Fiber optics

Principle

An optical fiber is a cylindrical light-isolated waveguide that transmits light along its axis by the process of total internal reflection (see Light: Fresnel equations). The fiber consists of a core surrounded by a cladding layer. To confine the optical signal in the core, the refractive index of the core must be greater than that of the cladding.

Optical fibers may be connected to each other by connectors or by splicing that is joining two fibers together to form a continuous optical waveguide. The complexity of this process is more difficult than splicing copper wire.

Multimode fiber (MMF) and multi-mode fiber

Fig. 1 The propagation of light through a SI-MMF.

A fiber with large core diameter (some tens of μm up to hundreds of μm) behaves in accordance with geometric optics. It is called a multimode fiber (MMF) since there are various modes of vibration given by the wave equations (see textbooks of physics).

When the boundary between the core and cladding is abrupt, the MMF is called a step-index (SI) fiber. When it is gradual it is a graded-index (GRIN) MMF.

In a SI MMF, rays of light are guided along the fiber core by total internal reflection. Rays (for instance the green one in Fig. 1) are completely reflected when they meet the core-cladding boundary at a higher angle (measured relative to a line normal to the boundary) than the critical angle Θ_c, the minimum angle for total internal reflection. The red ray in Fig. 1 impinges with the angle Θ_c. Θ_c is n_gladding/n_core. Rays that meet the boundary at a lower angle (the blue one in Fig. 2) are lost after many repeated reflections/refractions from the core into the cladding, and so do not convey light and hence information along the fiber.

Θ_c determines the acceptance angle of the fiber, also expressed in the numerical aperture NA (≡n₀∙Θ_c). A high NA allows light to propagate down the fiber in rays both close to the axis and at various angles, allowing efficient sending of light into the fiber. However, this high NA increases the amount of dispersion as rays at different angles have different path lengths and therefore take different times to traverse the fiber. This argues for a low NA.

Fig. 2. Paths of light rays in a GRIN fiber. The refractive index changes gradually from the center to the outer edge of the core.

In a GRIN fiber, n_core decreases continuously from the axis to the cladding. This causes light rays to bend smoothly as they approach the cladding, rather than reflecting abruptly from the core-cladding boundary. The resulting curved paths reduce multi-path dispersion because the undulations (see Fig.2) diminish the differences in path lengths. The difference in axial propagation speeds are minimized with an index profile which is very close to a parabolic relationship between the index and the distance from the axis.

FI and GRIN fibers suffer from Rayleigh scattering (see Light: scattering), which means that only wavelengths between 650 and 750 nm can be carried over significant distances.

Singlemode fiber (SMF)

This single glass fiber (core diameter generally 8 - 10 μm) has the axial pathway as solely mode of transmission, typically at near IR (1300 or 1550 nm). It carries higher bandwidth than multimode fiber, but requires a light source with a narrow spectral width. Single-mode fiber have a higher transmission pulse rate and cover up to 50 times more distance than multimode, but it also costs more. The small core and single light-wave virtually eliminate any distortion that could result from overlapping light pulses (little pulse dispersion), providing the least signal attenuation and the highest transmission speeds of any fiber cable type.

Image transmission 

It is impossible for a single fiber to transmit an image. An individual fiber can transmit only a spot of a certain color and intensity. To transmit an image, a large number of single fibers must be aligned and fused together. This means assembly of optical fibers in which the fibers are ordered in exactly the same way at both ends of the bundle to create an image. This type of fiber bundle is called a coherent bundle or image guide bundle. On the other hand, the assembly of optical fibers that are bundled but not ordered is called an incoherent bundle. An optical fiber which is incapable of producing an image is used in medical endoscopes, boroscopes, and fiberscopes as a light guide. The light guide, as well as the image guide, is essential to construct an image in any optical instrument. Light guides are much less expensive and easy to produce compared to image guides and are designed to maximize light carrying ability. In an image guide, the amount of image detail (resolving power) depends on the diameter of each fiber core. Generally, the individual fibers of a light guide are much thicker than fibers (MMFs) in image guides because resolution is not a factor.

Application

Medical

Optical fibers are used in transducers and bio-sensors for the measurement and monitoring of for instance body temperature, blood pressure, blood flow and oxygen saturation levels. In medical applications, the fiber length is so short (less than a few meters) that light loss and fiber dispersion are not of concern. Glass optical fibers are used in most endoscopes and are made with SI fibers.

1. Optical fibers are also used as transmission lines in equipment that is very sensitive to disturbance by electric fields, such as EEG amplifiers. At the other hand, they are applied to prevent the generation of a magnetic field due to current flowing in an electric cable. Even very small current produce magnetic fields strong enough to disturb MEG recordings (see Magnetoencephalography (MEG)). All these applications are based on SI MMFs.

The principle of fiber optics is also found in nature. Slender rods, as found in for instance frogs, and the visual sensory cells of arthropods, the ommatidia, act as wave guides.

General

Optical fiber cables are frequently used in ICT applications (such as cable television and all kind of data transport). For far distance transmission SMFs are used. MMFs can only be used for relative short distances, e.g. for ICT applications in a building.

More info

Consider Fig. 2 again. The ray incident on the face of the SI fiber at angle A₀ will be refracted inside the core and refracted into the cladding. At angle A₁ a ray will be refracted along the boundary of the core and the outside medium. The angle A_c is referred to as the maximum acceptance angle and θ_c is the critical angle for internal reflection. The angles A_c and θ_c are determined by the refractive indices of core and cladding. Therefore, a ray incident on the core-cladding boundary at an angle less than θ_c will not undergo total internal reflection and finally will be lost. However at an angle greater than θ_c, a ray will propagate inside the core by a series of internal reflections.

In Fig. 2 at the point P₁ it holds that:

n_o sin A_c = n₁ sin (90-θ_c)     (1)

Also at the point P₂:

n₁ sin θ_c = n₂ sin (90) = n₂  or Θ_c = arcsin(n₂/n₁)  (2)

Together they give:

n₀ sin A_c = n₁ cos θ_c = (n²₁ - n²₂)^1/2 = NA, or

A_c = arcsin(1-cos²Θ_c)^0.5 = arcsin(n₁sinΘ_c). (3)

NA is the numerical aperture of the SI fiber and is defined as the light-gathering power of an optical fiber. When the face of the fiber is in contact with air (n₀ = 1 for air), NA = sinθ_c. When n₂/n₁ = 0.99, then θ_c is 8.1^o and A_c is 12.2^o.

When total internal reflection occurs, there is also light transmission in the gladding, the evanescent wave (a very nearby standing wave). This can cause light leakage between two adjacent fibers even when the diameter of a fiber is many times greater than the wavelength. In SMFs, the energy transmitted via the evanescent wave is a significant fraction.

In SI fibers, the light rays zigzag in straight lines between the core/cladding on each side of the fiber axis. In GRIN fibers, the light travels in a curved trajectory, always being refracted back to the axis of the fiber. At angles > Θ_c, light never reaches the outer edge of the fiber. At angles< Θ_c, the light enters the adjacent fiber, traverses the guide and is absorbed on the periphery of the guide as in the case of the SI guide.

Glass optical fibers are mostly made from silica (SiO₂) with a refractive index of about 1.5. Typically the difference between core and cladding is less than one percent. For medical applications, due to the required properties (optical quality, mechanical strength, and flexibility) also plastic optical fibers are used. Plastic fibers have the advantages of much simpler and less demanding after-processing and plastic fibers are lighter and of lower cost than glass fibers.

Plastic is common in step-index multimode fiber with a core diameter of 1 mm and have more propagation losses than glass fiber (1 dB/m or higher).

A fiber with a core diameter < 10∙λ cannot be modeled using geometric optics, but must be analyzed as an electromagnetic structure, by solution of the electromagnetic wave equation, which describes the propagation of electromagnetic waves (see textbooks on physics).

The number of vibration modes in a SI MMF can be found from the V number:

V = (2πr/λ) (n²₁ - n²₂)^1/2,

where r is the core radius and λ wavelength. When n₀ =1, than V becomes (2πr/λ)NA. When V < 2.405 only the fundamental mode remains and so the fiber behaves as a SMF.

The electromagnetic analysis may also be required to understand behaviors such as speckles that occur when coherent light (same frequency and intensity) propagates in a MMF. (A speckle pattern is a random intensity pattern produced by the mutual interference of coherent wave fronts that are subject to phase differences and/or intensity fluctuations. See also Huygen’s Principle.) Speckles occur in optical coherence tomography and laser Doppler imaging.

A new type of crystals, photonic crystals led to the development of photonic crystal fiber (PCF). (Photonic crystals are periodic optical (nano)structures that are designed to affect the motion of photons in a similar way that periodicity of a semiconductor crystal affects the motion of electrons.) These fibers consist of a hexagonal bundle of hollow microtubes embedded in silica with in the center the fiber of photonic crystal. A PCF guides light by means of diffraction from a periodic structure, rather than total internal reflection. They can carry higher power than conventional fibers.