# Angle of Incidence, Propagation Constant and Wavelength

• says
In summary, the conversation discusses the guiding of light with a wavelength of 0.87 μm through a thin planar film with a thickness of 3.0 μm and refractive index of 1.6, surrounded by a medium with a refractive index of 1.4. The critical angle is determined to be 61.04° and the propagation constant and angle of incidence for the m = 1 TE mode are calculated using the equations NA = n0sinα0 and β = n1*(2π/λ0)*sinα0. The wavelength of this mode, measured along the z axis, is found to be longer than 2.9 μm.
says

## Homework Statement

Light of free-space wavelength λ0 = 0.87 μm is guided by a thin planar film of thickness d = 3.0 μm and refractive index n1 = 1.6, surrounded by a medium of refractive index n2 = 1.4
critical angle = 61.04°
n0 = 1.00

(a) Determine (i) the angle of incidence θ and (ii) the propagation constant β of the m = 1 TE mode (you will need to find a graphical or numerical approximate solution here).

(b) What is the wavelength of this mode, measured along the z axis?

## Homework Equations

M = [2dNA/λ0] + 1

M: number of modes
NA: Numerical aperture

NA = n0sinα0

β = n1*(2π/λ0)*sinα0

## The Attempt at a Solution

substituting NA = n0sinα0 and rearranging the equation to solve for sinα0

sinα0 = 8.7*10-7 / (2*3*10-7)

sinα0=0.145

arcsinα0(0.145)

α0=8.337° (Angle of Incidence)

Now that we have that we can calculate β

β = (1.6)*(2π/8.7*10-7)*sin(8.337)

β = 1.675*106 (Propagation constant of m=1 mode)

λ / 2d > cosθc

λ / (2*3*10-6) > cos(61.04°)

λ > cos(61.04°)(2*3*10-6)

λ > 2.9μm - Cut off wavelength (wavelength can be no shorter than 2.9μm, otherwise more modes will propagate in the fibre)

I'm pretty sure I've done the question correctly. But I'm not really sure about the propagation constant.

Is it correct?Also, I am not sure how to calculate the wavelength of the mode. Can someone please help me with this?

## 1. What is the angle of incidence?

The angle of incidence is the angle at which a ray of light or other electromagnetic radiation strikes a surface. It is measured between the incident ray and the normal (perpendicular) to the surface at the point of incidence.

## 2. How is the angle of incidence related to the angle of reflection?

The angle of incidence is equal to the angle of reflection, meaning that the incident ray and the reflected ray are at the same angle with respect to the surface's normal.

## 3. What is the propagation constant?

The propagation constant, also known as the phase constant, is a measure of how quickly a wave propagates through a medium. It is related to the wavelength and frequency of the wave and is typically denoted by the symbol "β" in equations.

## 4. How is the propagation constant related to the wavelength?

The propagation constant is inversely proportional to the wavelength. This means that as the wavelength decreases, the propagation constant increases and vice versa.

## 5. What is the relationship between wavelength and frequency?

Wavelength and frequency have an inverse relationship. This means that as the frequency increases, the wavelength decreases and vice versa. This relationship is described by the equation: wavelength = speed of light / frequency.

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