Small Signal Gain Coefficient Calculator

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✖Density of Atoms Final State represent the concentration of atoms in the respective energy levels.ⓘ Density of Atoms Final State [N₂]			+10% -10%
✖Degeneracy of Final State refers to the number of different quantum states with the same energy.ⓘ Degeneracy of Final State [g₂]			+10% -10%
✖Degeneracy of Initial State refers to the number of different quantum states with the same energy.ⓘ Degeneracy of Initial State [g₁]			+10% -10%
✖Density of Atoms Initial State represent the concentration of atoms in the respective energy levels.ⓘ Density of Atoms Initial State [N₁]			+10% -10%
✖Einstein Coefficient for Stimulated Absorption represents the probability per unit time for an atom in the lower energy state.ⓘ Einstein Coefficient for Stimulated Absorption [B₂₁]			+10% -10%
✖Frequency of Transition represents the energy difference between the two states divided by Planck's constant.ⓘ Frequency of Transition [v₂₁]			+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%

✖Signal Gain Coefficient is a parameter used to describe the amplification of an optical signal in a medium, typically within the context of lasers or optical amplifiers.ⓘ Small Signal Gain Coefficient [k_s]

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Formula

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Small Signal Gain Coefficient

Formula

`"k"_{"s"} = "N"_{"2"}-("g"_{"2"}/"g"_{"1"})*("N"_{"1"})*("B"_{"21"}*"[hP]"*"v"_{"21"}*"n"_{"ri"})/"[c]"`

Example

`"1.502"="1.502electrons/m³"-("24"/"12")*("1.85electrons/m³")*("1.52m³"*"[hP]"*"41Hz"*"1.01")/"[c]"`

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Small Signal Gain Coefficient Solution

STEP 0: Pre-Calculation Summary

Formula Used

Signal Gain Coefficient = Density of Atoms Final State-(Degeneracy of Final State/Degeneracy of Initial State)*(Density of Atoms Initial State)*(Einstein Coefficient for Stimulated Absorption*[hP]*Frequency of Transition*Refractive Index)/[c]
k_s = N₂-(g₂/g₁)*(N₁)*(B₂₁*[hP]*v₂₁*n_ri)/[c]
This formula uses 2 Constants, 8 Variables

Constants Used

[hP] - Planck constant Value Taken As 6.626070040E-34
[c] - Light speed in vacuum Value Taken As 299792458.0

Variables Used

Signal Gain Coefficient - Signal Gain Coefficient is a parameter used to describe the amplification of an optical signal in a medium, typically within the context of lasers or optical amplifiers.
Density of Atoms Final State - (Measured in Electrons per Cubic Meter) - Density of Atoms Final State represent the concentration of atoms in the respective energy levels.
Degeneracy of Final State - Degeneracy of Final State refers to the number of different quantum states with the same energy.
Degeneracy of Initial State - Degeneracy of Initial State refers to the number of different quantum states with the same energy.
Density of Atoms Initial State - (Measured in Electrons per Cubic Meter) - Density of Atoms Initial State represent the concentration of atoms in the respective energy levels.
Einstein Coefficient for Stimulated Absorption - (Measured in Cubic Meter) - Einstein Coefficient for Stimulated Absorption represents the probability per unit time for an atom in the lower energy state.
Frequency of Transition - (Measured in Hertz) - Frequency of Transition represents the energy difference between the two states divided by Planck's constant.
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.

STEP 1: Convert Input(s) to Base Unit

Density of Atoms Final State: 1.502 Electrons per Cubic Meter --> 1.502 Electrons per Cubic Meter No Conversion Required
Degeneracy of Final State: 24 --> No Conversion Required
Degeneracy of Initial State: 12 --> No Conversion Required
Density of Atoms Initial State: 1.85 Electrons per Cubic Meter --> 1.85 Electrons per Cubic Meter No Conversion Required
Einstein Coefficient for Stimulated Absorption: 1.52 Cubic Meter --> 1.52 Cubic Meter No Conversion Required
Frequency of Transition: 41 Hertz --> 41 Hertz No Conversion Required
Refractive Index: 1.01 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

k_s = N₂-(g₂/g₁)*(N₁)*(B₂₁*[hP]*v₂₁*n_ri)/[c] --> 1.502-(24/12)*(1.85)*(1.52*[hP]*41*1.01)/[c]

Evaluating ... ...

k_s = 1.502

STEP 3: Convert Result to Output's Unit

1.502 --> No Conversion Required

FINAL ANSWER

1.502 <-- Signal Gain Coefficient

(Calculation completed in 00.004 seconds)

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< 12 Lasers Calculators

Small Signal Gain Coefficient

Go Signal Gain Coefficient = Density of Atoms Final State-(Degeneracy of Final State/Degeneracy of Initial State)*(Density of Atoms Initial State)*(Einstein Coefficient for Stimulated Absorption*[hP]*Frequency of Transition*Refractive Index)/[c]

Absorption Co-Efficient

Go Absorption Coefficient = Degeneracy of Final State/Degeneracy of Initial State*(Density of Atoms Initial State-Density of Atoms Final State)*(Einstein Coefficient for Stimulated Absorption*[hP]*Frequency of Transition*Refractive Index)/[c]

Round Trip Gain

Go Round Trip Gain = Reflectances*Reflectances Separated by L*(exp(2*(Signal Gain Coefficient-Effective Loss Coefficient)*Length of Laser Cavity))

Transmittance

Go Transmittance = (sin(pi/Wavelength of Light*(Refractive Index)^3*Length of Fiber*Supply Voltage))^2

Ratio of Rate of Spontaneous and Stimulated Emission

Go Ratio of Rate of Spontaneous to Stimulus Emission = exp((([hP]*Frequency of Radiation)/([BoltZ]*Temperature))-1)

Irradiance

Go Irridance of Transmitted Beam = Irradiation of Light Incident*exp(Signal Gain Coefficient*Distance Travelled by Laser Beam)

Intensity of Signal at Distance

Go Intensity of Signal at Distance = Initial Intensity*exp(-Decay Constant*Distance of Measuring)

Variable Refractive Index of The GRIN Lens

Go Apparent Refractive Index = Refractive Index of Medium 1*(1-(Positive Constant*Radius of Lens^2)/2)

Half Wave Voltage

Go Half Wave Voltage = Wavelength of Light/(Length of Fiber*Refractive Index^3)

Plane of Transmission of Analyzer

Go Plane of Transmission of Analyzer = Plane of Polarizer/((cos(Theta))^2)

Plane of Polarizer

Go Plane of Polarizer = Plane of Transmission of Analyzer*(cos(Theta)^2)

Single Pinhole

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

Small Signal Gain Coefficient Formula

How is the Signal Gain Coefficient related to laser amplification?

In a laser system, the Signal Gain Coefficient is a key factor determining the amplification of the signal. It is associated with the rate of stimulated emission relative to the rate of absorption and spontaneous emission.

How to Calculate Small Signal Gain Coefficient?

Small Signal Gain Coefficient calculator uses Signal Gain Coefficient = Density of Atoms Final State-(Degeneracy of Final State/Degeneracy of Initial State)*(Density of Atoms Initial State)*(Einstein Coefficient for Stimulated Absorption*[hP]*Frequency of Transition*Refractive Index)/[c] to calculate the Signal Gain Coefficient, The Small Signal Gain Coefficient formula is defined as a parameter used to describe the amplification of an optical signal in a medium, typically within the context of lasers or optical amplifiers. Signal Gain Coefficient is denoted by k_s symbol.

How to calculate Small Signal Gain Coefficient using this online calculator? To use this online calculator for Small Signal Gain Coefficient, enter Density of Atoms Final State (N₂), Degeneracy of Final State (g₂), Degeneracy of Initial State (g₁), Density of Atoms Initial State (N₁), Einstein Coefficient for Stimulated Absorption (B₂₁), Frequency of Transition (v₂₁) & Refractive Index (n_ri) and hit the calculate button. Here is how the Small Signal Gain Coefficient calculation can be explained with given input values -> 1.502 = 1.502-(24/12)*(1.85)*(1.52*[hP]*41*1.01)/[c].

FAQ

What is Small Signal Gain Coefficient?

The Small Signal Gain Coefficient formula is defined as a parameter used to describe the amplification of an optical signal in a medium, typically within the context of lasers or optical amplifiers and is represented as k_s = N₂-(g₂/g₁)*(N₁)*(B₂₁*[hP]*v₂₁*n_ri)/[c] or Signal Gain Coefficient = Density of Atoms Final State-(Degeneracy of Final State/Degeneracy of Initial State)*(Density of Atoms Initial State)*(Einstein Coefficient for Stimulated Absorption*[hP]*Frequency of Transition*Refractive Index)/[c]. Density of Atoms Final State represent the concentration of atoms in the respective energy levels, Degeneracy of Final State refers to the number of different quantum states with the same energy, Degeneracy of Initial State refers to the number of different quantum states with the same energy, Density of Atoms Initial State represent the concentration of atoms in the respective energy levels, Einstein Coefficient for Stimulated Absorption represents the probability per unit time for an atom in the lower energy state, Frequency of Transition represents the energy difference between the two states divided by Planck's constant & 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.

How to calculate Small Signal Gain Coefficient?

The Small Signal Gain Coefficient formula is defined as a parameter used to describe the amplification of an optical signal in a medium, typically within the context of lasers or optical amplifiers is calculated using Signal Gain Coefficient = Density of Atoms Final State-(Degeneracy of Final State/Degeneracy of Initial State)*(Density of Atoms Initial State)*(Einstein Coefficient for Stimulated Absorption*[hP]*Frequency of Transition*Refractive Index)/[c]. To calculate Small Signal Gain Coefficient, you need Density of Atoms Final State (N₂), Degeneracy of Final State (g₂), Degeneracy of Initial State (g₁), Density of Atoms Initial State (N₁), Einstein Coefficient for Stimulated Absorption (B₂₁), Frequency of Transition (v₂₁) & Refractive Index (n_ri). With our tool, you need to enter the respective value for Density of Atoms Final State, Degeneracy of Final State, Degeneracy of Initial State, Density of Atoms Initial State, Einstein Coefficient for Stimulated Absorption, Frequency of Transition & Refractive Index 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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