles (also known as the law of brightness). However, if the emitting area of the source is smaller than the core area, a miniature lens may be placed between the source and the fiber to improve the powercoupling efficiency. The function of the microlens is to magnify the emitting area of the source to match exactly the core area of the fiber end face. If the emitting area is increased by a magnification factor M, the solid angle within which optical power is coupled to the fiber from the LED is increased by the same factor. Several possible lensing schemes are shown in Fig. 5-5. These include 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. Although these techniques can improve the source-to-fiber coupling efficiency, they also create additional complexities. One problem is that the lens size is similar to the source and fiber-core dimensions, which introduces fabrication and handling difficulties. In the case of the taper-ended fiber, the mechanical alignment must be carried out with greater precision since the coupling efficiency becomes a more sharply peaked function of the spatial alignment. However,alignment tolerances are increased for other types of lensing systems.

5.2.1 Nonimaging Microsphere one of the most efficient lensing methods is the use of a nonimaging microsphere. Let us first examine its use for a surface emitter, as shown in Fig 5-6. We first make the following practical assumptions: the spherical lens has a refractive index of about 2.0, the outside medium is air (n = 1.0), and the emitting area is circular. To collimate the output from the LED, the emitting surface should be located at the focal point of the lens. The focal point can be found from the gaussian lens formula

where s and q are the object and image distances, respectively, as measured from the lens surface, n is the refractive index of the lens, n l is the refractive index of the outside medium, and r is the radius of curvature of the lens surface. The following sign conventions are used with Eq. (5-l4):. 1. Light travels from left to right. 2. Object distances are measured as positive to the left of a vertex and negative to the right. 3. Image distances are measured as positive to the right of a vertex and negative to the left. 4. All convex surfaces encountered by the light have a positive radius of curvature, and concave surfaces have a negative radius. With the use of these conventions, we shall now find the focal point for the right-hand surface of the lens shown in Fig- 5-6. To find the focal point, we set q = ∞ and solve for s in Eq. (5-l4), where s is measured from point B. With n = 2.0, n' = l.0, q = ∞, and r = -RL, Eq. (5-l4) yields s =f = 2RL

Thus, the focal point is located on the lens surface at point A. (This, of course, changes if the refractive index of the sphere is not equal to 2.0.)

Placing the LED close to the lens surface thus results in a magnification M of the emitting area. This is given by the ratio of the cross-sectional area of the lens to that of the emitting area:

Using Eq. (5-4) we can show that, with the lens, the optical power PL that can be coupled into a full aperture angle 2θ is given by.

Where Ps is the total output power from the LED without the lens. The theoretical coupling efficiency that can be achieved is based on energy and radiance conservation principles.This efficiency is usually determined by the size of the fiber. For a fiber of radius a and numerical aperture NA, the maximum coupling efficiency ηmax is given by

Thus, when the radius of the emitting area is larger than the fiber radius, no improvement in coupling efficiency is possible with a lens. In this case, the best coupling efficiency is achieved by a direct-butt method. Based on Eq. (5-l7), the theoretical coupling efficiency as a function of the emitting diameter is shown in Fig. 5-7 for a fiber with a numerical aperture of 0.20 and 50μm core diameter.

5.2.2 Laser Diode-Fiber Coupling As we noted in Chap. 4, edge-emitting laser diodes have an emission pattern that nominally has a full width at half maximum (FWHM) of 30-50" in the plane perpendicular to the active-area junction and an FWHM of 5-10" in the plane parallel to the junction. Since the angular output distribution of the laser is greater than the fiber acceptance angle, and since the laser emitting area is much smaller than the fiber core, spherical or cylindrical lenseslo'll'l5 or optical fiber tapers can also be used to improve the coupling efficiency between edge-emitting laser diodes and optical fibers. This also works well for vertical-Cavity surface-emitting lasers (VCSELs), Here, coupling efficiencies to multimode fibers of 35 percent result for mass-produced connections of laser arrays to parallel optical fibers, and efficiencies of better than 90 percent are possible by direct (lensless) coupling from a single VCSEL source to a multimode fiber.

The use of homogeneous glass microsphere lenses has been tested in a series of several hundred laser diode assemblies by Khoe and Kyut. Spherical glass lenses with a refractive index of l.9 and diameters ranging between 50 and 60μm were epoxied to the ends of 50-μm corediameter graded-index fibers having a numerical aperture of 0.2. The measured FWHM values of the laser output beams were as follows: 1. Between 3 and 9 pm for the near-field parallel to the junction. 2. Between 30 and 60" for the field perpendicular to the junction. 3. Between l5 and 55' for the field parallel to the junction. Coupling efficiencies in these experiments ranged between 50 and 80 percent. 5.3 FIBER-TO-FIBER JOINTS A significant factor in any fiber optic system installation is the requirement to interconnect fibers in a low-loss manner. These interconnections occur at the optical source, at the photodetector, at intermediate points within a cable where two fibers are joined, and at intermediate points in a link where two cables are connected. The particular technique selected for joining the fibers depends on whether a permanent bond or an easily demountable connection is desired. A permanent bond is generally referred to as a splice, whereas a demountable joint is known as a connector. Every joining technique is subject to certain conditions which can cause various amounts of optical power loss at the joint. These losses depend on parameters such as the input power distribution to the joint, the length of the fiber between the optical source and the joint, the geometrical and waveguide characteristics of the two fiber ends at the joint, and the fiber end-face qualities. The optical power that can be coupled from one fiber to another is limited by the number of modes that can propagate in each fiber. For example, if a fiber in which 500 modes can propagate is connected to a fiber in which only 400 modes can propagate, then, at most, 80 percent of the optical power from the first fiber can be coupled into the second fiber (if we assume that all modes are equally excited). For a graded-index fiber with a core radius a and a cladding index r2, and with k = 2π/λ, the total number of modes can be found from the expression (the derivation of this is complex)

where n(r) defines the variation in the refractive-index profile of the core. This can be related to a general local numerical aperture NA(r) through Eq. (2-80) to yield

In general, any two fibers that are to be joined will have varying degrees of differences in their radii a, axial numerical apertures NA(0), and index profiles a. Thus, the fraction of energy coupled from one fiber to another is proportional to the common mode volume Mcomm(if a uniform distribution of energy over the modes is assumed). The fiber-to-fiber coupling efficiency ηF is given by ηF = Mcomm/ME (5-20) where ME is the number of modes in the emitting fiber (the fiber which launches power into the next fiber). The fiber-to-fiber coupling loss LF is given in terms of ηF as LF = -10log ηF (5-21) An analytical estimate of the optical power loss at a joint between multimode fibers is difficult to make, since the loss depends on the power distribution among the modes in the fiber. For example, consider first the case where all modes in a fiber are equally excited, as shown in Fig. 58a. The emerging optical beam thus fills the entire exit numerical aperture of this emitting fiber. Suppose now that a second identical fiber, which we shall call the receiving fiber, is to be joined to the emitting fiber. For the receiving fiber to accept all the optical power emitted by the first fiber, there must be perfect mechanical alignment between the two optical waveguides, and their geometric and waveguide characteristics must match precisely.

On the other hand, if steady-state modal equilibrium has been established in the emitting fiber, most of the energy is concentrated in the lower-order fiber modes. This means that the optical power is concentrated near the center of the fiber core, as shown in Fig. 5-8b. The optical power emerging from the fiber then fills only the equilibrium numerical aperture (see Fig. 5-4)- In this case, since the input NA of the receiving fiber is larger than the equilibrium NA of the emitting fiber, slight mechanical misalignments of the two joined fibers and small variations in their geometric characteristics do not contribute significantly to joint loss. Steady-state modal equilibrium is generally established in long fiber lengths (see Chap. 3). Thus, when estimating joint losses between long fibers, calculations based on a uniform modal power distribution tend to lead to results which may be too pessimistic. However, if a steady-state equilibrium modal distribution is assumed, the estimate may be too optimistic, since mechanical misalignments and fiber-to-fiber variations in characteristics cause a redistribution of power among the modes in the second fiber. As the power propagates along the second fiber, an additional loss will thus occur when a steady-state distribution is again established. An exact calculation of coupling loss between different optical fibers, which takes into account nonuniform distribution of power among the modes and propagation effects in the second fiber, is lengthy and involved. Here, we shall therefore make the assumption that all modes in the fiber are equally excited. Although this give a somewhat pessimistic prediction of joint loss, it will allow an estimate of the relative effects of losses resulting from mechanical misalignments, geometrical mismatches, and variations in the waveguide properties between two joined fibers.

5.3.l Mechanical Misalignment Mechanical alignment is a major problem when joining two fibers, owing to their. A standard multimode graded-index fiber core is 50-100μm microscopic size in diameter, which is roughly the thickness of a human hair, whereas single-mode fibers have diameters on the order of 9 um. Radiation losses result from mechanical misalignments because the radiation cone of the emitting fiber does not match the acceptance cone of the receiving fiber. The magnitude of the radiation loss depends on the degree of misalignment. The three fundamental types of misalignment between fibers are shown in Fig. 5-9. Longitudinal separation occurs when the fibers have the same axis but have a gap s between their end faces. Angular misalignment results when the two axes form an angle so that the fiber end has are no longer parallel. Axial displacement (which is also often called lateral displacement) results when the axes of the two fibers are separated by a distance d. The most common misalignment occurring in practice, which also causes the greatest power loss, is axial displacement. This axial offset reduces the overlap area of the two fiber-core end faces, as illustrated in Fig. 5-10, and consequently, reduces the amount of optical power that can be coupled from one fiber into the other. To illustrate the effects of axial misalignment, let us first consider the simple case of two identical step-index fibers of radii a. Suppose that their axes are offset by a separation d at the common junction, as is shown in Fig. 5-l0, and assume there is a uniform modal power distribution in the emitting fiber. Since the numerical aperture is constant across the end faces of the two fibers, the optical power coupled from one fiber to another is simply proportional to the common area Acomm of the two fiber cores. It is straightforward to show that this is (see Prob.5-9)

The calculation of power coupled from one graded-index fiber into another identical one is more complex, since the numerical aperture varies across the fiber end face. Because of this, the total power coupled into the receiving fiber at a given point in the common-core area is limited by the numerical aperture of the transmitting or receiving fiber, depending on which is smaller at that point.

If the end face of a graded-index fiber is uniformly illuminated, the optical power accepted by the core will be that power which falls within the numerical aperture of the fiber. The optical power density p(r) at a point r on the fiber end is proportional to the square of the local numerical aperture NA(r) at that point:

where NA(r) and NA(0)defined by Eqs(2-80a) and (2-80b), respectively. The parameter p(0) is the power density at the core axis, which is related to the total power P in the fiber by

For an arbitrary index profile, the double integral in Eq(5-25) must be evaluated numerically. However, an analytic expression can be found by using a fiber with a parabolic index profile (a =2.0). Using Eq. (2-80), the power density expression lat a point r given by Eq- (5-24) becomes

Using Eqs. (5-25) and (5-26), the relationship between the axial power densityp(0) land the total power P in the emitting fiber is

Let us now calculate the power transmitted across the butt joint of the two 1parabolic gradedindex fibers with an axial offset d, as shown in Fig. 5-ll. The overlap region must be considered separately for the areas Al and A2. In area Al the numerical aperture is limited by that of the emitting fiber, whereas in area A2 the numerical aperture of the receiving fiber is smaller than that of the emitting fiber. The vertical dashed line separating the two areas is the locus of points where the numerical apertures are equal. To determine the power coupled into the receiving fiber, the power density given by Eq. (5-26) is integrated separately over areas Al and A2. Since the .numerical aperture of the emitting fiber is smaller than that of the receiving fiber in area Al, all of the power emitted in this region will be accepted by the receiving fiber. The received power Pl in area Al is thus

In area A2 the emitting fiber has a larger numerical aperture than the receiving fiber. This means that the receiving fiber will accept only that fraction of the emitted optical power that falls within its own numerical aperture. This power can be found easily from symmetry considerations. The numerical aperture of the receiving fiber at a point x2 in area A2 is the same as the numerical aperture of the emitting fiber at the symmetrical point xl in area Al. Thus, the optical power accepted by the receiving fiber at any point x2 in area A2 is equal to that emitted from the symmetrical point xl in area Al. The total power P2 coupled across area A2 is thus equal to the power Pl coupled across area Al. Combining these results, we have that the total power PT accepted by the receiving fiber is

This is accurate to within l percent for d/a <0.4. The coupling loss for the offsets.. given by Eqs. (5-30) and (5-31) is

The effect of separating the two fiber ends longitudinally by a gap s is shown. in Fig. 5-l3. Not all the higher-mode optical power emitted in the ring of width x. will be intercepted by the receiving fiber. It is straightforward to show that, for a step-index fiber, the loss occurring in this case is

where θc is the critical acceptance angle of the fiber. When the axes of two joined fiber are angularly misaligned at the joint, the optical power that leaves the emitting fiber outside of the solid acceptance angle of the receiving fiber will be lost. For two step-index fibers that have an angular. Misalignment θ, the optical power loss at the joint has been shown to be

The derivation of Eq. (5-34) again assumes that all modes are uniformly excited.

An experimental comparison of the losses induced by the three types of mechanical misalignments is shown in Fig. 5-l4. The measurements were based on two independent experiments using LED sources and graded-index fibers. The core diameters were 50 and 55μm for the first and second experiments, respectively. Al.83-m-long fiber was used in the first test and 20m length in the second. In either case, the power output from the fibers was first optimized. The fibers were then cut at the center, so that the mechanical misalignment loss measurements were carried out on identical fibers. The axial offset and longitudinal separation losses are plotted as functions of misalignment normalized to the core radius. A normalized angular misalignment of 0.l corresponds to a l" angular offset.

Figure 5-l4 shows that, of the three mechanical misalignments, the dominant loss arises from lateral displacement. In practice, angular misalignments of less than l" are readily achievable in splices and connectors. From the experimental data shown in Fig- 5-l4, these misalignments result in losses of less than 0.5 dB. For splices, the separation losses are normally negligib1e, since the fibers should be in relatively close contact. In most connectors, the fiber ends are intentionally separated by a small gap. This prevents them from rubbing against each other and becoming damaged during connector engagement. Typical gaps in these applications range from 0.025 to 0.10 mm, which results in losses of less than 0.8 dB for a 50μm-diameter fiber. 5.3.2 Fiber-Related Losses In addition to mechanical misalignments, differences in the geometrical and wave-guide characteristics of any two waveguides being joined can have a profound effect on fiber-to-fiber coupling loss. These include variations in core diameter, core-area ellipticity, numerical aperture, refractive-index profile, and core-cladding concentricity of each fiber. Since these are manufacturer-related variations, the user generally has little control over them. Theoretical and experimental studies of the effects of these variations have shown that, for a given percentage mismatch, differences in core radii and numerical apertures have a significantly larger effect on joint loss than mismatches in the refractive-index profile or core ellipticity. The joint losses resulting from core diameter, numerical aperture, and core refractive-indexprofile mismatches can easily be found from Eqs. (5-l9) and (5-20). For simplicity, let the subscripts E and R refer to the emitting and receiving fibers, respectively. If the radii aE and aR are not equal but the axial numerical apertures and the index profiles are equal [NAE(0) = NAR(0) and aE = aR], then the coupling loss is

If the radii and the index profiles 0f the two c0uPled fibers are identical but their axial numerical apertures are different, then

Finally, if the radii and the axial numerical apertures are the same but the core refractive-index profiles differ in two j0ined fibers, then the coupling loss is

This results because for aR < aE the number of modes that can be supported by the receiving fiber is less than the number of modes in the emitting fiber. If aR > aE, then all modes in the emitting fiber can be captured by the receiving fiber. The derivations of Eqs.(5-35) to (5-37) are left as an exercise (see Probs.5-l3 through 5-l5) 5.3.3 Fiber End-Face Preparation one of the first steps that must be followed before fibers are connected or spliced to each other is to prepare the fiber end faces properly. In order not to have light deflected or scattered at the joint, the fiber ends must be flat, perpendicular to the fiber axis, and smooth. End-preparation techniques that have been extensively used include sawing, grinding and polishing, and controlled fracture. Conventional grinding and polishing techniques can produce a very smooth surface that is perpendicular to the fiber axis. However, this method is quite time-consuming and requires a fair amount of operator skill. Although it is often implemented in a controlled environment such as a laboratory or a factory, it is not readily adaptable for field use. The procedure employed in the grinding and polishing technique is to use successively finer abrasives to polish the fiber end face. The end face is polished with each successive abrasive until the scratches created by the previous abrasive material are replaced by the finer scratches of the present abrasive- The number of abrasives used depends on the degree of smooth-ness that is desired.

Controlled-fracture techniques are based on score-and-break methods for cleaving fibers. In this operation, the fiber to be cleaved is first scratched to create a stress concentration at the surface. The fiber is then bent over a curved form while tension is simultaneously applied, as shown in Fig. 5-l5. This action produces a stress distribution across the fiber. The maximum stress occurs at the scratch point so that a crack starts to propagate through the fiber. One can produce a highly smooth and perpendicular end face in this way. A number of different tools based on the controlled-fracture technique have been developed and are being used both in the field and in factory environments. However, the controlled-fracture method requires careful control of the curvature of the fiber and of the amount of tension applied. If the stress distribution across the crack is not properly controlle`1, the fracture propagating across the fiber can fork into several cracks. This forking produces defects such as a lip or a hackled fportion on the fiber end, as shown in Fig. 5-l6. The EIA Fiber Optic Test Procedures (FOTP) 57 and l79 define these and other common end-face defects as follows:

LiP. This is a sharp protrusion from the edge of a cleaved fiber that prevents the cores from coming in close contact. Excessive lip height can cause fiber damage.

Relief

This rounding-off of the edge of a fiber is the opposite condition to lipping. It is also known as breakover and can cause high insertion or splice loss. Chip. A chip is a localized fracture or break at the end of a cleaved fiber. Hackle. Figure 5-l6 shows this as severe irregularities across a fiber end face. Mist. This is similar to hackle but much less severe. Spiral or step. These are abrupt changes in the end-face surface topology. Shattering. This is the result of an uncontrolled fracture and has no definable cleavage or surface characteristics.

5.4 LED COUPLING TO SINGLE-MODE FIBERS In the early years of optical fiber applications, LEDs were traditionally considered only for multimode-fiber systems. However, around 1985, researchers recognized that edge-emitting LEDs can launch sufficient optical power into a single-mode fiber for transmission at data rates up to 560 Mb/s over several kilometers. The interest in this arose because of the cost and reliability advantages of LEDs over laser diodes. Edge-emitting LEDs are used for these applications since they have a laserlike output pattern in the direction perpendicular to the junction plane.

To rigorously evaluate the coupling between an LED and a single-mode fiber we need to use the formalism of electromagnetic theory rather than geometrical optics, because of the monomode nature of the fiber. However, coupling analyses of the output from an edge-emitting LED to a single-mode fiber can be carried out wherein the results of electromagnetic theory are interpreted from a geometrical point of view,45-47 which involves defining a numerical aperture for the single-mode fiber. Agreement with experimental measurements and with a more exact theory are quite good.

Here, we will use the analysis of Reith and Shumate to look at the fol1owing two cases: (l)direct coupling of an LED into a single-mode fiber, and (2)coupling into a single-mode fiber from a multimode flylead attached to the LED.In general, edge-emitting LEDs have gaussian near-field output profiles with l/e2full widths of approximately 0.9 and 22um in the directions perpendicular and parallel to the junction plane, respectively. The far-field patterns vary approximately as cos7θ in the Perpendicular direction and as cosθ(lambertian) in the parallel direction. For a source With a circularly asymmetric radiance B(As, Ωs), Eq.(5-3) is, in general, not separable into contributions from the perpendicular and parallel directions. However, we can approximate the independent contributions by evaluating Eq.(5-3) as if each component were a circularly symmetric source, and then taking the geometric mean to find the total coupling efficiency. Calling these the x (parallel) and y (perpendicular) directions, and letting τx and τy be the x and y power transmissivities (directional coupling efficiencies), respectively, we can find the maximum LED-to-fiber coupling efficiency n from the relation

where P. is the optical power launched into the fiber and Ps is the total source output power. Using a small-angle approximation, we first integrate over the effective solid acceptance angle of the fiber to get 7rNAs.' where the geometrical -op tics- based fiber numerical aperture NASM = 0.ll. Assuming a gaussian output for the source, then for butt coupling of the LED to the single-mode fiber of radius a, the coupling efficiency in the y direction is

where P in,y is the optical power coupled into the fiber from the y-direction source output, which has a l/e2 LED intensity radius op. One can write a similar set of integrals for τx Letting a = 4.5μm, ωx = l0.8μm, and ωy = 0.47μm, Reith and Shumate calculated τx = -l2.2 dB and τy = -6.6 dB to yield a total coupling efficiency n = -l8.8 dB. Thus, for example, if the LED emits 200μW (-7 dBm),then 2.6μW (-25.8 dBm) gets coupled into the single-mode fiber. When a l- to 2-m multimode-fiber flylead is attached to an edge-emitting LED, the near-field profile of the multimode fiber has the same asymmetry as the LED. In this case, one can assume that the multimode-fiber optical output is a simple gaussian with different beam widths along the x and y directions. Using a similar coupling analysis with effective beam widths of ωx = 19.6μm and ωy = l0.0μm, the directional coupling efficiencies are τx = -7.8 dB and τy = -5.2 dB, yielding a total LED-to-fiber coupling efficiency η = -l3.0dB. 5.5 FIBER SPLICING A fiber splice is a Permanent or semipermanent joint between two fibers. These are typically used to create long optical links or in situations where frequent connection and disconnection are not needed. In making and evaluating such splices, one must take into account the geometrical differences in the two fibers, fiber misalignments at the joint, and the mechanical strength of the splice- This section first addresses general splicing methods and then examines the factors contributing to loss when splicing single-mode fibers. 5.5.l Splicing Techniques Fiber splicing techniques include the fusion splice,"" the V-groove mechanical splice, and the elastic-tube splice.""' The first technique yields a permanent joint, whereas the other two types of splices can be disassembled if necessary. Fusion splices are made by thermally bonding together prepared fiber ends, as pictured in Fig.5-l7- In this method, the fiber ends are first prealigned and butted together. This is done either in a grooved fiber holder or under a microscope with micromanipulators. The butt joint is then heated with an electric arc or a laser pulse so that the fiber ends are momentarily melted and hence bonded together. This technique can produce very low splice losses (typically averaging less than 0.06 dB). However, care must be exercised in this technique, since surface damage due to handling, surface defect growth created during heating, and residual stresses induced near the joint as a result of changes in chemical composition arising from the material melting can produce a weak splice.

In the V-groove splice technique, the prepared fiber ends are first butted together in a V-shaped groove, as shown in Fig. 5-l8. They are then bonded together with an adhesive or are held in place by means of a cover plate. The V-shaped channel can be either a grooved si1icon, plastic, ceramic, or metal substrate. The splice loss in this method depends strongly on the fiber size (outside dimensions and core-diameter variations) and eccentricity (the position of the core relative to the center of the fiber).

The elastic-tube splice shown cross-sectionally in Fig. 5- l9 is a unique device that automatically performs lateral, longitudinal, and angular alignment. It splices multimode fibers to give losses in the same range as commercial fusion splices, but much less equipment and skill are needed. The splice mechanism is basically a tube made of an elastic material. The central hole diameter is slightly smaller than that of the fiber to be spliced and is tapered on each end for easy fiber insertion. When a fiber is inserted, it expands the hole diameter so that the elastic material exerts a symmetrical force on the fiber. This symmetry feature allows an accurate and automatic alignment of the axes of the two fibers to be joined. A wide range of fiber diameters can be inserted into the elastic tube. Thus, the fibers to be spliced do not have to be equal in diameter, since each fiber moves into position independently relative to the tube axis.

5.5.2 Splicing Single-Mode Fibers As is the case in multimode fibers, in single-mode fibers the lateral (axial) offset loss presents the most serious misalignment. This loss depends on the shape of the propagating mode. For gaussian-shaped beams the loss between identical fibers is

where the spot size W is the mode-field radius defined in Eq(2-74), and d is the lateral displacement shown in Fig. 5-9. Since the spot size is only a few micrometers in single-mode fibers, low-loss coupling requires a very high degree of mechanical precision in the axial dimension.

Example 5-5.A single-mode fiber has a normalized frequency V = 2.40, a core refractive index nl = l.47, a cladding refractive index n2 = l .465, and a core diameter 2a = 9 μm. Let us find the insertion losses of a fiber joint having a lateral offset of l μm. First, using the expression for the mode-field diameter from Prob. 2-24, we have W0 = a(0.65 + 1.619V-3/2+2.879(2.40)-6) =4.5[0.65 + l .6l9(2.40)-3/2 + 2.879(2.40)-6] = 4.95 pm Then, from Eq(5-4o), we have LSM,lat = -10 log{exp[-(l/4.95)2]} = 0. l8 dB For angular misalignment in single-mode fibers, the loss at a wavelength λ is

where n2 is the refractive index of the cladding, o is the angular misalignment in radians shown in Fig. 5-9, and W is the mode-field radius. Example 5-6. Consider the single-mode fiber described in Example 5-5. Let us find the loss at a joint having an angUlar misalignment of l" at a l3oo-nm wavelength. From Eq. (5-4l), we have

For a gap s with a material of index n3, and letting G = s/kW2, the gap loss for identical singlemode fiber splices is

See Eq. (5-43) for a more general equation for dissimilar fibers.

5.6 OPTICAL FIBER CONNECTORS A wide variety of optical fiber connectors has evolved for numerous different applications. Their uses range from simple single-channel fiber-to-fiber connectors in a benign location to multichannel connectors used in harsh military field environments. Some of the principal requirements of a good connector design are as follows: l. Low coupling losses. The connector assembly must maintain stringent alignment tolerances to assure low mating losses. These low losses must not change significantly during operation or after numerous connects and disconnects. 2. Interchangeability. Connectors of the same type must be compatible from one manufacturer to another. 3. Ease of assembly. A service technician should readily be able to install the connector in a field environment, that is, in a location other than the connector factory. The connector loss should also be fairly insensitive to the assembly skill of the technician. 4. Low environmental sensitivity. Conditions such as temperature, dust, and moisture should have a small effect on connector-loss variations. 5. Low-cost and reliable construction. The connector must have a precision suitable to the application, but its cost must not be a major factor in the fiber system. 6. Ease of connection. Generally, one should be able to mate and demate the connector, simply, by hand. 5.6.1 Connector Types Connectors are available in screw-on, bayonet-mount, and push-pull configurations. These include both single-channel and multi-channel assemblies for cable-to-cable and for cable-tocircuit card connections. The basic coupling mechanisms used in these connectors belong to either the butt-joint or the expanded-beam classes. Butt-joint connectors employ a metal, ceramic, or molded-plastic ferrule for Butt-joint connectors employ a metal, ceramic, or molded-plastic ferrule for each fiber and a precision sleeve into which the ferrule fit. The fiber is epoxied into a precision hole which has been drilled into the ferrule. The mechanical challenges of ferrule connectors include maintaining both the dimensions of the hole diameter and its position relative to the ferrule outer surface.

Figure 5-20 shows tlyo popular butt-joint alignment designs used in both multimode and single-mode fiber systems. These are the straight-sleeve and the tapered-sleeve (or biconical) mechanisms- In the straight-sleeve connector, the length of the sleeve and a guide ring on the ferrules determine the end separation of the fibers. The biconical connector uses a tapered sleeve to accept and guide tapered ferrules. Again, the sleeve length and the guide rings maintain a given fiber-end separation.. An expanded-beam connector, illustrated in Fig. 5-2l, employs lenses on the ends of the fibers. These lenses either collimate the light emerging from the transmitting fiber, or focus the expanded beam onto the core of the receiving fiber. The fiber-to-lens distance is equal to the focal length of the lens. The advantage of this scheme is that, since the beam is collimated, separation of the fiber ends may take place within the connector. Thus, the connector is less dependent on lateral alignments. In addition, optical processing elements, such as beam splitters and switches, can easily be inserted into the expanded beam between the fiber ends.

5.6.2 Single-Mode Fiber Connectors Because of the wide use of single-mode fiber optic links and because of the greater alignment precision required for these systems, this section addresses single-mode connector coupling losses. Based on the gaussian-beam model of single-mode fiber fields,63 Nemota and Makhaoto75 derived the following coupling loss (in decibe1s) between single-mode fibers that have unequal mode-field diameters (which is an intrinsic factor) and lateral, longitudinal, and angular offsets plus reflections (which are all extrinsic factors):

This general equation gives very good correlation with experimental investigations.

5.6.3 Connector Return Loss A connection point in an optical link can be categorized into four interface types. These consist of either a perpendicular or an angled end-face on the fiber, and either a direct physical contact between the fibers or a contact employing an index-matching material. Each of these methods has a basic application for which it is best suited. The physical-contact type connectors without indexmatching material are traditionally used in situations where frequent reconnections are required, such as within a building or on localized premises. Index-matching connectors are standardly employed in outside cable plants where the reconnections are infrequent, but need to have a low loss. This section gives some details on index-matched and direct physical contacts, and briefly discusses angled interfaces. In each case, these connections require high return losses (low reflection levels) and low insertion loses (high optical-signal throughput levels). The low reflectance levels are desired since optical reflections provide a source of unwanted feedback into the laser cavity. This can affect the optical frequency response, the linewidth, and the internal noise of the laser, which results in degradation of system performance. Figure 5-22 shows a model of an index-matched connection with perpendicular fiber end faces. In this figure and in the following analyses, offsets and angular misalignments are not taken into account. The connection model shows that the fiber end faces have a thin surface layer of thickness h having a high refractive index n2 relative to the core index, which is a result of fiber poli8hing. The fiber core has an index no, and the gap width d between the end faces is filled with index-matching material having a refractive index nl. The return loss RLIM in decibels for the index-matched gap region is given by

are the reflection coefficients through the core from the high-index layer and through the highindex layer from the core, respectively. The parameter δ= (4π/λ)n2h is the phase difference in the high-index layer- The factor 2 in Eq(5-44 accounts for reflections at both fiber end faces. The value of n2 of the glass surface layer varies from l.46 to l .6O, and the thickness h ranges from 0 to 0.15 μm.

When the perpendicular end faces are in direct physical contact, the return loss RLpc in decibels is given by

Here, R2 is the reflectivity at the discontinuity between the refractive indices of the fiber core and the high-index surface layer. In this case, the return loss at a given wavelength depends on the value of the refractive index n2 and the thickness h of the surface layer. Connections with angled end-faces are used in applications where an ultra-low reflection is required. Figure 5-23 shows a cross-sectional view of such a connection with a small gap of width d separating 'the fiber ends. The fiber

core has an index no, and the material in the gap has a refractive index nl. The end faces are polished at an angle θo with respect to the plane Perpendicular to the fiber axis. This angle is typically 8°. If Ii and It are the incident and throughput optical power intensities, respectively, then the transmitted efficiency T through the connector is

The insertion loss for this tyPe of connector with an 8" angle will vary from 0dB for n0 gap to 0.6 dB for an air gap of width d = l.0μm. Note that when an index matching material is used so that n0 = nl, then R = 0 and T = l. When n0 ≠ nl ,the transmitted efficiency (and hence the connector loss) has an oscilllatory behavior as a function of the wavelength and the end-face angle.

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