Fiber optics and fiber optic cables are used to transmit light energy and information over short or long distances. Over the past few decades, fiber optics have been combined with semiconductor laser diodes and optical receivers to enable the rapid growth of fiber optic communication systems. An optical fiber is a circular cross-section dielectric waveguide consisting of a core, a concentric cladding around the core, and a slightly lower refractive index (about 1%). Optical fibers are usually made of silicon dioxide with dopants such as GeO2, which changes the refractive index of the silicon dioxide. Fiber optic cables encapsulate the fiber in a protective layer that makes the fiber easier to handle, reduces crosstalk between adjacent fibers, and prevents damage to the fiber when it is pressed against rough surfaces. In addition to the advantages of light transmission, the confinement of light to a small area within the fiber core has facilitated the development of fiber lasers and photonic crystal fibers.
Fundamentals of Fiber Optics
Fig. 1 Schematic of critical angle and TIR (left). Light irradiated at the core-cladding interface at an angle greater than the critical angle is trapped inside the core of the fiber (right). Relationship between receiving angle (α), NA and refractive index.
Figure 1 shows the direction of the incident light as it encounters the interface of a light-sparse medium (i.e., n2 < n1, as when light travels from glass to air). According to Snell's law, light rays 1 and 2 are refracted, and the light rays are bent away from the normal after passing through the interface. At a particular angle of incidence, called the critical angle θc, the angle of refraction is 90° (ray 3), causing the light to travel along the interface between the two media. For any angle greater than θc, there are no refracted rays and light undergoes total reflection (TIR), which simply follows the law of reflection (shown in ray 4). When light is incident from a medium with a high index of refraction, Snell's law is used to determine θc= arcsin(n2 / n1). As shown below, it is the total reflection property that makes the propagation of light through an optical fiber possible.
An optical fiber is a circular dielectric waveguide with a core that has a higher refractive index than the cladding. As shown in Figure 1, if the angular condition of TIR is satisfied, then the light will be confined in the core. The NA of an optical fiber is defined as the sine of the maximum angle of incidence (α) of the TIR incident light in the core.NA is a qualitative measure of the ability of an optical fiber to concentrate light, and also indicates how easy it is to couple light into the fiber. The geometry and composition of an optical fiber determines the set of discrete electromagnetic fields or fiber modes that can propagate through the fiber. The modes fall into two broad categories: radiated and conducted modes. Light emitted outside of the specified angle of the fiber NA will excite radiation modes.
These modes carry energy out of the core and dissipate it quickly. Light emitted within the NA of the fiber typically produces conducted modes that are confined to the core. These modes propagate energy along the fiber, transmitting information and power. If the core of an optical fiber is large enough, it can support many conduction modes at the same time, i.e., multimode propagation. When light is incident into an optical fiber, the modes are excited to varying degrees depending on the incident conditions (e.g., input cone angle, spot size, axial center) and can exhibit a wide variety of spatial distributions. Much like the transverse modes of a laser, the lowest-order modes of an optical fiber have a near-Gaussian spatial distribution and therefore have many of the same advantages. This is the reason why it is often expected to maintain single mode transmission in optical fibers. The normalized frequency parameter of a fiber (also known as the V-number) is a very useful technical parameter that expresses the number of modes at a given wavelength based on the NA of the fiber and the radius of the core.
Figure 2 Typical spectral attenuation in a quartz fiber (left). As light travels along the fiber, dispersion causes individual light pulses to broaden in the time domain (top right). Example of multiple pulses representing a stream of information bits that become unrecognizable due to dispersion after propagation (bottom right).
The optical power propagating through an optical fiber decays exponentially with fiber length due to absorption and scattering losses (see Figure 2). Attenuation is the most important factor in a fiber optic communication system and directly affects the level of signal that can be received. In the NIR and VIS regions, the small absorption loss of pure silica is due to the tails of the absorption bands in FIR and UV. Impurities, especially water in the form of hydroxide ions, are a more dominant source of absorption in commercial optical fibers. Recent improvements in fiber purity have reduced attenuation loss to the order of 0.1 dB/km. Scattering loss can also lead to attenuation in the form of small refractive index fluctuations in the fiber when the fiber is cured and the core diameter and geometry are irregular.
The bandwidth of an optical fiber determines its data transmission rate. The mechanism that limits the bandwidth of an optical fiber is called dispersion. Dispersion is the broadening of light pulses that occurs as they propagate along the fiber. The result is that one pulse stretches into another and information becomes indistinguishable (see Figure 2).
Dispersion limits the bandwidth and distance over which information can be transmitted. There are two main types of dispersion: intra-modal dispersion and inter-modal dispersion. There are two different types of intra-modal dispersion: chromatic dispersion and polarization mode dispersion. Chromatic dispersion is simply the result of the refractive index of a material changing with wavelength. Polarization mode dispersion is due to orthogonal polarization modes traveling at different speeds in the fiber as a result of birefringence. Intermodal dispersion occurs because different propagation modes travel at different speeds. Therefore, intermodal dispersion only applies to multimode fibers.
Figure 3 Polarization control in an optical fiber triggered by squeezing the fiber from different directions.
Single-mode fibers support modes consisting of two orthogonally polarized modes. This is a consequence of the asymmetry of the cross-section of the fiber core. Typically, the external stresses are random, and the resulting induced birefringence helps to disturb or randomize the polarization states. Specialty fibers, called bias-preserving fibers, produce a consistent birefringence pattern over their length. This is achieved by optimizing the geometry of the fiber and the materials that produce a large amount of stress in one direction. This large induced birefringence dominates compared to random birefringence, allowing the polarization state to be maintained during propagation within the fiber. Controlling the polarization state in an optical fiber is analogous to free-space control by applying a waveplate that causes the phase of two orthogonal polarization states to change. This is achieved by stress induced birefringence of the fiber, which causes a delay, resulting in a waveguide based waveplate. A similar polarization device, including a fiber squeezer rotating around the fiber, is shown in Figure 3. Applying pressure to the optical fiber produces linear birefringence, effectively forming a fiber optic waveguide with a delay that varies with pressure.
