Laser Linewidth and Bandwidth Calculator

Analyze laser coherence properties and spectral characteristics with precision.

Calculate essential laser parameters including linewidth, bandwidth, coherence time, coherence length, and quality factor from your laser specifications.

Laser Examples

Click on any example to load typical laser specifications into the calculator.

Frequency-Stabilized HeNe Laser

stabilized

High-precision HeNe laser with frequency stabilization for interferometry and metrology applications.

λ: 632.8 nm

Δν: 1.00 kHz

n: 1.0

Single-Mode Diode Laser

diode

Typical single-mode semiconductor diode laser used in fiber optic communications and spectroscopy.

λ: 1550 nm

Δν: 10.00 MHz

n: 1.0

Free-Running Gas Laser

gas

Standard gas laser without stabilization, showing broader linewidth typical of free-running operation.

λ: 543.5 nm

Δν: 500.00 MHz

n: 1.0

Nd:YAG Laser

solid_state

Common solid-state laser used in industrial and scientific applications with moderate linewidth.

λ: 1064 nm

Δν: 100.00 MHz

n: 1.0

Other Titles
Understanding Laser Linewidth and Bandwidth: A Comprehensive Guide
Master the fundamental concepts of laser coherence, spectral properties, and bandwidth calculations essential for optical physics, laser spectroscopy, and precision measurements.

What is Laser Linewidth and Bandwidth?

  • Fundamental Concepts
  • Spectral Width Definition
  • Coherence Properties
Laser linewidth and bandwidth are fundamental parameters that characterize the spectral purity and coherence properties of laser light. Unlike broadband light sources that emit across a wide spectrum, lasers produce highly monochromatic light with a narrow spectral distribution. However, even the most stable lasers have some finite spectral width, which we call the linewidth. This parameter is crucial for applications requiring high spectral purity, such as precision interferometry, laser spectroscopy, and high-resolution optical measurements.
Understanding Spectral Width
The linewidth represents the frequency or wavelength range over which the laser's optical power is distributed. It's typically measured as the Full Width at Half Maximum (FWHM) of the laser's spectral profile. A smaller linewidth indicates higher spectral purity and better temporal coherence. The linewidth directly affects the laser's ability to maintain phase relationships over time and distance, which is essential for coherent optical processes.
Relationship to Coherence
Linewidth is inversely related to coherence time and coherence length. A laser with a narrow linewidth maintains its phase relationships for longer periods (longer coherence time) and over greater distances (longer coherence length). This relationship is fundamental to understanding how lasers behave in interferometric applications, holography, and precision measurements where phase stability is critical.
Physical Origins of Linewidth
Several physical mechanisms contribute to laser linewidth, including spontaneous emission noise, thermal fluctuations, mechanical vibrations, and electronic noise in the laser's driving circuitry. In gas lasers, collisional broadening and Doppler effects also play roles. Understanding these mechanisms helps in designing systems to minimize linewidth for applications requiring the highest spectral purity.

Typical Linewidth Ranges:

  • Ultra-stable laboratory lasers: 1 Hz - 1 kHz (extremely narrow)
  • Frequency-stabilized commercial lasers: 1 kHz - 100 kHz
  • Single-mode diode lasers: 100 kHz - 10 MHz
  • Free-running gas lasers: 10 MHz - 1 GHz
  • Multimode lasers: 1 GHz - 100 GHz (broad linewidth)

Step-by-Step Guide to Using the Calculator

  • Input Parameters
  • Measurement Considerations
  • Interpreting Results
This calculator provides comprehensive analysis of laser coherence properties from basic spectral measurements. Follow these guidelines to obtain accurate and meaningful results for your laser characterization needs.
1. Determining Center Wavelength
The center wavelength is the dominant wavelength of your laser's emission. This value can be found in your laser's specifications, measured with a spectrometer, or calculated from the laser's fundamental transition. For gas lasers, this corresponds to specific atomic or molecular transitions. For semiconductor lasers, it depends on the bandgap and cavity design. Enter this value in nanometers with appropriate precision.
2. Measuring or Specifying Linewidth
Linewidth can be measured using various techniques including Fabry-Perot interferometry, heterodyne detection, or delayed self-homodyne methods. If you don't have direct measurements, consult your laser's specifications or literature values for similar laser types. Remember that linewidth can vary with operating conditions, so ensure your value represents typical operating parameters.
3. Selecting Appropriate Refractive Index
The refractive index affects coherence length calculations and should match your measurement medium. Use 1.0 for air or vacuum measurements, 1.33 for water-based experiments, or the appropriate value for your optical medium. This parameter is crucial for accurate coherence length determination in interferometric applications.
4. Understanding Output Parameters
The calculator provides multiple related parameters: coherence time indicates how long phase relationships are maintained, coherence length shows the maximum path difference for interference, and quality factor quantifies the laser's spectral purity. Use these parameters to evaluate your laser's suitability for specific applications.

Measurement Techniques for Linewidth:

  • Fabry-Perot interferometry: High resolution, suitable for narrow linewidths
  • Heterodyne detection: Fast measurement, good for dynamic characterization
  • Delayed self-homodyne: Self-referencing, excellent for very narrow linewidths
  • Spectrum analyzer: Direct frequency domain measurement
  • Beat note analysis: Comparison with reference laser

Real-World Applications and Practical Considerations

  • Precision Interferometry
  • Laser Spectroscopy
  • Optical Communications
Understanding laser linewidth and bandwidth is essential for numerous high-precision optical applications. These parameters directly impact measurement accuracy, signal quality, and system performance across diverse fields.
Precision Interferometry and Metrology
In interferometric measurements, coherence length determines the maximum path difference that can be measured while maintaining fringe visibility. For LIGO gravitational wave detectors, extremely narrow linewidth lasers enable kilometer-scale interferometry. In precision manufacturing, coherence properties affect measurement accuracy in optical coordinate measuring machines and laser interferometers used for position feedback.
High-Resolution Spectroscopy
Laser linewidth fundamentally limits spectroscopic resolution. In Doppler-limited spectroscopy, the laser linewidth should be much smaller than the natural linewidth of the transition being studied. For sub-Doppler techniques like saturated absorption spectroscopy, narrow linewidth enables resolution of hyperfine structure and precise frequency measurements essential for atomic clocks and fundamental physics experiments.
Fiber Optic Communications
In coherent optical communication systems, laser linewidth affects phase noise and limits the achievable data rates. Dense wavelength division multiplexing (DWDM) systems require lasers with specific linewidth characteristics to prevent channel crosstalk. The linewidth also determines the effectiveness of dispersion compensation and the performance of advanced modulation formats.

Application-Specific Requirements:

  • Gravitational wave detection: < 1 Hz linewidth for kilometer-scale coherence
  • Atomic clocks: < 1 kHz for interrogating narrow atomic transitions
  • High-speed coherent communications: < 100 kHz for advanced modulation
  • Laser cooling and trapping: < 1 MHz for atomic manipulation
  • Industrial interferometry: < 10 MHz for precision manufacturing

Advanced Concepts and Measurement Techniques

  • Coherence Theory
  • Noise Contributions
  • Stabilization Methods
Advanced understanding of laser linewidth involves quantum mechanical and statistical considerations that govern the fundamental limits and practical measurements of laser coherence properties.
Quantum Limit and Schawlow-Townes Linewidth
The fundamental quantum limit of laser linewidth is given by the Schawlow-Townes formula, which predicts the minimum possible linewidth due to spontaneous emission. This quantum-limited linewidth is proportional to the square of the laser frequency and inversely proportional to the output power. Real lasers typically have linewidths much broader than this quantum limit due to technical noise sources.
Technical Noise Sources
Practical laser linewidths are dominated by technical noise including current noise in the pump source, thermal fluctuations affecting the cavity length, mechanical vibrations, and acoustical disturbances. Each noise source contributes to frequency fluctuations that broaden the effective linewidth. Understanding these contributions is essential for designing low-noise laser systems.
Active Stabilization Techniques
Modern narrow-linewidth lasers employ sophisticated stabilization schemes including Pound-Drever-Hall locking to high-finesse cavities, atomic or molecular references, and electronic feedback systems. These techniques can reduce linewidths by several orders of magnitude below the free-running value, enabling applications requiring exceptional frequency stability.

Stabilization Methods and Achievable Linewidths:

  • Pound-Drever-Hall cavity stabilization: 1 Hz - 1 kHz
  • Atomic reference stabilization: 10 Hz - 100 Hz
  • Electronic servo systems: 1 kHz - 1 MHz reduction
  • Temperature stabilization: Factor of 10-100 improvement
  • Vibration isolation: Reduces mechanical coupling by 100x

Mathematical Relationships and Calculations

  • Coherence Time Formula
  • Coherence Length Calculation
  • Quality Factor Definition
The mathematical relationships governing laser coherence provide quantitative tools for analyzing and predicting laser performance in various applications. These formulas connect measurable quantities to fundamental physical parameters.
Coherence Time Calculation
Coherence time (τc) is inversely related to linewidth: τc = 1/(π × Δν), where Δν is the FWHM linewidth in Hz. This represents the time scale over which the laser maintains its phase relationships. Longer coherence times enable longer integration times in precision measurements and are essential for applications requiring stable phase references over extended periods.
Coherence Length Formula
Coherence length (Lc) is given by: Lc = c × τc / n = c / (π × Δν × n), where c is the speed of light and n is the refractive index of the medium. This represents the maximum path difference over which interference fringes remain visible. In practical terms, it determines the maximum unequal-arm interferometer length that can be used.
Quality Factor and Finesse
The quality factor Q = ν0/Δν, where ν0 is the center frequency, quantifies the spectral purity of the laser. Higher Q values indicate more monochromatic light. This parameter is analogous to the finesse of an optical cavity and provides a dimensionless measure of laser coherence quality that can be compared across different wavelengths.

Practical Calculation Examples:

  • HeNe laser (1 kHz linewidth): Coherence time = 318 μs, Coherence length = 95 km
  • Diode laser (10 MHz linewidth): Coherence time = 32 ns, Coherence length = 9.5 m
  • Quality factor for 632.8 nm laser with 1 kHz linewidth: Q = 4.7 × 10¹¹
  • Wavelength linewidth conversion: Δλ = λ² × Δν / c