Laser Linewidth Calculator - Schawlow-Townes Hz Output

A laser linewidth calculator turns the fundamental wavelength, the cold-cavity linewidth Gamma, and the output power P into the FWHM of the optical spectrum using the Schawlow-Townes formula. Photonics students, laser engineers, and spectroscopy technicians reach for it to compare a measured laser against a manufacturer specification, predict coherence length, or convert a wavelength bandwidth from a diode data sheet into the frequency bandwidth their locking electronics actually see.

• • Predict coherence length: feed the linewidth into the inverse formula to estimate how far the laser stays phase-coherent.
• • Compare to a manufacturer spec: type the listed cavity linewidth and rated power to confirm a real He-Ne, diode, or fibre laser meets its kHz or MHz claim.
• • Convert wavelength bandwidth to frequency: supply Delta lambda from a data sheet to recover the THz or GHz frequency bandwidth.
• • Plan a photonics homework set: plug textbook values of lambda, Gamma, and P into the form for a clean numerical answer.

A real laser always emits a small range of frequencies, and the Schawlow-Townes formula expresses the lower bound as Delta nu = pi h nu Gamma squared divided by P. Doubling the cavity linewidth, the fundamental frequency, or halving the output power all widen the linewidth, which is why high-power narrow-linewidth sources pair a low-loss cavity with a long wavelength.

When the laser also has to be ranked against other sources by perceived brightness rather than linewidth, laser brightness calculator turns the same power and wavelength into a radiance and photopic comparison.

The form reads the wavelength, cavity linewidth, output power, and optional wavelength bandwidth, converts every value into SI base units, and evaluates the Schawlow-Townes formula and the wavelength-to-frequency bandwidth relation side by side. The result panel returns the FWHM linewidth, the fundamental frequency, the photon energy, and the converted frequency bandwidth.

• Delta nu: Laser linewidth (FWHM), reported in Hz, kHz, MHz, or GHz.
• h: Planck constant, 6.626e-34 J*s.
• nu: Fundamental frequency in vacuum, computed as c divided by the input wavelength.
• Gamma: Cold-cavity linewidth (FWHM of the passive resonator), in Hz to THz.
• P: Output power of the single laser mode in microwatts to kilowatts.

The wavelength-bandwidth converter is independent of the linewidth row and uses Delta nu = c / (lambda - Delta lambda / 2) - c / (lambda + Delta lambda / 2). The photon energy row uses h times nu, so the panel always shows a consistent energy per photon.

According to Omni Calculator Laser Linewidth, the laser linewidth equation is Delta nu = pi h nu Gamma^2 / P, and a He-Ne laser with P = 1 W, Gamma = 1 GHz, and lambda = 632.8 nm produces a linewidth of 0.9862 Hz.

Once the linewidth is in hand, the angular spread of the same beam at the target is the next number the optical design needs, and laser beam divergence calculator returns that divergence from two measured beam diameters and a distance.

Four ideas sit behind the laser linewidth formula and the bandwidth converter; each explains a piece of the result panel without leaning on quantum jargon.

These four ideas are independent, so a single page can hold both the Schawlow-Townes physics and the wavelength-bandwidth conversion. If Gamma grows but the FWHM shrinks, you probably typed a smaller cavity unit and the formula is still correct.

The phase diffusion that drives the Schawlow-Townes formula is a property of the underlying harmonic wave, and harmonic wave equation calculator is the right tool when a homework set needs the y(x,t) field that produces the measured spectrum.

Six short steps take you from a datasheet or measurement to the laser linewidth in hertz plus the wavelength-bandwidth conversion.

1. 1 Type the laser wavelength: Enter the fundamental wavelength. Use 632.8 nm for He-Ne, 1550 nm for telecom, or 1064 nm for Nd:YAG.
2. 2 Pick the wavelength unit: Nanometres for visible and near-IR lasers, micrometres for mid-IR, or millimetres for terahertz sources.
3. 3 Enter Gamma: Use the FWHM of the passive resonator from the data sheet or a ringdown measurement.
4. 4 Type P: Enter the output power of the single laser mode in microwatts to kilowatts.
5. 5 Enter Delta lambda: Optional. Type the wavelength bandwidth from the data sheet; set to 0 to skip.
6. 6 Read the panel: The primary output is the FWHM linewidth in Hz, kHz, MHz, or GHz; secondary rows show frequency, photon energy, and converted bandwidth.

Type 632.8 nm and pick nanometres. Enter 1 for the cavity linewidth and pick GHz, then 1 for output power and pick watts. Leave Delta lambda at 1 nm. The panel reports 0.9862 Hz linewidth and a 0.75 THz bandwidth for the 1 nm bandwidth at 632.8 nm.

Before recording the cavity linewidth and output power that feed this form, most labs resize the beam with a Galilean or Keplerian telescope, and laser beam expander calculator returns the expander magnification and the new output diameter.

Five concrete benefits show up when this laser linewidth calculator sits next to a measurement or a data sheet.

• • Skip the algebra: The page handles the unit conversions, the pi h factor, the Gamma squared scaling, and the bandwidth conversion in one pass.
• • Auto-scaled output units: The primary FWHM is reported in Hz, kHz, MHz, or GHz depending on magnitude, so 0.98 Hz and 19.7 kHz both display as readable numbers.
• • Two calculators in one page: The same form covers both the Schawlow-Townes linewidth and the wavelength-to-frequency bandwidth conversion.
• • Cross-checked against Omni Calculator examples: Three worked examples match the Omni He-Ne, red pointer, and He-Cd cases so the result panel can be trusted.
• • Useful secondary outputs: Fundamental frequency and photon energy ride alongside the linewidth, so the same form answers both how wide the spectrum is and how energetic each photon is.

These benefits show up most clearly during the early stages of an optics experiment, when you need to know whether a candidate laser will satisfy the linewidth budget of a spectroscopy or interferometry setup.

If the linewidth is being optimised for an imaging or LIDAR application, the same wavelength and aperture set a Rayleigh limit that angular resolution calculator converts into a two-point resolution in radians.

Four factors set the linewidth, plus two limitations to keep in mind when comparing to a measurement or data sheet.

• • The Schawlow-Townes formula is the quantum lower bound for an ideal laser with no extra noise sources, so any real linewidth that comes out smaller than the result is unphysical and points to a mistyped Gamma or P.
• • The wavelength-to-frequency conversion assumes Delta lambda is much smaller than lambda; if Delta lambda approaches lambda, the formula can report a large or unstable bandwidth.

These factors are independent, so cleaning up the cavity, raising the output power, and shifting to a longer wavelength can be combined in a single optimization pass. When the measured linewidth still sits above the prediction, the gap is usually driven by technical noise such as current ripple or acoustic pickup.

According to RP Photonics Linewidth, the linewidth of a laser is the width (typically the full width at half-maximum) of its optical spectrum, and the Schawlow-Townes equation sets the quantum-noise-limited lower bound as Delta nu = pi h nu Delta nu_c squared divided by P_out.

According to NIST CODATA Speed of Light, the speed of light in vacuum is exactly 299 792 458 m/s and is used to convert the He-Ne 632.8 nm line into a frequency of 473.755 THz.

When a residual gap between the predicted and measured linewidth traces back to mechanical vibration on the cavity mount, the natural frequency of the offending resonance is the next thing to identify, and vibration natural frequency calculator returns that natural frequency from the mass and stiffness of the mount.