A laser system

Abstract

A laser system 100 comprising a master laser 102 having a master laser frequency, at least one slave laser 1041 … 104n which is tuned to output laser light at a desired absolute frequency which is dif

Description

Field

[001] The present techniques relate to a laser system comprising a plurality of lasers each tuned to output laser light at a different frequency. The present techniques also relate to methods for tuning each laser in the laser system. Background

[002] Techniques to effectively manipulate and control quantum systems are becoming increasingly important. With their well controlled characteristics, laser systems are being applied to a wide range of areas to effectively control quantum systems, such as quantum information processing, and in particular the generation and control of quantum bits. Other such applications include atomic interferometry, gyroscopes, precision gravimeters and gravity gradiometers for gravitational wave detection.

[003] An important characteristic of laser systems for the manipulation and control of quantum systems is the frequency of the laser output light. It is often desirable to be able to lock the output frequency to a specific reference frequency or absolute reference frequency and the locking of the frequency of the light output of a laser in this way will be referred to as absolute referencing. A common technique for absolute referencing is to obtain an absolute frequency reference comprising a vapour cell which contains a pure atomic source. The reference is only applicable to the specific transition lines of the pure atomic source. Figure 1 illustrates an energy diagram of a Rubidium-87 transition line. Rubidium-87 is a commonly used isotope for the absolute referencing of laser systems for performing experiments on systems of atoms. Rubidium-87 has a relatively simple energy level structure, with a range of accessible transition lines between the energy levels of the structure. Each transition line may be used for a different purpose, e.g. Raman spectroscopy, atomic cooling or repumping. However, the range of frequencies accessible from the transition lines is limited to a few GHz.

[004] In addition to widely-used Rubidium-87 references mentioned above, other possible choices of isotopes are available for absolute referencing, such as Strontium (Sr), Ytterbium (Yb) and Mercury (Hg). The table below shows the typical wavelengths of such commercially available lasers. Transition Sr Yb Hg 1. Strong Cooling (nm) 460.9 (32 MHz) 389.9 (29 MHz) 184.9 (120 MHz) 2. Narrow Cooling (nm) 689.3 (7.5 kHz) 555.8(180 kHz) 253.7 (1.3 MHz) 3. Clock (nm) 698.4 (1 MHz) 578.4 (10 MHz) 256.6 (100 MHz) 4. Repump (nm) 707.2 770.2 546.1 5. Repump (nm) 679.3 649.1 404.6 6. Magic Wavelength (nm) 813.4 759.4 362.5

[005] Whilst such vapour cells provide access to a relatively large range of wavelengths and frequencies, a vapour cell containing Sr, for example, is extremely expensive. As a result, the use of such a vapour cell for absolute referencing is only commercially viable where significant financial resources are available. Hence, the present applicant has identified the need for a method of absolute referencing laser systems with broad commercial viability.

[006] The present applicant has identified the need for improved systems and methods of referencing the output frequency of laser systems. Summary

[007] According to the present invention there is provided a method and laser system as set forth in the appended claims. Other features of the invention will be apparent from the dependent claims, and the description which follows.

[008] In a first approach of the present techniques, there is provided a laser system comprising a master laser having a master laser frequency; at least one slave laser which is tuned to output laser light at a desired absolute frequency which is different to the master laser frequency; a frequency comb which generates a spectrum of laser light comprising a plurality of frequency comb lines which are all spaced by a discrete repetition frequency; at least one sensor for measuring a laser-comb beat signal which is generated by combining output from the at least one slave laser with output from the frequency comb; and a slave control circuit for tuning the at least one slave laser based on the measured laser-comb beat signal. For simplicity the discrete repetition frequency may be termed a repetition frequency and the desired absolute frequency may be termed a desired frequency and the terms may be used interchangeably.

[009] The beat signal may be a heterodyne beat signal. A beat signal is a known acoustic property which is an interference pattern between two sounds of slightly different frequencies (in this case the frequency of the laser and the frequency of a comb line of the frequency comb). A beat signal may be perceived as a periodic variation in volume whose frequency is the difference of the two slightly different frequencies. As the frequency of the slave laser is adjusted gradually (i.e. continuously over time), the frequency of the laser-comb beat signal will change. When the frequency of the laser exactly matches the frequency of a comb line, there will be no beat signal, in other words the frequency of the beat signal is zero. The beat signal between the slave laser and the frequency comb may be termed a slave-comb beat signal or laser-comb beat signal and the beat signal between the master laser and the frequency comb may be termed a master-comb beat signal.

[010] The known master frequency may be an absolute reference frequency of a spectroscopic reference (e.g. Rubidium-87, Strontium (Sr), Ytterbium (Yb) and Mercury (Hg)). In other words, there is a clear value or pinpoint in the frequency space. For simplicity, the absolute spectroscopic reference may be referred to as a spectroscopic reference. Moreover, the spectroscopic reference may be selected to ensure that the laser system outputs frequencies which are suitable for manipulating and controlling quantum systems such as those detailed in the background section.

[011] There may be a plurality of slave lasers each of which are separately tunable. Each of the plurality of slave lasers may thus be tuned to a different desired frequency. The slave lasers may be considered to act as a scalable chain of units that can span over a wide range of frequencies all related to the master laser. In this way, it is possible to create a system that is absolutely referenced over an entire desired spectrum for example over a range of frequencies spanning at least 50nm (30THz) or over the entire visible spectrum, e.g. over 500nm (300THz). Such a desired range can be achieved even though an arbitrary spectroscopic reference is chosen to reference the master laser. In other words, it is not necessary to engineer a specific laser design for the master laser. The lowest value in the range may be the value of the master reference value. The frequency comb spans the output frequencies of the master and slave lasers and may be considered to be an optical bridge linking all slave lasers on the chain to the master laser.

[012] The laser system may be compact and all components may be housed in the same housing.

[013] For each of the plurality of slave lasers, tuning the slave laser to output laser light at a desired frequency may comprise carrying out the steps described below sequentially or in parallel for each laser. These steps may be carried out by a slave control circuit. Thus, for each laser the tuning process may comprise calibrating the slave laser to a known frequency; gradually adjusting the frequency of the slave laser from the known frequency to an adjusted frequency; receiving, as the frequency is gradually adjusted, a measurement of the changing frequency of the generated slave-comb beat signal from the at least one sensor; counting instances at which the measured frequency of the laser-comb beat signal repeats (for example each instance the measured frequency is zero); obtaining, using the counted instances, a line number which indicates how many of the plurality of frequency comb lines have been crossed as the frequency is gradually adjusted to the adjusted frequency; calculating the adjusted frequency using the known frequency, the repetition frequency of the frequency comb, the determined line number and the measured beat signal and determining whether the adjusted frequency equals the desired frequency. When it is determined that the adjusted frequency does not equals the desired frequency, the steps of gradually adjusting, measuring, counting, obtaining, calculating and determining may be repeated. In this arrangement, when the adjusted frequency does equal the desired frequency, another laser may then be selected for tuning. Such a tuning method may be termed a counting method.

[014] This tuning process may be carried out independently for each slave laser. According to another aspect of the present techniques, there is provided a method of tuning a laser (i.e. a slave laser) to output laser light at a desired frequency, the method comprising setting (i.e. calibrating) the output laser light to a known frequency; generating a laser-comb beat signal by combining output from the laser with output from a frequency comb which generates a spectrum of laser light comprising a plurality of frequency comb lines which are all spaced by a repetition frequency; gradually adjusting the frequency of the laser from the known frequency to an adjusted frequency; measuring, as the frequency is gradually adjusted, a frequency of the generated laser-comb beat signal; counting instances at which the measured frequency of the laser-comb beat signal repeats (for example each repeating zero value); obtaining, using the counted instances, a line number which indicates how many of the plurality of frequency comb lines have been crossed as the frequency is gradually adjusted to the adjusted frequency; calculating the adjusted frequency using the known frequency, the repetition frequency of the frequency comb and the determined line number; and determining whether the adjusted frequency equals the desired frequency.

[015] The following features apply to both aspects.

[016] Calculating the adjusted frequency may be done for example using the following expression: few mfrep + fceo + fbeat where fcw is the adjusted frequency of a continuous wave (CW) laser, m is the obtained line number, frep is the repetition frequency of the frequency comb, fceo is an offset frequency of the frequency comb and fbeatis the frequency of the laser-comb beat signal.

[017] The method is an iterative one and thus when it is determined that the adjusted frequency does not equal the desired frequency, the steps of gradually adjusting, measuring, counting, obtaining, calculating and determining may be repeated. When it is determined that the adjusted frequency equals the desired frequency, no further tuning is required.

[018] Calibrating the slave laser to a known frequency may comprise adjusting the frequency of the slave laser to an initial value which is unknown; and using a dithering scheme which adjusts the repetition frequency of the frequency comb to determine the frequency of the initial value. Such a calibration may be used when the desired frequency of the slave laser is significantly different, e.g. tens of frequency comb lines different, from the master laser frequency. In such a case, it is not possible to first tune the slave laser to the master frequency to establish a known starting point. Thus, the laser system may further comprise a controller for implementing the dithering scheme which is used so that the frequency to which the slave laser has been set is known. The dithering scheme may comprise increasing the repetition frequency of the frequency comb over a pre-determined range. The slave control circuit may calibrate the slave laser by instructing the controller to increase the repetition frequency of the frequency comb; receiving, as the repetition frequency is increased, a measurement of the changing frequency of the generated laser-comb beat signal; counting instances at which the measured laser-comb beat signal repeats (e.g. is zero); estimating an index number for the frequency comb line closest in frequency to the initial value; determining, using the measured laser-comb beat signal, a directionality of the initial value relative to the frequency comb line with the estimated index number; and calculating the frequency of the initial value using the estimated index number, the repetition frequency, the determined directionality and the measured laser-comb beat signal.

[019] Estimating an index number may be done using the counted instances, the predetermined range and the measured laser-comb beat signal. For example, using &mfrep + fbeat ^beat 171 =----Af-------± Af--’ ^Trep ^Jrep where &beat is an experimental precision on the measured beat frequency, which is determined through a calibration stage, Afrep is a value of the pre-determined range given by hfrep = fr2ep -frep where f2ep is an upper limit of the of the pre-determined range, and fbeat is the final value of the measured frequency of the laser-comb beat signal. Depending on the determined directionality, calculating the frequency of the initial value f may be done using f fceo T ' frep + fbeat or f fceo T ’ frep fbeat where fceois a frequency offset for the frequency comb, m is the estimated index number, ffep is a lower limit of the pre-determined range, and fbeat is the final value of the measured frequency of the laser-comb beat signal.

[020] The dithering scheme allows the frequency of the slave laser to be determined and thus the dithering scheme allows a significant adjustment to the frequency of the slave laser. Thus adjusting the frequency of the output laser light from the laser to an initial value may comprise adjusting the frequency by more than 20 GHz, more than 30 THz and up to a maximum of 300THz. The adjustment may also be expressed as a number of frequency lines to be crossed and when more than 20 lines are to be crossed, such a large adjustment Gump) may be calculated theoretically and applied. The fine-tuning adjustments may be done using the counting method described above.

[021] The master laser may be used to calibrate the frequency of the slave laser to a known frequency using the counting method. Such a calibration is appropriate when the desired frequency of the slave laser is relatively close to the frequency of the master laser (e.g. within 20 frequency comb lines) and thus the master laser can be used to establish an absolute reference from which the slave laser can then be tuned. As an alternative, the dithering method described above may be used to establish a reference from which the slave laser can then be tuned by the counting method. The most appropriate calibration method may be selected, for example based on the physical properties of the slave and master lasers and / or the desired range of frequencies to be covered by the laser system. For example, each of the master and slave lasers may be made from the same crystal material and in such an example, the range of wavelengths which can be achieved by the system is relatively narrower so calibrating using the master laser is appropriate. In another example, the master and slave lasers may be made from different materials and some or all of the lasers may have frequencies which are significantly different (e.g. over 100nm apart). In such an example, the dithering scheme is more appropriate. In both cases, the frequency comb is important, particularly for bridging the large frequency gaps.

[022] The laser system may comprise a master control circuit which is used to tune the master laser to the known master frequency, e.g. the spectroscopic reference. In other words, calibrating the output laser light to a known frequency may comprise tuning, using a master control circuit, the frequency of output laser light from the master laser to a known master frequency. In such an arrangement, the master control circuit may be termed a master feedback control circuit and may use saturation absorption spectroscopy to generate an error signal which indicates whether the master frequency needs to be tuned or adjusted and the direction and value of any adjustment to be applied. Once the master frequency is locked, the slave control circuit may be used to tune the frequency of output laser light from the slave laser to the frequency of output laser light from the master laser.

[023] As an alternative to tuning to the master laser, using a feedback circuit, the laser system may comprise a modulator which shifts the frequency of output laser light from the master laser by a modulator frequency to generate a shifted frequency and a modulator control circuit for controlling the modulator frequency to lock the shifted frequency to a desired frequency. The process may comprise: calibrating the frequency of output laser light from the master laser to a known master frequency; shifting, using the modulator, the frequency of output laser light from the master laser by a modulator frequency; and controlling, using the modulator control circuit, the modulator frequency to lock the shifted frequency to a desired frequency.

[024] The modulator may be locked to the shifted frequency using saturation absorption techniques. For example, the system may comprise a spectroscopic reference; at least one reflector which directs light from the modulator through the spectroscopic reference in a first direction to saturate the spectroscopic reference; and at least one reflector which directs light from the modulator through the spectroscopic reference in a second direction which is opposite to the first direction whereby an error signal is generated when the frequency of the light from the modulator does not match a frequency of the saturated spectroscopic reference. The modulator control circuit may comprise a dithering module to generate a dithered signal which is mixed with the error signal received from the spectroscopic reference to generate a sharpened error signal; and a controller to determine a control signal which adjusts the modulator frequency based on the sharpened error signal, and send the control signal to the modulator to adjust the modulator frequency. In this way, the frequency of the modulator is adjusted as an alternative to directly adjusting the frequency of the master laser. The calibration of the master laser may be done using the feedback control circuit described above or any suitable technique.

[025] Once the shifted frequency is locked, the slave control circuit, may be used to tune the frequency of output laser light from the slave laser to the shifted frequency. For example, the slave control circuit may be configured to calibrate the at least one slave laser to a known frequency by receiving, from the at least one sensor, a measurement of a frequency of a generated shifted-slave beat signal which is generated by combining output from the modulator with output from the slave laser; determining, using the measured frequency of the shifted-slave beat signal, an error signal which indicates a direction in which the frequency of the slave laser needs to be adjusted to tune the frequency of output laser light from the slave laser to the frequency of output laser light from the modulator; and tuning the slave laser based on the determined error signal.

[026] This aspect of modulating the master frequency may be independent of tuning the slave laser and thus according to another aspect, there is provided a method of generating output laser light at a desired shifted frequency, the method comprising calibrating a laser (e.g. the master laser) to output laser light at a known frequency; shifting, using a modulator, the frequency of output laser light from the laser by a modulator frequency; controlling, using a modulator control circuit, the modulator frequency to lock the shifted frequency to the desired frequency; and outputting light from the modulator at the desired frequency. Similarly, according to another aspect there may be a laser system comprising a master laser having a master laser cavity and a master laser frequency; a modulator which is external to the master laser cavity and which shifts the frequency of output laser light from the master laser by a modulator frequency to generate a shifted frequency and which outputs light from the modulator at the desired frequency; and a modulator control circuit for controlling the modulator frequency to lock the shifted frequency to a desired frequency. Saturation absorption spectroscopy may be used to lock the shifted frequency to the desired frequency and the desired frequency may the frequency at which there is maximum absorption.

[027] When using the master laser as a reference, tuning each slave laser using the slave control circuit, may comprise generating a master-slave beat signal by combining output from the master laser with output from the slave laser; measuring a frequency of the generated master-slave beat signal; determining, using the measured master-slave beat signal, an error signal which indicates a direction in which the frequency of the slave laser needs to be adjusted to tune the frequency of output laser light from the slave laser to the frequency of output laser light from the master laser; and tuning the sI^va laser based on the determined error signal. A similar arrangement may be used to tune each slave laser to the shifted frequency but in this case a measured shifted-slave beat signal is measured. In such an arrangement, the slave control circuit may be termed a slave feedback control circuit because feedback in the form of an error signal is determined, and this is fed back into the laser. Each of these slave control circuits may comprise a processor (not shown) to implement the methods described. Each of the plurality of slave lasers may be set (e.g. initialised or calibrated) to a different known frequency.

[028] The frequency of the beat signal may be measured by any suitable sensor, for example a photo diode having a bandwidth which is chosen to resolve the spectral difference between each continuous wave laser (master or slave laser) and the nearest frequency line of the frequency comb. The bandwidth frequency fBW of the photo diode may be less than half of the repetition frequency frep of the frequency comb, namely: frep J BW < By setting the bandwidth in this way, the laser-comb beat signal will be measured only when its frequency is less than half the repetition frequency. Thus, the frequency of the measured laser-comb beat signal may be zero (and hence disappear), twice for each frequency comb line, when the frequencies are equal and when the frequency of the beat signal is near the mid-point between comb lines.

[029] Each of the slave and master lasers may comprise a laser cavity within which there are a plurality of mirrors, a laser crystal which is positioned between two of the plurality of mirrors and an actuation component which adjusts an optical path length between the plurality of mirrors, whereby the frequency of each laser is adjusted (tuned). The actuation component may be any suitable component, for example e.g. a piezoelectric transducer on one of the mirrors within the laser cavity and an electrooptic modulator within the laser cavity. Each of the slave and master lasers is a continuous wave laser. At least one of the slave lasers may be comprise four mirrors arranged in bow-tie resonator arrangement. The laser crystal may be any suitable material which is tunable over a wide emission range, for example chromium doped materials and Ti:Sapphire. Some or all of the slave lasers may contain laser crystals of different materials.

[030] The techniques further provide processor control code to implement the above-described methods, for example on a general purpose computer system or on a digital signal processor (DSP). The techniques also provide a carrier carrying processor control code to, when running, implement any of the above methods, in particular on a non-transitory data carrier. The code may be provided on a carrier such as a disk, a microprocessor, CD- or DVD-ROM, programmed memory such as non-volatile memory (e.g. Flash) or read-only memory (firmware), or on a data carrier such as an optical or electrical signal carrier. Code (and / or data) to implement embodiments of the techniques described herein may comprise source, object or executable code in a conventional programming language (interpreted or compiled) such as Python, C, or assembly code, code for setting up or controlling an ASIC (Application Specific Integrated Circuit) or FPGA (Field Programmable Gate Array), or code for a hardware description language such as Verilog (RTM) or VHDL (Very high speed integrated circuit Hardware Description Language). As the skilled person will appreciate, such code and / or data may be distributed between a plurality of coupled components in communication with one another. The techniques may comprise a controller which includes a microprocessor, working memory and program memory coupled to one or more of the components of the system. Brief description of the drawings

[031] Implementations of the present techniques will now be described, by way of example only, with reference to the accompanying drawings, in which:

[032] Figure 1 illustrates an energy diagram of a Rubidium-87 transition line;

[033] Figure 2 shows a laser system comprising a master laser and a plurality of slave lasers;

[034] Figure 3a is a schematic drawing of a master laser for use in the system of Figure 2;

[035] Figure 3b is a schematic drawing of a slave laser for use in the system of Figure 2;

[036] Figure 3c is a schematic drawing of a frequency comb for use in the system of Figure 2;

[037] Figure 4 is a flowchart showing the steps for one method for tuning each slave laser in the system of Figure 2 to a specific frequency using a frequency comb;

[038] Figure 5 is a schematic illustration of the frequency line spectrum of a frequency comb which is used in the system of Figure 2.

[039] Figures 6A to 6C show how a beat signal appears and disappears during one implementation of the method of Figure 3.

[040] Figure 7 is a flowchart showing the steps for a dithering scheme for tuning each slave laser in the system of Figure 2 to a specific frequency using a frequency comb;

[041] Figure 8A is a graph showing a measurement of a beat signal frequency using the dithering scheme of Figure 7

[042] Figures 8B to 8E illustrate frequency line spectrums as used in the dithering scheme of Figure 7;

[043] Figure 9 is a flowchart showing the steps for a combination method for tuning each slave laser in the system of Figure 2 to a specific frequency using a frequency comb;

[044] Figures 10a and 10b are two arrangements for locking a master laser to a master frequency;

[045] Figure 10c is a flowchart of the steps for locking a master laser using the arrangement of Figure 10b;

[046] Figure 10d is a spectral response of a saturated hyperfine structure showing amplitude varying with frequency;

[047] Figure 10e is a graph of a low amplitude dither signal which is shifted by k and which plots frequency versus time;

[048] Figure 10f is a graph of an error signal which shows variation in amplitude against time. Detailed description of the drawings

[049] Generally speaking, we describe a system comprising a master laser and a plurality of slave lasers each of which is locked to output laser light at different frequencies in a range of possible reference frequencies. The master and slave lasers are housed within the same housing to form a compact system. We also describe the method for locking the output laser light from each laser to a different frequency.

[050] Figure 2 shows a laser system 100 comprising a master laser 102, at least one slave laser 104i,..., 104n and an optical ruler in the form of a frequency comb laser 106 (which may be termed a frequency comb and the terms may be used interchangeably). The system 100 also comprises a plurality of avalanche photodiodes, APD, 112o,..., 112n; one for the master laser and one for each of the slave lasers. It will be appreciated that any suitable sensor may be used, and an avalanche photodiode is just one example. There is also a plurality of beam splitters 140 and mirrors (or other similar reflective elements) 150 to direct laser light within the system as explained in more detail below. All of these components are housed within a single housing 101.

[051] The master laser 102 may be configured to provide a precisely controlled output with a frequency fcw. For example, the master laser may be configured to operate on a single spectroscopic reference frequency provided by a spectroscopic reference 108. In other words, the master laser 102 may be absolutely referenced to the spectroscopic reference 108 which operates on a single reference frequency fref. For example, the spectroscopic reference 108 may be a Rubidium-87 vapour cell or any other appropriate spectroscopic reference. The master laser 102 may be a continuous wave, CW, laser operating on a frequency fcw. When the continuous wave master laser 102 operates on the frequency of the spectroscopic reference, the frequencies are equal and fcw = fref.

[052] The master laser may be configured to provide a precisely controlled output by means of a master control circuit 118. The master control circuit 118 provides an effective means of ensuring the stability of the output. The master control circuit 118 may be a master feedforward control circuit or a master feedback control circuit. In the case of a master feedback control circuit, the master feedback control circuit may comprise an error signal component and an actuation component. The error signal component may be configured to generate and measure an error signal. The actuation component typically adjusts the phase condition of the master laser by changing the optical path length of the laser and thus the error signal is fed back into the laser.

[053] Alternatively, rather than adjusting the operational frequency of the master laser 102 using the error signal, a master feedforward control circuit may comprise a modulator to adjust the output of the master laser 102 based on the error signal. The operational frequency of the master laser 102 itself is stable and unmodified. Examples of the master control circuits are described in Figures 10a to 10c. Each of these master control circuits may comprise a processor (not shown) to implement the methods described.

[054] Each of the slave lasers 104i . , 104n may similarly be configured to operate on a specific frequency by means of a corresponding slave feedback control circuit 120i,..., 120n. That is, each slave feedback control circuit may be used to lock the frequency of output laser light from each slave laser. As with the master feedback control circuit, the corresponding slave feedback control circuits 120i,..., 120n may comprise an error signal component and an actuation component. One illustrative arrangement for a slave laser and the slave feedback control circuit is described in more detail below with reference to Figure 3b.

[055] The frequency comb 106 produces a frequency line spectrum comprising a range of laser lines which are all discretely spaced by a repetition frequency frep. An example of such a frequency line spectrum is shown in Figure 5 and described in more detail below. The repetition frequency is usually less than 5GHz. Any frequency F may be defined by the following equation: J7 — f 4- n . f 1 Jceo ~ IL Jrep> where n is a number greater than or equal to 1 and fceo is an offset frequency which is typically less than 1GHz and is effectively the frequency of the first tooth of the comb. The frequency comb 106 may be an externally referenced frequency comb, for example as described in more detail in Figure 3c. Alternatively, the frequency comb may be a self-referenced frequency comb.

[056] The output of the master laser 102 may be combined with the output of the frequency comb 106 to generate an initial heterodyne beat signal which may also be termed a mastercomb beat signal. For conciseness, a heterodyne optical beat signal will be referred to as a beat signal herein. The frequency of the master-comb beat signal f°eat may be measured by the master APD 112o. Alternatively, the output of the master laser 102 may combine with the output of each slave laser 104i. , 104n to produce a master-slave heterodyne optical beat signal. Similarly, the output of each slave laser 104i,..., 104nmay combine with the output of the frequency comb 106 to produce a slave-comb heterodyne optical beat signal (this may also be termed a laser-comb beat signal and the terms are used interchangeably). The frequency of the beat signals resulting from the output of the first slave laser may be measured using a first slave APD 112i. Similarly, the frequency of the beat signals resulting from the output of the nth slave laser may be measured using an nth slave APD 112n.

[057] The bandwidth fBW of each of the master APD 112o and the slave APDs 112i, ..., 112n may be chosen such that a typical beat signal frequency falls within its bandwidth, i.e. so that fbeat1 < / bw- In other words, the bandwidth of each APD is chosen to resolve the spectral difference between each continuous wave laser (master or slave laser) and the nearest frequency line of the frequency comb. The bandwidth of the master and slave APDs may be adjusted by coupling each APD with a low-bandpass filter or a high-bandpass filter. The bandpass filters may serve to e.g. reduce the level of noise detected by the APDs. As explained below, each APD will detect the appearance of a beat signal when the beat signal frequency falls within its bandwidth as well as the disappearance of a beat signal when the beat signal frequency falls outside of its bandwidth.

[058] The system may also comprise a blocking component to select whether the output of each slave laser 104i,..., 104n is combined with the output of the master laser 102 or the output of the frequency comb 106. For example, as shown in Figure 2, the blocking component comprises a first beam block 114 and a second beam block 116. In a first master arrangement in which the output of the master laser 102 is combined with the output of each slave laser 104i,..., 104n (i.e. without the output of the frequency comb 106), the first beam block 114 is activated to block or impede the output of the frequency comb 106. The second beam block 116 is deactivated so that the output of the frequency comb 106 is not blocked. In a second frequency comb arrangement in which the output of the at least one slave laser 104i,..., 104n is combined with the output of the frequency comb (i.e. without the output of the master laser 102), the second beam block 116 is activated to block or impede the output of the master laser 102. The first beam block 114 is deactivated so that the output of the frequency comb 106 is not blocked. It will be appreciated that the beam blocks 114 and 116 are merely exemplary means of blocking or impeding the output of the master laser 104 or the frequency comb 106, and that any suitable blocking component for impeding or blocking may be used.

[059] Figure 3a shows an example arrangement of the master laser 102 which as shown may comprise a pair of opposing cavity mirrors 310, 312 with a laser crystal 314 positioned between the pair of mirrors. A piezo-electric transducer 316 (PZT) is mounted on one of the mirrors 312, each of which are highly reflective (e.g. 99.9% reflective). The PZT may be configured as an actuation component to adjust the distance between the cavity mirrors 310, 312, thereby adjusting the optical path length of the master laser and the phase condition of the master laser. The frequency of the master laser changes as a result of the change in the phase condition. Alternatively (or additionally), the actuation component may comprise an electrooptic modulator 318 (EOM) positioned within the laser cavity, i.e. between the cavity mirrors 310, 312. An applied voltage adjusts the refractive index of the EOM 318. As the light within the laser cavity traverses the EOM 318, the optical path length of the master laser changes as a result of the change in the refractive index. The changes in optical path length of the cavity are achieved relatively quickly with an EOM and relatively slowly with the PZT. It will be appreciated that the arrangement shown in Figure 3a is just one possible arrangement of the laser cavity for the master laser.

[060] Figure 3b shows an example of a slave laser arrangement which comprises a bow-tie resonator formed from four cavity mirrors 350, 352, 354, 356. A piezo-electric transducer 366 (PZT) is mounted on one of the mirrors 352. A laser crystal 364 is positioned between one pair of mirrors, in this example between the mirror with the PZT and another mirror. The PZT forms the actuation component which adjusts the phase condition of the slave laser by changing the optical path length of the laser as described above. One of the mirrors 356 acts as an output coupler to couple some output from the slave laser to the error signal component and is a partially reflective optic (e.g. 98% reflective). The mirrors which are not the output coupler are highly reflective (e.g. 99.9% reflective).

[061] As with the master feedback control circuit, the error signal component of the slave feedback control circuit is configured to generate and measure an error signal. In this example, the error signal component may comprise a mixer 342 and a high precision oscillator 334. The high precision oscillator 334 may generate a synthesised signal whose frequency is known to a high precision. The master-slave beat signal as measured by the photodiode 332 may be passed to the mixer 342 and mixed with the synthesised signal generated by the high precision oscillator 334. The mixed signal may be provided as input to a low bandpass filter 336 to generate a linear error signal which is measured by a sensor 338 (e.g. a PID). The characteristics of the linear error signal may be used to guide the actuation controller 340 which provides a signal to the PZT 366. For example, the linear error signal has a directionality, in other words is positive and negative around the lock point, so the actuation controller knows to feed back a negative or positive signal to keep the frequency locked.

[062] Figure 3c shows an example of an externally referenced laser comb 106 which may be used in the system of Figure 2. In this example, the laser comb 106 comprises three mirrors 380, 382, 384 with a PZT 386 mounted on one of the mirrors 384. The PZT may vary the optical path length with the frequency comb cavity as described above. A laser crystal 394 is positioned between one pair of mirrors, in this example, the mirrors without the PZT. One of the mirrors 384, in this example, the one with the PZT, acts as an output coupler to couple some output from the laser comb to the feedback control circuit. In this example, another of the mirrors 382 injects light output fFC from the frequency comb 106 into one of the slave lasers. The mirrors which are not the output coupler are highly reflective.

[063] Regarding the injection into the slave laser, although this is shown for a single slave laser, the frequency comb may inject output simultaneously into a plurality of slave lasers. By contrast, the master laser is referenced to the spectroscopic reference, rather than the frequency comb. As described above, one of the mirrors 356 in the slave laser acts as an output coupler to couple some output from the slave laser to the error signal component (which is not shown for ease of reference). The error signal component may comprise a photo-diode or APD to measure the slave-comb beat signal as described above. In other words, within each laser cavity may be less complex, with fewer components.

[064] Returning to the externally referenced nature of the frequency comb, a radio-frequency, RF, synthesiser 370 in combination with a laser diode pump source 372 is used to perform external referencing of the frequency comb 106. The laser diode pump source 372 may operate on a frequency fOffSet and the RF synthesiser 370 may have a pre-defined repetition frequency frRep. The offset frequency fceo of the frequency comb 106 may be tuned to the operating frequency foffset of the laser diode pump source 372 so that fceo = fOffSet. The repetition frequency frep of the frequency comb 106 may be tuned to the repetition frequency frRp of the RF synthesiser 370 so that frep = fRep.

[065] The laser diode pump source 372 may operate on a frequency fOffSet. The frequency foffset may be tuned using a laser driver 374. The laser driver 374 is a current source, wherein the current can be controlled with a high degree of precision. A change in the current of the laser driver 374 causes a change in the frequency foffset of the laser diode pump source 372. The repetition frequency frep of the frequency comb 106 may be tuned to the repetition frequency frRep of the RF synthesiser 370, for example using a feedback control circuit similar to the one used for tuning / locking the slave lasers. Thus, part of the output from the frequency comb may be passed to a photodiode 392 and then to the mixer 396 where it is mixed with the synthesised signal generated by the RF synthesiser 370. The mixed signal may be provided as input to a low bandpass filter 376 to generate a linear error signal which is measured by a sensor 378 (e.g. a PID). The characteristics of the linear error signal may be used to guide the actuation controller 390 which provides a signal to the PZT 386 to adjust the path length with the optical cavity and hence adjust the repetition frequency of the frequency comb.

[066] As an alternative to the externally referenced frequency comb in Figure 3c, a selfreferenced frequency comb may be produced by initially creating a frequency comb with an unknown offset fceo frequency and with a repetition frequency frep as set by a first RF synthesiser. The frequency comb may initially be created such that the lines of the frequency comb span an octave. That is, the offset frequency may be unknown, but the ratio between the first and last frequency comb lines may be fixed to 2:1. A beat signal between the signal of the first RF synthesiser and the first frequency comb line is measured. Similarly, a beat signal between the signal of the first RF synthesiser and the last frequency comb line is also measured. The measured beat signals between the first RF synthesiser and the first and last frequency comb lines allow a determination of the offset frequency fceo. The determined offset frequency may be used to set the offset frequency of a second RF synthesiser to generate a self-referenced frequency comb with the determined offset frequency fceo.

[067] Figure 4 is a flowchart showing how each of the slave lasers 104i,..., 104n can be tuned to different target reference frequencies using measurements of the beat signals by the APDs. Figure 5 is a schematic illustration of the frequency line spectrum 200 of a frequency comb which is used in the tuning method shown in Figure 4. As explained in more detail below, in this method the beat signals are counted using a counting procedure.

[068] In a first step S400 of Figure 4, the frequency fcw of the master laser is locked to the frequency fref of the spectroscopic reference, for example using the master feedback control circuit. The frequency comb is then activated so that at step S402, the frequency f°eat of the master-comb beat note which is generated by the combination of the output from the master laser and a line (or tooth) in the frequency comb can be measured by the master APD. These frequencies are illustrated in Figure 5 which shows the frequency fref of the spectroscopic reference as a dashed line. Merely for illustrative purposes, a small gap is shown between each of the reference frequency and the frequency of the master laser so that both lines are visible. Each line of the frequency comb is shown as a bold line and is labelled as m, m - 1, ..., m - 7. The frequency fcw of the master laser lies between the frequency of the mth and the m - 1th lines of the frequency comb.

[069] The manual counting procedure may comprise determining an initial index of a frequency line in the frequency comb using a measurement of the master-comb beat signal frequency. The frequency of the master-comb beat signal f°eat is given by the difference between the master laser frequency fcw and the frequency line fFC of the frequency comb: / ■0 f f r-i \ J beat — Jew JFC' k-U Furthermore, the master laser may be configured to operate on a single spectroscopic reference frequency such that fcw = fref. Hence, a measurement of the beat frequency fPeat and the known reference frequency fref allow the frequency fFC of the frequency line to be determined.

[070] The frequency fFC of the frequency line can also be expressed in terms of the characteristics of the frequency comb, namely the repetition frequency frep and an offset frequency fceo. Each of the frequencies of the frequency lines of the frequency comb may be expressed as: fpC fceo T ' frep> (2) where m is an integer which acts as in index of a particular frequency line. For example, if a frequency comb comprises 100 frequency lines, then m e {1,... ,100}. Re-arranging Eq. 2 above allows the index m of the frequency line to be determined at step S404 of Figure 4 when each of fFC, fceo and frep are known. Hence, a measurement of the master-comb beat frequency may be used to determine an index m of the frequency line when the operating frequency of the master laser is sufficiently close to the mth frequency line of the frequency comb to produce a beat signal within the bandwidth of the APD. The frequency of the mth frequency line of the frequency comb will also be denoted fm = fFC.

[071] At step S406 of Figure 4, the frequency f£w of the first slave laser may be tuned at time 0 to the frequency fcw = fref of the master laser. This may be done using any suitable technique, for example using a feedback control circuit as described above. The feedback may include combining the master laser output with the output of the first slave laser by activating the first beam block. The frequency of the first master-slave beat note is measured by the first APD. When the tuning is complete, the frequency fcW0 of the first slave laser will satisfy: fcW,0 = fref = few- (3)

[072] The first beam block may then be deactivated and the second beam block activated so that the output from the first slave laser is combined with the output from the frequency comb. By virtue of the condition in Eq. 3 above, the frequency of the first slave laser is sufficiently close to the frequency fm of the mth frequency line of the frequency comb to produce a beat signal which is detectable by the first slave APD. The frequency of the first slave-comb beat signal at time 0 f^eat# may be given by the difference: / ■1 __ f / -1 Jbeat,0 — Jm J CW- (4) Optionally, the frequency of the first slave-comb beat signal can be measured and the line number determined as above but given that the frequency of the first slave laser has been initially tuned to the frequency of the master laser, the line number should also be unchanged.

[073] The next step S408 is to adjust the frequency fBW of the slave laser. This may be done using any standard technique, for example using a feedback control circuit as described above. As the frequency is adjusted, its value is no longer known and needs to be calculated. As the frequency fBW changes, the frequency fBeat of the first slave-comb beat signal also changes. The bandwidth frequency fBW of the first slave APD is set to be less than half of the repetition frequency frep of the frequency comb, namely: (5) By setting the bandwidth of the APD in this way, the first slave-comb beat signal will be measured by the APD only when it is less than half the repetition frequency. Hence, between a given pair of frequency comb lines m and m - 1 separated by frep, there exists a pair of possible ranges for the frequency fBW of the first slave laser where a beat signal will be detected, namely: fm fBW <few fn> ($) fm-l<fc1W<fm-l + fBW (7) It will be appreciated that similar expressions can be written for each pair of frequency comb lines. Between any given pair of adjacent frequency comb lines, the beat signal will disappear twice. No beat signal is generated (i.e. disappears) when the slave laser frequency fcW is equal to the frequency of a comb line. The beat signal is not detected by the APD (i.e. disappears) when the frequency of the beat signal is near the midpoint between comb lines and thus falls outside both the ranges given in Eqs. 6 and 7 above.

[074] Figure 5 together with Figures 6A to 6C show how a beat signal appears and disappears. Initially, the first slave laser is tuned to the same frequency as the master laser, thus as shown in Figure 5, fCw=fcw,o- lf the first slave-comb beat note is measured at time 0, it will be equal to the master-comb beat note, i.e. fBeatfi = f°eat. The frequency of the first slave-comb beat note at time 0 is less than the bandwidth of the APD and thus the frequency of the first slave laser at time 0 meets the requirement of equation (6). The frequency of the first slave-comb beat note at time 0 can be measured by the first slave APD. Figure 6A shows an example of the measured beat signal frequency.

[075] Returning to Figure 5, at time t = 1, the frequency fcW1 of the first slave laser has decreased and is now closer to the m - 1th line than the mtfl line. The frequency of the first slave laser thus no longer satisfies the requirement of equation (6) and thus any slave-comb beat note generated by the combination of the frequency of the first slave laser and the mth comb line is not measureable by the APD. The frequency of the first slave laser also does not yet satisfy the requirement of equation (7) because the frequency is not yet close enough to the frequency of the m - 1th line. Thus any slave-comb beat note generated by the combination of the frequency of the first slave laser and the m - 1th comb line is outside the bandwidth of the APD. Figure 6B shows that no beat signal is detected by the APD. As a result, the beat signal disappears.

[076] Returning to Figure 5, at a later time t = k, the frequency f£wk of the first slave laser has further decreased and is now closer to the m - 1th line than at the previous time t = 1. In other words, the frequency ffwk of the first slave laser now meets the requirement of equation (7) and the beat signal can be measured by the APD. In other words, fbeat,k's within the bandwidth fBW. Figure 6C shows an example of the measured beat signal frequency at time t = k. It is noted that the beat signal will also have reappeared when the frequency of the first slave laser is on the other side of the m - 1th line but at a closer position than shown at time t = 1. The beat signal will also have disappeared when the frequency of the first slave laser equals that of the frequency of the m - 1th line. In other words, the slave-comb beat signal tunes and fades twice on each comb mode.

[077] The pattern of appearance and disappearance of the slave-comb beat signal illustrated in Figures 6A to 6C will be repeated for each pair of adjacent frequency lines e.g. m -1 and m - 2, m - 2 and m - 3 etc. Hence, as the frequency few the first slave laser changes across a series n of adjacent frequency comb line pairs, the first slave-comb beat signal appears and disappears 2n or 2n+1 times. For example, as shown in Figure 5, at time t = n, the frequency of the slave laser sits between the m - 5th and m - 6th lines and thus has crossed 5 lines. When the beat signal has appeared and disappeared 10 times, we can determine that the frequency ffw>n of the first slave laser is closer to the m - 5th line and when the beat signal has appeared and disappeared 11 times, we can determine that the frequency fcw,n °f first slave laser is closer to the m — 6th line but still above this line. Importantly, by counting the appearance and disappearance of the beat signal, we can determine the number m of frequency comb lines which have been crossed. In other words, we are counting the instances at which the beat signal repeats. We can calculate the instances at which the beat signal is equal to zero or any fixed value, e.g. 100MHz. We are determining the periodicity of the beat signal.

[078] The current slave-comb beat frequency fbeat,n’ the repetition frequency frep, the offset frequency fceo and the number m of frequency comb lines which have been crossed are thus known. At step S410 of Figure 4, the information can be used to determine the current frequency fcWn of the first slave laser using: fcw,n = mfrep T fceo T fbeat,n W At step S412, there is a determination as to whether the desired slave laser frequency has been reached and if not, the method loops back to adjusting the frequency of the slave laser and continues counting and recalculating the frequency as described above.

[079] When the first slave laser is set to the desired frequency, the next step S414 is to select the next slave laser to be tuned. The steps of tuning the next slave laser to the master laser (step S406) and then adjusting the frequency, counting the number of disappearances of the beat signal generated by the slave laser (steps S408 and S410) and calculating the current frequency are repeated. The slave-comb beat signal for the ittl slave laser at time n may be denoted by fbeat,n and may be inserted in each of the equations above. The exercise of tuning each slave laser to a desired and different frequency can be repeated n times for n continuous wave slave lasers. The slave lasers may be considered to be a chain of lasers and by separately tuning each slave laser, it is possible to create a system that is tunable and absolutely referenced over the entire desired spectrum (e.g. over the entire visible spectrum).

[080] It will be appreciated that the chain of lasers may be simultaneously tuned and that the steps of tuning each slave laser to the master laser (step S406) and then adjusting the frequency, counting the number of disappearances of the beat signal generated by the slave laser (steps S408 and S410) and calculating the current frequency may be done in parallel rather than sequentially as shown in Figure 4.

[081] When adjusting over a large frequency range, where each slave laser frequency is adjusted over a significant number (e.g. tens if not thousands) of frequency comb lines, it may be impractical to count the correspondingly large number of beat note appearances and disappearances. Figure 7 shows an alternative scheme for determining the frequency of the slave laser which is termed a dithering scheme.

[082] As shown in Figure 7, the first step S700 is to lock a frequency of laser light emitted from a slave laser (or each slave laser) to a particular frequency. At step S702, the repetition frequency frep of the frequency comb is then adjusted. The repetition frequency frep may vary or dither by means of a control interface coupled to the frequency comb. A controller (not shown) may be used to change the repetition frequency and may send a signal to the synthesiser to effect this change. The repetition frequency frep may be increased or scanned over a pre-determined range, e.g. from = 950 MHz to fr2ep = 1,050 MHz. The range of the repetition frequency scan may be given by Lfrep = f2ep - f^ep.

[083] While the repetition frequency is being increased over the pre-determined range, as shown at step S704, the changing beat note from the combined output from the slave laser and the frequency comb is measured. As mentioned above, the APD (or similar detector) may measure the appearance and disappearance of a beat signal when the beat frequency falls within the bandwidth of the APD. That is, as the beat signal frequency changes, the APD measures the appearance and disappearance of the beat signal. Figure 8a is a graph showing a measurement of the beat signal frequency and shows that the beat signal frequency increases, then decreases and ultimately disappears before increasing again.

[084] Figures 8b to 8e illustrate schematically the reasons for the changing beat frequency. Figure 8B shows a frequency comb with a repetition frequency frep. The current frequency 800 of a slave laser is marked with a line. Merely as an illustrative example, the slave laser frequency 800 is shown adjacent to the m - 1 frequency comb line and between the m - 1 and m - 2 frequency comb lines. A beat signal with frequency fbeat exists between one of the frequency comb lines (in this example the m -1 frequency comb line) and the slave laser frequency 800.

[085] Figure 8C shows a frequency comb with a different repetition frequency f^ep to the frequency comb of Figure 8B; specifically the repetition frequency is increased so that f'ep >frep. The spacing of the frequency comb lines m,m - l,m - 2,... of the frequency comb increases as a result of the increase in the repetition frequency. The slave laser frequency 800 is unchanged between Figures 8B and 8C and as shown the slave laser frequency 800 is now closer to the m -1 frequency comb line in Figure 8C than in Figure 8B. Thus, the beat frequency fbeat decreases, reflected by the decrease in the spacing between the frequency comb line and the slave laser frequency 800. It will be appreciated that if the repetition frequency frep is equal to the slave laser frequency 800, the beat note will disappear.

[086] Figure 8D shows a frequency comb which is the same as in Figure 8B and has a repetition frequency frep. In this example, the slave laser frequency 802 is to the right of the m - 1 frequency comb line rather than to the left of the m - 1 frequency comb line as shown in Figure 8B. In other words, the slave laser frequency 802 is between the m and m- 1 frequency comb lines. As in Figure 8B, a beat signal with frequency fbeat exists between the m - 1 frequency comb line and the slave laser frequency 802.

[087] Figure 8E shows a frequency comb which is the same as that shown in Figure 8C and has a larger repetition frequency f^p. The slave laser frequency 802 is unchanged between Figures 8D and 8E and as shown the slave laser frequency 802 is now further from the m - 1 frequency comb line in Figure 8E than in Figure 8D. The beat frequency fbeat may thus increase as a result of the increase in the repetition frequency, reflected by the increase in the spacing between the frequency comb line and the laser frequency line 802.

[088] As shown in Figures 8B to 8E, a beat signal may have a particular directionality which reflects the positioning of the slave laser frequency line 800, 802 with respect to a particular frequency comb line. The directionality may refer to whether slave laser frequency has a higher or lower frequency than a particular frequency comb line. The directionality may be determined based on whether the frequency of the beat signal increases or decreases when the repetition frequency of the frequency comb increases. It will be appreciated that the frequency of the slave laser does not change. As shown in Figures 8B and 8C, when the repetition frequency increases, the frequency of the slave laser is now closer to that of the frequency line and the frequency of the beat signal decreases. Thus, the slave laser frequency is to the left of a particular comb line (in this example : m-1). As shown in Figures 8D and 8E, when the repetition frequency increases, the frequency of the slave laser is now further away from the frequency of the frequency line and the frequency of the beat signal increases. Thus, the slave laser frequency 802 is to the right of a particular comb line.

[089] Figure 8A shows that the beat signal may appear and disappear a number of times, where the number of times reflects the number of frequency comb lines which have increased to a frequency above that of the laser frequency line as a result of the increase in the repetition frequency. That is, at the start of the scan of the repetition frequency, the laser frequency line may be adjacent to the m frequency comb line. At the end of the scan of the repetition frequency line, the laser frequency line may be adjacent to the m' frequency comb line, where m' = m + Am. The number of frequency lines which have increased to a frequency above that of the laser frequency line is reflected by Am. Returning to Figure 7, at step S706 the index m of the frequency comb line may be estimated, for example according to: ^mfrep + fbeat ^beat m =—Tf----(9) where &beat is the experimental precision on the measured beat frequency, bfrep is the range of the repetition scan given by &frep = ffep - ffep where frep is the upper limit of the frequency range, and fbeat is the frequency of the final measured beat signal. Thus, the dithering scheme may comprise counting the number of times the third beat signal appears and disappears when the repetition frequency changes.

[090] At step S708, the directionality of the frequency line is then determined, e.g. by considering whether the beat signal is increasing or decreasing. Now that we know the value of m, the frequency of the slave laser may be calculated at step S710. When the frequency directionality is above a comb line, the calculation may be: f fceo T ’ frep T fbeat> (10) where fceois the frequency offset, m is the index of the frequency comb line, ffep is the lower limit of the frequency range for dithering the repetition frequency, and fbeat is the frequency of the final measured beat signal. Similarly, when the frequency directionality is below a comb line, the calculation may be: f = fceo + ' frep - fbeat> (11)

[091] At step S712, there is a determination as to whether the desired slave laser frequency has been reached and if not, the method loops back to adjusting the frequency of the slave laser and repeats the calculation of the frequency as described above. When the first slave laser is set to the desired frequency, the next step S714 is to select the next slave laser to be tuned. The steps of tuning the slave laser and then calculating the current frequency as described above are repeated. The exercise of tuning each slave laser to a desired and different frequency can be repeated n times for n continuous wave slave lasers. The slave lasers may be considered to be a chain of lasers and by separately tuning each slave laser, it is possible to create a system that is tunable, and absolutely referenced over the entire desired spectrum (e.g. over the entire visible spectrum).

[092] Figure 9 is a flowchart showing how each of the slave lasers can be tuned using a dithering scheme as shown in Figure 7 in conjunction with a counting scheme as shown in Figure 4. The dithering scheme may be used to determine the frequency of the slave laser by measuring the beat signal frequency as the repetition frequency of the frequency comb is changed. The dithering scheme may be used after a first adjustment, which is typically significant (e.g. tens if not thousands of frequency comb lines or measured in hundreds of nanometres). The counting scheme may then be used to fine-tune the slave laser frequency.

[093] In a first step S900, the slave laser frequency f^w may be adjusted. As mentioned above, the frequency f^w may be adjusted using various methods. For example, the frequency f^w may be adjusted by adjusting the relative distance between opposing mirrors within the slave laser cavity. In this first step, the adjustment is typically significant, e.g. in the order of more than 10 THz, corresponding to a wavelength adjustment of more than lOnm. Such a significant adjustment may enable efficient tuning of the slave laser frequency across a significant portion the spectrum of visible light.

[094] At step S902, the dithering scheme may be used to estimate the index m of the frequency comb line which is closest to the adjusted slave laser frequency line. At step S904, the adjusted slave laser frequency may be calculated, for example using Eqs. 10 or 11 above, depending on the directionality of the beat note. As mentioned above, the directionality may be determined based on whether the frequency of the beat signal increases or decreases when the repetition frequency of the frequency comb increases. For conciseness, the details are not repeated here.

[095] At step S906, there is a determination as to whether the desired slave laser frequency has been reached or not. It will be appreciated that the probability of having reached the desired slave laser frequency after a significant adjustment is low. If the desired slave laser frequency has not yet been reached, there is a determination at step S908 of whether a further significant adjustment is required. This may be required if, for example, there is a significant discrepancy between the frequency calculated in step S904 and the desired slave laser frequency. If a further significant adjustment is required, then the method loops back to step S900 and continues recalculating the significantly adjusted slave laser frequency.

[096] When it is determined that a further significant adjustment is not required, at step 910, the slave laser frequency is fine-tuned using the beat note counting scheme described above in relation to Figure 4 using steps S406 to S414. In this case, the slave laser has a frequency which is significantly different (e.g. more than 10Onm different) from the master laser frequency and thus the slave laser is not tuned to the master laser. For conciseness, the details of steps S406 to S414 are not repeated here. Returning to Figure 9, at step 912, there is a determination of whether the desired slave laser frequency has been reached and if not, the method loops back to fine-tuning the slave laser frequency. The determination may comprise calculating the slave laser frequency, for example as described in equation (8).

[097] When the first slave laser is set to the desired frequency, the next step S914 is to select the next slave laser to be tuned. The steps of calculating the significantly adjusted slave laser frequency for the next slave laser to be tuned (steps S900 - S904), determining whether the desired slave laser frequency has been reached and whether a further significant adjustment is required (steps 906 and 908) and fine-tuning the slave laser frequency (steps S910 - 912) are repeated. As mentioned above in relation to Figure 4, the exercise of tuning each slave laser to a desired and different frequency can be repeated n times for n continuous wave slave lasers.

[098] Figures 10a and 10b are schematic diagrams of master control circuits according to the present techniques. As noted above the master control circuit enables the provision of a precisely controlled output of the master laser and may be a master feedforward control circuit or a master feedback control circuit. In the case of the feedback control circuit, the direct or immediate output of the master laser is used as part of a feedback loop to adjust the master laser frequency via the generation of an error signal related to any shift in the direct or immediate output of the master laser. By contrast, in the feedforward control circuit, the master laser frequency is stabilised to an on-board reference and is unchanged. A modulator is used to precisely control a shifted version of the output of the master laser.

[099] Figure 10a shows a schematic diagram of a master feedback control circuit 1050. The master laser 102 may be configured to operate on a spectroscopic reference frequency fcw = fref by means of the master feedback control circuit 1050. That is, the master feedback control circuit may be used to lock the frequency of output laser light from the master laser to that of a spectroscopic reference. The master feedback control circuit 1050 may comprise an error signal component and an actuation component. The error signal component may be configured to generate and measure an error signal. The actuation component typically adjusts the phase condition of the master laser by changing the optical path length of the laser. This can be done using any suitable technique and an example arrangement is described below with reference to Figure 3A. The first feedback control circuit 1050 may be configured to use the actuation component to adjust the master laser frequency until the error signal as generated and measured by the error signal component satisfies a particular condition. For example, the master laser frequency may be adjusted until the value of the error signal reaches a predetermined value.

[100] Merely, as an example, the error signal may be generated and measured by performing saturation absorption spectroscopy with the spectroscopic reference 1052. Saturation absorption spectroscopy is a well-known technique which exploits the fact that every atom has a unique set of absorption frequencies determined by the hyperfine structure of the electronic states. When the atoms are at rest, as light is propagated through the spectroscopic reference, light is only absorbed at these discrete transition frequencies. When some of the atoms are moving and other are stationary, only the atoms which are stationary will interact with the laser light at one of the hyperfine transition peaks. Atoms at speed v only interact with a laser frequency which is offset from the transition frequencies, and which satisfies a Doppler shift to a transition frequency. A frequency distribution of absorption with hyperfine dips results.

[101] Thus, as shown the error signal component may comprise two beam splitters 1054,1056 with the first beam splitter 1054 directing some of the light from the master laser towards the second beam splitter 1056. The second beam splitter 1056 directs a first portion of the directed light towards a first photodiode 1058 and a second portion of the directed light towards the spectroscopic reference 1052. There is a second counter-propagating beam (not shown) which travels through the spectroscopic reference 1052 and saturates the spectroscopic reference 1052 to allow an error signal to be created. A second photodiode 1060 detects any light which passes through the spectroscopic reference 1052. If the light is still tuned to the original frequency, the light will be completely absorbed by the reference. Otherwise, an error signal will be generated. It will be appreciated that using saturation absorption spectroscopy is just one method for generating the error signal and the error signal may be generated and measured by alternative means.

[102] Figure 10b shows a schematic diagram of an example of a feedforward control circuit 1000 according to the present techniques. Initially, the frequency of the master laser 102 may be pre-stabilised to the frequency of an on-board reference with a low frequency drift. That is, the master laser 102 may be pre-stabilised or pre-tuned to an on-board reference whose frequency is stable and remains within a narrow range for prolonged periods of time. The master laser 102 may be pre-stabilised by means of an actuation component, as described in relation to Figure 3A above. The on-board reference may be any appropriate reference frequency, and preferably in the optical range. For example, the on-board reference may be a Rubidium-87 absolute reference frequency. However, alternative on-board references may be used, provided they have a sufficiently low frequency drift. It will be appreciated that this step of pre-stabilising the master laser is distinct from the configuration of the master laser for the wider purpose of the present techniques, and is merely an initial, pre-stabilisation step.

[103] The output of the pre-stabilised master laser 102 is provided as input to an acousto-optic modulator, AOM, 1002. The purpose of the AOM is to apply a frequency shift fAOM to the frequency of the master laser fcw, for example the frequency shift may be 80KHz. The purpose of the frequency shift is to tune the shifted frequency (fcw + fA0M) to the peak absorption (i.e. the laser light is fully absorbed by the on-board reference) when using a saturation absorption spectroscopy scheme. The output of the pre-stabilised master laser 102 may undergo diffraction upon traversing the AOM 1002, resulting in a plurality of AOM output beams with orders of diffraction. That is the output of the AOM is a plurality of beams, wherein the nth beam in the plurality of beams represents an n^-order diffraction. The Ot / l-order diffraction may be blocked by a static beam block 1012. For the purposes of the present techniques, the 1st order diffraction may be the diffraction of interest. However, it will be appreciated that AOM beams corresponding to other diffraction orders may be of interest for other implementations of the present techniques. The lst-order diffraction AOM output beam may be transmitted from the AOM to a first beam splitter 10181. The first beam splitter 10181 may be a 90 / 10 beam splitter. The frequency of the lst-order diffraction AOM output beam fA0M's given by the frequency of the pre-stabilised master laser shifted by the AOM frequency fA0M. The frequency of the pre-stabilised master laser may be positively or negatively shifted by the AOM frequency: floM = few ± fAOM based on the error signal as explained below. It will be appreciated that a 90 / 10 beam splitter 1018i is provided by way of example only, and that beam splitters with alternative reflection characteristics may be used.

[104] The lst-order diffraction AOM output beam (referred to herein as the AOM output beam, for brevity) is split into two beams by the first beam splitter 1018i. As noted above, the first beam splitter may have a reflectivity of 90%. Therefore, 90% of the AOM output beam may be reflected and 10% may be transmitted through the first beam splitter 10181. That is, the AOM output beam may be split into a first reflected AOM output beam 1020 (which is shown as a dotted line) and a transmitted AOM output beam 1022 (which is shown as a dashed line). The first reflected AOM output beam 1020 may be polarised by a half waveplate 1024. It will be appreciated that a half waveplate is provided byway of example only, and that other suitable waveplates may be used. A second beam splitter 10182 may be used to split the transmitted AOM output beam 1022. The second beam splitter IOI82 may be identical to the first beam splitter 10181. Alternatively, the second beam splitter 10182 may be different to the first beam splitter 10181 and therefore the second beam splitter 10182 may have different reflection characteristics to the first beam splitter 10181.

[105] The second beam splitter 10182 may be used to split the transmitted AOM output beam into a second reflected AOM output beam 1026 and a transmitted master beam 1028 (both of which are shown as dashed lines). As noted above, the first reflected beam 1020 may be polarised by the half waveplate 1024. On the other hand, the second reflected AOM output beam 1026 retains the original polarisation of the pre-stabilised master laser. Therefore, the polarisation of the first reflected beam 1020 and the second reflected beam 1026 are different, for example orthogonal.

[106] A pair of polarising beam splitters, PBS, 1028 may be used to selectively transmit and / or reflected the first and second reflected beams 1020, 1026. By virtue of the splitting of beams being based on the polarisation of an incident beam to a PBS, the first and second reflected beams 1020, 1026 are split based on their polarisation. For example, one PBS may be significantly transparent to beams with the polarisation of the first reflected beam 1020, whilst the other may be significantly transparent to beams with the polarisation of the second reflected beam 1026 (or vice versa). Alternatively, the transparencies of each PBS may be the same. In the example shown in Figure 10b, each PBS is significantly transparent to the second reflected beam 1026, and highly reflective to the first reflected beam 1020.

[107] After being transmitted or reflected by the pair of PBS 1028, the second reflected beam may be used to saturate a spectroscopic reference 1032, for example, a Rubidium-87 vapour cell. By saturating the spectroscopic reference 1032 with the second reflected beam 1026, when the first reflected beam 1020 passes through the spectroscopic reference 1032, a spectral response such as that shown in Figure 10d is created. The second reflected beam 1026 may be termed a pump signal. As shown in Figure 10d, the spectral response has a single Lorentzian peak at around 5MHz in this example. If the spectroscopic reference 1032 was not saturated, the spectral response would be a noisy signal. The pump signal may be considered to be preparing the spectroscopic reference 1032 so that the error signal can be created.

[108] The first reflected beam 1020 passes through the spectroscopic reference 1032 in a counter direction to the pump signal. When the frequency of the reflected beams matches that of the saturated spectroscopic reference 1032, the reflected beams will be completely absorbed and there is no input to the photodiode 1034. However, when the frequency of the reflected beams does not match, for example because of a drift in the master laser frequency which means that the shifted frequency no longer satisfies the requirement for maximum absorption, an error signal will the input to the photodiode. Any output signal from the spectroscopic reference 1032 is then reflected by a PBS from the PBS pair 1028 and provided as input to a sensor such as the photodiode 1034.

[109] The output of the photodiode may be provided as input to the feedforward control circuit, more specifically a modulator feedback loop 1008 which controls the frequency fA0M of the acousto-optic modulator. The modulator feedback loop 1008 may be used to control the shifted frequency in response to drifts of fcw within the bandwidth kfAOM- That is, if the frequency fcw drifts within the bandwidth, then the AOM may be used to adjust the shifted frequency fcw ± fA0M back to the desired frequency. No change is made to the frequency fcw of the master laser. However, if the frequency fcw drifts beyond the range of the AOM bandwidth kfA0M, then the AOM may no longer be used to adjust the shifted frequency and the frequency of the master laser will need to be reset.

[110] The modulator feedback loop 1008 may comprise a proportional-integral-derivative, PID, controller 1010 which controls the frequency of the AOM 1002 over its bandwidth kfA0M- The modulator feedback loop 1008 may also comprise a dithering module 1012, a first second mixer 1014 and an adder 1015. An error signal received from the PID 1034 is typically without sign dependence and thus when the frequency of the master laser moves from the fixed frequency in either direction, it will increase the error signal. The dithering module 1012 may be used, for example using an RF synthesiser, to generate a phase offset sine wave signal from the original error signal and an example is shown in Figure 10e. This phase offset sine wave signal which may be expressed as sin(A*wt-TT) is mixed with the original error signal which may be expressed as sin(A*wt) in the mixer 1014 and input to the PID controller 1010. The mixing creates a sharp error signal such as the one shown in Figure 10f. As shown in Figure 10f, when the laser is locked it sits at the zero point which around the peak absorption is close to linear. In this example, if the frequency moves to the left (e.g. down in frequency), this generates a positive error and similarly, if the frequency moves to the right (e.g. up in frequency) this generates a negative error. Thus a sign-dependent error signal is obtained and the appropriate adjustment can be made to adjust the frequency of the AOM. A similar dither can be applied to the beat note signals and it is noted that the beat note signal is effectively the same as the saturation dip shown in Figure 10d but inverted.

[111] The AOM may be configured to operate on the fixed frequency fA0M by means of a voltage-controlled oscillator, VCO, 1004 which provides a signal provided as input to the AOM 1002. The VCO 1004 receives an output from the PID controller 1010 which indicates any adjustment to be made to the modulator frequency fA0M. The output from the PID controller 1010 may have been added with a signal from the dithering module using the adder 1015. Adding the signals in this way, demodulates the dither signal and removes the original sine wave to generate the necessary DC signal which is then sent to the VCO. An amplifier 1006 may be configured to amplify the signal of the VCO 1004 before being provided as input to the AOM 1002. The AOM 1002 also has a bandwidth &fA0M which is typically around 10 Hz and thus as an example the frequency shift may be in the range of 70 to 90kHz.

[112] Figure 10c is a flowchart showing how a master laser output may be manipulated and controlled using a feedforward control circuit according to the present techniques. At step S1000, the master laser is set to a master laser frequency, for example by pre-stabilising on an on-board reference to provide an initial output frequency with a low frequency drift (e.g. ±5MHz). The on-board reference may be a spectroscopic reference and may have a value of 780nm. Alternatively, the on-board reference may be any appropriate reference with a low frequency drift. At step S1002, a frequency shift for an external actuator is set. The external actuator may be an acousto-optic modulator, AOM or an electro-optic modulator, EOM or any suitable high-speed modulator. For example, the initial frequency shift may be 80MHz and the AOM may have a bandwidth of 10MHz whereby better stability can be achieved. At step S1004, the master laser frequency is adjusted by applying the frequency shift. In this example, the adjusted (shifted) output may have a frequency of rubidium minus 80MHz. The shift to the laser frequency may be to meet the precondition of maximum absorption.

[113] At the next step S1006, absorption spectroscopy is performed using a spectroscopic reference using the shifted output to generate an error signal. Absorption spectroscopy may be performed using a Rubidium-87 vapour cell or another suitable spectroscopic reference (which was used in the pre-stabilising step). At step S1008, the generated error signal is processed by a feedback loop. The feedback loop may comprise a PID controller and optionally a dithering module and one or more mixers and adders to sharpen and convert the error signal as described above and shown in Figures 10e and 10f. The PID controller controls the AOM frequency over its bandwidth.

[114] At step S1010, a determination is made as to whether an adjustment is required to the shifted output frequency by processing the generated error signal using the feedback loop. If an adjustment is not required, then at step S1014 the shifted output may be output, e.g. to the slave laser(s). The shifted output may be further monitored by looping back to step S1006 to perform absorption spectroscopy and repeat the processing and determining steps.

[115] The generated error signal may indicate that a negative adjustment to the shifted output is required. Conversely, the error signal may indicate that a positive adjustment to the shifted output is required. If an adjustment is required, then there may be a determination as to whether the necessary adjustment is within the bandwidth of the AOM at step S1012. If the adjustment is not within the bandwidth, e.g. in the example above needs to be above 10MHz, the process loops back to the start S1000 to calibrate the master laser. However, if the adjustment is within the bandwidth of the AOM, the process loops to step S1002 to set the frequency shift of the AOM (actuator). In other words, the external actuator may be used to reshift the shifted output. Such an adjustment can be done relatively quickly, particularly when compared to recalibration of the master laser. The AOM is external to the master laser and is thus outside the laser cavity of the master laser and may be considered an external actuator. As explained above, the AOM does not alter the frequency within the master laser but shifts the frequency after it has been output from the master laser.

[116] In either case described in relation to Figures 10a and 10b above, the frequency of the precisely controlled output of the master laser fcw or the shifted fcw ± fA0M is output to be used in conjunction with the slave lasers described above. In the case of Figure 10a, the output fcw corresponds to a master laser frequency whose operational frequency has been adjusted by a feedback control circuit. In the case of Figure 10b, the output fcw ± fA0M may correspond to a master laser frequency which is not directly adjusted but is shifted by an external actuator whose frequency can be quickly adjusted. The Figure 10b arrangement may be termed a feedforward control circuit.

[117] Various combinations of optional features have been described herein, and it will be appreciated that described features may be combined in any suitable combination. In particular, the features of any one example embodiment may be combined with features of any other embodiment, as appropriate, except where such combinations are mutually exclusive. Throughout this specification, the term “comprising” or “comprises” means including the component(s) specified but not to the exclusion of the presence of others.

[118] Attention is directed to all papers and documents which are filed concurrently with or previous to this specification in connection with this application and which are open to public inspection with this specification, and the contents of all such papers and documents are incorporated herein by reference.

[119] All of the features disclosed in this specification (including any accompanying claims, abstract and drawings), and / or all of the steps of any method or process so disclosed, may be combined in any combination, except combinations where at least some of such features and / or steps are mutually exclusive. Each feature disclosed in this specification (including any accompanying claims, abstract and drawings) may be replaced by alternative features serving the same, equivalent or similar purpose, unless expressly stated otherwise. Thus, unless expressly stated otherwise, each feature disclosed is one example only of a generic series of equivalent or similar features.

[120] The invention is not restricted to the details of the foregoing embodiment(s). The invention extends to any novel one, or any novel combination, of the features disclosed in this specification (including any accompanying claims, abstract and drawings), or to any novel one, or any novel combination, of the steps of any method or process so disclosed. Although a few preferred embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes and modifications might be made without departing from the scope of the invention, as defined in the appended claims.

Claims

1. A laser system comprisinga master laser having a master laser frequency;at least one slave laser which is tuned to output laser light at a desired absolute frequency which is different to the master laser frequency;a frequency comb which generates a spectrum of laser light comprising a plurality of frequency comb lines which are all spaced by a discrete repetition frequency;at least one sensor for measuring a laser-comb beat signal which is generated by combining output from the at least one slave laser with output from the frequency comb; anda slave control circuit for tuning the at least one slave laser based on the measured laser-comb beat signal.

2. The laser system of claim 1, comprising a plurality of slave lasers each tuned to a different frequency.

3. The laser system of claim 1 or claim 2, wherein the laser system outputs a range of frequencies of laser light and the range spans at least 50nm.

4. The laser system of claim 3, wherein the range of frequencies is suitable for controlling quantum systems.

5. The laser system of any one of the preceding claims, wherein the slave control circuit is configured to tune the at least one slave laser by:calibrating the at least one slave laser to a known frequency;gradually adjusting the frequency of the at least one slave laser from the known frequency to an adjusted frequency;receiving, as the frequency is gradually adjusted, a measurement of the changing frequency of the laser-comb beat signal;counting instances at which the frequency of the measured laser-comb beat signal is zero;obtaining, using the counted instances, a line number which indicates how many of the plurality of frequency comb lines have been crossed as the frequency is gradually adjusted to the adjusted frequency;calculating the adjusted frequency using the known frequency, the repetition frequency of the frequency comb , the measured laser-comb beat signal and the determined linenumber;determining whether the adjusted frequency equals the desired frequency andwhen it is determined that the adjusted frequency does not equal the desired frequency, repeating the steps of gradually adjusting, receiving, counting, obtaining, calculating and determining.

6. The laser system of any one of the preceding claims, further comprising a controller for implementing a dithering scheme which adjusts the repetition frequency of the frequency comb.

7. The laser system of claim 6, wherein the slave control circuit is configured to tune the at least one slave laser by:adjusting the frequency of the at least one slave laser to an initial value which is unknown;instructing the controller to increase the repetition frequency of the frequency comb over a pre-determined range;receiving, as the repetition frequency is increased, a measurement of a changing frequency of the generated laser-comb beat signal from the at least one sensor;counting instances at which the measured laser-comb beat signal repeats;estimating, using the counted instances, the pre-determined range and the measured laser-comb beat signal, an index number for the frequency comb line closest in frequency to the initial value;determining, using the measured laser-comb beat signal, a directionality of the initial value relative to the frequency comb line with the estimated index number; andcalculating the frequency of the initial value using the estimated index number, the repetition frequency, the determined directionality and the measured laser-comb beat signal.

8. The laser system of claim 6, when dependent on claim 5, wherein the slave control circuit is configured to calibrate the at least one slave laser to a known frequency by:adjusting the frequency of the at least one slave laser to an initial value which is unknown;instructing the controller to increase the repetition frequency of the frequency comb over a pre-determined range;receiving, as the repetition frequency is increased, a measurement of a changing frequency of the generated laser-comb beat signal from the at least one sensor;counting instances at which the measured laser-comb beat signal repeats;estimating, using the counted instances, the pre-determined range and the measured laser-comb beat signal, an index number for the frequency comb line closest in frequency to the initial value;determining, using the measured laser-comb beat signal, a directionality of the initial value relative to the frequency comb line with the estimated index number; andcalculating the frequency of the initial value using the estimated index number, the repetition frequency, the determined directionality and the measured laser-comb beat signal.

9. The laser system of claim 7 or claim 8, wherein adjusting the frequency of the at least one slave laser to an initial value comprises adjusting the frequency by more than 250 THz.

10. The laser system of any one of the preceding claims, further comprising a master control circuit for locking the frequency of output laser light from the master laser to the known master frequency using saturation absorption spectroscopy.

11. The laser system of claim 10, when dependent on claim 5, wherein the slave control circuit is configured to calibrate the at least one slave laser to a known frequency by:receiving, from the at least one sensor, a measurement of a frequency of a generated master-slave beat signal which is generated by combining output from the master laser with output from the slave laser;determining, using the measured frequency of the master-slave beat signal, an error signal which indicates a direction in which the frequency of the slave laser needs to be adjusted to tune the frequency of output laser light from the slave laser to the frequency of output laser light from the master laser; andtuning the slave laser based on the determined error signal.

12. The laser system of any one of the preceding claims, further comprisinga modulator which shifts the frequency of output laser light from the master laser by a modulator frequency to generate a shifted frequency and which outputs light from the modulator at the desired frequency anda modulator control circuit for controlling the modulator frequency to lock the shifted frequency to a desired frequency.

13. A laser system comprisinga master laser having a master laser cavity and a master laser frequency;a modulator which is external to the master laser cavity and which shifts the frequencyof output laser light from the master laser by a modulator frequency to generate a shifted frequency and which outputs light from the modulator at the desired frequency; anda modulator control circuit for controlling the modulator frequency to lock the shifted frequency to a desired frequency.

14. The laser system of claim 12 or claim 13, wherein the modulator control circuit uses saturation absorption spectroscopy to lock the shifted frequency to the desired frequency.

15. The laser system of claim 14, further comprisinga spectroscopic reference;at least one reflector which directs light from the modulator through the spectroscopic reference in a first direction to saturate the spectroscopic reference;at least one reflector which directs light from the modulator through the spectroscopic reference in a second direction which is opposite to the first direction whereby an error signal is generated when the frequency of the light from the modulator does not match a frequency of the saturated spectroscopic reference; andwherein the modulator control circuit comprisesa dithering module to generate a dithered signal which is mixed with the error signal received from the spectroscopic reference to generate a sharpened error signal; anda controller todetermine a control signal which adjusts the modulator frequency based on the sharpened error signal, andsend the control signal to the modulator to adjust the modulator frequency.

16. The laser system of any one of claims 12 to 15, when dependent on claim 5, wherein the slave control circuit is configured to calibrate the at least one slave laser to a known frequency equal to the shifted frequency byreceiving, from the at least one sensor, a measurement of a frequency of a generated shifted-slave beat signal which is generated by combining output from the modulator with output from the slave laser;determining, using the measured frequency of the shifted-slave beat signal, an error signal which indicates a direction in which the frequency of the slave laser needs to be adjusted to tune the frequency of output laser light from the slave laser to the frequency of output laser light from the modulator; andtuning the slave laser based on the determined error signal.

17. The laser system of any one of the preceding claims, wherein the at least one sensor is a photo diode having a bandwidth which is less than half the bandwidth of the repetition frequency of the frequency comb.

18. The laser system of any one of the preceding claims, further comprising an actuation component for each slave laser and master laser to adjust an optical path length within each slave laser and master laser to adjust the output frequency.

19. A method of tuning a slave laser in a laser system comprising at least one slave laser and a frequency comb to link each slave laser, the method comprisingcalibrating the slave laser to a known frequency;generating a laser-comb beat signal by combining output from the slave laser with output from the frequency comb which generates a spectrum of laser light comprising a plurality of frequency comb lines which are all spaced by a repetition frequency;gradually adjusting the frequency of the slave laser from the known frequency to an adjusted frequency;measuring, as the frequency is gradually adjusted, a changing frequency of the generated laser-comb beat signal;counting instances at which the frequency of the measured laser-comb beat signal repeats;obtaining, using the counted instances, a line number which indicates how many of the plurality of frequency comb lines have been crossed as the frequency is gradually adjusted to the adjusted frequency;calculating the adjusted frequency using the known frequency, the repetition frequency of the frequency comb and the determined line number;determining whether the adjusted frequency of the output laser light equals the desired frequency; and when it is determined that the adjusted frequency does not equal the desired frequency, repeating the steps of gradually adjusting, measuring, counting, obtaining, calculating and determining.

20. The method according to claim 19, wherein calibrating a slave laser to a known frequency comprisesadjusting the frequency of the at least one slave laser to an initial value which is unknown;increasing a repetition frequency of the frequency comb over a pre-determined range, wherein the repetition frequency defines a spacing between a plurality of frequency comb lines of the frequency comb;receiving, as the repetition frequency is increased, a measurement of a changing frequency of the generated laser-comb beat signal from the at least one sensor;counting instances at which the measured laser-comb beat signal repeats;estimating, using the counted instances, the pre-determined range and the measured laser-comb beat signal, an index number for the frequency comb line closest in frequency to the initial value;determining, using the measured laser-comb beat signal, a directionality of the initial value relative to the frequency comb line with the estimated index number; andcalculating the frequency of the initial value using the estimated index number, the repetition frequency, the determined directionality and the measured laser-comb beat signal.

21. The method according to claim 19 or claim 20, wherein calibrating a slave laser to a known frequency comprisesmeasuring a frequency of a master-slave beat signal which is generated by combining output from the slave laser with output from a master laser which is tuned to a master reference frequency;determining, using the measured frequency of the master-slave beat signal, an error signal which indicates a direction in which the frequency of the slave laser needs to be adjusted to tune the frequency of output laser light from the slave laser to the master reference frequency; andtuning the slave laser based on the determined error signal.

22. The method according to any one of claims 19 to 21, wherein calibrating a slave laser to a known frequency comprisesmeasuring a frequency of a generated shifted-slave beat signal which is generated by combining output from the slave laser with a modulator which shifts the frequency of output laser light from a master laser by a modulator frequency to generate a shifted frequency;determining, using the measured frequency of the shifted -slave beat signal, an error signal which indicates a direction in which the frequency of the slave laser needs to be adjusted to tune the frequency of output laser light from the slave laser to the shifted frequency; andtuning the slave laser based on the determined error signal.

23. A method of generating output laser light at a desired frequency, the method comprising calibrating a master laser to output laser light at a known master reference frequency; shifting, using a modulator which is external to the master laser, the frequency of output laser light from the master laser by a modulator frequency;controlling, using a modulator control circuit, the modulator frequency to lock the shifted frequency to the desired frequency; andoutputting light from the modulator at the desired frequency.

24. A non-transitory data carrier carrying code which, when implemented on a processor, causes the processor to carry out any of the methods of claims 19 to 23.

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