Probability of Detecting Photons Calculator

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✖The variance of probability distribution function is a measure of how data points differ from the mean in probability and statistics.ⓘ Variance of Probability Distribution Function [z_var]			+10% -10%
✖Number of Incident Photons refers to the quantity of individual photons (particles of light) that strike or interact with a surface, detector, or material within a given period or area.ⓘ Number of Incident Photons [N_p]			+10% -10%

✖The probability of finding a photon can be regarded as a probability function whose intensity at any point in space defines the probability of finding a photon there.ⓘ Probability of Detecting Photons [P_(z)]

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Formula

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Probability of Detecting Photons

Formula

`"P"_{"(z)"} = (("z"_{"var"}^("N"_{"p"}))*exp(-"z"_{"var"}))/("N"_{"p"}!)`

Example

`"0.025386"=((("2.3")^("6.25"))*exp(-"2.3"))/("6.25"!)`

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Probability of Detecting Photons Solution

STEP 0: Pre-Calculation Summary

Formula Used

Probability of Finding a Photon = ((Variance of Probability Distribution Function^(Number of Incident Photons))*exp(-Variance of Probability Distribution Function))/(Number of Incident Photons!)
P_(z) = ((z_var^(N_p))*exp(-z_var))/(N_p!)
This formula uses 1 Functions, 3 Variables

Functions Used

exp - n an exponential function, the value of the function changes by a constant factor for every unit change in the independent variable., exp(Number)

Variables Used

Probability of Finding a Photon - The probability of finding a photon can be regarded as a probability function whose intensity at any point in space defines the probability of finding a photon there.
Variance of Probability Distribution Function - The variance of probability distribution function is a measure of how data points differ from the mean in probability and statistics.
Number of Incident Photons - Number of Incident Photons refers to the quantity of individual photons (particles of light) that strike or interact with a surface, detector, or material within a given period or area.

STEP 1: Convert Input(s) to Base Unit

Variance of Probability Distribution Function: 2.3 --> No Conversion Required
Number of Incident Photons: 6.25 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P_(z) = ((z_var^(N_p))*exp(-z_var))/(N_p!) --> ((2.3^(6.25))*exp(-2.3))/(6.25!)

Evaluating ... ...

P_(z) = 0.0253857015728346

STEP 3: Convert Result to Output's Unit

0.0253857015728346 --> No Conversion Required

FINAL ANSWER

0.0253857015728346 ≈ 0.025386 <-- Probability of Finding a Photon

(Calculation completed in 00.004 seconds)

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Created by Vaidehi Singh

Prabhat Engineering College (P.E.C.), Uttar Pradesh

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Chandigarh University (CU), Punjab

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< 25 Optical Detectors Calculators

SNR of Good Avalanche Photodiode ADP Receiver in decibels

Go Signal to Noise Ratio = 10*log10((Multiplication Factor^2*Photocurrent^2)/(2*[Charge-e]*Post Detection Bandwidth*(Photocurrent+Dark Current)*Multiplication Factor^2.3+((4*[BoltZ]*Temperature*Post Detection Bandwidth*1.26)/Load Resistance)))

Photocurrent due to Incident Light

Go Photocurrent = (Incident Power*[Charge-e]*(1-Reflection Coefficient))/([hP]*Frequency Of Incident Light)*(1-exp(-Absorption Coefficient*Width of Absorption Region))

Probability of Detecting Photons

Go Probability of Finding a Photon = ((Variance of Probability Distribution Function^(Number of Incident Photons))*exp(-Variance of Probability Distribution Function))/(Number of Incident Photons!)

Excess Avalanche Noise Factor

Go Excess Avalanche Noise Factor = Multiplication Factor*(1+((1-Impact Ionization Coefficient)/Impact Ionization Coefficient)*((Multiplication Factor-1)/Multiplication Factor)^2)

Total Photodiode Current

Go Output Current = Dark Current*(exp(([Charge-e]*Photodiode Voltage)/(2*[BoltZ]*Temperature))-1)+Photocurrent

Optical Gain of Phototransistors

Go Optical Gain of Phototransistor = (([hP]*[c])/(Wavelength of Light*[Charge-e]))*(Collector Current of Phototransistor/Incident Power)

Average Number of Photons Detected

Go Average Number Of Photons Detected = (Quantum Efficiency*Average Received Optical Power*Time Period)/(Frequency Of Incident Light*[hP])

Single Pass Phase Shift through Fabry-Perot Amplifier

Go Single-Pass Phase Shift = (pi*(Frequency Of Incident Light-Fabry–Perot Resonant Frequency))/Free Spectral Range of Fabry-Pérot Interferometer

Total Root Mean Square Noise Current

Go Total Root Mean Square Noise Current = sqrt(Total Shot Noise^2+Dark Current Noise^2+Thermal Noise Current^2)

Average Received Optical Power

Go Average Received Optical Power = (20.7*[hP]*Frequency Of Incident Light)/(Time Period*Quantum Efficiency)

Total Power Accepted by Fiber

Go Total Power Accepted by Fiber = Incident Power*(1-(8*Axial Displacement)/(3*pi*Radius of Core))

Multiplied Photocurrent

Go Multiplied Photocurrent = Optical Gain of Phototransistor*Responsivity of Photodetector*Incident Power

Temperature Effect on Dark Current

Go Dark Current in raised temperature = Dark Current*2^((Changed Temperature-Previous Temperature)/10)

Incident Photon Rate

Go Incident Photon Rate = Incident Optical Power/([hP]*Frequency Of Light Wave)

Maximum Photodiode 3 dB Bandwidth

Go Maximum 3db Bandwidth = Carrier Velocity/(2*pi*Depletion Layer Width)

Maximum 3dB Bandwidth of Metal Photodetector

Go Maximum 3db Bandwidth = 1/(2*pi*Transit Time*PhotoConductive Gain)

Bandwidth Penalty

Go Post Detection Bandwidth = 1/(2*pi*Load Resistance*Capacitance)

Long Wavelength Cutoff Point

Go Wavelength Cutoff Point = [hP]*[c]/Bandgap Energy

Quantum Efficiency of Photodetector

Go Quantum Efficiency = Number of Electrons/Number of Incident Photons

Multiplication Factor

Go Multiplication Factor = Output Current/Initial Photocurrent

Electron Rate in Detector

Go Electron Rate = Quantum Efficiency*Incident Photon Rate

Transit Time with respect to Minority Carrier Diffusion

Go Diffusion Time = Distance^2/(2*Diffusion Coefficient)

Longest Transit Time

Go Transit Time = Depletion Layer Width/Drift Velocity

3 dB Bandwidth of Metal Photodetectors

Go Maximum 3db Bandwidth = 1/(2*pi*Transit Time)

Detectivity of Photodetector

Go Detectivity = 1/Noise Equivalent Power

Probability of Detecting Photons Formula

What is Probability of Detecting Photons?

Probability is a branch of mathematics that deals with the likelihood of occurrence of an event. It is a measure of the likelihood of an event to occur.
In fiber optics, the probability of finding a photon in fiber optics can be understood from the perspective of wave-particle duality. The light waves, as electromagnetic continuous waves, can be regarded as a probability function whose intensity at any point in space defines the probability of finding a photon there.

How to Calculate Probability of Detecting Photons?

Probability of Detecting Photons calculator uses Probability of Finding a Photon = ((Variance of Probability Distribution Function^(Number of Incident Photons))*exp(-Variance of Probability Distribution Function))/(Number of Incident Photons!) to calculate the Probability of Finding a Photon, The Probability of Detecting Photons is a measure of the likelihood of an event to occur. The probability of an event is a number between 0 and 1. Here, 0 indicates that an event will not occur, and 1 indicates that an event is certain to occur. According to this logic, the probability of finding a photon is the possibility of that photon being present. This probability can be computed by this equation. Probability of Finding a Photon is denoted by P_(z) symbol.

How to calculate Probability of Detecting Photons using this online calculator? To use this online calculator for Probability of Detecting Photons, enter Variance of Probability Distribution Function (z_var) & Number of Incident Photons (N_p) and hit the calculate button. Here is how the Probability of Detecting Photons calculation can be explained with given input values -> 0.025386 = ((2.3^(6.25))*exp(-2.3))/(6.25!).

FAQ

What is Probability of Detecting Photons?

The Probability of Detecting Photons is a measure of the likelihood of an event to occur. The probability of an event is a number between 0 and 1. Here, 0 indicates that an event will not occur, and 1 indicates that an event is certain to occur. According to this logic, the probability of finding a photon is the possibility of that photon being present. This probability can be computed by this equation and is represented as P_(z) = ((z_var^(N_p))*exp(-z_var))/(N_p!) or Probability of Finding a Photon = ((Variance of Probability Distribution Function^(Number of Incident Photons))*exp(-Variance of Probability Distribution Function))/(Number of Incident Photons!). The variance of probability distribution function is a measure of how data points differ from the mean in probability and statistics & Number of Incident Photons refers to the quantity of individual photons (particles of light) that strike or interact with a surface, detector, or material within a given period or area.

How to calculate Probability of Detecting Photons?

The Probability of Detecting Photons is a measure of the likelihood of an event to occur. The probability of an event is a number between 0 and 1. Here, 0 indicates that an event will not occur, and 1 indicates that an event is certain to occur. According to this logic, the probability of finding a photon is the possibility of that photon being present. This probability can be computed by this equation is calculated using Probability of Finding a Photon = ((Variance of Probability Distribution Function^(Number of Incident Photons))*exp(-Variance of Probability Distribution Function))/(Number of Incident Photons!). To calculate Probability of Detecting Photons, you need Variance of Probability Distribution Function (z_var) & Number of Incident Photons (N_p). With our tool, you need to enter the respective value for Variance of Probability Distribution Function & Number of Incident Photons 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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