Fiber_Optics_Physics_Technology

angle, and quarter-wave plates (λ/4 plates) which can transform, e.g., linear polarization into circular polarization or the other way round. Such birefringent elements can also be built in all-fiber technology.

A fiber loop, by virtue of the bending, is birefringent, and its birefringence is given by [93]

where b = 0.133 is an empirical constant, r the fiber radius, and R the bend radius. This birefringence provides a phase di erence between the orthogonal polarization components parallel and perpendicular to the plane of the loop, given by

with W the number of turns. To understand the e ect one can mentally decompose the state of polarization of the incoming light into the component along the fast axis (in the loop plane) and that along the slow axis (parallel to the loop’s axis) (see Fig. 8.8). This allows to follow both components individually, putting them together after the loop produces the change of polarization state. By rotating the loop around the axis given by the incoming fiber, one changes the projection and thus the change of polarization state. The e ect is equivalent to the rotation of a conventional wave plate around the beam direction.

Figure 8.8: Torsion of a fiber rotates the birefringent axes. If, e.g., the incoming light is linearly polarized as A, then it oscillates in the fast axis of the nontwisted fiber (B) and the state of polarization is maintained. If the fiber gets twisted, though, the polarization plane is at an angle with the resulting axis (C); then the state of polarization will evolve upon further propagation in the loop.

In order to make a fiber-optic polarizer, one can insert a slab of dichroitic material in a gap in the fiber. Alternatively, one can polish down a fiber from the side until its cross-section has the form of the letter D and the core is nearly exposed just beneath the flat surface. If the flat surface is then coated with metal, one obtains polarization-dependent losses.

8.6Direction-Dependent Devices

8.6.1Isolators

Isolators are well known in conventional bulk optics and play a role in laser technology. These are devices which let light pass through in one direction, but block it in the opposite direction. They are also called optical diodes.

Optical diodes rely on the Faraday e ect, the rotation of the plane of polarization of linearly polarized light in a material subject to an external longitudinal magnetic field. The physical mechanism is based on the splitting of atomic energy levels into Zeeman substates due to the magnetic field; this yields a circular birefringence. The resulting angle of rotation of the plane of polarization is given, assuming a homogenous magnetic field, by

where H is the magnetic field strength and L the length of the light path through the material. V is Verdet’s constant.2 This material constant has units of rad/(m A/m) = rad A−1. Since in most instances nonmagnetic materials are considered, often Eq. (8.4) is written using B instead of H; then, units are rad/(T m). Verdet’s constant depends on wavelength; according to classical theory it is given by

where e is the elementary charge and me the electron mass. The table shows selected typical values of V ; for a measurement across the entire visible range for fused silica (Suprasil), see [153].

2Marcel Emile Verdet 1824–1866.

In the context of practical components, it is not only Verdet’s constant that is relevant, but also the ratio of this constant and the optical loss at the operational wavelength. For visible light, it turns out that TGG (terbium gallium garnet Tb3Ga5O12) is a useful material. In the near infrared, YIG (yttrium iron garnet Y3Fe5O12) is important. Using YIG and a powerful permanent magnet (e.g., a samarium–cobalt type), path lengths of a few millimeters su ce to obtain a rotation of = 45◦. In the interest of long-term stability, one chooses the magnetic field strength high enough to drive the material into magnetic saturation. That typically happens at B ≈ 1 T, in the case of YIG at 0.178 T. Then the rotational angle becomes independent of fluctuations of the magnetic field strength.

If one places one polarizer each before and after the Faraday rotator and sets their angle at 45◦ relative to each other, light can pass with minimal loss (in principle, lossless; in practice, often under 1 dB). Light propagating in the opposite direction is projected onto the 45◦ direction at the rear polarizer, is rotated by another 45◦, and arrives at the front polarizer with a total rotation of 90◦ so that it is perfectly blocked (Fig. 8.10). In practical devices the blocking is not perfect; one obtains attenuations around 30 dB, in stark contrast to the forward attenuation of ≈1 dB (Fig. 8.11).

Occasionally, the fiber itself has been used as a Faraday rotator, in order to make an all-fiber isolator [138]. Unfortunately, Verdet’s constant for fused silica is quite small so that extremely powerful (bulky, power-hungry, expensive) magnets are required. Even with superconducting magnets, one still needs to use many meters of fiber to obtain a rotation angle of 45◦. This is why in practical devices, almost always TGG or YIG is used.

There is a distinction between polarizing and polarization-independent isolators. The former are built as just described. Polarization-independent isolators first split the incoming light with birefringent polarizers into two polarization

Figure 8.10: Principle of an optical isolator based on the Faraday e ect: As linearly polarized light in 0◦ orientation passes in forward direction (A → B), it can pass through both polarizers without attenuation because they have just the right position. Backtraveling light (B → A) may be partially blocked by the rear polarizer, but inasmuch as it passes, it is rotated further and hits the front polarizer at 90◦ polarization orientation so that it is blocked there.

Figure 8.11: An optical isolator. It comes with two fibers attached, known as “pigtails”. The engraved arrow indicates the forward direction. A 1 Euro coin is shown for size comparison.

components. These components are then sent through the isolator on parallel but separate paths; each is rotated. Finally both components are recombined. The result is an optical diode which is “transparent” to any forward light, but blocks any backtraveling light, in full independence of its state of polarization.

8.6.2Circulators

Circulators are well-known devices in microwave engineering and have been introduced recently to fiber optics. These are multiport components (at least three “ports”). Each port can serve as an input or an output for signals. A signal launched into port 1 appears as an output at port 2, a signal launched into port 2 appears as an output at port 3, and so on – in the ideal case with cyclic permutation.

An optical circulator is based on an optical isolator (Fig. 8.12). The only modification is that the front polarizer is replaced with a version which acts as a polarizing beam splitter. The backtraveling beam is then not absorbed

Figure 8.12: An optical circulator conveys signals in the directions A → B and

B → C.

(eliminated) but directed to an additional output, the third port where another fiber is attached. This way one obtains a three-port circulator with the functions A → B and B → C. This already su ces for a variety of useful applications. A typical example is the combination with a fiber-Bragg grating (see Sect. 9.7.2). Ports A and C are placed in the signal path; the grating is attached at port B. Fiber-Bragg gratings, which are band reject filters by their nature, are thus converted into band-pass filters which can be used to filter out a single wavelength from a wide spectrum.

8.7Couplers

There would be no way to set up a network of fiber-optic links without having the possibility to branch between several fibers. Often it is required that a signal be split into two fibers, or two signals from two fibers are to be combined into one fiber. The same goes for larger numbers of fibers.

8.7.1Power Splitting/Combining Couplers

The simplest case of coupling is shown schematically in Fig. 8.13. Such a coupler can be made of discrete bulk optical elements, but is neither practical, cost- e ective, nor lossless.

Fortunately one can obtain nearly the same functionality in an all-fiber concept. Two fibers are brought together side by side over a length of a few

Figure 8.13: A discrete fiber coupler connects four fibers with the help of four collimation lenses and a beam splitter of, e.g., 50% reflection. However, such a setup requires delicate adjustments and has a rather large footprint; therefore, it is not of practical relevance. We show it solely to demonstrate the concept.

Figure 8.14: Construction of a fused fiber coupler. Two fibers are fused together over a certain well-defined length such that both cores are at a well-defined mutual distance. The distance sets the coupling coe cient of the modes; in combination with the interaction length, the branching ratio is defined. The power of a signal which is launched at A is split between B and D according to the branching ratio, etc.

centimeters (Fig. 8.14). Then both are fused together by heating. The modes in each fiber penetrate into the cladding as we have seen; in the fused coupler, the mode of one fiber has a nonvanishing spatial overlap with the mode of the other fiber. This implies that they are coupled to a certain degree. When part of the energy guided in one fiber can make the transfer to the other fiber, in that second fiber one obtains a buildup of power – accompanied by a corresponding reduction of power in the first fiber, of course. Let us consider a symmetric coupler (two like fibers) in which the phases of the wave in both fibers evolve in the same way. Then, the powers as a function of common path length z evolve as

where the coupling coe cient κ is sensitively dependent on the spatial distance of both fiber cores. By judicious choice of coupling coe cient and interaction length, one can tune the branching ratio of the coupler to virtually any desired value; 0% does not make much sense, but 100% is possible; more useful are values in between. Very often a 50:50 branching ratio is required. In that case there is a 3-dB attenuation for each direction so that this case is called a 3-dB coupler. Also, 10:90 branching ratio couplers (10 dB couplers) and some other values are employed (Fig. 8.15).

In an alternate procedure, two fibers are polished down from the side until the (initially circular) cross-section acquires the shape of the letter D. Then, the

Figure 8.15: A typical fused fiber coupler. It comes with four pigtails.