Unit III Fibre Optics | PHY 110 Engineering Physics |B.tech

 Fiber Optics

1. Introduction to Fiber Optics

• Fundamental Principle: Fiber optics involves the transmission of data through glass or plastic fibers using light signals. Light signals carry information in the form of pulses that are transmitted through the core of the fiber by a process called total internal reflection.

• Structure of an Optical Fiber:

  • Core: The central part of the fiber, typically made from glass or plastic, through which the light signal travels.
  • Cladding: A layer surrounding the core, made from a material with a lower refractive index than the core. It helps contain the light within the core by reflecting it back into the core via total internal reflection.
  • Buffer Coating: A protective outer layer that shields the fiber from mechanical damage, moisture, and contamination.
  • Jacket: An additional layer that provides physical protection against environmental conditions like UV radiation or physical abrasions.

• Types of Optical Fibers:

  • Single-Mode Fiber (SMF): Designed for long-distance communication. It allows light to travel in a single path (mode) and is used for high-speed, high-bandwidth applications. It has a small core diameter (typically around 8-10 micrometers).
  • Multimode Fiber (MMF): Used for shorter distances, multimode fiber supports multiple paths or modes for light to travel. It has a larger core diameter (50-100 micrometers) and is commonly used in data centers and local area networks (LANs).

---

2. Optical Fiber as a Dielectric Waveguide

• Waveguide Function: An optical fiber operates as a dielectric waveguide, meaning it guides light through its core due to the principle of total internal reflection. The light is confined within the core because of the difference in the refractive index between the core and the cladding.

  • The refractive index of the core is higher than that of the cladding, allowing light to be confined to the core, even when the fiber is bent.

• Optical Power Propagation:

  • As light is transmitted through the fiber, it bounces off the core-cladding interface, following a zigzag pattern. This ensures the light stays inside the core over long distances, even with bends or curves in the fiber.
  • Light propagation in fibers can be described using mode theory, where light modes correspond to different light paths and behaviors within the fiber.

---

3. Total Internal Reflection (TIR)

• Key Concept: Total internal reflection occurs when light traveling through a denser medium (core) strikes a boundary with a less dense medium (cladding) at an angle greater than the critical angle, resulting in the light being reflected back into the core rather than refracting into the cladding.

• Critical Angle: The angle of incidence at which light will no longer refract into the cladding but instead reflect entirely within the core. It is given by:

  $$\theta_c = \sin^{-1}\left( \frac{n_{\text{cladding}}}{n_{\text{core}}} \right)$$

  Where:

  • $\$ = critical angle.
  • $n_{\text{core}}$ = refractive index of the core.
  • $n_{\text{cladding}}$ = refractive index of the cladding.

  This principle ensures that the light signal remains confined to the core, allowing for effective transmission over long distances.

---

4. Acceptance Angle

• Definition: The acceptance angle is the maximum angle at which light can enter the fiber and still undergo total internal reflection to propagate down the fiber. It is the largest angle at which light can be coupled into the core without escaping the fiber.

• Formula: The acceptance angle $\theta_0$ is related to the numerical aperture (NA) by the following relationship:

  $$\sin \theta_0 = \text{NA}$$

  Where NA is the numerical aperture of the fiber. The larger the numerical aperture, the larger the acceptance angle, meaning the fiber can accept light from a wider range of angles.

---

5. Numerical Aperture (NA)

• Definition: The numerical aperture (NA) of a fiber is a dimensionless number that characterizes the range of angles over which the fiber can accept light. It essentially defines the light-gathering ability of the fiber.

• Formula:

  $$\text{NA} = \sqrt{n_{\text{core}}^2 - n_{\text{cladding}}^2}$$

  Where:

  • $n_{\text{core}}$ is the refractive index of the core.
  • $n_{\text{cladding}}$ is the refractive index of the cladding.

• Interpretation:

  • Larger NA: The fiber can accept light at larger angles and is used for short-distance transmission.
  • Smaller NA: The fiber accepts light at smaller angles, typically used for longer-distance, high-quality transmission (e.g., single-mode fibers).

---

6. Relative Refractive Index (Δ)

• Definition: The relative refractive index difference between the core and cladding determines how efficiently the fiber guides light and impacts the modes the fiber can support. It is a percentage and is given by:

  $$\Delta = \frac{n_{\text{core}} - n_{\text{cladding}}}{n_{\text{core}}} \times 100$$

• Impact of Δ:

  • A larger Δ increases the number of modes the fiber can support but also increases modal dispersion, which can degrade performance over longer distances.
  • Smaller Δ results in a narrower core and often supports single-mode operation with minimal modal dispersion.

---

7. V-Number (Normalized Frequency)

• Definition: The V-number (or normalized frequency) is a dimensionless parameter that describes the number of modes a fiber can support. It depends on the fiber's diameter, wavelength of the light, and the numerical aperture (NA).

• Formula:

  $$V = \frac{2\pi a}{\lambda} \text{NA}$$

  Where:

  • a= radius of the core.
  • $\lambda$ = wavelength of the light being used.
  • $\text{NA}$= numerical aperture.

• Mode Behavior Based on V:

  • V < 2.405: The fiber is single-mode, supporting only the fundamental mode.
  • V > 2.405: The fiber is multimode and supports multiple modes.

---

8. Step Index vs. Graded Index Fiber

• Step Index Fiber:

  • The refractive index of the core is uniform and there is a sharp boundary between the core and cladding.
  • This abrupt change in refractive index results in light reflecting at discrete steps.
  • Disadvantages: Causes significant modal dispersion, which can distort signals over long distances, making it unsuitable for high-speed, long-distance transmission.
  • Applications: Short-distance transmission like local area networks (LANs).

• Graded Index Fiber:

  • The refractive index of the core decreases gradually from the center of the core to the cladding.
  • Light traveling along the fiber's core is refracted toward the axis, minimizing modal dispersion because all light rays reach the destination at the same time.
  • Advantages: Less modal dispersion and better performance over longer distances.
  • Applications: High-speed data transmission for medium distances, such as in LANs and multi-building networks.

---

9. Losses Associated with Optical Fibers

• Attenuation: The reduction in signal strength as light propagates through the fiber. This occurs due to:

  • Scattering: Primarily Rayleigh scattering, where imperfections in the fiber cause light to scatter. This effect increases as the wavelength decreases (shorter wavelengths suffer more scattering).
  • Absorption: Light is absorbed by the fiber material (glass or plastic) and is converted to heat, reducing signal strength.
  • Bending Loss: Bends in the fiber can cause light to escape from the core, reducing the signal intensity.
  • Connector and Splice Losses: Losses occur when fibers are connected or spliced together. Misalignment of the fibers or imperfect connections can cause significant losses.

• Other Types of Loss:

  • Modal Dispersion: In multimode fibers, different light modes take different paths and travel at different speeds. This causes pulse broadening and signal degradation over long distances.
  • Chromatic Dispersion: Light of different wavelengths (colors) travels at different speeds through the fiber, leading to pulse spreading and signal distortion.
  • Polarization Mode Dispersion (PMD): In single-mode fibers, different polarization modes of light travel at different speeds, causing timing errors in high-speed systems.

• Loss Calculation: The attenuation is typically measured in decibels per kilometer (dB/km), and is calculated as:

  $$\alpha = \frac{10}{L} \log \left( \frac{P_0}{P_L} \right)$$

  Where:

  • $P_0$ = initial power.
  • $P_L$ = power after transmission through the fiber.
  • $L$ = length of the fiber.