Phase Shift of Jth Channel Calculator

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Fiber Modelling Parameters

Fiber Design Characteristics

✖Non Linear Parameter refers to the attenuation coefficient or attenuation rate of optical fibers.ⓘ Non Linear Parameter [γ]			+10% -10%
✖Effective Interaction Length used to describe the distance over which light can interact with or propagate through the fiber before certain optical effects become significant.ⓘ Effective Interaction Length [L_eff]			+10% -10%
✖Power of Jth signal denotes the power of the "j-th" signal, which could be any optical signal in the system.ⓘ Power of Jth signal [P_j]			+10% -10%
✖Range of Other Channels Except J is the specific range for m is determined by the number of optical channels being considered in the analysis of XPM.ⓘ Range of Other Channels Except J [m]			+10% -10%
✖Power of Mth signal denotes the power of the "m-th" signal, which is another optical signal propagating concurrently with the Pj signal.ⓘ Power of Mth signal [P_m]			+10% -10%

✖Phase Shift Jth Channel refers to the change in the phase of the optical signal in the "jth channel" induced by the presence of another optical signal.ⓘ Phase Shift of Jth Channel [Øj^NL]

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Formula

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Phase Shift of Jth Channel

Formula

`"Øj"^{"NL"} = "γ"*"L"_{"eff"}*("P"_{"j"}+2*sum(x,1,"m","P"_{"m"}))`

Example

`"540.175rad"="5dB/m"*"0.3485m"*("40W"+2*sum(x,1,"5","27W"))`

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Phase Shift of Jth Channel Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
Øj^NL = γ*L_eff*(P_j+2*sum(x,1,m,P_m))
This formula uses 1 Functions, 6 Variables

Functions Used

sum - Summation or sigma (∑) notation is a method used to write out a long sum in a concise way., sum(i, from, to, expr)

Variables Used

Phase Shift Jth Channel - (Measured in Radian) - Phase Shift Jth Channel refers to the change in the phase of the optical signal in the "jth channel" induced by the presence of another optical signal.
Non Linear Parameter - (Measured in Decibel per Meter) - Non Linear Parameter refers to the attenuation coefficient or attenuation rate of optical fibers.
Effective Interaction Length - (Measured in Meter) - Effective Interaction Length used to describe the distance over which light can interact with or propagate through the fiber before certain optical effects become significant.
Power of Jth signal - (Measured in Watt) - Power of Jth signal denotes the power of the "j-th" signal, which could be any optical signal in the system.
Range of Other Channels Except J - Range of Other Channels Except J is the specific range for m is determined by the number of optical channels being considered in the analysis of XPM.
Power of Mth signal - (Measured in Watt) - Power of Mth signal denotes the power of the "m-th" signal, which is another optical signal propagating concurrently with the Pj signal.

STEP 1: Convert Input(s) to Base Unit

Non Linear Parameter: 5 Decibel per Meter --> 5 Decibel per Meter No Conversion Required
Effective Interaction Length: 0.3485 Meter --> 0.3485 Meter No Conversion Required
Power of Jth signal: 40 Watt --> 40 Watt No Conversion Required
Range of Other Channels Except J: 5 --> No Conversion Required
Power of Mth signal: 27 Watt --> 27 Watt No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Øj^NL = γ*L_eff*(P_j+2*sum(x,1,m,P_m)) --> 5*0.3485*(40+2*sum(x,1,5,27))

Evaluating ... ...

Øj^NL = 540.175

STEP 3: Convert Result to Output's Unit

540.175 Radian --> No Conversion Required

FINAL ANSWER

540.175 Radian <-- Phase Shift Jth Channel

(Calculation completed in 00.004 seconds)

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Created by Zaheer Sheik

Seshadri Rao Gudlavalleru Engineering College (SRGEC), Gudlavalleru

Zaheer Sheik has created this Calculator and 10+ more calculators!

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< 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

Phase Shift of Jth Channel Formula

What is Cross-Phase Modulation?

Cross-phase modulation (XPM) is a nonlinear optical phenomenon occurring in fiber optic communication systems. It results from the interaction between different optical signals (channels) propagating through the same fiber, the intensity of one optical signal (the pump or modulating signal) induces changes in the refractive index of the fiber, which modulates the phase of another optical signal (the probe or modulated signal). This modulation can lead to various effects, including phase shifts, frequency shifts, signal distortion, and the generation of new optical frequencies through nonlinear mixing processes.

How to Calculate Phase Shift of Jth Channel?

Phase Shift of Jth Channel calculator uses 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)) to calculate the Phase Shift Jth Channel, The Phase Shift of Jth Channel occurs when two or more optical channels are transmitted simultaneously inside an optical fiber using the WDM technique. In such systems, the nonlinear phase shift for a specific channel depends not only on the power of that channel but also on the power of other channels. Phase Shift Jth Channel is denoted by Øj^NL symbol.

How to calculate Phase Shift of Jth Channel using this online calculator? To use this online calculator for Phase Shift of Jth Channel, enter Non Linear Parameter (γ), Effective Interaction Length (L_eff), Power of Jth signal (P_j), Range of Other Channels Except J (m) & Power of Mth signal (P_m) and hit the calculate button. Here is how the Phase Shift of Jth Channel calculation can be explained with given input values -> 540.175 = 5*0.3485*(40+2*sum(x,1,5,27)).

FAQ

What is Phase Shift of Jth Channel?

The Phase Shift of Jth Channel occurs when two or more optical channels are transmitted simultaneously inside an optical fiber using the WDM technique. In such systems, the nonlinear phase shift for a specific channel depends not only on the power of that channel but also on the power of other channels and is represented as Øj^NL = γ*L_eff*(P_j+2*sum(x,1,m,P_m)) or 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)). Non Linear Parameter refers to the attenuation coefficient or attenuation rate of optical fibers, Effective Interaction Length used to describe the distance over which light can interact with or propagate through the fiber before certain optical effects become significant, Power of Jth signal denotes the power of the "j-th" signal, which could be any optical signal in the system, Range of Other Channels Except J is the specific range for m is determined by the number of optical channels being considered in the analysis of XPM & Power of Mth signal denotes the power of the "m-th" signal, which is another optical signal propagating concurrently with the Pj signal.

How to calculate Phase Shift of Jth Channel?

The Phase Shift of Jth Channel occurs when two or more optical channels are transmitted simultaneously inside an optical fiber using the WDM technique. In such systems, the nonlinear phase shift for a specific channel depends not only on the power of that channel but also on the power of other channels is calculated using 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)). To calculate Phase Shift of Jth Channel, you need Non Linear Parameter (γ), Effective Interaction Length (L_eff), Power of Jth signal (P_j), Range of Other Channels Except J (m) & Power of Mth signal (P_m). With our tool, you need to enter the respective value for Non Linear Parameter, Effective Interaction Length, Power of Jth signal, Range of Other Channels Except J & Power of Mth signal 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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