Optical Cavity

Optical Gain

The photons released by stimulated emission can cause further stimulations as long as there is population inversion. This process is called optical gain. 只要存在粒子数反转，由受激发射释放的光子就能进一步引发更多的受激发射。这一过程被称为Optical Gain。

The gain obtained in a single travel in the active region is small. 在有源区内单次传播获得的增益很小。

To increase the optical gain, multiple passes of a wave must occur. This can be achieved by an optical cavity which is essentially a resonant cavity in which the photons have multiple reflections. 为了增加光学增益，光波必须进行多次传播。这可以通过光学腔体来实现，光学腔体本质上是一个谐振腔，光子在其中进行多次反射。

For semiconductor lasers, the most widely used cavity is the Fabry-Perot cavity. 对于半导体激光器，最广泛使用的腔体是法布里-佩罗谐振腔。

Fabry-Perot Cavity

• (a) A typical laser structure showing the Fabry-Perot cavity. 展示法布里-佩罗谐振腔的典型激光结构。
  • The Fabry-Perot Cavity is formed by mirrored surfaces on two sides (left and right). The other two sides (front and back) are roughened. 法布里-佩罗谐振腔由两侧（左侧和右侧）的镜面形成，其他两侧（前侧和后侧）粗糙。
• (b) The stationary states of the cavity. 谐振腔的稳定状态。
  • The photons to be emitted towards these mirrored sides are multiple reflected back. Photons at resonant modes are allowed to build up through stimulated emission. 光子向这些镜面发射时会被多次反射。光子在谐振模式下通过受激辐射积累。
• (c) The variation of refractive index (or dielectric constant) responsible for optical confinement. 负责光限制的折射率（或介电常数）的变化。

Resonant Modes

• Resonant modes are those for which integer multiple half wavelength of the light in the cavity equals the length of the cavity:orwhere:
  • is an integer
  • is the cavity length
  • is the refractive index of the cavity
  • is the light wavelength
• Many values of can satisfy the resonance condition but only those within the spontaneous emission spectrum will be produced. 许多  的值可以满足谐振条件，但只有波长在自发辐射光谱内的会被产生。
• Due to optical loss, only the strongest can survive. 由于光损耗，只有最强的可以留存
• The separation between the allowed modes in the longitudinal (propagating) direction is the difference in the wavelengths corresponding to and .
  • It can be obtained by differentiating and is expressed as
  • Although is a function of but the change is very small. . Therefore,