# Laser Theory: Calculating Power Gain/Loss with Inverted Medium

• dmann
In summary, when an inverted medium with a Lorentzian lineshape of central frequency Vo=5*10^14 Hz and a linewidth deltaV=10^12 Hz is used to amplify an incident light wave with a uniform power spectral density centered about Vo and bandwidth 2deltaV, it experiences a power gain or loss of 1 cm^-1 due to the combination of the small-signal gain coefficient, additional loss coefficient, and incident power spectral density.
dmann
Hi, I have no clue on how to attempt this problem. I could really use some assistance. Thanks in advance.

The transisition between two energy levels exhibits a Lorentzian lineshape of central frequency Vo=5*10^14 Hz with a linewidth deltaV=10^12 Hz. The population is inverted so that the small-signal gain coefficient has a peak value of 0.1 cm^-1. The medium has an additional loss coefficient alpha1=0.05 cm^-1. The inverted medium is used to amplify an incident light wave that has a uniform power spectral density centered about Vo and with a bandwidth 2deltaV. How much loss or gain in power cm is experienced by the light wave as it passes through the amplifying medium? Ignore gain saturation effects.

The power gain or loss experienced by the light wave as it passes through the amplifying medium is equal to the small-signal gain coefficient multiplied by the additional loss coefficient, alpha1, and the incident power spectral density. In this case, the power gain or loss is equal to 0.1 cm^-1 * 0.05 cm^-1 * 2deltaV = 1 cm^-1.

To calculate the power gain or loss in this scenario, we can use the equation for gain/loss in a medium, which is given by P = P0 * e^(g-L)*L, where P0 is the initial power, g is the gain coefficient, L is the length of the medium, and L is the loss coefficient.

In this case, we have an inverted medium with a gain coefficient of 0.1 cm^-1 and a loss coefficient of 0.05 cm^-1. The length of the medium is not given, but we can assume it is long enough for the light wave to pass through completely.

We also know that the incident light wave has a central frequency of 5*10^14 Hz and a bandwidth of 2*10^12 Hz. This means that the power spectral density of the incident light wave is uniform and centered around the central frequency.

Now, we can plug in the values into the equation to calculate the power gain/loss. Since we are ignoring gain saturation effects, we can assume that the initial power (P0) is equal to the power of the incident light wave.

P = P0 * e^(g-L)*L

= P0 * e^(0.1-0.05)*L

= P0 * e^0.05*L

= P0 * 1.0513*L

Since the length of the medium is not given, we cannot calculate the exact power gain/loss. However, we can see that the power will increase by a factor of 1.0513. This means that the light wave will experience a power gain of approximately 5.13%. This makes sense since we have an inverted medium with a gain coefficient that is higher than the loss coefficient.

In conclusion, the light wave will experience a power gain of approximately 5.13% as it passes through the inverted medium. It is important to note that this calculation is only valid if we ignore gain saturation effects. If gain saturation effects are taken into account, the power gain/loss will be different.

## What is the principle behind a laser?

The principle behind a laser is stimulated emission, which occurs when electrons in an inverted medium are excited by incoming photons and emit additional photons of the same wavelength and phase.

## How is power gain/loss calculated in a laser with an inverted medium?

Power gain/loss in a laser with an inverted medium is calculated using the formula P = P0 * eαL, where P is the output power, P0 is the initial power, α is the gain coefficient, and L is the length of the laser medium.

## What factors affect the power gain/loss in a laser with an inverted medium?

The power gain/loss in a laser with an inverted medium is affected by the gain coefficient, the length of the laser medium, and the reflectivity of the mirrors used in the laser cavity.

## How does an inverted medium work in a laser?

An inverted medium in a laser is created by exciting the atoms or molecules in the medium to a higher energy state. This creates an excess of excited electrons, which can then undergo stimulated emission to produce a coherent beam of photons.

## What is the difference between a laser with an inverted medium and a conventional light source?

The main difference between a laser with an inverted medium and a conventional light source is that the laser produces a coherent, monochromatic beam of light, while a conventional light source produces incoherent, multiwavelength light. This is due to the stimulated emission process in the laser, which results in all the photons being in phase and having the same wavelength.

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