# Optical Fibres: Wavelength for Zero net Dispersion

• Engineering
• Master1022
In summary: This one doesn't even need the quadratic formula=it factors: multiplying by 100 we get ## (\lambda-100) (\lambda+50)=0 ##.
Master1022
Homework Statement
An optical fibre transmission system uses a step-index multimode optical fibre which has a core refractive index of 1.49 and a cladding refractive index of 1.48. The fibre is also subject to material dispersion which is a function of wavelength ## \lambda ##. The material dispersion coefficient D is given by:
$$D = a \lambda^2 + b\lambda + C \text{ps/km}$$
where ## a = 0.01 ##, ##b = 0.50 ## and ## c = 50## and ## \lambda ## is the wavelength in nanometres. Estimate the wavelength at which the fibre has zero net dispersion.
Relevant Equations
D = 0
Hi,

I was working on the problem below:

Question:
An optical fibre transmission system uses a step-index multimode optical fibre which has a core refractive index of 1.49 and a cladding refractive index of 1.48. The fibre is also subject to material dispersion which is a function of wavelength ## \lambda ##. The material dispersion coefficient D is given by:
$$D = a \lambda^2 + b\lambda + C \text{ps/km}$$
where ## a = 0.01 ##, ##b = 0.50 ## and ## c = 50## and ##\lambda ## is the wavelength in nanometres. Estimate the wavelength at which the fibre has zero net dispersion.

Attempt:
Do we just let D = 0 and solve the quadratic equation? Is is that simple...

I was slightly confused as I know ## D = -\frac{\lambda}{c} \frac{d^2 n}{d \lambda^2} ## and perhaps there was a trick that we needed to use this.

Nonetheless, the first method yields the answers 4999 nm and 1 nm. Not sure how to choose between them, but I think the higher value might be correct as it is closer to the order of magnitude that we saw in a graph in the lectures (order of microns).

Any help or guidance would be appreciated

You need at least one of the coefficients of the dispersion function ## D ## to be negative if you are going to have a positive root ## \lambda ##.

Master1022
You need at least one of the coefficients of the dispersion function ## D ## to be negative if you are going to have a positive root ## \lambda ##.
Ah yes, you are right! Sorry, I think I forgot the -ve sign on ## b ##.

Master1022 said:
Ah yes, you are right! Sorry, I think I forgot the -ve sign on ## b ##.
I think "c" also might need a minus sign, or you get imaginary roots. Please check your arithmetic=putting in minus signs on "b" and "c", I get roots of ## \lambda=+100 ## nm, and ## \lambda=-50 ## nm.

This one doesn't even need the quadratic formula=it factors: multiplying by 100 we get ## (\lambda-100) (\lambda+50)=0 ##.

Last edited:

## 1. What is zero net dispersion in optical fibers?

Zero net dispersion refers to the state in which the different wavelengths of light traveling through an optical fiber experience no overall dispersion or distortion. This means that all wavelengths arrive at the end of the fiber at the same time, resulting in high-quality transmission of data and signals.

## 2. How is zero net dispersion achieved in optical fibers?

Zero net dispersion is achieved through the use of specialized fibers that have been designed to have a specific refractive index profile. This profile helps to balance the dispersion effects of different wavelengths, resulting in zero net dispersion.

## 3. Why is zero net dispersion important in optical fibers?

Zero net dispersion is important because it allows for high-speed and high-quality transmission of data and signals over long distances in optical fibers. This is crucial for applications such as telecommunications, internet connectivity, and medical imaging.

## 4. What is the role of wavelength in achieving zero net dispersion?

The wavelength of light plays a critical role in achieving zero net dispersion in optical fibers. This is because different wavelengths of light have different speeds and can experience different levels of dispersion. By carefully selecting the wavelength, it is possible to achieve zero net dispersion in the fiber.

## 5. Are there any limitations to achieving zero net dispersion in optical fibers?

While zero net dispersion is highly desirable in optical fibers, it is not always possible to achieve it completely. This is due to factors such as manufacturing limitations, external environmental factors, and the use of multiple fibers in a network. However, significant efforts are being made to minimize the dispersion effects and achieve as close to zero net dispersion as possible.

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