Wavelength stabilisation method and apparatus

Abstract

A wavelength stabilisation method and system. The wavelength stabilisation method comprises setting an desired wavelength of the laser, passing the laser through a gas cell containing a gas, measuring the intensity of the laser through the gas, altering the desired wavelength of the laser and repeating the passing and measuring steps through a range of desired wavelengths to obtain a set of stabilising intensity measurements, wherein the stabilising intensity measurements comprise an intensity gas line associated with the gas contained in the gas cell. The method further comprises converting the set of stabilising intensity measurements into a set of absorption measurements comprising an absorption gas line, determining a stabilising peak value of the absorption gas line, determining an absorption offset based on the stabilising peak value and an desired peak value, and tuning the wavelength of the laser based on the absorption offset.

Description

[0001] WAVELENGTH STABILISATION METHOD AND APPARATUS

[0002] Technical Field

[0003] Embodiments described herein relate to methods and apparatus for stabilising a wavelength, and in particular for stabilising a wavelength of a laser or laser diode.

[0004] Background

[0005] Wavelength stabilisation techniques may be used to reduce or avoid fluctuations in emission wavelength for a laser or laser diode. Wavelength stabilisation is commonly used in many fields using lasers, as many components forming an optical system may have a wavelength dependent characteristic such as transmission or isolation. An example of a field in which wavelength stabilisation is widely used is interferometry. In interferometry, measurements may be inherently linked to laser emission wavelength, and hence it is desirable to reduce any unintentional deviation in laser emission wavelength.

[0006] In known wavelength stabilisation processes, a fixed feature is identified or created within the bandwidth of laser emission, for example a feature such as an absorption line or an interference feature such as an optical cavity. Methods for detecting or creating such a feature include the use of an optical cavity, the specific use of a Fabry-Perot etalon optical cavity, the use of an atomic absorption reference. Molecular absorption references include probing an atomic element in a gaseous state using an optical beam and determining the energies absorbed by the gas; these excitation energy levels may be determined as absorption features or gas lines. These detection methods may then generate an error signal that is analysed and combined with an active feedback system that controls one or more laser parameters, or mechanical components, to lock the laser emission wavelength to the selected reference feature.

[0007] Known wavelength stabilisation techniques may be suitable for laser wavelength modulation covering zero to low wavelength modulation cases. That is, known wavelength stabilisation techniques may be suitable for cases in which modulation depths are below the order of a standard absorption linewidth. Modulation depth refers to a maximum change in absorption or reflectance which can be induced by incident light with a given wavelength. However, such wavelength stabilisation techniques may not be suitable within wider wavelength modulation regimes. An example regime which may use wider wavelength modulation is Range-Resolved Interferometry (RRI). RRI may be suitable for wide-modulation scenarios, where the modulation depth is several orders of magnitude greater than standard references (e.g. GHz). RRI uses a widely-wavelength modulated laser diode with a modulation amplitude at least an order of magnitude higher than the linewidth of existing frequency references. In RRI, a wider modulation depth results in increased spatial resolution of optical path differences and as with most laser interferometric techniques, the emission frequency / wavelength of the laser diode inherently affects any measurements made. RRI has previously been applied to fibre-optic strain, shape sensing, multi-surface vibrometry, multi-dimensional optical encoding and gas sensing.

[0008] However, there is a lack of stabilisation techniques suitable for use in RRI. For precision techniques such as range-resolved interferometry (RRI) that typically use very large wavelength modulation amplitudes of many 10s of Gigahertz, the modulation far exceeds absorption or interference reference linewidths that are typically on the order of 1 GHz, and there is a need to develop new techniques for long-term laser stabilisation.

[0009] There are two main factors that affect the ability of existing techniques to stabilise a widely- modulated laser diode. In RRI, a large sinusoidal modulation is applied (for example via injection current modulation) which results in a sinusoidal wavelength modulation with a large modulation depth. The wavelength modulation depth may be of particular issue for techniques that use the harmonic content of the modulation signal as the signal energy for the first harmonic signal, which is typically used by techniques such as harmonic frequency stabilisation (HFS) or techniques utilising resonance cavities, is diluted into hundreds of harmonics and therefore determination of the correct locking conditions may become extremely complex.

[0010] In addition to the large wavelength modulation depths it may also be necessary to account for the intensity modulation of the laser, which is phase offset from the frequency modulation, in the stabilisation technique if modulation is performed on the laser diode. This may add further complication to the processing. For injection current modulation in diode lasers, another issue that complicates stabilisation may stem from the presence of harmonics in the resulting wavelength modulation waveform, even when a perfectly sinusoidal injection current modulation waveform is used. This may lead to the introduction of second, third and further harmonics of the modulation frequency into the frequency modulation with associated amplitudes and phase offsets that may then need to be considered when demodulating the combined signal. Accordingly, phase offset between the intensity and wavelength modulations of the lasers may cause significant skewing in the detected signal so direct measurement techniques may be less effective.

[0011] Summary

[0012] It is an object of the present disclosure to provide methods and devices for stabilising a wavelength, and in particular for stabilising a wavelength of a laser (which may be a laser diode), which at least partially address one or more challenges discussed above. In particular, it is an object of the present disclosure to provide methods and devices for stabilising a wavelength of a laser that are suitable for wider wavelength modulation regimes.

[0013] The present disclosure provides a method for stabilising a wavelength of a laser. The method comprises setting a desired wavelength of the laser, passing the laser through a gas cell containing a gas, measuring the intensity of the laser through the gas, and altering the desired wavelength of the laser and repeating the passing and measuring steps through a range of desired wavelengths to obtain a set of stabilising intensity measurements, wherein the stabilising intensity measurements comprise an intensity gas line associated with the gas contained in the gas cell. The method further comprises converting the set of stabilising intensity measurements into a set of absorption measurements comprising an absorption gas line, determining a stabilising peak value of the absorption gas line, determining an absorption offset based on the stabilising peak value and a desired peak value, and tuning the wavelength of the laser based on the absorption offset.

[0014] The present disclosure further provides a system for stabilising the wavelength of a laser comprising a photodetector and a processor. The processor is configured to set a desired wavelength of the laser and pass the laser through a gas cell containing a gas. The photodetector is configured to measure the intensity of the laser through the gas. The processor is further configured to: alter the desired wavelength of the laser and repeat the passing step and measuring steps through a range of desired wavelengths to obtain a set of stabilising intensity measurements, wherein the stabilising intensity measurements comprise an intensity gas line associated with the gas contained in the gas cell, convert the set of stabilising intensity measurements into a set of absorption measurements comprising an absorption gas line, determine a stabilising peak value of the absorption gas line, determine an absorption offset based on the stabilising peak value and a desired peak value, and tune the wavelength of the laser based on the absorption offset. Brief Description of Drawings

[0015] The present disclosure is described, by way of example only, with reference to the following figures, in which:

[0016] Figure 1A and Figure 1 B (collectively referred to as Figure 1) are flowcharts showing a wavelength stabilisation method according to aspects of embodiments;

[0017] Figure 2A and Figure 2B (collectively referred to as Figure 2) are plots of laser intensity measurements over time in accordance with aspects of embodiments;

[0018] Figure 3A, Figure 3B, Figure 3C and Figure 3D (collectively referred to as Figure 3) are graphical overviews of a wavelength locking mechanism in accordance with specific aspects of embodiments;

[0019] Figure 4 is a graphical overview relating to a peak skew phenomena in relation to the wavelength locking mechanism;

[0020] Figure 5 is a graphical overview relating to a further wavelength locking mechanism in accordance with specific aspects of embodiments;

[0021] Figure 6 is a schematic overview of a system implementing a wavelength stabilisation method in accordance with aspects of embodiments;

[0022] Figure 7 is a graphical overview associated with a further wavelength stabilisation method according to aspects of embodiments;

[0023] Figure 8 is a further graphical overview associated with the further wavelength stabilisation method according to aspects of embodiments;

[0024] Figure 9 is a flowchart showing a further wavelength stabilisation method according to aspects of embodiments; and

[0025] Figure 10 is a further schematic overview of a system implementing a wavelength stabilisation method in accordance with aspects of embodiments. Detailed Description

[0026] For the purpose of explanation, details are set forth in the following description in order to provide a thorough understanding of the embodiments disclosed. It will be apparent, however, to those skilled in the art that the embodiments may be implemented without these specific details or with an equivalent arrangement.

[0027] Aspects of embodiments provide a method for wavelength stabilisation in wider wavelength modulation regimes using swept absorption line locking. Figure 1 is a flowchart showing a wavelength stabilisation method S100 according to aspects of embodiments. As shown in Figure 1A, the method may comprise Step S101 of obtaining a set of stabilising intensity measurements for a laser passing through a gas cell. The stabilising intensity measurements may comprise an intensity gas line associated with the gas contained in the gas cell. The steps that may be taken to obtain the set of stabilising intensity measurements of S101 are shown in Figure 1B.

[0028] In Step S111 of the Figure 1 B method, a desired wavelength of a laser is fixed. The laser of this step is the laser to which the wavelength stabilisation method is being applied. The desired wavelength of the laser may be the wavelength that would be expected to be transmitted by the laser, were no errors present in the laser. Errors present in the laser may include variations to the emitted wavelength caused by heating in the laser, electrical errors in the laser, miscalibration of the laser, and the like. Once the desired wavelength of the laser is fixed, the laser may be passed or swept through a gas cell as shown in Step S112 of Figure 1 B.

[0029] The gas cell may be filled with a known gas that has a known absorption feature and / or known gas line. An example of a suitable gas to be held in the gas cell may be acetylene. As shown in Step S113 of Figure 1 B, the intensity of the laser through the gas cell may be measured. If the laser is passed through a gas cell and is directly incident on a photodetector, the measured intensity / (t) may be given by the Beer-Lambert Law, recited in Equation 1 :

[0030] Z(t) = 10~AIo(t) Equation 1 where / 0(t) is the original laser intensity, and A is the absorbance of the gas. The absorbance may be dependent on laser wavelength A(A) and as such for specific laser wavelength the absorbance of the gas may peak or significantly increase. The desired wavelength of the laser may then be altered as shown in Step S114 of Figure 1 B, and then Steps S112-S113 repeated. That is, as shown in Step S115 of Figure 1 B, the passing and measuring steps of the method of Figure 1 B may be repeated in order to obtain a set of stabilising intensity measurements. The altering step (S114 of Figure 1 B) may also be repeated. Steps S112, S113, and / or S114 may be repeated once, or may be repeated a plurality of times in order to obtain larger amounts of data. A gas line corresponds to such a peak in absorbance (which may be referred to as an absorption feature), and a set of stabilising intensity measurements of present embodiments may comprise one or more gas lines.

[0031] The minimum number of repetitions or samples that may be performed may be determined by the Nyquist-Shannon sampling theorem; the Nyquist-Shannon sampling theorem provides a correlation between the sampling rate to the highest frequency component of the signal. In the present embodiments, the Nyquist-Shannon sampling theorem may provide a correlation or ratio between the gas absorption line and the wavelength range.

[0032] The minimum wavelength range over which stabilising intensity measurements may be taken may be determined by the ability of the detector to measure the resultant absorption modulation, which in turn may be limited by the detector sensitivity and noise. In specific embodiments, the minimum range at which measurements may be taken may be of the linewidth of the gas line (or gas linewidth), which may be on the order of picometers.

[0033] Figure 2A and Figure 2B depict two plots of laser intensity measurements taken over a period of time which may be used as part of a swept absorption line locking method in accordance with Figure 1. These plots may be considered to be stabilising intensity measurements as obtained by the method steps of Figure 1 B. As detailed above, throughout the duration of the time period over which laser intensity is recorded the wavelength of the laser may be modulated to provide multiple different desired wavelength values. The laser wavelength may be modulated by manipulating one or more of: current, voltage, and / or power provided to the laser. In a specific example, the modulation applied to the laser wavelength may be sinusoidal. For example, the laser wavelength may be modulated using sinusoidal injection current modulation, which may produce a sinusoidal wavelength / frequency modulation as well as a sinusoidal intensity modulation. Both may considered in the first order to scale proportional to the intensity modulation, within the lasing current thresholds of the laser diode. Alternatively, laser wavelength may be modulated by manipulating the temperature of the laser. For a specific example where the laser is modulated using sinusoidal injection current modulation, the wavelength may undergo a sinusoidal wavelength modulation with a modulation period t. In a single period of the laser modulation, the emission of a laser diode modulated with a sinusoidal modulation waveform may "sweep" through a range Ac± 8A where Acis the central laser emission wavelength, and 8A is the modulation depth of the laser. This sinusoidal waveform may have a modulation period t that is the same as that of the injection current modulation waveform, but alternatively may have a phase offset 0Xdetermined by laser diode and driver characteristics. Meanwhile, the intensity modulation may occur in-phase with the injection current modulation. The wavelength modulation as a result of sinusoidal injection current modulation with modulation frequency fm, can be described by Equation 2:

[0034] A(t) = Ac+ 8Asin(27r / jnt + 0^ + 0Q)

[0035] Equation 2 where 0Ois the original phase of the modulation waveform. The intensity modulation may be assumed, within the lasing current thresholds, to be proportional to the injection current of the laser. Accordingly, the intensity modulation waveform / 0(t) may be described using Equation 3:

[0036] Io(t) = IC+ sin(2n fmt + 0X+ 0O) Equation 3 where 81 is intensity amplitude and Icis central intensity. The sets of stabilising intensity measurements depicted in Figure 2A and Figure 2B are for a specific example of a laser modulated using sinusoidal injection current modulation and thus Equation 1 and Equation 2 are applicable to these specific examples. However, as detailed above, the laser wavelength may be modulated by any suitable means.

[0037] As can be seen in Figure 2A and Figure 2B, a gas line is present in the modulation period as shown by the sharp reduction in intensity at a specific time corresponding to a sharp increase in absorbance A(A). That is, as a result of the result of the interaction with the reference cell, for a single modulation period an absorption feature within the wavelength range Ac± 8A may cause significant dips in the measured intensity resulting in gas lines.

[0038] The specific examples of Figure 2A and 2B both contain an absorption feature producing two gas lines, however a set of stabilising intensity measurements may only comprise one gas line or may comprise more than two gas lines. Two gas lines associated with the same absorption feature being present in a set of stabilising intensity measurements may be indicative of a forward and reverse sweep of the wavelength modulation of the laser over a set wavelength caused by the sinusoidal modulation of the laser wavelength. Accordingly, aspects of the present disclosure may include the stabilising intensity measurements comprising a first gas line and a second gas line and the first and second gas lines may further correspond to the same absorption feature. In such aspects, the method may further comprise: converting the set of stabilising intensity measurements into a set of absorption measurements comprising a first absorption gas line and a second absorption gas line, determining a first stabilising peak value of the first absorption gas line and a second stabilising peak value of the second absorption gas line, determining a first absorption offset based on the first stabilising peak value and a first desired peak value and a second absorption offset based on the second stabilising peak value and a second desired peak value, and tuning the wavelength of the laser based on the first absorption offset and the second absorption offset.

[0039] In the specific example of Figure 2A, the two gas lines are separated by a period wherein t is the modulation period of the laser. In the specific example of Figure 2B, the two gas lines are separated by a period + x where x is an offset. For specific examples comprising two or more gas lines, and in particular where the two or more gas lines correspond to the same absorption feature, an additional locking or stabilising mechanism may be performed wherein the laser emission wavelength is adjusted until x = 0 such that the laser emission wavelength is locked to the case where the separation of the two gas lines is equal to The laser emission wavelength may be adjusted using any suitable means, for example injection current tuning or temperature tuning. This additional locking mechanism may provide a fixed reference point for the central wavelength Ac, to correct for drifting in the laser wavelength over time, which may result from operation of the laser diode (for example, heating of the laser diode).

[0040] As can be seen in Figures 2A and 2B, data sets may comprise multiple gas lines corresponding to different absorption features. That is, in Figure 2A the gas lines separated by a period correspond to the same absorption feature at laser wavelength however other discontinuities are present in the data set; these further discontinuities are gas lines corresponding to other absorption features at other laser wavelengths. Similarly, in Figure 2B the gas lines separated by a period + x correspond to the same absorption feature at laser wavelength however other discontinuities are present in the data set; these further discontinuities are gas lines corresponding to other absorption features at other laser wavelengths. These discontinuities may be treated as errors and removed from the data set or may be used as further locking mechanisms using the same method discussed above. For the avoidance of doubt, the term “absorption feature” is used herein to refer to the physical properties of a gas that causes increased absorption of incident light at particular wavelengths as defined by Equation 1. The term “gas line” is used herein to refer to the resulting sharp change in measured laser intensity of the laser after passing through the gas at a particular laser wavelength associated with an absorption feature. Accordingly, when a laser wavelength is sinusoidally modulated overtime as detailed above, a single absorption feature may produce multiple gas lines in a single data set over time.

[0041] Figure 3 is a graphical overview of the steps undertaken to lock the laser emission wavelength to the case where the separation of the two gas lines is equal to Figure 3A depicts a specific example of raw data from a set of stabilising intensity measurements. As shown in Figure 3B, a first derivative of the photodiode signal over time may be taken in order to identify the gas line(s) present in the set of stabilising intensity measurements. Discontinuities present in the set of stabilising intensity measurements may then be compared to a threshold value in order to identify gas lines and remove any minor fluctuations in photodiode value resulting from errors. The threshold may be selected manually. Selections of data surrounding the threshold crossings as shown in Figure 3B may be removed as shown in Figure 3C. A suitable fitted sine function can then be compared to the remaining data as shown in Figure 3C; this fitted sine may be considered equivalent to incident intensity / o( in Equation 1. Accordingly, the Beer-Lambert Law of Equation 1 may be rearranged as show below in Equation 4 to determine a suitable fitted sine function: wherein A(t) is gas absorbance, / 0(t) is a background intensity measurement at the time t and / (t) is a stabilising intensity measurement at time t. By applying the Beer-Lambert Law the fitted sine may be subtracted from the remaining data in order to remove the sinusoidal aspect of the intensity modulation waveform may be removed as shown in Figure 3D to produce a resultant absorbance spectrum.

[0042] The resultant absorbance spectrum may comprise two clear gas lines or peaks per wavelength forming an absorbance peak on an approximately flat base line. The time between the peak centres may be calculated, and the laser emission wavelength may be adjusted using any suitable means until the separation between the two peaks is equal to For example, the laser emission wavelength may be adjusted using a Proportional Integral Differential (PID) controller or PID loop which may regulate temperature, flow, pressure, speed and other process variables of the system in order to manipulate laser emission wavelength. This locking mechanism is applicable to wider wavelength modulation regimes, for example where the modulation is greater than an order of magnitude larger than the absorption linewidths, but may not account for peak skew in the intensity peak values. Peak skew may be particularly significant in cases where the absorption or intensity lines form a greater proportion of modulation depth. This locking mechanism may also have further reduced effectiveness for cases where absorption or intensity lines form a greater proportion of modulation depth, due to a lack of available data once the selections of data surrounding threshold crossings is removed from the data set.

[0043] An example case where a lack of available data would occur if masking was applied is shown in Figure 4. The top plot of Figure 4 depicts a raw data set compared to a background sinusoidal function calculated using Equation 4, for a set of stabilising intensity measurements taken away from any absorption features or gas lines. The bottom plot of Figure 4 depicts the raw data compared to the same fitted background function for a set of stabilising intensity measurements taken close to an absorption feature / gas line. The dashed line in the bottom plot of Figure 4 is an expected background fit BG(L, t) found using empirical data (for example as shown in Figure 5 and discussed below). As can be seen from Figure 4, when considering data around an absorption feature it may not be suitable to form a background fit from the raw data due to the width of the absorption line. That is, there would be no remaining data after the selections of data surrounding the threshold crossing(s) is removed from the data set. Accordingly, for specific examples where the modulations in laser intensity resulting from laser wavelength modulations are sinusoidal in nature (for example, using sinusoidal injection current modulation) this sinusoidal fit experiences a peak skew close to gas lines. This may reduce the accuracy of wavelength locking mechanisms that calculate a background sinusoidal function using Equation 4.

[0044] In further specific examples, specific embodiments of the present disclosure may further comprise repeating the altering, passing, and measuring steps of Figure 2 (Steps S112, S113, and S114) through a second range of wavelengths of the laser to obtain a set of background intensity measurements / 0(t). Specific embodiments may further comprise determining a background function based on the set of background intensity measurements, and removing the background function from the stabilising intensity measurements. In a further specific embodiment, the second range of wavelengths is a range of wavelengths separate from known absorption lines of the gas in the gas cell. Alternatively or additionally, the method may further comprise identifying the stabilising peak value using the Beer-Lambert law as detailed in Equation 4.

[0045] Accordingly, any undesirable intensity modulations resulting from the chosen method of modulating laser wavelength can be removed through the use of a fitted background function BG IL, t) generated using a set of background intensity measurements in place of the Beer- Lambert Law of Equation 4. The background function BG IL, t) may be a function of laser current ILand time t. This may increase the accuracy of the removal of background intensity modulations and allow for background intensity modulations to be removed when the modulations are not sinusoidal.

[0046] In some specific examples, the background fit BG IL, t) may be determined using a masked scan over a range of modulation centre currents. A specific example that determines the background fit BG IL, t) using a masked scan is depicted in Figure 5. The masked scan may be performed over a range of modulation centre laser currents in order to fit both linear intensity variation with current and sinusoidal intensity modulation from wavelength variation. For the masked scan of Figure 5, a scan of the photodiode signal over time and varying laser diode current is performed. This scan is then plotted in order to achieve a 2-dimensional plot such as that shown in Figure 5. After this, a first derivative of the photodiode signal in laser current dBG

[0047] — is taken for each column (that is, each time sample) in order to identify the gas line(s) d / Lpresent. Once the gas line(s) have been identified, the data surrounding the gas line(s) can be removed (for example as shown in Figure 3B).

[0048] As shown in Figure 1A, method S100 may comprise Step S102 of converting the set of stabilising intensity measurements into a set of absorption measurements comprising an absorption gas line. Method S100 may further comprise Step S103 of determining a stabilising peak value of the absorption gas line. In specific examples, determining the offset of the line centre of the absorption gas line may comprise applying a Voigt model to the set of absorption measurements. The Voigt model may be a Voigt function, or may be a pseudo-Voigt function. Accordingly, any model approximating the shape of a gas line (which in turn may be dependent on the gas species, temperature, and / or pressure of the gas) may be used. Method S100 may then further comprise Step S104 of determining an absorption offset based on the stabilising peak value and a desired peak value, and Step S105 of tuning the wavelength of the laser based on the absorption offset. An apparatus or system 600 for implementing a wavelength stabilisation method in accordance with aspects of an embodiment is shown in Figure 6. The apparatus as shown in Figure 6 may be suitable for obtaining the stabilising intensity measurements shown in Figure 1A and Figure 1 B. Optical fibres in Figure 6 are denoted as a solid line, and electric connections are denoted with a narrow dashed line.

[0049] The system 600 of Figure 6 may comprise a processor 601. The processor 601 may be an electronic signal processing unit. The processor 601 may be configured to perform Steps S111 , S112, and / or S114 of Figure 1 B. The processor 601 may be further configured to perform any of Steps S101 , S102, S103, S104, and / or S105 of Figure 1A. In specific examples, the processor 601 may be configured to perform method S100.

[0050] The system 600 of Figure 6 may additionally comprise a photodetector 602. The photodetector 602 may be configured to perform Step S113 of Figure 1 B. Accordingly, the photodetector may be configured to measure the intensity of the laser through the gas. The photodetector 602 may be connected to the processor 601 via a connection 608. The processor may further send a feedback signal 609 to the laser 605. The connection 608 may be a voltage connection and may facilitate interaction and communication between the processor 601 and photodetector 602. The photodetector 602, processor 601 , feedback signal 609, and connection 608 may be configured to perform Step S101 of Figure 1A. Accordingly, the photodetector 602, processor 601 , feedback signal 609, and connection 608 may be configured to perform Steps S111-S115 of Figure 1 B. The system 600 may further comprise a sealed gas cell 603, through which the laser is swept. The sealed gas cell may contain a gas with a known gas line or absorption linewidth, for example acetylene which produces gas lines for wavelengths of 1510- 1540nm and / or hydrogen cyanide ( I 'AC 'AN) which produces gas lines for wavelengths of 1525-1565nm. However, any gas that produces an absorption feature or gas line may be used. Accordingly, further examples of gases suitable for use in the sealed gas cell 603 include: Iodine ( / 2) which, for example, produces gas lines for lasers operating at wavelengths of 514.5nm and 532nm, and Rubidium (Rb) which produces gas lines for wavelengths in the region of approximately 780nm.

[0051] The system 600 may comprise a wavelength modulation unit 604, configured to modulate the desired wavelength of the laser using any suitable means. For example, the wavelength modulation unit 604 may be configured to modulate the laser desired wavelength by manipulating one or more of: current, voltage, and / or power provided to the laser, or temperature of the laser. In a specific example, the wavelength modulation unit may be an injection-current modulation unit 604, which may be configured to inject a sinusoidal injection current modulation as detailed above.

[0052] The system 600 may further comprise a laser 605. The laser 605 may be the laser to which the wavelength stabilisation method is being applied. The laser 605 may be a fibre-coupled diode laser, or any other suitable type of laser. The system 600 may further comprise an fibre splitter and a fibre lead to a further application 607, to allow the laser 605 to be used for other purposes whilst connected to the wavelength stabilisation system 600. Accordingly, the fibre splitter and fibre lead to a further application 607 may allow the laser 605 to be used at the same time as undertaking the wavelength stabilisation process of present embodiments. Optionally, the system 600 may further comprise an isolator 606 to prevent back reflections entering the laser which may cause instability in the laser.

[0053] In a specific example of present embodiments, the method S100 may comprise mapping the absorption measurements into a wavelength space. In a preferred specific embodiment, the method S100 may further comprise mapping the absorption measurements into a normalised wavelength space. For example, mapping the absorption measurements into a normalised wavelength space comprising using Equation 5 below:

[0054] 2nx w(x) = sin(— + p)

[0055] Equation 5 wherein w(x) is the normalised wavelength associated with an absorption measurement, x is the sample number of the absorption measurement, p is the sampling phase of the absorption measurement, and N is the total number of measurements forming the set of absorption measurements. Equation 5 assumes a sinusoidal wavelength modulation, however as detailed above the wavelength modulation may follow another function (for example, linear). Accordingly, any suitable modulation function may be substituted into Equation 5 in order to map the absorption measurements into the normalised wavelength space. In such a case, Equation 5 would be any suitable function of sample number x, total number of measurements forming the set of absorption measurements N, and sampling phase of the absorption measurement p.

[0056] In a further specific embodiment, the desired peak value may correspond to a value of 0 in the normalised wavelength space and determining the offset of the line centre of the absorption gas line may comprise determining the absorption offset relative to a normalised wavelength of 0. Accordingly, in such an embodiment there is a change in conceptualisation from fitting peaks to find a time period between absorption or gas line crossings to fitting peaks to find a gas line relative to a laser centre wavelength.

[0057] In order to fit the set of stabilising intensity measurements to a model function (which may be a function of desired wavelength Ao, central wavelength Acand / or phase offset 0A) the absolute wavelengths associated with the set of stabilising intensity measurements may need to be known. By using of a normalised wavelength space as detailed above, it is not necessary to know the absolute wavelengths associated with the set of stabilising intensity measurements. Accordingly, the absorption measurements may be converted into a normalised wavelength space defined as spanning from -1 to +1 , with 0 as the central normalised wavelength. A function or fit can then be applied as a function of the absorption line centre in the normalised wavelength space, such that parameters associated with the absorption gas line can then be determined from the fit. Parameters associated with the absorption gas line may include: central wavelength Ac, desired wavelength Ao, line width and line height.

[0058] Figure 7 depicts an example of a set of absorption measurements, comprising a first scan through an absorption feature and a second return scan through the same absorption feature in order to obtain two gas lines, and a conversion of the set of absorption measurements from being a function of absorption and time to a function of absorption and normalised wavelength. The fit applied to the data in Figure 7 is a Voigt fit. As can be seen in the absorption-time plot, there is a slight skew in the applied fit due to errors in background normalisation as detailed above.

[0059] There may be a further non-linear skew in the absorption measurements when compared to the Voigt fit. This non-linear skew may be a result of the difference in wavelength intervals between samples or data points. The non-linear skew may be able to be accounted for when the absolute wavelengths for each absorption measurement or data point are known. However, the use of normalised wavelength space allows for these skews to be accounted for even when the absolute wavelengths for each absorption measurement are not known. Accordingly, the use of a normalised wavelength space improves the accuracy of applying a Voigt function model to the set of absorption measurements in order to determine the offset of the line centre of the absorption gas line.

[0060] Figure 8 depicts a further example of a set of absorption measurements, comprising a merged absorption feature, and a conversion of the set of absorption measurements from being a function of absorption and time to a function of absorption and normalised wavelength. As detailed above, converting absorption measurements into the normalised wavelength space allows for a determination of an absorption offset relative to a normalised wavelength of zero, which is then used to tune the wavelength of the laser. That is, rather than trying to determine a time separation between two peaks and control the separation to be set at Accordingly, methods that involve converting absorption measurements into the normalised wavelength space determine an offset of the absorption gas line from a normalised wavelength of 0 and then control the offset to be set at 0. As shown in Figure 8, methods that involve converting absorption measurements into the normalised wavelength space no longer require that the two scans of the absorption feature are fully resolved and thus appear as two separate gas lines (that is, such methods no longer require two or more gas lines associated with the same absorption feature to be present). Instead only a single gas line (and thus a single absorption feature) is needed; this is also in contrast to methods based on a time space, which require two resolved peaks.

[0061] For sets of absorption measurements which only comprise a single absorption feature, the centre of the gas line may still be shown after conversion into the normalised wavelength space based around either extreme of the normalised wavelength (either +1 or -1) as shown in Figure 8. From this, the peak of the gas line may still be calculated using a Voigt fit modelled to the data.

[0062] Alternatively, the method S100 may further comprise mapping the absorption measurements into a non-normalised wavelength space. However, for some particular implementations of this mapping, a-priori information about the absolute wavelength range of the modulation and centre emission wavelength at all times in the measurement may need to be known in order to map the data points; this in turn may nullify the need for any fitting or stabilisation process, and this data may not be available. Furthermore, in order to fit a model for the absolute centre wavelength and wavelength range with a-priori information about the absorption line wavelength, line width and line height, multiple calculations may be required for each iteration of the fit this would require multiple calculations. This would be computationally slower, and may require further a-priori information about the gas line. Accordingly, it is preferred to map the absorption measurements into a normalised wavelength space.

[0063] In specific examples of present embodiments, tuning the wavelength of the laser based on the offset of the absorption gas line may comprise generating a tuning parameter, and applying the tuning parameter to the laser. In further specific examples of present embodiments, method S100 may further comprise determining a line width of the absorption gas line. Gas line width may give an indirect measurement of the wavelength modulation range (particularly in cases where the desired line width of the reference gas is known). Alternatively or additionally, method S100 may further comprise determining a line height of the absorption gas line. Line height may be used to differentiate between absolute gas lines, and / or determine where there are multiple gas lines visible within the wavelength modulation range.

[0064] Figure 9 depicts a further wavelength stabilisation method S900 according to specific embodiments. As shown in Figure 9, method S900 begins at step S901. At Step S902, the wavelength of the laser is modulated in time t and passed through a gas cell and then at Step S903 the laser is absorbed at specific wavelengths as it passes through the gas cell. A photodiode measures the intensity / (t) at each time t of the laser passing through the gas cell at Step S904, and then at Step S905 the absorption A(t) at each time t is calculated using the Beer-Lambert Law as shown in Equation 4. Following this, at Step S906 the time of each sample is remapped into a normalised wavelength A between -1 and +1 , where 0 is the centre wavelength and +1 / -1 form the extremes of modulation. This results in the determination of an absorption per normalised wavelength 4(A), and from this at Step S907 a gas line model function is fitted to the absorption per normalised wavelength 4(A) to determine a line centre and optionally a line width in terms of normalised wavelength and optionally in terms of line height. At Step S908, an offset of the line centre from A = 0 (which may model the absorption line at the centre of the modulation sweep) is calculated to generate an error signal, and at Step S909 the error signal is processed using proportional, integral and / or differential calculations to form a feedback value. A tuning parameter AILand / or AT may be calculated from the feedback value at Step S910 and applied to the laser diode in order to tuning the wavelength of the laser, where AILis a tuning parameter for laser current and AT is a tuning parameter for laser temperature.

[0065] Concurrently with this process, the method S900 of Figure 9 comprises recording a calibration background map as a function of control variable temperature T and / or laser injection current ILat Step S911 . That is, a second set of data measurements may be performed as previously discussed in order to generate a calibration background map. From this, the region of the absorption line is masked at Step S912 such that the data surrounding the absorption line is removed, and at Step S913 a model for background intensity variation BG(t, I, T) is fitted or generated using the remaining calibration background data. From this, at Step S914 a set of background intensity measurements BG(t) is determined and fed into the Beer-Lambert law calculations at Step S905.

[0066] Figure 10 depicts a schematic overview of a system 1000 implementing a wavelength stabilisation method in accordance with aspects of embodiments. System 1000 comprises the same components as the system 600 depicted in Figure 6. Accordingly, system 1000 comprises a processor 1001 , photodetector 1002, sealed gas cell 1003, wavelength modulation unit 1004, connection 1008, feedback signal 1009, and laser 1005; these components may be configured in the same manner as discussed with reference to the system 600 of Figure 6. System 1000 additionally comprises an integrated interferometric setup 1007 optionally connected to an isolator 1006 as a specific example of the further application 607 of Figure 6. The integrated interferometric setup 1007 of Figure 10 comprises an optical circulator, collimating lens, laser, glass block, and mirror. The depicted integrated interferometric setup 1007 may be suitable for interrogation using range-resolved interferometry. Solid lines in Figure 10 denote optical fibre connections, and narrow dashed lines represent electrical connections and broad dashed lines denote free-space laser paths.

[0067] Above examples are presented with reference to a system including a gas cell. However, the technique of the present disclosure may be applied to any standard stability reference. For example, the gas cell of any of the examples disclosed above may be replaced with one of the following: an Etalon, an interference filter, an in-fibre filter, an interferometer, and / or a cell comprising a substance configured to allow molecular absorption.

[0068] Aspects of the present disclosure aim to provide methods of wavelength stabilisation suitable for wide-modulation scenarios such as RRI. Specific aspects of the present disclosure aim to provide methods of wavelength stabilisation which are more precise and / or accurate than known methods, in particular by providing methods of accounting for background fluctuations in wavelength that are more precise than known methods. Further specific aspects of the present disclosure aim to provide methods of wavelength stabilisation that are more efficient than known methods, in particular by providing methods that only require the presence of a single absorption feature (and thus a single gas line in the measured data) and do not require prior knowledge of the absolute wavelength(s) associated with the measured data.

[0069] In general, the various exemplary embodiments may be implemented in hardware or special purpose circuits, software, logic or any combination thereof. For example, some aspects may be implemented in hardware, while other aspects may be implemented in firmware or software which may be executed by a controller, microprocessor or other computing device, although the disclosure is not limited thereto. While various aspects of the exemplary embodiments of this disclosure may be illustrated and described as block diagrams, flow charts, or using some other pictorial representation, it is well understood that these blocks, apparatus, systems, techniques or methods described herein may be implemented in, as non-limiting examples, hardware, software, firmware, special purpose circuits or logic, general purpose hardware or controller or other computing devices, or some combination thereof.

[0070] As such, it should be appreciated that at least some aspects of the exemplary embodiments of the disclosure may be practiced in various components such as integrated circuit chips and modules. It should thus be appreciated that the exemplary embodiments of this disclosure may be realized in an apparatus that incorporates an integrated circuit, where the integrated circuit may comprise circuitry (as well as possibly firmware) for embodying at least one or more of a data processor, a digital signal processor, baseband circuitry and radio frequency circuitry that are configurable so as to operate in accordance with the exemplary embodiments of this disclosure.

[0071] References in the present disclosure to “one embodiment”, “an embodiment” and so on, indicate that the embodiment described may include a particular feature, structure, or characteristic, but it is not necessary that every embodiment includes the particular feature, structure, or characteristic. Moreover, such phrases are not necessarily referring to the same embodiment. Further, when a particular feature, structure, or characteristic is described in connection with an embodiment, it is submitted that it is within the knowledge of one skilled in the art to implement such feature, structure, or characteristic in connection with other embodiments whether or not explicitly described.

[0072] It should be understood that, although the terms “first”, “second” and so on may be used herein to describe various elements, these elements should not be limited by these terms. These terms are only used to distinguish one element from another. For example, a first element could be termed a second element, and similarly, a second element could be termed a first element, without departing from the scope of the disclosure. As used herein, the term “and / or” includes any and all combinations of one or more of the associated listed terms.

[0073] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the present disclosure. As used herein, the singular forms “a”, “an” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms “comprises”, “comprising”, “has”, “having”, “includes” and / or “including”, when used herein, specify the presence of stated features, elements, and / or components, but do not preclude the presence or addition of one or more other features, elements, components and / or combinations thereof. The terms “connect”, “connects”, “connecting” and / or “connected” used herein cover the direct and / or indirect connection between two elements.

[0074] The present disclosure includes any novel feature or combination of features disclosed herein either explicitly or any generalization thereof. Various modifications and adaptations to the foregoing exemplary embodiments of this disclosure may become apparent to those skilled in the relevant arts in view of the foregoing description, when read in conjunction with the accompanying drawings. However, any and all modifications will still fall within the scope of the non-limiting and exemplary embodiments of this disclosure. For the avoidance of doubt, the scope of the disclosure is defined by the claims.

Claims

CLAIMS1. A method of stabilising a wavelength of a laser, comprising: setting a desired wavelength of the laser; passing the laser through a gas cell containing a gas; measuring the intensity of the laser through the gas; altering the desired wavelength of the laser and repeating the passing and measuring steps through a range of desired wavelengths to obtain a set of stabilising intensity measurements, wherein the stabilising intensity measurements comprise an intensity gas line associated with the gas contained in the gas cell; converting the set of stabilising intensity measurements into a set of absorption measurements comprising an absorption gas line; determining a stabilising peak value of the absorption gas line; determining an absorption offset based on the stabilising peak value and a desired peak value; and tuning the wavelength of the laser based on the absorption offset.

2. A method as claimed in Claim 1 , wherein the method further comprises: mapping the absorption measurements into a normalised wavelength space.

3. A method as claimed in Claim 2, wherein mapping the absorption measurements into a normalised wavelength space comprising using the equation2nx w(x) = sin(— + p) wherein w(x) is the normalised wavelength associated with an absorption measurement, x is the sample number of the absorption measurement, p is the sampling phase of the absorption measurement, and N is the total number of measurements forming the set of absorption measurements.

4. A method as claimed in any of Claims 2 or 3, wherein the desired peak value corresponds to a value of 0 in the normalised wavelength space and determining the offset of the line centre of the absorption gas line comprises: determining the absorption offset relative to a normalised wavelength of 0.

5. A method as claimed in any preceding claim, wherein determining the offset of the line centre of the absorption gas line comprises: applying a Voigt model to the set of absorption measurements.

6. A method as claimed in any preceding claim, wherein the method further comprises: repeating the altering, passing and measuring steps of Claim 1 through a second range of wavelengths of the laser to obtain a set of background intensity measurements; determining a background function based on the set of background intensity measurements; and removing the background function from the stabilising intensity measurements.

7. A method as claimed in Claim 6, wherein the second range of wavelengths is a range of wavelengths separate from known absorption lines of the gas in the gas cell.

8. A method as claimed in any of Claims 6 or 7, wherein the method further comprises identifying the stabilising peak value using the Beer-Lambert law, the Beer-Lambert law corresponding to the equation:wherein A(t) is an absorption measurement at a time t, / o( is a background intensity measurement at the time t and / (t) is a stabilising intensity measurement at time t.

9. A method as claimed in any preceding claim, wherein tuning the wavelength of the laser based on the offset of the absorption gas line comprises: generating a tuning parameter, and applying the tuning parameter to the laser.

10. A method as claimed in any preceding claim, wherein the method further comprises: determining a line width of the absorption gas line.

11. A method as claimed in any preceding claim, wherein the method further comprises: determining a line height of the absorption gas line.

12. A method as claimed in any preceding claim, wherein the stabilising intensity measurements comprise a first gas line and a second gas line, and wherein the method further comprises: converting the set of stabilising intensity measurements into a set of absorption measurements comprising a first absorption gas line and a second absorption gas line; determining a first stabilising peak value of the first absorption gas line and a second stabilising peak value of the second absorption gas line;determining a first absorption offset based on the first stabilising peak value and a first desired peak value and a second absorption offset based on the second stabilising peak value and a second desired peak value; and tuning the wavelength of the laser based on the first absorption offset and the second absorption offset.

13. A system for stabilising the wavelength of a laser comprising a photodetector and a processor, wherein: the processor is configured to: set a desired wavelength of the laser; pass the laser through a gas cell containing a gas; the photodetector is configured to: measure the intensity of the laser through the gas; and the processor is further configured to: alter the desired wavelength of the laser and repeat the passing step and measuring steps through a range of desired wavelengths to obtain a set of stabilising intensity measurements, wherein the stabilising intensity measurements comprise an intensity gas line associated with the gas contained in the gas cell; convert the set of stabilising intensity measurements into a set of absorption measurements comprising an absorption gas line; determine a stabilising peak value of the absorption gas line; determine an absorption offset based on the stabilising peak value and a desired peak value; and tune the wavelength of the laser based on the absorption offset.

14. A system as claimed in Claim 13, wherein the processor is further configured to: map the absorption measurements into a normalised wavelength space.

15. A system as claimed in Claim 14, wherein mapping the absorption measurements into a normalised wavelength space comprising using the equation2nx w(x) = sin(— + p) wherein w(x) is the normalised wavelength associated with an absorption measurement, x is the sample number of the absorption measurement, p is the sampling phase of the absorption measurement, and N is the total number of measurements forming the set of absorption measurements.

16. A method as claimed in any of Claims 14 or 15, wherein the desired peak value corresponds to a value of 0 in the normalised wavelength space and determining the offset of the line centre of the absorption gas line comprises: determining the absorption offset relative to a normalised wavelength of 0.

17. A system as claimed in any of Claims 13 to 16, wherein determining the offset of the line centre of the absorption gas line comprises: applying a Voigt model to the set of absorption measurements.

18. A system as claimed in any of Claims 13 to 17, wherein the processor is further configured to: repeat the altering, passing, and measuring steps of Claim 13 through a second range of wavelengths of the laser to obtain a set of background intensity measurements; determine a background function based on the set of background intensity measurements; and remove the background function from the stabilising intensity measurements.

19. A system as claimed in Claim 18, wherein the second range of wavelengths is a range of wavelengths separate from known absorption lines of the gas in the gas cell.

20. A method as claimed in any of Claims 18 or 19, wherein the processor is further configured to identify the stabilising peak value using the Beer-Lambert law, the Beer- Lambert law corresponding to the equation:70(t)A(t) = logio -^7 7 (I) wherein A(t) is an absorption measurement at a time t, / 0(t) is a background intensity measurement at the time t and / (t) is a stabilising intensity measurement at time t.

21. A system as claimed in any of Claims 13 to 20, wherein the processor is further configured to tune the wavelength of the laser based on the offset of the absorption gas line by: generating a tuning parameter, and applying the tuning parameter to the laser.

22. A system as claimed in any of Claims 13 to 21, wherein the processor is further configured to: determine a line width of the absorption gas line.

23. A system as claimed in any of Claims 13 to 22, wherein the processor is further configured to: determine a line height of the absorption gas line.

24. A system as claimed in any of Claims 13 to 23, wherein the stabilising intensity measurements comprise a first gas line and a second gas line, and wherein the processor is further configured to: convert the set of stabilising intensity measurements into a set of absorption measurements comprising a first absorption gas line and a second absorption gas line; determine a first stabilising peak value of the first absorption gas line and a second stabilising peak value of the second absorption gas line; determine a first absorption offset based on the first stabilising peak value and a first desired peak value and a second absorption offset based on the second stabilising peak value and a second desired peak value; and tune the wavelength of the laser based on the first absorption offset and the second absorption offset.

25. A system as claimed in any of Claims 13 to 24, wherein the system further comprises a fibre splitter.

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