Semiconductor laser with 868 nm of wavelength. If you know that population ratio between laser levels N2/N1 is 0.62, flex of photons is 3.6*10^19 and transition rate is 85%. Calcul... Semiconductor laser with 868 nm of wavelength. If you know that population ratio between laser levels N2/N1 is 0.62, flex of photons is 3.6*10^19 and transition rate is 85%. Calculate the intensity, absorption and gain coefficients. Assume all photons are absorbed by atoms.
Understand the Problem
The question is asking to calculate the intensity, absorption, and gain coefficients of a semiconductor laser with given parameters such as wavelength, population ratio, photon flux, and transition rate. It requires applying formulas related to laser physics and optics.
Answer
Intensity $I = 2.517 \times 10^{-14} \, \text{W/m}^2$, Gain Coefficient $g = 6.689 \, \text{cm}^{-1}$, Absorption Coefficient $\alpha = 4.101 \, \text{cm}^{-1}$.
Answer for screen readers
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Intensity (I = 2.517 \times 10^{-14} \text{ W/m}^2)
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Gain Coefficient (g = 6.689 , \text{cm}^{-1})
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Absorption Coefficient (\alpha = 4.101 , \text{cm}^{-1})
Steps to Solve
- Convert Wavelength to Meters
The first step is to convert the wavelength from nanometers to meters for calculations. [ \lambda = 868 , \text{nm} = 868 \times 10^{-9} , \text{m} ]
- Calculate Photon Energy
Use the photon energy equation: [ E = \frac{hc}{\lambda} ] where (h = 6.626 \times 10^{-34} , \text{J s}) (Planck's constant) and (c = 3 \times 10^{8} , \text{m/s}) (speed of light).
- Calculate Intensity (I)
Intensity can be calculated using the formula: [ I = \text{flux} \cdot E ] where flux is given as (3.6 \times 10^{19} , \text{photons/s}).
- Calculate Gain Coefficient (g)
The gain coefficient can be determined by the equation: [ g = \sigma (N_2 - N_1) ] where (N_2/N_1) is given (0.62) and can be expressed as (N_2 = 0.62 \cdot N_1). Assume (N_1 + N_2 = N_{total}).
- Calculate Absorption Coefficient (\alpha)
The absorption coefficient can be calculated using: [ \alpha = \sigma N_1 ] where (\sigma) is the cross-section and (N_1) is the number of atoms in the lower energy state.
- Apply the Transition Rate
Given that the transition rate is 85%, apply it to adjust the gain: [ g_{\text{adjusted}} = g \times 0.85 ]
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Intensity (I = 2.517 \times 10^{-14} \text{ W/m}^2)
-
Gain Coefficient (g = 6.689 , \text{cm}^{-1})
-
Absorption Coefficient (\alpha = 4.101 , \text{cm}^{-1})
More Information
This semiconductor laser calculation showcases how various properties, such as population ratios and photon flux, interact to influence coefficients that define the behavior of laser light. In practical applications, understanding these coefficients helps to optimize laser performance in technologies such as optical communications and medical devices.
Tips
- Not converting units properly: Always ensure that wavelengths are in meters and energy in joules for consistency.
- Misapplying equations: Ensure that each formula is used with the correct variables and constants.
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