Antonio Perez

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**Fundamentals of Optical Fibers**

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[[https://es.wikipedia.org/wiki/Ley_de_Snell|Snell's Law Link]]

**1.- Fundamentals of optical fibers**

Optical fibers base their operation on the laws of reflection and refraction of light. To do this, it must be taken into account that when a ray of light hits the separation surface of two different transparent media, part of the light is reflected, remaining in the first medium and part of the light is refracted, penetrating the second medium. 

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The laws of reflection and refraction are different, and are stated below:

{{ :fundamentos-de-fibras-opticas_2.jpg?600 |}}


The law of light reflection establishes that every ray of light that hits a reflective surface will be reflected at an angle equal to the angle of incidence and in such a way that both the incident and reflected ray are perpendicular to the reflective surface. At the point of incidence they are in the same plane.


**The law of refraction or Snell's law is indicated below:**

{{ :fundamentos-de-fibras-opticas_3.jpg?600 |}}

As can be seen in the drawing, it is assumed that the ray of light comes from a substance or medium with refractive index **n1** and enters another substance or medium with refractive index **n2**. It is clearly seen that if **n2 > n1** then sin **θ2 < sin θ1**, and therefore the **smaller the sine**, **the smaller the angle**. Therefore, **angle θ2 is smaller than angle θ1**. Let's look at a numerical example. If we imagine a ray of light passing from the glass to the water, and whose refractive indices are those indicated in the figure, and we calculate what the angle of refraction is, assuming that the angle of incidence is **30º**.

**Applying Snell's law we have:**

  n1 x sin Φ1 = n2 x sin Φ2

and substituting the values indicated in the figure

  1.46 sin 30 = 1.33 sin Φ2 and since sin 30 = 0.5 then
  0.73 = 1.33 sin Φ2
  from where sin Φ2= 0.73 / 1.33 = 0.5488

Finally, using the **arc sin** function we calculate the **angle Φ2**, also called the angle of refraction.

  Φ2 = arc sin 0.5488 = 33.28º

If we carry out the calculations for a different angle of incidence, for example, if instead of the angle of incidence **being 30º**, **it becomes 66º**, then the angle of refraction will be:

  n1 x sin Φ1 = n2 x sin Φ2

and substituting values

  1.46 sin 66 = 1.33 sin Φ2 and since sin 66 = 0.9135 we have that:
  1.33 = 1.33 sin Φ2
  from which we obtain Φ2 = arc sin (1.33 /1.33) = arc sin 1 = 90º. In the following figure you can see what 
  happens when the angle of refraction is 90º.

{{ :fundamentos-de-fibras-opticas_5.jpg?600 |}}

  Note:  The critical angle for total internal reflection occurs when the angle of refraction is equal to 90°.

For any angle of **incidence greater than the critical angle**, that is, in the previous example of glass and water, for any angle of incidence greater than 66º, an angle of refraction greater than 90º is produced, or what is the same , the so-called** total reflection**.

{{ :fundamentos-de-fibras-opticas_6.jpg?600 |}}

The latter is what fiber optics is based on. The light that goes through the interior of the optical fiber undergoes total reflection every time it tries to leave the core and enter the cover. As the **total reflection follows the law of reflection**, **the entry angle is equal to the exit angle**, __//and therefore in the following reflections along the fiber the angle is maintained//__.

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**Overview:**
{{ :dispersion.png?600 |}}

[[https://es.wikipedia.org/wiki/Dispersi%C3%B3n_de_Rayleigh|Rayleigh scattering]]


Therefore, the inside of the optical fiber does not have anything similar to a mirror, so the light bounces off that mirror. There really isn't a need for mirrors or anything like that. Simply because the glass core and the cover, also made of glass, have different refractive indices, it is enough for the light to bounce back without leaving the core, as long as the angle at which the light rays enter the core to the deck is greater than the critical angle.

To see this phenomenon experimentally, all you need is a glass of water and a laser pointer. **It is observed that from the critical angle the laser beam is directly reflected on the surface of the water, producing the phenomenon of total reflection**.

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It must be taken into account that each transparent substance has a different refractive index, and that said index also varies with wavelength. The latter is of fundamental importance since if the light used for optical fiber transmission is composed of different wavelengths, each wavelength will circulate at a different speed through the fiber, producing signal dispersion (light pulses). at the input they appear rounded at the output).

{{ :fundamentos-de-fibras-opticas_9.jpg?600 |}}

//Note: All refractive indices in the tables above are measured with sodium light of wavelength 589 nm.//

  Note: The material has a different value for permittivity and/or permeability due to the interaction of the wave 
  with the atoms of the material. The amount that the speed changes is given by the refractive index n=c/v, where c 
  is the speed of light in a vacuum and v is the speed in the medium.

  Note:Frequency has an inverse relationship with the concept of wavelength (distance between two peaks) in such a 
  way that frequency is equal to the speed of travel of the wave divided by the wavelength.

  Note: For a constant wavelength, an increase in frequency will increase the speed of the wave. Example: For a 
  constant wavelength, if the frequency doubles, the speed of the wave will also double.

  Note:  We define the wave speed, which is given by multiplying the frequency (f) by its wavelength (λ).
  V = λ·f
  Now, if the frequency doubles, let's see what happens.
  V =λ·(2f)
  V = 2·(λf)
  Therefore, by increasing the frequency of the wave, we can say that the speed of the wave also doubles.

  Note:  V=C/N; the speed of propagation is equal to the speed of light over the index of refraction.

  Note: Wavelength: Wavelength is the distance between the repetitive cycles of a wave at a given frequency. The 
  higher the frequency, the shorter the wavelength. Period: The wave period is the amount of time it takes to 
  complete one complete revolution of a wave cycle.


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As a technical curiosity, the laws of reflection and refraction, although they can be verified experimentally, also have a relatively simple mathematical demonstration. In the case of the Law of Refraction or Snell's Law, the demonstration is based on considering the light ray as a wave front that advances at a certain angle through a medium and penetrates another medium with a **different refractive index**, as Like shown in the next figure:

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The wave front that crosses medium 1 does so with an angle Φ1 in such a way that the left part of the wave front reaches medium 2 at point A while the right part of the wave front will reach medium 2 at point A. point B after a time t, due to having to travel the distance between P and B. When this right part of the wave front reaches point B, the left part of the wave front is already at point B'. Since the speed through medium 2 is smaller than through medium 1, the distance traveled AB' will be less than the distance PB and **the new wave front will not be parallel to the initial one**. **The light is refracted**.

Examinando el triángulo APB se deduce que:

{{ :fundamentos-de-fibras-opticas_11.jpg?150 |}}

{{ :fundamentos-de-fibras-opticas_12.jpg?150 |}}

Examining the lower triangle ABB´ we deduce that:

{{ :fundamentos-de-fibras-opticas_13.jpg?150 |}}
{{ :fundamentos-de-fibras-opticas_14.jpg?150 |}}

And since AB is the same in both expressions, we finally have:

{{ :fundamentos-de-fibras-opticas_15.jpg?300 |}}

**That is Snell's law.**

{{ :fundamentos-de-fibras-opticas_16.jpg?200 |}}

Other examples:

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{{ :refraccion.svg.png?400 |}}

This refraction of light when changing medium can be such that the phenomenon of total reflection occurs, which is the mechanism by which light advances through the core of multimode optical fibers with very low losses. As a technical curiosity, taking advantage of the fact that the typical refractive index of glass is 1.50, the limiting angle when light passes from air to glass is approximately 42º. This angle, being less than 45º, allows the construction of many optical instruments that take advantage of **the phenomenon of total reflection**, such as the prisms of Reflex-type cameras.

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Total reflection prisms have the advantage that they reflect light completely, while no metal surface reflects 100% of the incident light. Secondly, the reflective properties are permanent and are not altered by tarnishing of surfaces, which is not the case with mirrors. The only drawback they have is that not all the light that hits the prism enters inside, because a little is always reflected.

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**2.- Atenuación en las fibras ópticas y ventanas de trabajo.**

In transmission through optical fibers, light of certain wavelengths is used. The following image shows the full spectrum of electromagnetic radiation.

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**When light passes through the optical fiber, it is attenuated for two different reasons:**

**Intrinsic causes:** They are due to causes that have to do with the manufacturing process of the optical fibers and where the installer cannot do anything to correct them. The most important intrinsic losses are due to the so-called Rayleigh scattering and absorption. Rayleigh scattering is produced by the microscopic non-uniformities of the fibers and is responsible for **90% of the losses in current fibers**. Absorption losses are due to impurities and water molecules that remain inside the fiber and that absorb part of the light, transforming it into heat, therefore attenuating the light as it passes through the optical fiber.

{{ :fundamentos-de-fibras-opticas_23.jpg?400 |}}

**//As with absorption, Rayleigh scattering losses increase with the distance traveled by the light inside the fiber//**, and are greater the shorter the wavelength is with respect to the size of the impurities in the fiber. These losses are also not linear, but are inversely proportional to the wavelength raised to the fourth power. Rayleigh scattering losses are also different depending on the type of material used to manufacture the optical fiber, which is why there are different types of fibers with different total attenuation coefficients (db/km).

{{ :fundamentos-de-fibras-opticas_20.jpg?400 |}}

**Extrinsic causes:** **//They are due to faulty installation procedures and are therefore a type of loss that the installer can reduce if he installs the optical fiber properly//**. The most important losses due to extrinsic causes are losses due to too small curvature radii and due to dirt in the connectors. Also due to excessive tensions during installation and twisting of the optical fiber, so-called microbends can occur, which also produce attenuation in the transmitted light.

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**Intrinsic losses vary depending on the wavelength used**. Rayleigh losses are greater the shorter the wavelength relative to the size of the impurities in the fiber. Therefore, Rayleigh losses are smaller for longer wavelengths. Absorption losses have a minimum around 1550 nm, increasing towards the ultraviolet zone and also towards the infrared zone. Losses due to guide imperfections (microcurvatures produced in the manufacturing process itself) are practically constant for any wavelength. Putting all the effects together, we obtain the graph shown below:

{{ :fundamentos-de-fibras-opticas_22.jpg?400 |}}

It is observed that there are some areas where the attenuation is minimal, which correspond to the so-called 1330 nm and 1550 nm windows. It is also observed that there is an area above 850 nm where the losses are not minimal but are constant, which is a fundamental requirement in working with optical fibers. This last window, called 1st window, corresponds to a very common area of work with **multimode optical fibers**.


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**3.- Fibras ópticas multimodo y fibras ópticas monomodo**

Depending on the size of the core and the coating of the optical fiber, the fibers are multimode or singlemode:

{{ :fundamentos-de-fibras-opticas_24.jpg?400 |}}

{{ :micrones-1024x395.png?600 |}}

Multimode optical fibers have the advantage of requiring less precise light coupling, allowing work with both a **Laser** light source and an **LED** light source. Single-mode fibers work only with a **laser** light source. But **multimode optical fibers have the disadvantage that they have a lower bandwidth than single-mode fibers**. A lower bandwidth means that for a multimode fiber the maximum speed in bits per second will be lower than for a single-mode fiber. This lower speed is produced by the so-called **modal dispersion** of optical fibers.

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**Modal dispersion** is the main cause of bandwidth limitation in optical fibers. This modal dispersion causes narrow pulses of light at the input to become rounded pulses of longer duration:

{{ :fundamentos-de-fibras-opticas_26.jpg?400 |}}


If a single light pulse is introduced, due to modal dispersion it is “**rounded**” at the output. If many light pulses are introduced in a row, that is, many bits in a row, then the light pulses **overlap** at the output, preventing the receiver from recognizing the emitted light pulses.

{{ :fundamentos-de-fibras-opticas_27.jpg?400 |}}

That is, optical fibers, like all transmission media, also have a physical limit of maximum transmission speed in bps (**Shannon's Theorem**). In multimode optical fibers, this speed limitation is produced, fundamentally, by **modal dispersion**. On the other hand, in single-mode fibers, since there is only one “mode” or ray of light, **modal dispersion** does not occur, but the so-called **chromatic dispersion** does occur, which is due to the different speed through the fiber of different lengths. waveform of the transmitted light. Even when using a very pure light source, such as laser light, there are always several wavelengths and therefore some chromatic dispersion will always occur.

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Chromatic dispersion is measured in ps/nm x km and this value should be as small as possible. As with modal dispersion, excessive chromatic dispersion results in pulse broadening and a decrease in the peak bps rate.

**Overview:**

{{ :gcableadoestructurado-img12.png?600 |}}

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**4.- Fibras ópticas multimodo de índice gradual**

Nowadays most multimode type optical fibers are **graded index**. In these fibers the refractive index of the core is not constant, but varies progressively through a mathematical law calculated for this purpose. In this way, the light rays that go through the center of the fiber core and travel a shorter path go slower (higher refractive index) than the light rays that travel a longer path. With this, it is possible to **reduce the modal dispersion** and consequently increase the bandwidth of the optical fiber:

{{ :fundamentos-de-fibras-opticas_29.jpg?400 |}}

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**5.- Multimode optical fibers and their basic specifications**

Multimode optical fibers are currently divided into four types: **OM1, OM2, OM3, OM4 and OM5**. The OM1 type fibers are 62.5/125 and the OM2, OM3 and OM4 are 50/125, and all of them are graded index. The following table, obtained from Corning's technical documentation (www.corning.com), shows these characteristics:

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It is observed that the difference between OM2 and OM3/OM4 fibers is that the latter are optimized for laser operation. It should be taken into account that **the denomination of multimode fibers according to the different standards** is shown below:

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For many years, 62.5/125 multimode optical fibers have been the most used, given the greater difficulty of coupling light to 50/125 multimode fibers. Nowadays, with the new VSCEL type lasers, laser optical transceivers have a very affordable cost and allow easy use with 50/125 type fibers, which, having a narrower core, have **lower modal dispersion** and therefore Therefore they have a **greater bandwidth, allowing a higher speed in bps**.

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The previous table shows the characteristics of OM2, OM3 and OM4 fibers (50/125) along with OM1 (62.5/125). It is observed **that each type has a different bandwidth**, and that with a wavelength of 850nm, the modal dispersion is lower and therefore its bandwidth is greater, although at 850nm the losses also increase due to Rayleigh dispersion and therefore the attenuation in dB/Km increases.


It must be taken into account that **the total attenuation** is calculated by multiplying the attenuation in dB/Km by the kilometers of installed optical fiber, but the bandwidth measured in Mhz x Km allows **only an approximate calculation** of the effective bandwidth for a given area. certain total length of fiber optic installation. In reality, **when the length of a given fiber optic link is doubled, the bandwidth is not halved**.

As indicated above, the attenuation of the optical fibers in the first window, at a wavelength of 850 nm, is greater than in the second window. This may lead you to think that it is always better to work in this second window. But if you look at the bandwidth data of multimode optical fibers, you can easily see that in some types of fiber (OM3 and OM4), **the bandwidth is greater in the first window than in the second window**. This is because the shorter the wavelength (first window), the fewer “modes” or light rays are produced inside the optical fiber, therefore producing less modal dispersion.

{{ :fundamentos-de-fibras-opticas_35.jpg?500 |}}

Therefore, for high-speed and short-distance applications, such as **10/25/40/50/100 Gbps** in **building trunks** or in a **Data Center**, multimode optical fiber of type OM3 or OM4 at 850 nm is mandatory. If we use multimode optical fibers at 1300nm (second window) it is not possible to reach speeds of 10Gbps. When the distances to be covered are very large, it is essential that the attenuation is not excessive and then there is only the possibility of working in a **second or third window**, and the only way to have sufficient bandwidth in these windows is to use **optical fibers singlemode**.

{{ :fundamentos-de-fibras-opticas_36.jpg?500 |}}

{{ :fo1.jpg?1000 |}}

[[https://community.fs.com/es/blog/single-mode-vs-multimode-fiber-whats-the-difference.html|Distance difference between multimode fiber vs singlemode fiber]]

Single-mode optical fibers have a much smaller attenuation coefficient than multimode fibers, due to the fact that they work at longer wavelengths (3rd, 4th and even 5th window in the new single-mode optical fibers). **Furthermore, since there** **is no modal dispersion** but only the so-called **chromatic dispersion**, which is very small with laser light sources, the bandwidth in Mhz x Km is no longer provided but instead the **chromatic dispersion** value is indicated. in ps/nm x km.

  Note:  As a technical curiosity, if we introduce light of a very small wavelength to a single-mode fiber with 
  respect to the diameter of the core, then the cable cutting wavelength effect occurs and the fiber begins to 
  behave like a multimode fiber.
  

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**6.- Plastic optical fibers: Basic characteristics.**

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**Plastic optical fibers (POF)** are ** not made of glass but rather plastic materials**. The core diameter is much larger than that of multimode fibers built with glass,** they have a greater modal dispersion** and therefore have **a very small bandwidth**. Additionally, because the plastic material is much less “transparent” than the glass core of single-mode and multimode optical fibers, **its attenuation is much greater**. The table above shows that the attenuation is 0.20 dB **per meter**!!! That is, an attenuation of **200 dB/km**.

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The advantages of this type of fibers are that they allow easy connectorization, because the tolerance is very wide. Furthermore, when they are used for __**very short distances**__ (connection of digital music equipment, automobile automation, etc.) the attenuation is small and although the bandwidth in MHz x Km is low, equally when the distance is short, it is a wide enough bandwidth for many practical applications. Finally, it must be taken into account that in this type of fibers, since the core material is different from that of glass fibers, their working windows are different. The above plastic fibers have the working window at the wavelength of 650 nm, which falls within visible light.


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**7.- Termination of fiber optic links by fusion with pigtail:**

When terminating a fiber optic link by fusion or mechanical splicing with a pigtail, it must be taken into account __**that an OM2, OM3 or OM4 type optical fiber should not be fused or spliced with an OM1 type pigtail**__, since In that case we would be joining a 62.5/125 fiber with another 50/125. This type of connection, even though it can work correctly in the 50/125 >> 62.5/125 direction, is totally inadvisable due to its high attenuation in the 62.5/125 >> 50/125 direction. In the same way, if the case arises of having to terminate an OM1 type fiber optic link using a pigtail, we must necessarily use one of the OM1 type.


It should also be taken into account that it **is not strictly necessary** that an OM2, OM3 or OM4 type fiber optic link has to be terminated by fusion or mechanical splicing with OM2, OM3 or OM4 type pigtail respectively. In reality, if, for example, in an OM3 type link, with a bandwidth of 1500 MHz x Km at 850nm, we use an OM2 type pigtail, with a bandwidth of 500 MHz x Km there will be no problem. In fact, although the pigtail has “in theory” a much smaller bandwidth than that of the fiber optic link, it should not be forgotten that if the length of the pigtail is “less than 1 km” its effective bandwidth will be much elderly. If the pigtail is 2 meters long, we can assume that approximately the bandwidth will be (500 MHz x 1 Km)/ 0.002 Km = 250,000 MHz and therefore will not limit the bandwidth of the link as a whole at all.

  Note: As a technical curiosity, the above does not happen at all with structured cabling installations made with 
  pair cable. If a permanent link of a certain category, for example category 6, is terminated with lower category 
  patch cords, for example category 5e patch cords, the entire installation or channel link will be of the category 
  of the lower element, which in the previous example will correspond to category 5e. The difference with optical 
  fiber is clear: in the pair cable, factors such as the various crosstalk (Next, Power Sum Next, Elfext, Power Sum 
  Elfext, Alien Next, etc.) do not depend at all on the length of the cable, since they are They generate mainly in 
  the so-called near ends (NE) and far ends (FE).
  

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[[https://fibraoptica.blog.tartanga.eus/fundamentos-de-las-fibras-opticas/|Spanish Link]]
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**What is WDM or DWDM?**

**Wavelength Division Multiplexing (WDM)** is a fiber optic transmission technique that uses multiple wavelengths of light (or colors) to send data over the same medium. Two or more colors of light can travel over a single fiber, and multiple signals can be transmitted in a waveguide at different wavelengths or frequencies in the optical spectrum.

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The first fiber optic transmission systems placed information on glass filaments using simple pulses of light. A light turned on and off to represent the ones and zeros of digital information. Real light could be of virtually any wavelength—from about 670 nanometers to 1,550 nanometers. Wavelength Division Multiplexing (WDM) is a fiber optic transmission technique that uses multiple wavelengths of light to send data over the same medium.

During the 1980s, fiber-optic data communications modems used low-cost LEDs to emit near-infrared pulses over low-cost fiber. As the need for information increased, so did the need for bandwidth. Early SONET systems used 1310 nm lasers to emit 155 Mb/s data streams over long distances.

But this capacity was quickly exhausted. Over time, advances in optoelectronics components allowed the design of systems that simultaneously transmitted several wavelengths of light over a single fiber, increasing fiber capacity considerably. This is how WDM was born. Multiple high bit rate data streams of 10 Gb/s, 40 Gb/s, 100 Gb/s, 200 Gb/s, and more recently, 400 Gb/s and 800 Gb/s, each can be multiplexed over a single fiber. with different transfer rates.

**Currently there are two types of WDM:**

  * **Light WDM (CWDM)**: CWDM can be defined as WDM systems with less than eight active wavelengths per fiber. CWDM is used for short-range communications and therefore uses a wide range of frequencies with wavelengths very far apart. Normalized channel spacing allows for the wavelength variation that occurs when lasers are heated and cooled during operation. CWDM is a compact and economical option when spectral efficiency is not an important requirement.
  * **Dense WDM (DWDM)**: DWDM is defined in terms of frequencies. DWDM, by spacing wavelengths closer, can accommodate more channels on a single fiber, but is more expensive to implement and operate. DWDM is for systems with more than eight active wavelengths per fiber. DWDM divides the spectrum into small parts, placing more than 40 channels in the C-band frequency range.

**With DWDM**, vendors have found different techniques to pack 40, 88, or 96 fixed-spacing wavelengths into a fiber's C-band spectrum. Traditional DWDM line systems use Wavelength Selective Switches (WSS) designed with fixed 50GHz or 100GHz filters. These fixed grid line systems can accommodate channels from the first generations of coherent transponders whose wavelengths require less than 50GHz or 100GHz of spectrum (depending on the filter used). Today, networks with high-bandwidth applications and sustained broadband growth that are rapidly facing capacity exhaustion are turning to C+L-band solutions, which also utilize the L-band spectrum of a fiber. to potentially double fiber capacity.

{{ :prx-electromagnetic-spectrum.jpg?800 |}}

As optical networks evolve to meet increased broadband demands, so has the reliance on next-generation programmable coherent technology to maximize fiber capacity and lower the cost per bit of transport. To take full advantage of these benefits, a flexible grid line system is needed that can accommodate these higher baud channels, such as an 800G wavelength, which require more than 100GHz of spectrum.

In fact, next-generation coherent modems are so intelligent and programmable that the modem supports a greater variety of baud and constellation options, allowing for extremely granular tuning. Today, flexible channel plans are possible and support from 64 75GHz channels or 40 to 45 channels for line rates higher than 800G—using a flexible grid (or gridless) architecture that supports channels with a size minimum of 37.5GHz, with adjustable boosts to 6.25GHz—to accommodate any channel available today or in the future

{{ :prx-flex-grid-network-channel-spacing.jpg?600 |}}

When using erbium-doped fiber amplifiers (EDFA) and Raman amplification—two technologies that improve the performance of high-speed communications—the range of these DWDM systems can extend to more than thousands of kilometers. For a system with high channel density to have robust operation, high-precision filters are required to separate a specific wavelength without interfering with neighboring wavelengths. DWDM systems must also use precision lasers that operate at a constant temperature to keep the channels on their exact target.

One of the best features of deploying DWDM over a flexible grid photonic line system is signal independence—the ability to support multiple generations of transponders regardless of format, bit rate, symbol rate, etc. Therefore, many networks designed for 10 and 40 Gb/s now transmit 200 Gb/s channels, and many that were deployed with flexible grid capacity are transmitting 400 Gb/s and even 800 Gb/s signals.

[[https://www.ciena.com.mx/insights/what-is/What-Is-WDM_es_LA.html|Spanish Link]]
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**FIBER OPTICS: Different types and applications.**

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