Active laser medium

 ( Laser Science ) 

The active laser medium (also called a gain medium or lasing medium) is the source of optical gain within a laser. The gain results from the stimulated emission of photons through electronic or molecular transitions to a lower energy state from a higher energy state previously populated by a laser pumping.

Examples of active laser media include:

• Certain , typically doped with rare-earth (e.g. neodymium, ytterbium, or erbium) or transition metal ions (titanium or chromium); most often yttrium aluminium garnet (yttrium₃aluminium₅Oxygen₁₂), yttrium orthovanadate (YVO₄), or sapphire (Al₂O₃);Hecht, Jeff. The Laser Guidebook: Second Edition. McGraw-Hill, 1992. (Chapter 22) and not often caesium cadmium bromide (caesiumCadmiumbromine₃) (solid-state lasers)
• , e.g. silicate or phosphate glasses, doped with laser-active ions;Hecht, Chapter 22
• , e.g. mixtures of helium and neon (HeNe), nitrogen, argon, krypton, carbon monoxide, carbon dioxide, or metal vapors;Hecht, Chapters 7-15 ()
• , e.g. gallium arsenide (GaAs), indium gallium arsenide (InGaAs), or gallium nitride (GaN).Hecht, Chapters 18–21
• Liquids, in the form of dye solutions as used in dye lasers.F. J. Duarte and L. W. Hillman (Eds.), Dye Laser Principles (Academic, New York, 1990).F. P. Schäfer (Ed.), Dye Lasers, 2nd Edition (Springer-Verlag, Berlin, 1990).

In order to fire a laser, the active gain medium must be changed into a state in which population inversion occurs. The preparation of this state requires an external energy source and is known as laser pumping. Pumping may be achieved with electrical currents (e.g. semiconductors, or gases via glow discharge) or with light, generated by or by other lasers (semiconductor lasers). More exotic gain media can be pumped by chemical reactions, nuclear fission, or with high-energy . Encyclopedia of laser physics and technology

---

Example of a model of gain medium The simplest model of optical gain in real systems includes just two, energetically well separated, groups of sub-levels. Within each sub-level group, fast transitions ensure that thermal equilibrium is reached quickly. Stimulated emissions between upper and lower groups, essential for gain, require the upper levels to be more populated than the corresponding lower ones. This situation is called population-inversion. It is more readily achieved if unstimulated transition rates between the two groups are slow, i.e. the upper levels are metastable. Population inversions are more easily produced when only the lowest sublevels are occupied, requiring either low temperatures or well energetically split groups.

In the case of Amplifier of optical signals, the lasing frequency is called signal frequency. If the externally provided energy required for the signal's amplification is optical, it would necessarily be at the same or higher pump frequency.

---

Cross-sections The simple medium can be characterized with effective cross-sections of absorption and emission at frequencies $~\backslash omega\_\{\backslash rm\; p\}~$ and $~\backslash omega\_\{\backslash rm\; s\}$.

• Have $~N~$ be concentration of active centers in the solid-state lasers.
• Have $~N\_1~$ be concentration of active centers in the ground state.
• Have $~N\_2~$ be concentration of excited centers.
• Have $~N\_1+N\_2=N$.

The relative concentrations can be defined as $~n\_1=N\_1/N~$ and $~n\_2=N\_2/N$.

The rate of transitions of an active center from the ground state to the excited state can be expressed like this: $~\; W\_\{\backslash rm\; u\}=\backslash frac\{I\_\{\backslash rm\; p\}\backslash sigma\_\{\backslash rm\; ap\}\}\{\; \backslash hbar\; \backslash omega\_\{\backslash rm\; p\}\; \}+\backslash frac\{I\_\{\backslash rm\; s\}\backslash sigma\_\{\backslash rm\; as\}\}\{\; \backslash hbar\; \backslash omega\_\{\backslash rm\; s\}\; \}\; ~$.

While the rate of transitions back to the ground state can be expressed like: $~W\_\{\backslash rm\; d\}=\backslash frac\{\; I\_\{\backslash rm\; p\}\; \backslash sigma\_\{\backslash rm\; ep\}\}\{\; \backslash hbar\; \backslash omega\_\{\backslash rm\; p\}\; \}+\backslash frac\{I\_\{\backslash rm\; s\}\backslash sigma\_\{\backslash rm\; es\}\}\{\; \backslash hbar\; \backslash omega\_\{\backslash rm\; s\}\; \}\; +\backslash frac\{1\}\{\backslash tau\}~$, where $~\backslash sigma\_\{\backslash rm\; as\}\; ~$ and $~\backslash sigma\_\{\backslash rm\; ap\}\; ~$ are effective cross-sections of absorption at the frequencies of the signal and the pump, $~\backslash sigma\_\{\backslash rm\; es\}\; ~$ and $~\backslash sigma\_\{\backslash rm\; ep\}\; ~$ are the same for stimulated emission, and $~\backslash frac\{1\}\{\backslash tau\}~$ is rate of the spontaneous decay of the upper level.

Then, the kinetic equation for relative populations can be written as follows:

$~\; \backslash frac\; .$

The dynamic saturation intensities can be defined:

$~\; I\_\{\backslash rm\; po\}=\backslash frac\{\backslash hbar\; \backslash omega\_\{\backslash rm\; p\}\}\{(\backslash sigma\_\{\backslash rm\; ap\}+\backslash sigma\_\{\backslash rm\; ep\})\backslash tau\}\; ~$, $~\; I\_\{\backslash rm\; so\}=\backslash frac\{\backslash hbar\; \backslash omega\_\{\backslash rm\; s\}\}\{(\backslash sigma\_\{\backslash rm\; as\}+\backslash sigma\_\{\backslash rm\; es\})\backslash tau\}\; ~$.

The absorption at strong signal: $~\; A\_0=\backslash frac\{ND\}\{\backslash sigma\_\{\backslash rm\; as\}+\backslash sigma\_\{\backslash rm\; es\}\}~$.

The gain at strong pump: $~\; G\_0=\backslash frac\{ND\}\{\backslash sigma\_\{\backslash rm\; ap\}+\backslash sigma\_\{\backslash rm\; ep\}\}~$, where $~\; D=\; \backslash sigma\_\{\backslash rm\; pa\}\; \backslash sigma\_\{\backslash rm\; se\}\; -\; \backslash sigma\_\{\backslash rm\; pe\}\; \backslash sigma\_\{\backslash rm\; sa\}\; ~$ is determinant of cross-section.

Gain never exceeds value $~G\_0~$, and absorption never exceeds value $~A\_0\; U~$.

At given intensities $~I\_\{\backslash rm\; p\}~$, $~I\_\{\backslash rm\; s\}~$ of pump and signal, the gain and absorption can be expressed as follows:

$~A=A\_0\backslash frac\{U+s\}\{1+p+s\}~$, $~G=G\_0\backslash frac\{p-V\}\{1+p+s\}~$,

where $~p=I\_\{\backslash rm\; p\}/I\_\{\backslash rm\; po\}~$, $~s=I\_\{\backslash rm\; s\}/I\_\{\backslash rm\; so\}~$, $~U=\backslash frac\{(\backslash sigma\_\{\backslash rm\; as\}+\backslash sigma\_\{\backslash rm\; es\})\backslash sigma\_\{\backslash rm\; ap\}\}\{D\}~$, $~V=\backslash frac\{(\backslash sigma\_\{\backslash rm\; ap\}+\backslash sigma\_\{\backslash rm\; ep\})\backslash sigma\_\{\backslash rm\; as\}\}\{D\}~$ .

---

Identities The following identities take place: $U-V=1\; ~$, $~\; A/A\_0\; +G/G\_0=1~.\backslash$

The state of gain medium can be characterized with a single parameter, such as population of the upper level, gain or absorption.

---

Efficiency of the gain medium The efficiency of a gain medium can be defined as $~\; E\; =\backslash frac\{I\_\{\backslash rm\; s\}\; G\}\{I\_\{\backslash rm\; p\}A\}~$.

Within the same model, the efficiency can be expressed as follows: $~E\; =\backslash frac\{\backslash omega\_\{\backslash rm\; s\}\}\{\backslash omega\_\{\backslash rm\; p\}\}\; \backslash frac\{1-V/p\}\{1+U/s\}~$.

For efficient operation, both intensities—pump and signal—should exceed their saturation intensities: $~\backslash frac\{p\}\{V\}\backslash gg\; 1~$, and $~\backslash frac\{s\}\{U\}\backslash gg\; 1~$.

The estimates above are valid for a medium uniformly filled with pump and signal light. Spatial hole burning may slightly reduce the efficiency because some regions are pumped well, but the pump is not efficiently withdrawn by the signal in the nodes of the interference of counter-propagating waves.

---

See also

• Population inversion
• Laser construction
• Laser science
• List of laser articles
• List of laser types

---

References and notes

---

External links

• Gain media Encyclopedia of Laser Physics and Technology

Categories: Laser Science

Post Comment