7.2 Gain and feedback in semiconductor lasers

Gain and feedback are crucial for semiconductor lasers to function. These processes allow light amplification and sustained lasing. We'll explore how optical gain is achieved, the conditions for lasing, and the role of cavity structures in shaping laser output.

Laser resonators and cavity modes determine the laser's output characteristics. We'll examine different resonator designs, from simple Fabry-Perot to more complex DFB and DBR structures. Understanding these concepts is key to grasping how semiconductor lasers work and their applications.

Gain and Threshold

Optical Gain in Semiconductor Lasers

Top images from around the web for Optical Gain in Semiconductor Lasers

• 

  Frontiers | Single-Mode Semiconductor Nanowire Lasers With Coupled Cavities View original

  Is this image relevant?

• 

  Dominant factors limiting the optical gain in layered two-dimensional halide perovskite thin ... View original

  Is this image relevant?

• 

  Frontiers | Single-Mode Semiconductor Nanowire Lasers With Coupled Cavities View original

  Is this image relevant?

• 

  Dominant factors limiting the optical gain in layered two-dimensional halide perovskite thin ... View original

  Is this image relevant?

1 of 2

Top images from around the web for Optical Gain in Semiconductor Lasers

• 

  Frontiers | Single-Mode Semiconductor Nanowire Lasers With Coupled Cavities View original

  Is this image relevant?

• 

  Dominant factors limiting the optical gain in layered two-dimensional halide perovskite thin ... View original

  Is this image relevant?

• 

  Frontiers | Single-Mode Semiconductor Nanowire Lasers With Coupled Cavities View original

  Is this image relevant?

• 

  Dominant factors limiting the optical gain in layered two-dimensional halide perovskite thin ... View original

  Is this image relevant?

1 of 2

• Optical gain occurs when stimulated emission exceeds absorption in a semiconductor material
• Achieved by injecting current into the active region of the laser diode
• Current injection increases the carrier density, leading to population inversion
• Population inversion is a condition where more electrons are in the excited state than the ground state
• Optical gain is proportional to the difference between the quasi-Fermi levels of the conduction and valence bands
• Higher current injection leads to higher optical gain until saturation occurs (gain saturation)

Threshold Current and Lasing Conditions

• Threshold current is the minimum current required for a laser diode to start lasing
• At threshold, the optical gain equals the total losses in the laser cavity (mirror losses and internal losses)
• Lasing occurs when the round-trip gain is greater than or equal to the round-trip losses
• Round-trip gain depends on the optical gain and the length of the active region
• Round-trip losses include mirror losses (determined by the reflectivity of the laser facets) and internal losses (absorption and scattering)
• Threshold current depends on factors such as the material properties, cavity design, and operating temperature

Mode Competition and Gain Saturation

• Mode competition occurs when multiple cavity modes compete for the available gain in the laser cavity
• Each mode experiences different gain and loss, depending on its wavelength and spatial distribution
• Modes with higher gain and lower loss will dominate and suppress other modes (mode suppression)
• Gain saturation occurs when the optical gain decreases with increasing photon density in the cavity
• At high photon densities, the gain medium becomes depleted, limiting the maximum output power of the laser
• Gain saturation affects the dynamic behavior of the laser, such as the modulation response and noise characteristics

Laser Resonator Structures

Fabry-Perot Resonator

• Fabry-Perot resonator is the simplest type of laser cavity, consisting of two parallel mirrors
• One mirror is highly reflective (rear mirror), while the other is partially transmissive (output coupler)
• Light bounces back and forth between the mirrors, amplifying the optical signal
• Resonance occurs when the round-trip phase shift is an integer multiple of 2π
• Fabry-Perot lasers have multiple longitudinal modes, determined by the cavity length and refractive index
• Advantages include simple fabrication and low cost, but they suffer from mode instability and broad linewidth

Distributed Feedback (DFB) Laser

• DFB lasers have a periodic structure (grating) embedded in the active region
• The grating provides optical feedback and wavelength selectivity
• Light is scattered by the grating, creating a standing wave pattern in the cavity
• DFB lasers operate in a single longitudinal mode, determined by the grating period and effective refractive index
• Advantages include stable single-mode operation, narrow linewidth, and high output power
• Widely used in optical communication systems and sensing applications

Distributed Bragg Reflector (DBR) Laser

• DBR lasers have separate gain and reflector sections
• The gain section provides optical amplification, while the reflector section acts as a wavelength-selective mirror
• The reflector section contains a Bragg grating, which reflects light at a specific wavelength
• DBR lasers offer single-mode operation and wavelength tunability
• Tuning is achieved by adjusting the refractive index of the reflector section (using current injection or temperature control)
• Advantages include high output power, narrow linewidth, and wide wavelength tuning range
• Used in wavelength-division multiplexing (WDM) systems and tunable laser applications

Laser Cavity Modes

Cavity Modes and Resonance Conditions

• Cavity modes are the allowed electromagnetic field distributions in a laser resonator
• Determined by the boundary conditions imposed by the cavity geometry and refractive index
• Resonance occurs when the phase shift accumulated over a round trip is an integer multiple of 2π
• The resonance condition is given by: $2L = mλ/n$, where $L$ is the cavity length, $m$ is an integer, $λ$ is the wavelength, and $n$ is the refractive index
• Cavity modes are characterized by their frequency, wavelength, and spatial distribution
• The frequency spacing between adjacent modes is called the free spectral range (FSR), given by: $FSR = c/(2nL)$, where $c$ is the speed of light

Longitudinal Modes

• Longitudinal modes are cavity modes that differ in their propagation direction along the cavity axis
• Characterized by the number of half-wavelengths that fit within the cavity length
• The wavelength of each longitudinal mode is given by: $λ_m = 2nL/m$, where $m$ is the mode number
• The frequency of each longitudinal mode is given by: $f_m = mc/(2nL)$
• Longitudinal modes are separated by the FSR in frequency domain
• The number of longitudinal modes depends on the gain bandwidth of the laser medium and the cavity length
• Single-mode lasers (DFB, DBR) have only one dominant longitudinal mode, while multi-mode lasers (Fabry-Perot) have multiple longitudinal modes

Transverse Modes

• Transverse modes are cavity modes that differ in their spatial distribution perpendicular to the cavity axis
• Characterized by the intensity profile and the number of nodes in the transverse plane
• Described by the transverse mode indices (p, q) for rectangular cavities or (l, m) for circular cavities
• The fundamental transverse mode (TEM00) has a Gaussian intensity profile and the lowest diffraction loss
• Higher-order transverse modes have more complex intensity profiles and higher diffraction losses
• The number of supported transverse modes depends on the cavity geometry and the Fresnel number ($N_F = a^2/(λL)$, where $a$ is the cavity aperture size)
• Single-mode lasers have a small cavity aperture and operate in the fundamental transverse mode, while multi-mode lasers have a larger aperture and support multiple transverse modes
• Transverse mode control is important for beam quality, focusing, and coupling efficiency in applications such as fiber optics and laser material processing