Soliton generation in micro-resonators

Abstract

Disclosed is a method for generating a broadband microcomb, that includes generating a comb signal by a pump laser, at a pump wavelength corresponding to a resonance of a micro-resonator, wherein the micro-resonator operates with two modes with a mode separation of a predefined range, heating 5 the micro-resonator using a heater, and deterministically generating broadband microcombs including octave spanning solitons by the micro-resonator by bi- directional tuning of the heater voltage, wherein the bi-directional tuning of the heater voltage tunes the resonance wavelengths of the two modes, and alters the wavelength separation of two modes. 10

Description

[0001] Title

[0002] Soliton Generation in Micro-resonators

[0003] Field

[0004] The present invention relates to soliton generation in micro-resonators, and more specifically to generating frequency combs based on thermally controlled dual-mode micro-resonators.

[0005] Background

[0006] Comb sources are key optical sources for use in a variety of applications. Of particular interest is the optical frequency reference which requires an octave spanning soliton that can be easily and reliably generated. Optical comb sources have a large range of applications including the development of an optical frequency synthesizer (an optical reference source with central frequency of about 1193 THz with a frequency accuracy of 1 Hz, a range in excess of 1014.) They are crucial for applications such as optical atomic clocks, optical metrology, astronomical spectrometer calibration, and GPS technology.

[0007] Extending the frequency comb to cover an octave is a key advancement, enabling characterization through the ‘f-2f self-referencing technique, which allows for the accurate determination of carrier offset frequencies. Solitons are highly stabilized combs in which the individual lines of the combs are locked together and whose frequencies are then precisely known. Using a dual-mode scheme where two resonances are very close to one another, the soliton comb can be stabilized and allowed to exist over a large range of frequencies, called a soliton existence range. However, the dual-modes require very precise control on fabrication and variations in the thickness, width and radius of the micro resonator can strongly affect the dual-mode separation. Typically, accessing soliton microcombs involves tuning the pump wavelength to match the resonances of the microresonator, which requires the use of tunable lasers as pump sources. This process involves complex control mechanisms to counteract thermal effects and stabilize solitons, such as employing fast sweeping techniques with additional modulators or using an auxiliary laser.

[0008] Alternatively, solitons can be initiated by keeping the pump wavelength constant while tuning the resonance either mechanically or thermally. In this case, a fiber laser or a semiconductor laser, which is locked to a whispering gallery mode resonator or an ultra-stable cavity, can serve as the pump, offering significantly reduced phase noise. Additionally, piezoelectric or thermal control methods can be implemented with a low-cost source meter, avoiding the need for a complex setup involving modulators or auxiliary lasers. However, the current piezocontrolled soliton microcomb sources have been limited to a narrow comb spectral bandwidth, falling short of an octave-spanning range. For the thermal tuning method, the thermal instability during the soliton formation remains and thus cannot be regarded as a universal solution.

[0009] Summary of the Invention

[0010] According to the invention there is provided, as set out in the appended claims, a method for generating a broadband microcomb, that includes generating a comb signal by a pump laser, at a pump wavelength corresponding to a resonance of a micro-resonator, wherein the micro-resonator operates with two modes with a mode separation of a predefined range, heating the microresonator using a heater, and deterministically generating broadband microcombs including octave spanning solitons by the micro-resonator by bidirectional tuning of the heater voltage, wherein the bi-directional tuning of the heater voltage tunes the resonance wavelengths of the two modes, and alters the wavelength separation of two modes. In an embodiment of the present invention, the micro-resonator includes a dualmode 1-THz ring resonator with TE or TM polarization, with a repetition rate ranging from 100 GHZ to 1 THz and a mode separation ranging from 67 pm to 260 pm. The heating the micro-resonator increases the refractive indices of the materials via the thermo-optic effect, thereby tuning the resonances of two modes to longer wavelengths, and adjusting the mode separation to a regime conducive to soliton microcomb formation.

[0011] In an embodiment of the present invention, the method further includes initially heating the micro-resonator by applying a first heater voltage, wherein the application of the first heater voltage shifts current resonance wavelengths of the two modes towards wavelengths greater than that of the pump laser and decreases current mode separation between the two modes, and deterministically generate soliton combs by the micro-resonator upon applying a second heater voltage that is less than the first heater voltage, wherein the application of the second heater voltage decreases current mode separation and current resonance wavelengths of the two modes.

[0012] In an embodiment of the present invention, the heating the micro resonator demonstrates substantial tunability, shifting the resonances by more than one free spectral range at maximum heater power.

[0013] In an embodiment of the present invention, the method further includes changing the heater voltage either gradually or through rapid pulsed operation.

[0014] In an embodiment of the present invention, the method further includes performing bi-directional tuning of the wavelength of pump laser along with bidirectional tuning of heater voltage to tune the mode separation.

[0015] In an embodiment of the present invention, the method further includes reducing the wavelength of the pump laser to reduce the number of soliton combs. In an embodiment of the present invention, the method further includes, the micro-resonator is made from a material selected from a group consisting of: Silicon carbide, Silica, Silicon, Lithium niobate, and Aluminium nitride.

[0016] In an embodiment of the present invention, the method further includes comprising applying four-stage thermal control method to deterministically generate single soliton combs, wherein the four-stage control method comprises performing backward resonance tuning of the resonator at first stage to form an initial comb state by decreasing current heater voltage; performing forward resonance tuning of the resonator at second stage by decreasing current heater voltage in order to reduce detuning between the fundamental cavity resonance and pump frequency, and thereby ensuring a deterministic transition from a multi-soliton to a single-soliton state; performing another backward resonance tuning at third stage to reduce degradation in soliton spectral bandwidth and comb conversion efficiency; and performing further backward resonance tuning at fourth stage to yield an optimized single-soliton output under constant heater voltage.

[0017] In an embodiment of the present invention, the method further includes integrating a second micro-resonator with a GHz repetition rate soliton microcomb with the broadband microcomb on same chip, triggering the two microcombs with a single pump laser locked to an atomic transition frequency; and thermally tuning the two microcombs using two heaters.

[0018] In an embodiment of the present invention, the method includes measuring power of output signal of the micro-resonator, and adjusting the heater voltage in the event of reduction of the measured power.

[0019] In an embodiment of the present invention, the method includes tuning carrier envelope offset frequency and repetition rate of the soliton microcombs based on bi-directional tuning of the heater voltage. In an embodiment of the present invention, the method includes generating octave spanning soliton microcombs with pump wavelengths that are precisely aligned with rubidium atomic transitions.

[0020] In an embodiment of the present invention, the method includes comprising maximising the bandwidth of the broadband microcomb through the refractive index dispersion.

[0021] In another aspect of the present invention, there is provided a system for generating a broadband microcomb. The system includes a pump laser for generating a comb signal at a pump wavelength corresponding to a resonance of a micro-resonator, the micro-resonator coupled to an output of the pump laser, wherein the micro-resonator operates with two modes with a mode separation of a predefined range in order to stabilize soliton formation over a broad range of pump wavelengths, and a heater for heating the micro-resonator upon applying a heater voltage, wherein the micro-resonator deterministically generate broadband microcombs including octave spanning solitons through bidirectional tuning of the heater voltage, wherein the bi-directional tuning of the heater voltage tunes the resonance wavelengths of the two modes, and alters the wavelength separation of two modes.

[0022] There is also provided a computer program comprising program instructions for causing a computer program to carry out the above method which may be embodied on a recording medium, carrier signal or read-only memory.

[0023] Various embodiments of the present invention provide a system and method to generate self-referenced octave-spanning frequency combs using thermally controlled dual-mode microresonators. By integrating a simple heater into the design of dual-mode resonators, effective tuning of the mode separation is realized, which is crucial for soliton generation, thus addressing the key challenges such as thermal instability and low yield of the desirable resonators. By adjusting the heater power through either gradual change or rapid pulsed operation, the present approach facilitates straightforward soliton formation without additional electro-optic equipment to mitigate the thermal effect, thus reducing the cost and complexity. This flexibility also supports a smooth and reliable transition from multi-soliton and single-soliton regimes with optimized bandwidth and power. The thermal control method not only simplifies the soliton generation process but also offers fine-tuning capabilities for both carrierenvelope offset frequency (fceo) and the repetition rate (frep) measurements, with results of -0.37 GHz / mW -21 MHz / mW, respectively, found in one particular case. Notably, octave-spanning solitons with pump wavelengths are achieved that are precisely aligned with rubidium atomic transitions, highlighting the potential for atomic-referenced optical clocks. The ability to achieve high-yield octave-spanning solitons with reduced fceo is crucial for further advancements in soliton-based technologies. The future integration of GHz soliton microcombs with such octave-spanning combs on the same chip could lead to simplified and more cost-effective systems for precise timekeeping and frequency measurements. These provide a solid foundation for future efforts in designing efficient and scalable soliton microcomb systems with improved production and performance, facilitating the development of low-cost, integrated optical clocks and frequency synthesizers.

[0024] The novelty here is that in the scheme that the voltage is varied, and therefore the heating ensures (i) solitons are created deterministically by adjusting the separation of the two modes in the dual mode scheme and (ii) the bandwidth of the soliton microcomb is maximised through design of the refractive index dispersion as is well known in the literature. A simple feedback system is envisaged that may measure the comb power. The feedback could be implemented by tapping off a small amount of the comb power. Any reduction in this power can then be compensated by adjusting the voltage on the heaters.

[0025] Brief Description of the Drawings The invention will be more clearly understood from the following description of an embodiment thereof, given by way of example only, with reference to the accompanying drawings, in which:-

[0026] FIG.1A illustrates a system for achieving octave-spanning soliton microcombs, in accordance with an embodiment of the present invention;

[0027] FIG.1 B presents schematic diagram of the thermally controlled generation of soliton microcomb, and more specifically a schematic diagram of the thermal control method of the resonator, in accordance with an embodiment of the present invention;

[0028] FIG.1C illustrates simulated temperature change in the ring resonator over time, in accordance with an embodiment of the present invention;

[0029] FIG.1 D illustrates experimental transmission spectra of the dual-mode resonator at various electrical powers to the heater, in accordance with an embodiment of the present invention;

[0030] FIG.1 E illustrates resonance wavelengths shift and the separation between the adjacent TE modes versus electrical power;

[0031] FIG.2A illustrates how comb power varies with time for a set of different pump wavelengths (lower part of diagram) with voltage versus time corresponding to each wavelength shown in the upper part;

[0032] FIG.2B illustrates microcomb spectra of single-soliton, two-soliton, and three- soliton states, in accordance with an embodiment of the present invention;

[0033] FIG.2C illustrates pulsed operation of the heater voltage to trigger soliton states, in accordance with an embodiment of the present invention; FIG.2D illustrates long-term stability of the single-soliton, in accordance with an embodiment of the present invention;

[0034] FIG.2E illustrates a detailed view of the soliton formation phase, in accordance with an embodiment of the present invention;

[0035] FIGs.3A-3C illustrate bi-directional four-stage thermal tuning to achieve singlesolitons, in accordance with an embodiment of the present invention;

[0036] FIG.4A illustrates single-soliton microcomb spectra obtained at different electrical input powers;

[0037] FIG.4B illustrates a zoom-in view of the comb lines at low frequencies used to determine fceo,

[0038] FIG.4C.D illustrates retrieved comb frequencies fceoand frepas a function of the electrical power; and

[0039] FIGs.5A-5B demonstrate thermally controlled single-solitons from two different dual-mode resonators with different frep(~1THz and -390 THz), in accordance with an embodiment of the present invention.

[0040] Detailed Description of the Drawings

[0041] FIG.1A illustrates a system 100 for generating self-referenced octave-spanning soliton microcombs using thermally controlled dual-mode micro-resonators. The system 100 includes a pump laser 102, a polarization controller (PC) 104, an erbium-doped fiber amplifier (EDFA) 106, a ring resonator 108, a heater 109, an optical spectrum analyzer (OSA) 110, a fiber Bragg grating (FBG) 112, a photodiode (PD) 114, and a digital storage oscilloscope (DSO) 116. The signal generated by the pump laser 102 is amplified by an erbium-doped fiber amplifier (EDFA) 104, which is further coupled into the ring resonator 108, that is equipped with an advanced heater module 109.

[0042] In operation, the light from the pump laser 102 enters the polarization controller 104 where the polarization is selected to match the transverse electric (TE) or transverse magnetic (TM) modes of the micro-resonator 108. The light exiting the micro-resonator 108 enters the optical spectrum analyser 110 where the spectrum of the comb is shown. Some of the light also goes through the fiber Bragg grating 112 to remove the strong pump and then to allow to measure the comb power on the digital oscilloscope 116. The source meter 118 provides a voltage to the heater 109 to increase the temperature of the micro-resonator 108.

[0043] In an example, the heater module 109 includes a 1.5 pm wide ring metal heater and the ring resonator is a SisN4 ring resonator, each embedded within an SiO2 layer, with a distance between them as 1.7 pm. In an example, the ring resonator 108 is a dual-mode 1-THz resonators (TE00-TE10) with mode separation ranging from 127 pm and approximately 260 pm. In an embodiment of the present invention, the ring resonator and the heater may be implemented as an integrated module.

[0044] The micro-heater 109 is integrated directly on top of the resonator 108. Applying a voltage to the heater 109 increases the temperature of the resonator 108 and this tunes the cavity resonances. Crucially, it also changes the separation of the dual-modes and in this way, the solitons can be generated deterministically. The integrated heater 109 enables precise tuning of both the resonance wavelength and the separation between the dual modes, allowing a large number of devices to be adjusted into soliton regimes. It is to be noted that the entering the soliton state is often accompanied by a reduction in power in the micro-resonator 108. This affects the temperature of the micro-resonator 108 causing it to tune to shorter wavelengths resulting in the pump laser no longer being on resonance and so the soliton comb stops. The dual modes can occur in a number of different ways. Examples are (i) a TEoo and TE10 mode occur that are very close in wavelength to one another with TE10 at longer wavelength, (ii) A TEoo and TMoo mode occur that are very close in wavelength to one another. When the resonator 108 is now pumped in the region of the dual mode, most of the power is absorbed by the TEoo mode, but as the soliton state is entered, the power in the TEoo mode decreases, but at the same time, the power in the TE10 mode increases thereby stabilising the soliton generation. In this way, the range of frequencies over which the soliton can be observed is greatly increased. Other combinations of modes, for example the TE10 mode occurring at shorter wavelength can occur, and also the dual modes with the polarization case TM modes.

[0045] In an embodiment of the present invention, the resonance of the ring resonator is thermally tuned by injecting electrical energy into the heater contact and thereby increasing the refractive indices of the materials via the thermo-optic effect, thus tuning the resonances to longer wavelength. The integrated heater 109 not only effectively tunes the resonance wavelengths but crucially adjusts the mode separation to a regime conducive to soliton formation, significantly increasing the yield of dual-mode resonators. Solitons are deterministically produced by simply varying the heater power at any speed, without the need to manage slow thermal effects.

[0046] FIG.1 B presents schematic diagram of the thermally controlled generation of soliton microcomb, and more specifically a schematic of thermal control method of the resonator 106 to deterministically trigger the soliton state. Throughout the process, the pump laser 102, operating at sufficient power, is fixed at a constant wavelength. In the initial stage I (cold cavity) without electrical heating, the TEoo and TE10 modes exhibit their largest spacing, with the pumping not occupying either mode. As the voltage increases to stage II, the resonator 106 heats up, shifting the resonances towards longer wavelengths that are now on the righthand side of the pump output. Meanwhile, the mode separation (difference in wavelength of the two modes) is also changed due to the different shifts of the TEoo and TE10 modes with temperature. Specifically, the separation may be reduced since the fundamental TEoo mode is more sensitive to temperature change. By leveraging these characteristics, the dual-mode cases can be effectively modified especially for those with too large spacing initially for effective thermal compensation. In stage III, solitons may be stably achieved by tuning the resonance by altering the voltage from a high to a low level.

[0047] FIG.1C illustrates simulated temperature change in the ring resonator 108 over time when a 34 mW electrical power is applied. In an example, the ring resonator 108 has a radius of 24.23 pm and a cross-section of 1.74 pm x 0.79 pm (width x height). The inset shows the temperature profile across the resonator 108 in the steady state. It can be seen that with 34 mW power injected into the metal heater, the temperature of the ring resonator 108 experiences a rapid initial rise, followed by a slower increase to a steady state. The inset displays a steady temperature distribution, with the highest temperature near the heater and decreasing outward through the SisN4, SiO2, and Si layers. An average change (ATSIN) of approximately 54 K is observed, corresponding to a ratio (dTsiN / dPheater) of -1.59 K / mW.

[0048] FIG.1 D illustrates experimental transmission spectra of the dual-mode resonator 108 at various electrical powers, with two close modes in the C-band, measured with a low on-chip pump power (Pin) of around -16 dBm. As the electrical power (PEIGC) increases, both resonances exhibit a red shift to longer wavelength as anticipated. The TEoo mode, characterized by a high extinction ratio and narrow linewidth, shows a greater shift compared to the TE10 mode, similar to results observed using a thermoelectric cooler (TEC) under the substrate. The integrated heater demonstrates substantial tunability, shifting the resonances by more than one free spectral range (FSR, -8 nm) if using the maximum PEIGC of around 350 mW.

[0049] FIG.1 E illustrates resonance wavelengths and the separation between the adjacent TE modes versus electrical power. The highlighted region indicates the power range or mode separation range where stable soliton generation is observed. As shown in FIG. 1 E, the resonance wavelengths increase almost linearly with increasing PEIGC, with ratios of approximately -28.69 pm / mW and -28.00 pm / mW for the TEoo and TE10 modes, respectively. The initial mode separation (AA = A - Aoo) of 227 pm can be adjusted down to 33 pm when EIGC is 283 mW. Initially, by sweeping the pump wavelength, the soliton states can be accessed when AA (PEIGC) falls within the range of 122 to 67 pm (150 to 234 mW). Notably, the soliton existence range (SER), which is the tuning range of pump frequency that can support soliton states, can exceed 30 GHz when the electrical power is 183 mW (AA = 100 pm). This thorough examination of thermal tuning in optical micro-resonators provides valuable insights for designing and optimizing the dual-mode characteristics to achieve octave spanning solitons.

[0050] FIG.2A illustrates thermally controlled solitons generation at an on-chip power Pin of 250 mW and presents the power traces of the generated combs as the heater voltage is adjusted, while fixing the pump wavelength in 1558, 1560.5, 1561.5, 1562, 1562.5, and 1564 nm. The upper stack displays the repeated voltage scans at six different levels, with the sweeping speed (how voltage changes with time) being much slower than the thermal response time of the micro-resonator 108. As the voltage level increases from (i) to (vi), the pump wavelength may also be incremented accordingly so as to keep it aligned with the resonances. Similar to the forward tuning of the laser, decreasing the voltage allows the pump to engage with the resonance, where primary and modulation instability microcombs can be excited. Further decreasing the voltage results in generating the soliton. The step-like features in the comb power traces indicate the soliton state, with the step level corresponding to the number (A / ) of the soliton pulse within the cavity. At pump wavelengths (AP) of 1558 nm (i) and 1564 nm (vi), solitons are not observed due to insufficient or excessive thermal compensation of the mode separation, respectively. At APvalues of 1560.5 nm (ii), 1561.5 nm (iii), and 1562.5 nm (v), decreasing the voltage reveals a stair-like pattern, highlighted by the shaded regions, indicating the presence of multiple solitons. At / Pof 1562 nm (iv), the system can access a single soliton state, though not deterministically. Therefore, precise adjustment of the heater voltage (i.e., PEIGC) is effective for tuning the microcomb into soliton regimes, particularly when the initial dual-mode has a relatively large separation (>125 pm).

[0051] FIG.2B illustrates microcomb spectra of single-soliton, two-soliton, and three- soliton states aUP=1562 nm with increasing pump power generating the higher number of solitons. A pronounced dispersive wave (DW) is observed at -309 THz, contributing to the extension of the spectral bandwidth to nearly 1.5 octaves. By engineering the electrical injection, a smooth transition is demonstrated from multi-soliton to single-soliton regimes while optimizing the comb line power. These advancements make a significant contribution to the development of cost-effective and practical Kerr frequency combs for applications in optical clocks and frequency synthesizers.

[0052] FIG.2C illustrates pulsed operation of the heater voltage to trigger soliton states. In addition to adiabatic sweep tuning, soliton generation can be effectively achieved via the pulsed operation of the heater voltage, eliminating the need to vary pump wavelength. Additionally, the heater’s bidirectional tuning capability supports a smooth transition from multi-soliton to single-soliton states. In this approach, the voltage alternates between 6 and 4.5 V, while the comb power is monitored. At 6 V, the pump stands on the left-detuned side of the resonance without coupling or comb generation. Then reducing the voltage to 4.5 V reliably activates the soliton state with a 100% success rate, although the number of solitons can vary among 1 , 2, and 3.

[0053] FIG.2D illustrates long-term stability of the single-soliton. The solitons produced under these conditions exhibit robust long-term stability, indicating stable thermal behavior once the soliton state is established. FIG.2E illustrates a detailed view of the soliton formation phase. Despite a rapid voltage switching time of approximately 10 ps, the resonator’s slow thermal response requires about 300-400 ps to stabilize a soliton state, consistent with the thermal relaxation simulations. Therefore, by carefully modifying the dual-mode and mitigating thermal effects, solitons can be activated either through gradual or fast voltage adjustment. This approach implies that the initial design of the dualmode resonators and the fabrication tolerances can be relaxed, thus potentially increasing the yield of resonators capable of easy soliton generation.

[0054] In many applications, the spectrum of a single soliton is of paramount interest due to its smooth spectrum and well-defined repetition rate. It has been demonstrated that starting with a high-order soliton (e.g a two-soliton state) and performing an adiabatic backward pump tuning (slowly reducing the wavelength of the pump) can successively reduce the soliton number. Utilizing a dualpumping scheme (e.g. the TE00 / TE10 modes as outlined above), deterministic single-soliton can be achieved through bi-directional (increasing and decreasing the wavelength of the pump laser) pump tuning by engineering the thermal compensation to achieve the desired separation of the TEoo and TE10 modes.

[0055] FIGs.3A-3C illustrate bi-directional four-stage thermal tuning to achieve singlesolitons, with APand Pin being fixed at 1561.5 nm and 250 mW, respectively. FIG.3A illustrates normalized comb power (solid lines) as a function of a four- stage engineered heater voltage (dashed lines). FIG.3B illustrates a diagram illustrating the relationship between the pump and resonances at different detuning levels. FIG.3C illustrates five single-soliton microcomb spectra during Stage III. Solid curves correspond to the sech2 fitting profiles. Dash-dot lines indicate the center of the soliton peak. The 3-d B bandwidth refers to the width of the spectrum at 3 dB below the power level of the soliton peak. Recoil denotes spacing between the soliton peak center and pump.

[0056] The four-stage thermal control method includes four stages l-IV. Stage I involves an initial multi-soliton formation through backward resonance tuning (by reducing the voltage). During multi-soliton states (N=2 or 3), a voltage adjustment is applied in the reverse direction (stage II, forward tuning by increasing the voltage) to reduce the effective detuning (<5eff), the detuning between the hot cavity resonance (TEoo) and pump frequency [referred to FIG.3(b)], This forward tuning ensures a deterministic transition from a multisoliton to a single-soliton state (3— >2— >1 , or 2— >1 ). However, upon reaching the single-soliton and further increasing the voltage, a gradual reduction in comb power is observed due to a decrease in <5eff, indicating a degradation in soliton spectral bandwidth and comb conversion efficiency. The spectral bandwidth is the range of wavelength of the comb lines from the shortest to longest. It is desired that this is always as broad as possible, and the four stage process ensures the maximum bandwidth. The comb conversion efficiency is the ratio of the comb power to the pump power. The higher this ratio is the better.

[0057] To address this issue, another backward tuning may be introduced as stage III, followed by stage IV, which yields an optimized single-soliton output under a constant electrical injection. Single soliton usually exists at the lower power level. Spectrum of single soliton is simpler than other cases, so easier to use. To better explain this mechanism, FIG. 3(b) illustrates the shift of the resonances relative to the pump during the tuning process. The different stacks correspond to the detuning marked in FIG.3(a). It should be noted that the shift of the soliton resonances is too small to be neglected. FIG. 3(c) presents the spectral evolution of single-solitons at various detuning, with the top and bottom corresponding to states @ and @, respectively. All the spectra fit well with the sech2function, and the soliton center shifts to the right side, referred to as soliton recoil, caused by the interaction between DW and the Raman-induced soliton self-frequency shift. As <5eff increases, the 3-dB bandwidth, intensity of the DW, and the soliton recoil amplitude are enhanced. While this four-stage voltage programming may not always be necessary, it is demonstrated here as a universal scheme for deterministic single-soliton generation. This method could be automated incorporating monitoring of comb power and feedback control of the heater voltage to achieve the single-soliton deterministically. FIG.4A illustrates single-soliton microcomb spectra obtained at different electrical input powers, with varying pumps as shown in the enlarged view on the right. FIG.4B illustrates a zoom-in view of the comb lines at low frequencies, where the dash arrow lines indicate the comb lines with different j (mode number relative to the pump mode). FIG.4C illustrates retrieved fceoand frepas a function of the electrical power. For use in multiple applications, the two key frequencies, fceo and frep , need to be determined as a function of temperature. We do this here in an optical measurement by changing the power level of the heater.

[0058] The four-stage heater control provides a robust method to deterministically access single-solitons despite variations in electrical inputs and pump frequencies. As illustrated in FIG.4A, single-solitons are reliably produced when the PEIGC ranges between 167 mW and 228 mW for the resonator of FIG.1A, corresponding to an approximate 97 K temperature change. The right plot shows a closer view of the corresponding pump line, which can tuned from 1560.48 to 1562.5 nm (-248 GHz change). The dashed lines in FIG.4(b) represent the actual comb lines with a relative mode numbers j of -67, -68, and -69 (with respect to the pump). The other weak comb lines spaced by approximately half of the FSR are observed due to the second-order diffraction of the OSA. The frequency difference Af between the real comb line (with a mode number of m) and the nearby weak line (half frequency of the comb line with a mode number of 2m) can be expressed as fm-f2m=(fceo'*' m*frep)-(fceo+ 2m*frep) / 2=fceo / 2, where the fceo and frepindicate the carrier-envelope offset frequency and repetition rate, respectively. As shown in FIG.4(c), the estimated fceo from different orders of modes show excellent agreement and can be tuned from approximately 150 GHz to 128.4 GHz by heating the resonator. The ratio between the fceo variation and the Paec change exhibits a linear fitted slope of - 0.37 GHz / mW (approximately -0.23 GHz / K). Thus, thermal operation enables tunability in both fceo and pump frequency, with a ratio of approximately 9.1 %, consistent with investigations using a buried heater where an auxiliary laser was employed for single-soliton formation. Furthermore, by dividing the frequency spacing between the comb line with j = -69 (f =-69) and the pump line (fp), the frep is evaluated as a function of PEIGC, as the triangles depicted in FIG.4D. The frep decreases with an increase in heater power, exhibiting a linear fitted slope of approximately -21 MHz / mW (approximately -13.21 MHz / K). Using the fCeo, the frep are also retrieved by the equation of f= / ceo + mxfrep and plotted with circle symbols in FIG.4D, where fPand m=198 represent the pump frequency and the actual mode number of the pump, respectively. Despite the relatively low accuracy due to the limitation of the OSA’s precision, the frepcalculated by both methods show excellent agreement. The estimated ratio of -13.21 MHz / K shows reasonable agreement with the results demonstrated in SisN4. Therefore, thermal control not only modifies the mode separation to simplify soliton generation but also shows promise for fine-tuning both fceoand frepfor locking operations.

[0059] For optical atomic clocks, octave-spanning soliton microcombs that enable fceomeasurement are essential for achieving high-precision microwave repetition rates through down conversion. To reduce the size and complexity of optical clocks, an integrated optical clock has been proposed, utilizing a microcomb system via frequency division. This system employs a pair of microcombs with frep of 1 THz and 22 GHz to generate the clock output tone, where the pump wavelength (1556.2 nm) for the latter comb is phase-locked to the Rb two- photon transition. However, the pump wavelength of the THz soliton needs to be interlocked with the GHz comb. Here, the robust thermal control and high- yield dual-mode resonators offer an effective method for effectively tuning the pump wavelength easily. The combination of the dual-modes and the variable heating gives a new level of control.

[0060] FIGs.5A-5C demonstrate thermally controlled single-solitons from three different dual-mode resonators. In order for soliton combs to become a widely used technology, it is essential that devices can be designed and fabricated with high yield. Yield means the number of devices that make it all the way to operating in particular applications. A high yield will lower costs and drive the technology forward. This invention combing the dual mode scheme with a thermal tuning scheme increases the number of devices that show the octave spanning soliton and so the scheme will benefit attempts to use micro-resonators in comb applications. FIGs. 5A-5C showcases additional thermally accessed ~1-THz and ~393-GHz dual mode (TE00 / TE10) soliton microcombs with pump wavelengths of 1556.2 nm and 1563.16 nm. FIG.5A shows the transmission curves. FIG.5B shows the comb power versus voltage, and FIG.5C presents the soliton microcomb spectra. For device 2 (~1-THz resonator), the pump wavelength is set to 1556.2 nm, which can be frequency doubled to the Rb atomic transition lines: two-photon transition, as shown by the insets in FIG.5C. As depicted in FIG.5A, without any electrical power input, the ~1-THz and ~393- GHz resonators exhibit separation of 260, and 67 pm, respectively, which are too large to access the soliton state thermally. By applying a voltage of 5.5, and 4.2 V, the separations are effectively reduced to 105, and 52 pm, respectively, enabling soliton formation. FIG.5B shows the comb power traces versus voltage tuning, with two attempts for each device. For device 2 (D2, ~1-THz repetition ratre), the initial multi-soliton ( / \ / = 2 or 3) is commonly produced by tuning the resonance backward. Subsequently, forward resonance tuning is used to reduce the soliton number and access a single-soliton. Another backward tuning is then employed to enhance the power of the single-soliton, which is maintained with an optimal voltage. For device 3 (D3, ~393-GHz repetition rate), the two-solitons or single-solitons can be accessed directly via pulse tuning of the voltage. The comb power at the single-soliton state surpasses that of the two-soliton state due to the presence of an auxiliary mode-based microcomb, as shown in FIG. 5C. FIG.5C shows the spectra of the achieved single-soliton microcombs, where the pump wavelength of D2 is 1556.2 nm, while for D3 it is set at 1563.16 nm. Their frepdifference are caused by the differences in ring radius. Recent research demonstrates an atom-referenced soliton microcomb with a 7.3-GHz-frep and 100-nm span using a dual-mode crystalline resonator. The employed pump source is a low-cost semiconductor laser, phase-stabilized to Rb atomic transition. In the future, a similar GHz soliton microcomb may be integrated with an octave-spanning comb (as demonstrated in this work) on the same SisN4 chip. With thermal control, the two microcombs can be triggered with the same pump, which is locked to the atomic transition frequency, thereby simplifying the system for clock output. Compared to the dispersion profile and dual-mode resonance designs, fceois much harder to design and control due to its sensitivity to the cavity geometry variations caused by fabrication errors. Therefore, an octave-spanning soliton with a smaller frepof less than 100 GHz would be highly desirable to provide a smaller fceothat can be measured electronically. Furthermore, the octave-spanning solitons that share the same pump wavelength could be used to characterize the frepand fceowith a Vernier effect even if the fceois not electronically detectable.

[0061] The embodiments in the invention described with reference to the drawings comprise a computer apparatus and / or processes performed in a computer apparatus. However, the invention also extends to computer programs, particularly computer programs stored on or in a carrier adapted to bring the invention into practice. The program may be in the form of source code, object code, or a code intermediate source and object code, such as in partially compiled form or in any other form suitable for use in the implementation of the method according to the invention. The carrier may comprise a storage medium such as ROM, e.g. a memory stick or hard disk. The carrier may be an electrical or optical signal which may be transmitted via an electrical or an optical cable or by radio or other means.

[0062] In the specification the terms "comprise, comprises, comprised and comprising" or any variation thereof and the terms include, includes, included and including" or any variation thereof are considered to be totally interchangeable, and they should all be afforded the widest possible interpretation and vice versa.

[0063] The invention is not limited to the embodiments hereinbefore described but may be varied in both construction and detail.

Claims

Claims1 . A method for generating a broadband microcomb, comprising: generating a comb signal by a pump laser, at a pump wavelength corresponding to a resonance of a micro-resonator, wherein the microresonator operates with two modes with a mode separation of a predefined range; heating the micro-resonator using a heater; and deterministically generating broadband microcombs including octave spanning solitons by the micro-resonator by bi-directional tuning of the heater voltage, wherein the bi-directional tuning of the heater voltage tunes the resonance wavelengths of the two modes, and alters the wavelength separation of two modes.

2. The method as claimed in claim 1 , wherein the micro-resonator includes a dual-mode 1-THz ring resonator with TE or TM polarization, with a repetition rate ranging from 100 GHZ to 1 THz and a mode separation ranging from 67 pm to 260 pm.

3. The method as claimed in any preceding claim, wherein the heating the micro-resonator increases the refractive indices of the materials via the thermooptic effect, thereby tuning the resonances of two modes to longer wavelengths, and adjusting the mode separation to a regime conducive to soliton microcomb formation.

4. The method as claimed in any preceding claim further comprising:initially heating the micro-resonator by applying a first heater voltage, wherein the application of the first heater voltage shifts current resonance wavelengths of the two modes towards wavelengths greater than that of the pump laser and decreases current mode separation between the two modes; and deterministically generating soliton combs by the micro- re senator upon applying a second heater voltage that is less than the first heater voltage, wherein the application of the second heater voltage decreases current mode separation and current resonance wavelengths of the two modes.

5. The method as claimed in any preceding claim, wherein the heating the micro resonator demonstrates substantial tunability, shifting the resonances by more than one free spectral range at maximum heater power.

6. The method as claimed in any preceding claim further comprising changing the heater voltage either gradually or through rapid pulsed operation.

7. The method as claimed in any preceding claim further comprising performing bi-directional tuning of the wavelength of pump laser along with bidirectional tuning of heater voltage to tune the mode separation.

8. The method as claimed in any preceding claim further comprising reducing the wavelength of the pump laser to reduce the number of soliton combs.

9. The method as claimed in any preceding claim, wherein the microresonator is made from a material selected from a group consisting of: Silicon carbide, Silica, Silicon, Lithium niobate, and Aluminium nitride.

10. The method as claimed in any preceding claim further comprising applying four-stage thermal control method to deterministically generate single soliton combs, wherein the four-stage control method comprises: performing backward resonance tuning of the resonator at first stage to form an initial comb state by decreasing current heater voltage; performing forward resonance tuning of the resonator at second stage by decreasing current heater voltage in order to reduce detuning between the fundamental cavity resonance and pump frequency, and thereby ensuring a deterministic transition from a multi-soliton to a single-soliton state; performing another backward resonance tuning at third stage to reduce degradation in soliton spectral bandwidth and comb conversion efficiency; and performing further backward resonance tuning at fourth stage to yield an optimized single-soliton output under constant heater voltage.11 . The method as claimed in any preceding claim further comprising: integrating a second micro-resonator with a GHz repetition rate soliton microcomb with the broadband microcomb on same chip; triggering the two microcombs with a single pump laser locked to an atomic transition frequency; and thermally tuning the two microcombs using two heaters.

12. The method as claimed in any preceding claim further comprising measuring power of output signal of the micro-resonator, and adjusting the heater voltage in the event of reduction of the measured power.

13. The method as claimed in any preceding claim further comprising tuning carrier envelope offset frequency and repetition rate of the soliton microcombs based on bi-directional tuning of the heater voltage.

14. The method as claimed in any preceding claim further comprising generating octave spanning soliton microcombs with pump wavelengths that are precisely aligned with rubidium atomic transitions.

15. The method as claimed in any preceding claim further comprising maximising the bandwidth of the broadband microcomb through the refractive index dispersion.

16. A system for generating a broadband microcomb, comprising: a pump laser for generating a comb signal at a pump wavelength corresponding to a resonance of a micro-resonator; the micro-resonator coupled to an output of the pump laser, wherein the micro-resonator operates with two modes with a mode separation of a predefined range in order to stabilize soliton formation over a broad range of pump wavelengths; and a heater for heating the micro-resonator upon applying a heater voltage, wherein the micro-resonator deterministically generate broadband microcombs including octave spanning solitons through bidirectional tuning of the heater voltage, wherein the bi-directional tuning of the heater voltage tunes the resonance wavelengths of the two modes, and alters the wavelength separation of two modes.

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