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Guided Modes Number Formula

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Guided Modes Number in a waveguide is to describe the different allowed electromagnetic modes or propagation patterns within the waveguide structure. Check FAQs

M g = {(\frac{π \cdot r core}{λ})}^{2} \cdot ({η core}^{2} - {η clad}^{2})

M_g - Guided Modes Number?r_core - Radius of Core?λ - Wavelength of Light?η_core - Refractive Index of Core?η_clad - Refractive Index of Cladding?π - Archimedes' constant?

Guided Modes Number Example

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Here is how the Guided Modes Number equation looks like with Values.

Here is how the Guided Modes Number equation looks like with Units.

Here is how the Guided Modes Number equation looks like.

112.2593 = {(\frac{3.1416 \cdot 13}{1.55})}^{2} \cdot ({1.335}^{2} - {1.273}^{2})

112.2593 = {(\frac{3.1416 \cdot 13μm}{1.55μm})}^{2} \cdot ({1.335}^{2} - {1.273}^{2})

112.2593 = {(\frac{3.1416 \cdot 13}{1.55})}^{2} \cdot ({1.335}^{2} - {1.273}^{2})

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Guided Modes Number Solution

Follow our step by step solution on how to calculate Guided Modes Number?

FIRST Step Consider the formula

M g = {(\frac{π \cdot r core}{λ})}^{2} \cdot ({η core}^{2} - {η clad}^{2})

Next Step Substitute values of Variables

∴

M g = {(\frac{π \cdot 13μm}{1.55μm})}^{2} \cdot ({1.335}^{2} - {1.273}^{2})

Next Step Substitute values of Constants

∴

M g = {(\frac{3.1416 \cdot 13μm}{1.55μm})}^{2} \cdot ({1.335}^{2} - {1.273}^{2})

Next Step Convert Units

∴

M g = {(\frac{3.1416 \cdot 1.3E-5m}{1.6E-6m})}^{2} \cdot ({1.335}^{2} - {1.273}^{2})

Next Step Prepare to Evaluate

∴

M g = {(\frac{3.1416 \cdot 1.3E-5}{1.6E-6})}^{2} \cdot ({1.335}^{2} - {1.273}^{2})

Next Step Evaluate

∴

M g = 112.259300102941

LAST Step Rounding Answer

∴

M g = 112.2593

Guided Modes Number Formula Elements

Variables

Constants

Guided Modes Number

Guided Modes Number in a waveguide is to describe the different allowed electromagnetic modes or propagation patterns within the waveguide structure.

Symbol: M_g

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Guided Modes Number

Radius of Core

Radius of Core is the length measured from the center of the core to the core-cladding interface.

Symbol: r_core

Measurement: LengthUnit: μm

Note: Value should be greater than 0.

Formulas to find Radius of Core

Wavelength of Light

Wavelength of Light refers to the distance between two consecutive peaks or troughs of an electromagnetic wave in the optical spectrum.

Symbol: λ

Measurement: LengthUnit: μm

Note: Value should be greater than 0.

Formulas to find Wavelength of Light

Refractive Index of Core

The Refractive Index of Core is defined as how the light travels through that medium. It defines how much a light ray can bend when it enters from one medium to the other.

Symbol: η_core

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Refractive Index of Core

Refractive Index of Cladding

Refractive Index of Cladding is the measure of bending of a ray of light when passing from one medium(surrounding) into another.

Symbol: η_clad

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Refractive Index of Cladding

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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How to Evaluate Guided Modes Number?

Guided Modes Number evaluator uses Guided Modes Number = ((pi*Radius of Core)/Wavelength of Light)^2*(Refractive Index of Core^2-Refractive Index of Cladding^2) to evaluate the Guided Modes Number, Guided Modes Number, often referred to as the mode number, is a term used in the context of waveguides, such as optical fibers or dielectric waveguides, to describe the different allowed electromagnetic modes or propagation patterns within the waveguide structure. Guided Modes Number is denoted by M_g symbol.

How to evaluate Guided Modes Number using this online evaluator? To use this online evaluator for Guided Modes Number, enter Radius of Core (r_core), Wavelength of Light (λ), Refractive Index of Core (η_core) & Refractive Index of Cladding (η_clad) and hit the calculate button.

FAQs on Guided Modes Number

What is the formula to find Guided Modes Number?

The formula of Guided Modes Number is expressed as Guided Modes Number = ((pi*Radius of Core)/Wavelength of Light)^2*(Refractive Index of Core^2-Refractive Index of Cladding^2). Here is an example- 112.2593 = ((pi*1.3E-05)/1.55E-06)^2*(1.335^2-1.273^2).

How to calculate Guided Modes Number?

With Radius of Core (r_core), Wavelength of Light (λ), Refractive Index of Core (η_core) & Refractive Index of Cladding (η_clad) we can find Guided Modes Number using the formula - Guided Modes Number = ((pi*Radius of Core)/Wavelength of Light)^2*(Refractive Index of Core^2-Refractive Index of Cladding^2). This formula also uses Archimedes' constant .

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Guided Modes Number Formula

Guided Modes Number Example

Guided Modes Number Solution

Guided Modes Number Formula Elements

Other formulas in Transmission Measurements category

How to Evaluate Guided Modes Number?

FAQs on Guided Modes Number

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