Number of Modes Calculator

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Fiber Modelling Parameters

Fiber Design Characteristics

✖Radius of Core is the length measured from the center of the core to the core-cladding interface.ⓘ Radius of Core [r_core]			+10% -10%
✖Numerical Aperture is a measure of the light-gathering or light-capturing ability of an optical fiber or an optical system.ⓘ Numerical Aperture [NA]			+10% -10%
✖Wavelength of Light refers to the distance between two consecutive peaks or troughs of an electromagnetic wave in the optical spectrum.ⓘ Wavelength of Light [λ]			+10% -10%

✖Number of Modes refers to the different spatial propagation paths or patterns that an optical signal can take within a multimode optical fiber.ⓘ Number of Modes [N_M]

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Formula

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Number of Modes

Formula

`"N"_{"M"} = (2*pi*"r"_{"core"}*"NA")/"λ"`

Example

`"21.07907"=(2*pi*"13μm"*"0.4")/"1.55μm"`

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Number of Modes Solution

STEP 0: Pre-Calculation Summary

Formula Used

Number of Modes = (2*pi*Radius of Core*Numerical Aperture)/Wavelength of Light
N_M = (2*pi*r_core*NA)/λ
This formula uses 1 Constants, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Number of Modes - Number of Modes refers to the different spatial propagation paths or patterns that an optical signal can take within a multimode optical fiber.
Radius of Core - (Measured in Meter) - Radius of Core is the length measured from the center of the core to the core-cladding interface.
Numerical Aperture - Numerical Aperture is a measure of the light-gathering or light-capturing ability of an optical fiber or an optical system.
Wavelength of Light - (Measured in Meter) - Wavelength of Light refers to the distance between two consecutive peaks or troughs of an electromagnetic wave in the optical spectrum.

STEP 1: Convert Input(s) to Base Unit

Radius of Core: 13 Micrometer --> 1.3E-05 Meter (Check conversion here)
Numerical Aperture: 0.4 --> No Conversion Required
Wavelength of Light: 1.55 Micrometer --> 1.55E-06 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

N_M = (2*pi*r_core*NA)/λ --> (2*pi*1.3E-05*0.4)/1.55E-06

Evaluating ... ...

N_M = 21.0790732886025

STEP 3: Convert Result to Output's Unit

21.0790732886025 --> No Conversion Required

FINAL ANSWER

21.0790732886025 ≈ 21.07907 <-- Number of Modes

(Calculation completed in 00.004 seconds)

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Credits

Created by Saiju Shah

Jayawantrao Sawant College of Engineering (JSCOE), Pune

Saiju Shah has created this Calculator and 4 more calculators!

Verified by Swapneel Shah

Vidya Pratishthans College of Engineering (VPCOE), Baramati

Swapneel Shah has verified this Calculator and 5 more calculators!

< 19 Fiber Modelling Parameters Calculators

Total Amplifier Gain for EDFA

Go Total Amplifier Gain for an EDFA = Confinement Factor*exp(int((Emission Cross Section*Population Density of Higher Energy Level-Absorption Cross Section*Population Density of Lower Energy Level)*x,x,0,Length of Fiber))

Photo Current Generated to Incident Optical Power

Go Photo Current Generated to Incident Optical Power = Photodetector Responsivity for Channel M*Power of Mth Channel+sum(x,1,Number of Channels,Photodetector Responsivity for Channel N*Filter Transmittivity for Channel N*Power in Nth Channel)

Phase Shift of Jth Channel

Go Phase Shift Jth Channel = Non Linear Parameter*Effective Interaction Length*(Power of Jth signal+2*sum(x,1,Range of Other Channels Except J,Power of Mth signal))

External Quantum Efficiency

Go External Quantum Efficiency = (1/(4*pi))*int(Fresnel Transmissivity*(2*pi*sin(x)),x,0,Cone of Acceptance Angle)

Effective Interaction Length

Go Effective Interaction Length = (1-exp(-(Attenuation Loss*Length of Fiber)))/Attenuation Loss

Non Linear Phase Shift

Go Non Linear Phase Shift = int(Non Linear Parameter*Optical Power,x,0,Length of Fiber)

Optical Dispersion

Go Optical Fiber Dispersion = (2*pi*[c]*Propagation Constant)/Wavelength of Light^2

Diameter of Fiber

Go Diameter of Fiber = (Wavelength of Light*Number of Modes)/(pi*Numerical Aperture)

Number of Modes

Go Number of Modes = (2*pi*Radius of Core*Numerical Aperture)/Wavelength of Light

Power Loss in Fiber

Go Power Loss Fiber = Input Power*exp(Attenuation Coefficient*Length of Fiber)

Gaussian Pulse

Go Gaussian Pulse = Optical Pulse Duration/(Length of Fiber*Optical Fiber Dispersion)

Brillouin Shift

Go Brillouin shift = (2*Mode Index*Acoustic Velocity)/Pump Wavelength

Modal Birefringence Degree

Go Modal Birefringence Degree = modulus(Mode Index X-Mode Index Y)

Rayleigh Scattering

Go Rayleigh Scattering = Fiber Constant/(Wavelength of Light^4)

Beat Length

Go Beat Length = Wavelength of Light/Modal Birefringence Degree

Group Velocity

Go Group Velocity = Length of Fiber/Group Delay

Fiber Length

Go Length of Fiber = Group Velocity*Group Delay

Fiber Attenuation Coefficient

Go Attenuation Coefficient = Attenuation Loss/4.343

Number of Modes using Normalized Frequency

Go Number of Modes = Normalized Frequency^2/2

Number of Modes Formula

Number of Modes = (2*pi*Radius of Core*Numerical Aperture)/Wavelength of Light
N_M = (2*pi*r_core*NA)/λ

What is the V number of fiber or normalized frequency of fiber?

For a single-mode fiber, it is required that the normalized frequency, satisfies the condition V < 2.4048. For a step index fiber, the mode volume of that fiber is directionally proportional to the square of the normalized frequency, that is V2.

How to Calculate Number of Modes?

Number of Modes calculator uses Number of Modes = (2*pi*Radius of Core*Numerical Aperture)/Wavelength of Light to calculate the Number of Modes, Number of Modes refers to the different spatial propagation paths or patterns that an optical signal can take within a multimode optical fiber. Multimode fibers are designed to support multiple propagation modes, which are characterized by distinct optical paths that the light can follow as it travels through the fiber. Each mode corresponds to a different pattern of light rays bouncing off the inner walls of the fiber. Number of Modes is denoted by N_M symbol.

How to calculate Number of Modes using this online calculator? To use this online calculator for Number of Modes, enter Radius of Core (r_core), Numerical Aperture (NA) & Wavelength of Light (λ) and hit the calculate button. Here is how the Number of Modes calculation can be explained with given input values -> 21.07907 = (2*pi*1.3E-05*0.4)/1.55E-06.

FAQ

What is Number of Modes?

Number of Modes refers to the different spatial propagation paths or patterns that an optical signal can take within a multimode optical fiber. Multimode fibers are designed to support multiple propagation modes, which are characterized by distinct optical paths that the light can follow as it travels through the fiber. Each mode corresponds to a different pattern of light rays bouncing off the inner walls of the fiber and is represented as N_M = (2*pi*r_core*NA)/λ or Number of Modes = (2*pi*Radius of Core*Numerical Aperture)/Wavelength of Light. Radius of Core is the length measured from the center of the core to the core-cladding interface, Numerical Aperture is a measure of the light-gathering or light-capturing ability of an optical fiber or an optical system & Wavelength of Light refers to the distance between two consecutive peaks or troughs of an electromagnetic wave in the optical spectrum.

How to calculate Number of Modes?

Number of Modes refers to the different spatial propagation paths or patterns that an optical signal can take within a multimode optical fiber. Multimode fibers are designed to support multiple propagation modes, which are characterized by distinct optical paths that the light can follow as it travels through the fiber. Each mode corresponds to a different pattern of light rays bouncing off the inner walls of the fiber is calculated using Number of Modes = (2*pi*Radius of Core*Numerical Aperture)/Wavelength of Light. To calculate Number of Modes, you need Radius of Core (r_core), Numerical Aperture (NA) & Wavelength of Light (λ). With our tool, you need to enter the respective value for Radius of Core, Numerical Aperture & Wavelength of Light and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Number of Modes?

In this formula, Number of Modes uses Radius of Core, Numerical Aperture & Wavelength of Light. We can use 1 other way(s) to calculate the same, which is/are as follows -

Number of Modes = Normalized Frequency^2/2

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