Mode Number Calculator

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Photonics Devices

Devices with Optical Components

Lasers

✖Length of Cavity is a physical measure representing the distance between the two reflective surfaces (mirrors) of an optical cavity.ⓘ Length of Cavity [L_c]			+10% -10%
✖Refractive Index is a dimensionless quantity that describes how much light is slowed down or refracted when entering a medium compared to its speed in a vacuum.ⓘ Refractive Index [n_ri]			+10% -10%
✖Photon Wavelength refers to the distance between consecutive peaks (or troughs) in the oscillating electric and magnetic fields of a photon's electromagnetic wave.ⓘ Photon Wavelength [λ]			+10% -10%

✖Mode Number indicates the number of half-wavelengths that fit into the given space.ⓘ Mode Number [m]

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Formula

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Mode Number

Formula

`"m" = (2*"L"_{"c"}*"n"_{"ri"})/"λ"`

Example

`"4.029641"=(2*"7.78m"*"1.01")/"3.9m"`

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Mode Number Solution

STEP 0: Pre-Calculation Summary

Formula Used

Mode Number = (2*Length of Cavity*Refractive Index)/Photon Wavelength
m = (2*L_c*n_ri)/λ
This formula uses 4 Variables

Variables Used

Mode Number - Mode Number indicates the number of half-wavelengths that fit into the given space.
Length of Cavity - (Measured in Meter) - Length of Cavity is a physical measure representing the distance between the two reflective surfaces (mirrors) of an optical cavity.
Refractive Index - Refractive Index is a dimensionless quantity that describes how much light is slowed down or refracted when entering a medium compared to its speed in a vacuum.
Photon Wavelength - (Measured in Meter) - Photon Wavelength refers to the distance between consecutive peaks (or troughs) in the oscillating electric and magnetic fields of a photon's electromagnetic wave.

STEP 1: Convert Input(s) to Base Unit

Length of Cavity: 7.78 Meter --> 7.78 Meter No Conversion Required
Refractive Index: 1.01 --> No Conversion Required
Photon Wavelength: 3.9 Meter --> 3.9 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

m = (2*L_c*n_ri)/λ --> (2*7.78*1.01)/3.9

Evaluating ... ...

m = 4.02964102564103

STEP 3: Convert Result to Output's Unit

4.02964102564103 --> No Conversion Required

FINAL ANSWER

4.02964102564103 ≈ 4.029641 <-- Mode Number

(Calculation completed in 00.004 seconds)

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Created by Gowthaman N

Vellore Institute of Technology (VIT University), Chennai

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Verified by Parminder Singh

Chandigarh University (CU), Punjab

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< 13 Photonics Devices Calculators

Saturation Current Density

Go Saturation Current Density = [Charge-e]*((Diffusion Coefficient of Hole)/Diffusion Length of Hole*Hole Concentration in n-Region+(Electron Diffusion Coefficient)/Diffusion Length of Electron*Electron Concentration in p-Region)

Spectral Radiant Emittance

Go Spectral Radiant Emittance = (2*pi*[hP]*[c]^3)/Wavelength of Visible Light^5*1/(exp(([hP]*[c])/(Wavelength of Visible Light*[BoltZ]*Absolute Temperature))-1)

Contact Potential Difference

Go Voltage Across PN Junction = ([BoltZ]*Absolute Temperature)/[Charge-e]*ln((Acceptor Concentration*Donor Concentration)/(Intrinsic Carrier Concentration)^2)

Energy Density given Einstein Co-Efficients

Go Energy Density = (8*[hP]*Frequency of Radiation^3)/[c]^3*(1/(exp((Planck's Constant*Frequency of Radiation)/([BoltZ]*Temperature))-1))

Proton Concentration under Unbalanced Condition

Go Proton Concentration = Intrinsic Electron Concentration*exp((Intrinsic Energy Level of Semiconductor-Quasi Fermi Level of Electrons)/([BoltZ]*Absolute Temperature))

Total Current Density

Go Total Current Density = Saturation Current Density*(exp(([Charge-e]*Voltage Across PN Junction)/([BoltZ]*Absolute Temperature))-1)

Net Phase Shift

Go Net Phase Shift = pi/Wavelength of Light*(Refractive Index)^3*Length of Fiber*Supply Voltage

Relative Population

Go Relative Population = exp(-([hP]*Relative Frequency)/([BoltZ]*Absolute Temperature))

Optical Power Radiated

Go Optical Power Radiated = Emissivity*[Stefan-BoltZ]*Area of Source*Temperature^4

Mode Number

Go Mode Number = (2*Length of Cavity*Refractive Index)/Photon Wavelength

Wavelength of Radiation in Vaccum

Go Wavelength of Wave = Apex Angle*(180/pi)*2*Single Pinhole

Wavelength of Output Light

Go Wavelength of Light = Refractive Index*Photon Wavelength

Length of Cavity

Go Length of Cavity = (Photon Wavelength*Mode Number)/2

Mode Number Formula

Mode Number = (2*Length of Cavity*Refractive Index)/Photon Wavelength
m = (2*L_c*n_ri)/λ

How does mode number affect interference fringes?

The mode number determines the order of interference fringes, influencing their spacing and arrangement in a double-slit experiment. Higher m values correspond to more distant and narrower fringes, providing a theoretical understanding of the interference pattern's characteristics.

How to Calculate Mode Number?

Mode Number calculator uses Mode Number = (2*Length of Cavity*Refractive Index)/Photon Wavelength to calculate the Mode Number, The Mode Number formula expresses the conditions for constructive interference in the double-slit pattern. Mode Number is denoted by m symbol.

How to calculate Mode Number using this online calculator? To use this online calculator for Mode Number, enter Length of Cavity (L_c), Refractive Index (n_ri) & Photon Wavelength (λ) and hit the calculate button. Here is how the Mode Number calculation can be explained with given input values -> 4.04 = (2*7.78*1.01)/3.9.

FAQ

What is Mode Number?

The Mode Number formula expresses the conditions for constructive interference in the double-slit pattern and is represented as m = (2*L_c*n_ri)/λ or Mode Number = (2*Length of Cavity*Refractive Index)/Photon Wavelength. Length of Cavity is a physical measure representing the distance between the two reflective surfaces (mirrors) of an optical cavity, Refractive Index is a dimensionless quantity that describes how much light is slowed down or refracted when entering a medium compared to its speed in a vacuum & Photon Wavelength refers to the distance between consecutive peaks (or troughs) in the oscillating electric and magnetic fields of a photon's electromagnetic wave.

How to calculate Mode Number?

The Mode Number formula expresses the conditions for constructive interference in the double-slit pattern is calculated using Mode Number = (2*Length of Cavity*Refractive Index)/Photon Wavelength. To calculate Mode Number, you need Length of Cavity (L_c), Refractive Index (n_ri) & Photon Wavelength (λ). With our tool, you need to enter the respective value for Length of Cavity, Refractive Index & Photon Wavelength and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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