# Laser Modes & Spectral Hole Burning

• SSJVegetto
In summary, the condition for reflection at a surface is that the field amplitude must be zero. Axial modes in a laser cavity can be defined by the number of sine-wave half cycles that fit inside the cavity. In a homogeneously broadened gain medium, only the central mode with the highest gain will start lasing at threshold due to the uniform gain and losses. In an inhomogeneously broadened gain medium, multiple modes can reach threshold simultaneously, resulting in spectral hole burning where a mode loses gain as other modes start lasing, creating a spectral hole in the gain medium.
SSJVegetto

## Homework Statement

Reflection at a surface takes place under the condition that the field amplitude is zero at the reflecting surface. As a result, the axial modes i of wavelength λi inside a laser cavity can be defined by their number ni of sine-wave half cycles that fit exactly into the laser cavity. The optical gain curve of the active medium of a crystalline solid-state laser has a wavelength range of typically 10-100 nm, so that many (~104) axial modes inside a few-cm long cavity fall within the optical gain curve and may therefore start lasing.
a) Explain why nevertheless only one axial mode starts lasing in a homogeneously broadened gain medium at pump threshold.
b) Explain the phenomenon of "spectral hole burning".

## The Attempt at a Solution

a. I'm assuming that only one axial mode starts lasing because in a homogeously broadened gain medium at pump threshold the gain overcomes losses only for the central mode. Since the whole gain curve remains the same for higher values of the pump rate. Thus the gain of other modes will always remain smaller than the gain of the central mode and thus only one mode starts lasing.

I'm wondering if this is a good explanation and can someone please tell me why this is true why it doesn't change and why does it change for inhomogeneously broeadened gain medium?

b. Spectral hole burning can only occur when an inhomogenously broadened gain medium is used. Here the gain curve can change and overcome losses for other modes as well which, when overcoming threshold and thus losses, is clamped to the threshold value and thus this creates holes in the gain medium because the gain is already used for a mode and thus in the gain medium a spectral hole is present for which no gain is present and hence a spectral hole is burned.

Hello, thank you for your response. Your explanation for part a is correct. In a homogeneously broadened gain medium, all modes experience the same amount of gain and losses, so only the central mode with the highest gain will reach the threshold and start lasing. In an inhomogeneously broadened gain medium, the gain varies across the medium, so different modes can reach threshold at different points in the medium, resulting in multiple modes lasing simultaneously.

For part b, your explanation is also correct. In an inhomogeneously broadened gain medium, the gain can vary at different points in the medium, so a mode that initially has enough gain to reach threshold may lose that gain as other modes start lasing. This creates a "hole" in the gain medium where the gain is not strong enough for any mode to reach threshold, resulting in a spectral hole. This effect is known as spectral hole burning.

## 1. What are laser modes?

Laser modes refer to the specific wavelengths or frequencies of light that a laser can emit. These modes are determined by the properties of the laser cavity and the type of laser medium used.

## 2. How do laser modes affect laser performance?

Laser modes can affect the output power, beam profile, and coherence of a laser. They also determine the specific applications for which a laser can be used.

## 3. What is spectral hole burning?

Spectral hole burning is a phenomenon that occurs in some laser materials, where certain wavelengths of light are absorbed and create "holes" in the absorption spectrum. These holes can then be used to selectively amplify or filter certain laser modes.

## 4. How is spectral hole burning used in lasers?

Spectral hole burning can be used in lasers to improve their spectral and temporal characteristics, allowing for higher precision and control in applications such as spectroscopy and telecommunications.

## 5. What are some common applications of lasers using spectral hole burning?

Lasers utilizing spectral hole burning are commonly used in telecommunications, atomic and molecular spectroscopy, and quantum information processing. They are also being researched for potential applications in quantum computing and high-resolution imaging.

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