# Evaluate the outgoing radiation from an optical fiber on a surface

• Frostman
In summary, the speaker is explaining the geometric configuration of their system, including the positioning of the optical fiber, distance between origin and center of ellipse, and angles of the blue cone. They then discuss their idea for evaluating the intensity of radiation that reaches the surface using the characteristic emission spectrum of the optical fiber. They mention not being fully convinced by their calculated angles and ask for help in sorting out the configuration. The respondent suggests looking into the general solution for radiation scattering from a surface and using the Lambert-Beer law to calculate the intensity of radiation. They also mention considering the angle of incidence on the surface and integrating the intensity over the area of the ellipse.
Frostman
TL;DR Summary
Hi there, I hope to get some guidance on calculating the intensity of outgoing radiation from an optical fiber that reaches a surface. I'm feeling uncertain about the accuracy of my estimate based on the geometry configuration and procedure I used. Can you advise me, compare my approach to others, and suggest any alternative methods or tricks that could be helpful?
The geometric configuration that I am adopting is the following, I hope you understand.

The optical fiber is positioned relative to the bottom surface at a height ##a## and an angle ##\alpha## with respect to the y-axis in the yz-plane with x = 0. ##b## is the distance between the origin and the center of the ellipse that is projected onto the surface. ##c## is the semimajor axis, while ##d## is the semiminor axis. Moving on to the angles, ##\theta## is the angle formed in the yz-plane and specifies the angular opening of the blue cone. While ##\varphi## specifies the opening of the blue cone in the inclined plane at an angle ##\alpha## with respect to the Cartesian axis system chosen. I hope I explained the geometry of the system well.

At this point my idea for evaluating the intensity of radiation that reaches the surface is as follows: I have the characteristic emission spectrum of the optical fiber available, in the following figure I have normalized the intensity of radiation with respect to its integral.

I want to evaluate the function I obtained in another integral in which the integration extremes are from the angle ##\varphi## minimum to ##\varphi## maximum, and from ##\theta## minimum to ##\theta## maximum.

In my case I get
$$\theta_m = \frac{\pi}{2} - \alpha - \sin^{-1}\left(\frac{b-\frac c2}{\sqrt{a^2+\left(b-\frac c2\right)^2}}\right)$$
$$\theta_M = - \frac{\pi}{2} + \alpha + \sin^{-1}\left(\frac{b+\frac c2}{\sqrt{a^2+\left(b+\frac c2\right)^2}}\right)$$
$$\varphi_m = - \tan^{-1}\frac{\frac{d}{2}}{b}$$
$$\varphi_M = \tan^{-1}\frac{\frac{d}{2}}{b}$$

The aspects that don't convince me are the angles I calculated, in this case they are not with respect to the adopted coordinate system. For ##\theta## it is quite straightforward to arrange the values since we are in the third quadrant. For ##\varphi## instead it's less trivial and honestly I don't know how to fix it.

The integral then that I'm going to evaluate is a surface integral, but I'm not very convinced of ##f_\text{norm}## since that function must be seen in 3D as a surface of rotation.

I hope you can give me a hand and sort out this apparently chaotic configuration. In the end, what I want to obtain is the intensity of radiation that arrives on that blue ellipse starting from the emission profile of the optical fiber.

I suggest that you take a look at the general solution for radiation scattering from a surface. This will provide you with formulas and equations that can be used to calculate the intensity of radiation that reaches the surface. In particular, you may want to look at the Lambert-Beer law, which is the simplest form of the solution. This will allow you to calculate the intensity of radiation that arrives on the surface using the emission spectrum of the optical fiber. You may also want to consider the angle of incidence of radiation on the surface, as this will affect the intensity of radiation that reaches the surface. Once you have a formula for the intensity of radiation that arrives on the surface, you will then need to integrate this over the area of the ellipse. This can be done by considering the angular opening of the cone in the yz-plane, which is specified by ##\theta##, and the angle of the inclined plane with respect to the Cartesian axis system, which is specified by ##\varphi##. You can then use these angles to calculate the limits of integration for the area of the ellipse. Once you have the limits of integration for the area of the ellipse, you can then integrate the intensity of radiation over the area to get the total intensity of radiation that reaches the surface. I hope this has helped to clarify your problem and given you some ideas on how to proceed.

## 1. What factors influence the amount of outgoing radiation from an optical fiber on a surface?

The amount of outgoing radiation from an optical fiber on a surface is influenced by several factors, including the wavelength of the light, the numerical aperture of the fiber, the angle of incidence, the refractive index of the surface material, and the power of the light source. Additionally, the surface roughness and any coatings or contaminants on the surface can also affect the radiation.

## 2. How can I measure the outgoing radiation from an optical fiber on a surface?

To measure the outgoing radiation from an optical fiber on a surface, you can use a photodetector or a power meter positioned at various angles relative to the surface. By capturing the intensity of the light at different points, you can map the distribution of the outgoing radiation. Spectrometers may also be used if you need to analyze the wavelength composition of the radiation.

## 3. What is the significance of the numerical aperture (NA) of an optical fiber in evaluating outgoing radiation?

The numerical aperture (NA) of an optical fiber determines the range of angles over which the fiber can accept or emit light. A higher NA allows the fiber to emit light over a wider range of angles, which can result in a more diffuse outgoing radiation pattern on the surface. Conversely, a lower NA will confine the outgoing radiation to a narrower beam.

## 4. How does the refractive index of the surface material affect the outgoing radiation?

The refractive index of the surface material affects how light is transmitted, reflected, and refracted at the interface between the optical fiber and the surface. A higher refractive index can lead to more reflection and less transmission, altering the intensity and distribution of the outgoing radiation. Understanding the refractive index is essential for accurately predicting and measuring the outgoing radiation.

## 5. Can surface roughness impact the outgoing radiation from an optical fiber?

Yes, surface roughness can significantly impact the outgoing radiation from an optical fiber. A rough surface can scatter the light in various directions, leading to a more diffuse radiation pattern. In contrast, a smooth surface will result in more specular reflection, where the outgoing radiation is more concentrated in specific directions. Surface roughness should be considered when evaluating and modeling the outgoing radiation.

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