Precise Metrology Measurements using Spectroscopy and Coherence-Tailored Diode Lasers

Topics Covered

Introduction into Precision Metrology
Linewidth and Coherence
    Coherence Length Measurements
    What Influences the Coherence Length?
    Coherence Control of Diode Lasers
    Lowest Coherence
Laser Spectroscopy
    Application Example: Ultra-Precise Spectroscopy
    Application Example: Optical Pumping of Helium-3

Introduction into Metrology

Metrology, the science of measurement, is one of the oldest branches of science. For example, time was measured by tracking the movements of the moon and the sun over the horizon before the birth of modern technology. This allowed people to establish the best time to plant and harvest crops and prepare for the coming winter.

Figure 1. Stonehenge is a famous example of the value that ancient civilizations placed on the measurement of times passage.
Vicky Jirayu | Shutterstock

Time and seasonality was of such high importance almost all cultures had their own religious sites dedicated to the celestial bodies, the moon and the sun, that displayed the passage of time. In more recent history accurate clocks were developed when it was realized that the accurate measurement of time is required for navigation.

In the present, highly accurate measurements of time and frequencies uses trapped ions or cold atoms to provide length and time standards and to enhance the resolution of global positioning systems (GPS). Fundamental constants such as the Rydberg constant or the fine structure constant are determined using these measurements.

Rotations and gravity can be measured using atom interferometers with excellent accuracy. These instruments can be used to find natural resources, to study volcano eruptions and earthquakes, and to test earth tide models and more.

Figure 2. An antique atomic clock.
karenfoleyphotography | Shutterstock


Spectroscopic gas analysis can be used to track the flow of gases. Isotope ratio determination can be used to measure pollution and advanced laser-based techniques can be used for trace gas analysis.

Here, we explore how coherent, narrow-linewidth lasers and laser optimization in spectroscopy can be used to add to the precision that is required for modern metrology.

Linewidth and Coherence

In the context of laser physics, two different properties of coherence can be described, i.e. spatial and temporal coherence. Whereas temporal coherence refers to the time at which the wave’s phase is considerably altered.

The coherence length refers to the propagation length that occurs during this time. Spatial coherence represents the distance between two points of a wave, and these points impede with one another over the wave. The focusability of a laser beam is dependend on the spatial coherence. Low spatial coherence is required in confocal microscopy to prevent speckle patterns (Figure 3).

Figure 3. Some laser imaging methods like confocal microscopy require a low spatial coherence, in order to avoid speckle patterns.

When the range of frequencies is large in a given wave, the phase correlation will be lost equally faster. Both the coherence length and the linewidth, Δv, are inversely proportional to one-another. In the case of a rectangular emission spectrum the coherence length lc is given by:

Where, c represents the speed of light and Δv represents the full width half maximum of the laser linewidth.

The coherence length in the case of a Gaussian spectral distribution is given by:

In SI units this gives a coherence length of around 132 m divided by the linewidth in MHz in practical units. It must be noted that that Equation 2 is independent from the absolute wavelength.

Considering the case of  a 405 nm violet diode laser's emission spectrum (Figure 4). The spectrum has a halfwidth of 0.5 nm or 900 GHz due to lack of frequency stabilization. Therefore, the coherence length is determined to be roughly 150 µm.

Figure 4. Typical emission spectrum of a violet laser diode, recorded with a grating spectrometer.

In cases were an external-cavity configuration is used for a diode laser, the diode’s spectrum is significantly narrowed by the diffraction grating. This results in a coherence length above 100 m for a linewidth of 1 MHz (i.e. 0.0005 µm). The grating changes the coherence properties by nearly six orders of magnitude.

However, it is not possible to universally implement this approach and the intermediate range has been considered as a major gap in the coherence length spectrum of lasers. Specifically, it has been difficult to obtain coherence lengths in the millimeter to 50 m range. This following methods demonstrate several technologies to close this inherent gap, and to expand the coherence length spectrum to relatively shorter and longer values.

Coherence Length Measurements

There is no universal method to determine either coherence lengths or laser linewidths. One method, delayed self-heterodyne measurement, is a suitable option for narrow laser lines ranging from 100 kHz to 100 MHz (Figure 5).

Figure 5. Delayed self-heterodyne linewidth measurement.

Using this method the laser that is being measured's output beam is divided into two probe beams. One of these probe beams is then frequency-shifted and combined into a fiber delay using an acousto-optical modulator. The beams are then re-combined and a fast photo diode is used to detect the beat-signal. The output of the photo diode is linked to an RF spectrum analyzer.

Variations in frequency within the delay time contribute to the beat note, which has a width of roughly double the lasers linewidth. This technique can be easily implemented as it allows short measurement times and does not require laser stabilization or moving components. Toptica uses dual set-ups with single-mode fiber delays of 1 km and 20 km. This enables a linewidth assessment on time scales of 5 µs to 100 µs.

However, this technique fails to give data regarding the long-term linewidth and is also limited as the coherence length must be shorter than the fiber delay. Measurements can still be performed if this is not the case but data interpretation of the beat signal becomes more inherently complex and requires intensive data processing.

A scanning Fabry-Perot interferometer (FPI) can be used to define wider spectral profiles (Figure 6).

Figure 6. Scanning Fabry-Perot interferometer (FPI).

FPIs that are commercially available in the market have a finesse of 100 to 1000, and free spectral ranges from several 100 MHz to 10 GHz. FPIs are perfect for measuring laser linewidths in the MHz to GHz range.

However, the FPI also has some limitations. When the laser line begins to fragment into multiple longitudinal modes, which tends to occur for lasers with frequencies in the GHz range, the FPI does not accurately assess the spacing of the different modes, meaning they may appear superimposed.

For these situtations the coherence length can be directly determined with a Michelson interferometer. This coherence length then corresponds with the path length difference, at which point the fringe visibility contrast reduces to one half of its initial value. The measurement’s resolution and range are depends on the design of the interferometer design.

A simple lab setup can also be used to assess coherence lengths from 100 µm to 100 cm. This approach can be applied to multi-mode lasers, although the fringe contrast no longer shows a monotonous decrease.

A grating spectrometer can be used to assess lasers with a spectral width between 50 to 100 µm .

The time scale of the measurement should always be stated for laser linewidth specifications. This is because frequency fluctuations that are relatively faster than the rate of measurement add to the laser's linewidth, whereas slower processes will induce a frequency drift between consecutive measurements.

What Influences the Coherence Length?

The Schawlow-Townes formula can be used to acquire the coherence length of a laser. This coherence length is proportional to the output power, which is divided by the square of the cavity round-trip time. Different sources of noise often make it difficult to achieve this limit.

In case the noise is the result of spontaneous emission, then low resonator losses, a long resonator length and a high intracavity power will augment the coherence length, resulting in a decreased laser linewidth. When a diode laser is used for practical applications, coupling between phase noise and intensity, technical excess noise and drift factors further affect the coherence.

Air, humidity, pressure, temperature drifts as well as piezo creep, in the case of external-cavity lasers, induce long-term drifts which range from seconds to hours (Figure 7). Acoustic perturbations and current noise impact the laser’s linewidth on a time scale of µs or ms.

Figure 7. Influences on the coherence of an external-cavity diode laser and their respective time scale.

It is important to perform efficient coherence control on the right timescale, or to put it simply, the bandwidth is integral to linewidth broadening and narrowing concepts. Diode lasers can directly apply high frequency electric fields to the laser chip, unlike other types of lasers.

Table 1 shows some examples of laser coherence lengths.

Table 1. Typical examples of laser coherence lengths.

Laser Type Typical coherence length
Lamp pumped Nd:YAG 1 cm
HeNe (non-stabilized) 20 cm
HeNe (stabilized) 1 km
Argon/Krypton 1 cm
Argon/Krypton + Etalon 1 m
Dye Laser 5 .. 250 m
Fiber Laser (non-stabilized) 50 µm
Fiber Laser (stabilized) 100 km
Free running diode laser < 1mm
External-cavity diode laser 100 .. 1000 m

Coherence Control of Diode Lasers

It is possible to use diode lasers in a wide range of configurations. Free-running diodes with no spectrally selective means can be used in applications where spectral control is not required. Some examples include flow cytometry, laser microscopy, microlithography and disc mastering.

Despite their short coherence length diode lasers are sensitive to a phenomenon called “fringe revival” that is related to the non-monotonous fringe visibility decrease of laser light composed of a plurality of longitudinal modes. After some distance, the fringes appear again and promote speckle effects and unwanted interference. This occurs due to constructive interference between the independent modes. This issue can be overcome by using TOPTICA’s electronic speckle killer. This device comes as an option for the industrial-grade diode laser modules that are part of the iBeam smart series (Figure 8).

Figure 8. iBeam smart 405 – ultra-compact diode laser with upto 300 mW output and 150 µm coherence length.

When there is a need for spectral tunability and single frequency emission, grating-stabilized external-cavity geometries are used. The coherence gain, from spectral filtering using a grating, covers up to six orders of magnitude. Over the years, higher coherences have had to be compromised for output power.

The BlueMode technology, that was developed by Toptica’s engineers, is capable of delivering up to 50 mW output from a blue-violet diode laser (Figure 9). The technology allows a coherence length which is greater than 25 m with single-line emission. Table 2 shows the linewidth, output power, and coherence length of Toptica’s blue-violet diode lasers.

Figure 9. TopMode: High-power diode laser with high coherence (405 nm, 50 mW, > 25 m)

Table 2. Typical linewidth, coherence length and output power of TOPTICA’s blue-violet diode lasers.

Laser Linewidth Coh. Length Power
iBeam 900 GHz 150 µm up to 300 mW
TopMode < 5 MHz > 25 m 50 mW
TA-SHG pro < 2 MHz 65 m up to 100 mW

Lowest Coherence

The gain profile of a diode laser restricts its spectral width at the distant end of the scale. Superluminescent LEDs (SLEDs) are the spectrally broadest diodes. They provide a spectral width of up to 50 nm spectral , which matches with a coherence length on the scale of 10 µm. Optical coherence tomography (OCT) applications use SLEDs where increased an spatial resolution is achieved through a low temporal coherence.

In cases where this spectral width is inadequate ultrafast pulsed lasers can be used to produce a supercontinuum. It was observed that a feasible coherence spectrum of semiconductor lasers spans over 12 orders of magnitude, setting new records in terms of frequency resolution and spectrally broad violet diodes. This means, precision analyses of hydrogen transitions, laser-based imaging, and other similar applications can now be carried out easily.

Laser Spectroscopy

Spectroscopy techniques are used extensively to study the molecular constituents of gases. When a laser is transmitted through a gas its  frequency is changed and its intensity is reduced. The laser frequencies which are absorbed correspond to particlular atomic and molecular species, and the depth of the absorption is related to the molecular or atomic gas’s density. It is possible to determine a gases composition and the partial density of individual components of the gas. In addition, high-resolution spectroscopy of molecules and atoms can be used to analyze their internal structures.

Toptica supplies industrial, and research-grade lasers at different wavelengths for spectroscopic applications (Figure 10).

Figure 10. TOPTICAs tunable lasers are ideal tools for spectroscopic applications.


The company develops tunable lasers for almost every wavelength spanning from 200 to 3500 nm. The linewidth of the lasers can also be customized to suit the needs of different spectroscopic applications. Toptica provides the widest wavelength coverage for research-grade diode lasers.

Application Example: Ultra-Precise Spectroscopy

Metrology, quantum optics, and precision spectroscopy demand narrow laser linewidths. Forbidden transitions between atomic energy levels exhibit halfwidths between several Hz and kHz. The 243 nm 1s to 2s transition of hydrogen is an excellent example of this. Hydrogen gas exhibits a natural linewidth of 1.3 Hz.

One way to match these narrow lineshapes is to ensure that the laser’s linewidth is a few decades smaller than the external-cavitysystems. Toptica’s FALC 110 is a fast analogue linewidth control module, and the Digilock 110 is its digital counterpart (Figure 11). A PID regulator with a 10 MHz bandwidth is integrated into these control modules to regulate the driver current of anexternal-cavity laser diode.

Figure 11. DigiLock 110 and FALC 110: modules for linewidth narrowing.

Scientists at the Max Planck Institute for Quantum Optics have successfully used the FALC 110 module to decrease the linewidth of a 972 nm diode laser to 0.5 Hz. This gives a coherence length of 664,000 km, i.e. two thirds of the distance between the Earth and the Moon.

Application Example: Optical Pumping of Helium-3

Experiments such as the optical pumping or molecular spectroscopy of Doppler-broadened gases have absorption signatures that are several hundreds of MHz wide. In these cases an artificially broadened laser linewidth is required, which is difficult to achieve with diode lasers. This is because free-running diodes are relatively broad, while the external-cavity equipment is spectrally too narrow.

When the amplitude of the modulation is changed using a coherence control unit, the laser linewidth can be adjusted accurately. Thus, laser linewidths in the GHz range can be achieved as linewidths without  any major measurable broadening. This makes it possible to match a diode laser’s spectral profile to a specified absorption profile, whilst the laser continues to stay tuned to the resonance frequency.

Using a set up such as this the magnetic resonance imaging of human lungs usingspin-polarized Helium-3 gas is possible (Figure 12).

Figure 12. In vivo image of a human lung, recorded with magnetic resonance tomography using spin-polarized Helium-3.

Helium-3 has ½ nuclear spin and a result it carries a magnetic moment. When the small nuclear magnets are aligned, the gas turns magnetic, allowing hte in vivo imaging of internal airway and lung structure. Through this approach, smoking-induced defects can be detected, the gas inflow via the bronchi and trachea can be visualized and oxygen concentrations within the lungs can be determined.


This information has been sourced, reviewed and adapted from materials provided by Toptica Photonics.

For more information on this source, please visit Toptica Photonics.

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