Single and multiple soliton generation device and method

Abstract

A soliton generation apparatus comprising: an optical resonator; a pumping laser for providing light at a pumping wavelength into the optical resonator; a generator for generating multiple solitons in the optical resonator; a detuning device for changing the wavelength detuning between the pumping laser wavelength and an optical resonance wavelength of the optical resonator to remove at least one soliton of the generated multiple solitons to provide (i) a plurality of solitons that comprises at least one less soliton than that of the generated multiple solitons or (ii) a single soliton in the optical resonator.

Claims

1. A soliton generation apparatus comprising: an optical resonator for generating multiple solitons; a pumping laser for providing light at a pumping wavelength into the optical resonator; a tuning device for tuning the pumping wavelength across an optical resonance wavelength of the optical resonator or the optical resonance wavelength of the optical resonator across the pumping wavelength to generate multiple solitons inside the optical resonator, and for changing the wavelength detuning between the pumping laser wavelength and the optical resonance wavelength of the optical resonator to remove at least one soliton of the generated multiple solitons to provide (i) a plurality of solitons that comprises at least one less soliton than that of the generated multiple solitons or (ii) a single soliton in the optical resonator; a photodetector for receiving light output from the optical resonator and producing a corresponding output signal; a processor configured to control the tuning device to generate multiple solitons in the optical resonator and to change the wavelength detuning between the pumping laser wavelength and an optical resonance wavelength of the optical resonator to remove at least one soliton of the generated multiple solitons, process the output signal to determine a removal of a soliton from the optical resonator through the identification of a step profile in the corresponding output signal, stop detuning when the removal of the at least one soliton is determined from the corresponding output signal, and control the detuning device to tune at a tuning speed slower than a thermal relaxation rate of the optical resonator.

2. Apparatus according to claim 1, wherein the detuning device comprises a thermal tuner configured to apply or remove thermal energy to or from the optical resonator to displace the optical resonance wavelength of the optical resonator towards the pumping wavelength.

3. Apparatus according to claim 2, wherein the thermal tuner is configured to apply or remove thermal energy to or from the optical resonator to displace the optical resonance wavelength of the optical resonator across the pumping wavelength to generate the multiple solitons in the optical resonator.

4. Apparatus according to claim 1, wherein the pumping laser is configured to provide light at a first wavelength into the optical resonator; and the apparatus includes: a laser tuning controller configured to: (a) forward tune the pumping laser to tune the pumping laser light from the first wavelength, across a cavity resonance of the optical resonator, to a second wavelength to generate a frequency comb and multiple solitons in the optical resonator, the second wavelength being longer than the first wavelength; and configured to (b) backward tune the pumping laser light from the second wavelength to a third wavelength to remove at least one soliton of the generated multiple solitons to provide (i) a plurality of solitons that comprises at least one less soliton than that of the generated multiple solitons or (ii) a single soliton in the optical resonator, the third wavelength being shorter than the second wavelength.

5. Apparatus according to claim 4, wherein the processor is configured to determine the removal of a least one soliton during forward and/or backward tuning from the optical resonator light output signal.

6. Apparatus according to claim 5, wherein the processor is configured to control the laser tuning controller to stop tuning when the removal of a least one soliton is determined.

7. Apparatus according to claim 5, wherein the processor is configured to control the laser tuning controller to carry out further backward tuning until a single soliton remains in the optical resonator based on determined soliton removals.

8. Apparatus according to claim 5, wherein the processor is configured to control the laser tuning controller to backward tune the laser light from the second wavelength to the third wavelength to remove solely one soliton of the generated multiple solitons to provide (i) a plurality of solitons that comprises one less soliton than that of the generated multiple solitons or (ii) a single soliton in the optical resonator.

9. Apparatus according to claim 5, wherein the processor is configured to control the laser tuning controller to backward tune the laser light from the third wavelength to lower wavelengths to remove solitons of the plurality of solitons one-by-one to provide a single soliton in the optical resonator.

10. Apparatus according to claim 5, wherein the processor is configured to control the laser tuning controller to adiabatically backward tune the laser light.

11. Apparatus according to claim 5, wherein the processor is configured to control the laser tuning controller to backward tune the laser light at a tuning speed that is slower than a thermal relaxation rate of the optical resonator.

12. Apparatus according to claim 1, wherein the optical resonator is a crystalline resonator or an on-chip resonator.

13. Apparatus according to claim 1, further including a phase modulator for modulating the pumping laser light to non-destructively probe soliton generation in the optical resonator.

14. Apparatus according to claim 13, further including a modulation response analyzer for receiving an optical response signal outputted by the optical resonator and configured to determine a modulation response signal representing the response of the optical resonator to the phase modulation of the pumping laser light.

15. Apparatus according to claim 14, further including a processor configured to determine, from the modulation response signal, an effective pump detuning value representing the detuning of the pump laser frequency/wavelength from a cavity resonance frequency/wavelength of the optical resonator during the apparatus operation or pumping.

16. Apparatus according to claim 15, wherein the processor is configured to monitor the effective pump detuning value to maintain a soliton state in the optical resonator.

17. Apparatus according to claim 16, wherein the processor is configured to adjust the effective pump detuning value by controlling the laser tuning controller to tune the pump laser frequency/wavelength to maintain a soliton state in the optical resonator.

18. Apparatus according to claim 14, further including a processor configured to monitor the evolution of the modulation response signal or the effective pump detuning value while carrying out backward tuning to determine the extinction of one single soliton state in the optical resonator.

19. Apparatus according to claim 18, wherein the processor is configured to monitor the evolution of the modulation response signal or the evolution of the effective pump detuning value during backward tuning to determine successive extinctions of individual solitons, and configured to control the laser tuning controller to stop tuning to provide a single soliton in the optical resonator.

20. Apparatus according to claim 19, wherein the processor is configured to monitor the effective pump detuning value and to control the tuning device or the laser tuning controller to tune the pump laser frequency/wavelength to maintain the single soliton state in the optical resonator.

21. Soliton generation apparatus according claim 1, wherein the optical resonator is a crystalline resonator or an on-chip resonator and the apparatus further includes a coupling waveguide optically coupled to the optical resonator, the pumping laser light being provided to the optical resonator via the coupling waveguide.

22. A soliton generation method including the steps of: introducing pumping laser light at a pumping wavelength into an optical resonator; generating multiple solitons in the optical resonator by tuning the pumping wavelength across an optical resonance wavelength of the optical resonator or tuning the optical resonance wavelength of the optical resonator across the pumping wavelength; providing light output from the optical resonator to a photodetector to produce a corresponding output signal; and changing the wavelength detuning between the pumping laser wavelength and the optical resonance wavelength of the optical resonator to remove at least one soliton of the generated multiple solitons to provide (i) a plurality of solitons that comprises at least one less soliton than that of the generated multiple solitons or (ii) a single soliton in the optical resonator, wherein the corresponding output signal is processed to determine a removal of a soliton from the optical resonator through the identification of a step profile in the corresponding output signal, and detuning is stopped when the removal of the at least one soliton is determined from the corresponding output signal to provide (i) a plurality of solitons that comprises at least one less soliton than that of the generated multiple solitons or (ii) a single soliton in the optical resonator, wherein the detuning device is tuned at a tuning speed slower than a thermal relaxation rate of the optical resonator.

23. Method according to claim 22, wherein the step of changing the wavelength detuning is carried out by applying or removing thermal energy to or from the optical resonator to displace the optical resonance wavelength of the optical resonator towards the pumping wavelength.

24. Method according to claim 22, wherein the step of generating multiple solitons is carried out by applying or removing thermal energy to or from the optical resonator to displace the optical resonance wavelength of the optical resonator across the pumping wavelength to generate the multiple solitons in the optical resonator.

25. Method according to claim 22 further including the steps of: introducing the pumping laser light at a first wavelength into the optical resonator; forward tuning the pumping laser light from the first wavelength, across theft cavity resonance of the optical resonator, to a second wavelength to generate a frequency comb and multiple solitons in the optical resonator, the second wavelength being longer than the first wavelength; and backward tuning the pumping laser light from the second wavelength to a third wavelength to remove at least one soliton of the generated multiple solitons to provide (i) a plurality of solitons that comprises at least one less soliton than that of the generated multiple solitons or (ii) a single soliton in the optical resonator, the third wavelength being shorter than the second wavelength.

26. Method according to claim 25, wherein the step of backward tuning the laser light from the second wavelength to the third wavelength removes solely one soliton of the generated multiple solitons to provide (i) a plurality of solitons that comprises one less soliton than that of the generated multiple solitons or (ii) a single soliton in the optical resonator.

27. Method according to claim 26, further including the step of backward tuning the laser light from the third wavelength to lower wavelengths to remove solitons of the plurality of solitons one-by-one to provide a single soliton in the optical resonator.

28. Method according to claim 25, wherein the backward tuning of the laser light is carried out adiabatically.

29. Method according to claim 25, wherein the backward tuning of the laser light is carried out at a tuning speed that is slower than a thermal relaxation rate of the optical resonator.

30. Method according to claim 25, wherein the backward tuning of the laser light is carried out at a constant tuning speed.

31. Method according to claim 25, wherein the intensity of the pumping laser light is substantially constant.

32. Method according to claim 25, wherein the soliton is a dissipative Kerr soliton and/or the optical resonator is a crystalline resonator or an on-chip resonator.

33. Method according to claim 22, further including the step of phase modulating the pumping laser light to non-destructively probe soliton generation in the optical resonator.

34. Method according to claim 33, further including the step of measuring an optical response signal outputted by the optical resonator and determining a modulation response signal to non-destructively probe soliton generation in the optical resonator.

35. Method according to claim 34, further including the step of determining, from the modulation response signal, an effective pump detuning value representing the detuning of the pump laser frequency/wavelength from they cavity resonance frequency/wavelength of the optical resonator during the apparatus operation or pumping.

36. Method according to claim 35, further including the step of monitoring the effective pump detuning value to maintain a soliton state in the optical resonator.

37. Method according to claim 36, further including the step of adjusting the effective pump detuning value by tuning the optical resonance wavelength of the optical resonator or the pump laser frequency/wavelength to maintain a soliton state in the optical resonator.

38. Method according to claim 34, further including the step of monitoring the evolution of the modulation response signal or the effective pump detuning value while carrying out backward tuning to determine the extinction of one single soliton state in the optical resonator.

39. Method according to claim 32, wherein monitoring of the modulation response signal or the evolution of the effective pump detuning value is carried out while carrying out backward tuning to determine successive extinctions of individual solitons and provide a single soliton in the optical resonator.

40. Method according to claim 39, further including the steps of monitoring and adjusting the effective pump detuning value to maintain the single soliton state in the optical resonator.

Description

A BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

(1) FIG. 1a shows a schematic view of an apparatus according to one embodiment;

(2) FIG. 1b shows the principle of microresonator frequency comb generation and the formation of dissipative Kerr solitons;

(3) FIG. 2 shows SEM image of a Si.sub.3N.sub.4 on-chip microresonator with a free spectral range (FSR) of 100 GHz;

(4) FIG. 3 is a picture of a MgF.sub.2 crystalline resonator with FSR of 14 GHz;

(5) FIG. 4 shows a scheme of a laser tuning method for the soliton generation in optical microresonators where the pump laser is tuned over the resonance from short to long wavelengths (forward tuning), the hatched region indicates the pump detuning range of multiple solitons (MS);

(6) FIG. 5 is a histogram plot of 200 overlaid experimental traces of the output comb light in the pump forward tuning over the resonance with the same pump power and tuning speed, which reveals the formation of a predominant multiple soliton state with N=6; the noise pattern in the forward detuning was not captured by the measurements due to the averaging in the photodetector;

(7) FIG. 6 shows a scheme of the laser backward tuning, where to initiate the sequence, the forward tuning is first applied, and the pump is stopped in a multiple soliton state (which can be stable by suitable choice of the laser tuning speed); in the second stage, the pump is tuned back to short wavelengths, which leads to successive soliton switching, N.fwdarw.N1.fwdarw. . . . .fwdarw.1; the MS area indicates the detuning range of multiple soliton states, which is much larger compared to the forward tuning method, there also exists the range of the single soliton state (SS);

(8) FIG. 7 shows a measured experimental trace in the forward tuning (top curve) followed by one trace in the backward tuning (bottom curve) with successive transitions of multiple-soliton states from N=7 to N=0 (no solitons);

(9) FIG. 8 to FIG. 10 show frequency comb spectra in soliton states with N=1, 2, 3, measured during the backward tuning in a 100 GHz Si.sub.3N.sub.4 microresonator;

(10) FIG. 11a shows a schematic view of an apparatus according to another embodiment;

(11) FIG. 11b shows an exemplary apparatus or setup scheme used for soliton generation, non-destructive soliton probing and deterministic soliton switching and which includes an external cavity diode laser (CW pump) used as a pump source, an arbitrary function generator (AFG), an erbium doped amplifier (EDFA); a fiber polarization controller (FPC), a wavelength meter (WM), vector network analyzer (VNA), OSA, an optical spectrum analyzer (OSA), an oscilloscope (OSC); photodiodes (PD), an electro-optical phase modulator (EOM), a phase modulator (PD) and a fiber Bragg grating (FBG);

(12) FIG. 12 shows a diagram of the double-resonance modulation response in the soliton state (Left, top) where the power trace of the soliton component is indicated which is evolved from the high-intensity branch of the bistability, the pump is tuned in the bistability range (in the effective-red detuned regime); therefore, both the soliton branch and the low-intensity continuous (CW) branch (bottom line) are supported in the system, each corresponds to a resonance, i.e. the S-resonance and the -resonance; a double-resonance modulation response from VNA is also shown (left, down) in which the high-frequency peak indicates the C-resonance and the low frequency is the S-resonance; Four stages of the microresonator frequency comb formation and corresponding VNA modulation response when the pump laser is forward tuned over the resonance is also shown (middle) with (I) No comb, the pump is blue-detuned; (II) Chaotic MI comb state; (III) Soliton state; (IV) No comb, the pump is red-detuned; Frequency comb spectra corresponding to the chaotic MI operation regime and the single soliton state is also presented (right);

(13) FIG. 13 to FIG. 16 show measured Experimental double-resonance responses of various multiple-soliton states at different detunings for MgF.sub.2 and Si.sub.3N.sub.4 microresonators;

(14) FIG. 17 and FIG. 18 show simulated double-resonance responses for a Si.sub.3N.sub.4 microresonator;

(15) FIG. 19 shows the power trace of the generated light obtained from 100 GHz Si.sub.3N.sub.4 microresonator with the backward pump tuning from multiple-soliton with N=6 (effectively red detuned) to the effectively blue detuned regime (top); shows a set of 500 concatenated VNA traces that were taken during the backward tuning, an arrow indicates the transition from a single soliton state to no-soliton state, while the pump is still red detuned with respect to the cavity resonance, a second arrow indicates the transition from the red detuned operating regime to the blue detuned regime (middle); and shows the evolution of the modulation response during the backward tuning process in the effectively red detuned regime, with no soliton presented (N=0) as well as the evolution of the modulation response in the multiple-soliton state with N=6 (bottom);

(16) FIG. 20 shows the power trace of the generated light obtained from 14 GHz MgF.sub.2 crystalline resonator with the backward pump tuning from multiple-soliton state with N=6 (effectively red detuned) to the effectively blue detuned regime (top), a set of 1700 concatenated VNA traces that were taken during the backward tuning are also shown (middle); the Evolution of the modulation response during backward tuning in the state with no soliton is presented as well as the Evolution of modulation response in the multiple-soliton state with N=6 (bottom);

(17) FIG. 21 shows Experimental measurements of the generated comb light with respect to the absolute detuning, a top curve shows the trace in the forward tuning and a bottom curve indicates the entire soliton existence range, Zero absolute detuning corresponds to 1553.4 nm.

(18) FIG. 22 shows an Experimental trace from FIG. 21 plotted in terms of the effective detuning measured from the modulation response with the VNA, Hypothetical trace of forward tuning is shown in a dashed line, because the effective detuning in this process cannot be reliably measured with the VNA; and

(19) FIG. 23 and FIG. 24 show Numerical simulations and analytical solutions of the backward tuning in Si.sub.3N.sub.4 with (FIG. 23) and without (FIG. 24) thermal effects where normalized detuning used in the simulation: =2(.sub.0.sub.p)/, where .sub.0 is the resonance frequency, .sub.p is the pump frequency and is the resonance linewidth, dashed lines indicate initial excitation of a multiple-soliton state in the forward tuning, solid lines indicate the backward tuning, the stable branch of the nonlinear induced tilted resonance (in the CW mode) is also indicated, dashed lines indicate the unstable branch.

(20) Herein, identical reference numerals are used, where possible, to designate identical elements that are common to the figures.

DETAILED DESCRIPTION OF THE SEVERAL EMBODIMENTS

(21) The present invention relates to a novel mechanism which makes it possible to reduce deterministically the number of solitons, one by one, i.e. N.fwdarw.N1.fwdarw. . . . .fwdarw.1. By applying for example weak phase modulation, the soliton state is directly characterized via a double-resonance response. The dynamical probing demonstrates that transitions occur in a predictable way, and thereby enables to map experimentally the underlying multi-stability diagram of dissipative Kerr solitons. These measurements reveal the lifted degeneracy of soliton states as a result of the power-dependent thermal shift of the cavity resonance (i.e. the thermal nonlinearity). The experimental results are in agreement with theoretical and numerical analysis that incorporate the thermal nonlinearity.

(22) By studying two different microresonator platforms (integrated Si.sub.3N.sub.4 microresonators and crystalline MgF.sub.2 resonators) it is confirmed that these effects have a universal nature. Beyond elucidating the fundamental dynamical properties of dissipative Kerr solitons, the observed phenomena are also of practical relevance, providing a manipulation toolbox which enables to sequentially reduce, monitor and stabilize the number N of solitons, preventing it from decay. Achieving reliable single soliton operation and stabilization in this manner in optical resonators is imperative to applications.

(23) The present invention allows to induce deterministically transitions to states with less solitons (i.e. from N to N1), and thereby to reliably reach a single soliton state. The phenomenon is not explained by standard theoretical simulations based on the Lugiato-Lefever equation (LLE) or coupled mode equations models. A detailed analysis of the observed phenomenon is presented, in two microresonator platforms where the thermal locking is possible, and demonstrates its universal nature. The findings allow to switch between multiple-soliton states by sequentially reducing the number N of initially created solitons (with a routine simple enough to be carried out by a micro-controller), to monitor and control the switching, and to hold the targeted soliton state, preventing it from decay.

(24) In particular, the single soliton state can be deterministically and reliably induced, which is imperative to a wide range of applications. The presented results contribute to the physical understanding of switching behavior of the DKS, highlight the influence of thermal effects and provide a rich toolbox for the study of the multiple-soliton dynamics. From an applied perspective, the results present a route to make, for example, reliable pulse sources and frequency combs based on DKS at microwave repetition rates in optical microresonators.

(25) One embodiment of the present disclosure concerns an apparatus and method for soliton generation. FIG. 1a schematically illustrates an example of such an apparatus 1. The soliton generation apparatus 1 can include an optical resonator 3, a pumping optical source such as a pumping laser 5 for providing light at a first wavelength into the optical resonator 3 and a tuning device 7. According to one embodiment, the tuning device 7 comprises or is, for example, a laser tuning controller 7 configured to forward tune the pumping laser 5 to tune the pumping laser light from the first wavelength, across a cavity resonance of the optical resonator 3, to a second wavelength to generate a frequency comb and multiple solitons in the optical resonator 3, where the second wavelength is longer than the first wavelength.

(26) A non-limiting example of the laser tuning controller 7 is a (internal) motor which is activated to move a cavity mirror of the laser to carry out tuning, for example, course tuning of the laser cavity. Finer tuning can be implemented using a piezo element which provides smooth and precise tuning of the mirror by applying a voltage. The pumping laser can be for example a tunable External Cavity Diode Laser (ECDL) that includes such control systems embedded. Alternatively, the laser can be tuned using alternative ways such by a heater or a MEMS structure for tuning the cavity length. An array of lasers, each at a different wavelength, can be used with switching between lasers being used to changes the wavelength in a coarse manner and a heater being used for fine tuning.

(27) The laser tuning controller 7 is also configured to backward tune the pumping laser light from the second wavelength to a third wavelength to remove at least one soliton of the generated multiple solitons to provide either a plurality of solitons that comprises at least one less soliton than that of the generated multiple solitons or a single soliton in the optical resonator 3, where the third wavelength is shorter than the second wavelength.

(28) According to another embodiment, the detuning device 7 is or comprises, for example, a thermal tuner configured to apply or remove thermal energy to or from the optical resonator 3 to displace the optical resonance wavelength of the optical resonator 3 towards the pumping wavelength. The thermal tuner 7 is configured to apply or remove thermal energy to or from the optical resonator 3 to displace the optical resonance wavelength of the optical resonator 3 across the pumping wavelength to generate the multiple solitons in the optical resonator 3. Non-limiting examples of the thermal tuner are a peltier element or for example a simple resistive heater (temperature increased by applying a voltage to a high-resistance element) which can be a separate device or even deposited on the resonator 3.

(29) The apparatus 1 may also further include a photo-detector 9 for receiving the optical resonator light output from the optical resonator 3 and for producing a corresponding output signal 11 that is received by a processor or micro-controller 15. FIG. 7 shows an example of such a signal 11. The processor 15 is configured to process the signal 11 determine the removal of a soliton from an optical resonator light output signal. This is done, for example, through the identification of a step profile in the signal 11. The processor 15 is also configured to determine the removal of a soliton during both forward and backward tuning of the laser pump wavelength from the optical resonator light output signal. This is done, for example, during forward tuning through the identification of a step profile in the signal 11 as shown in FIG. 5. The processor 15 is configured to control the tuning device, for example, the laser tuning controller 7 to carry out forward and backward tuning, and to stop backward tuning when the removal of one soliton is determined from the signal 11. The processor 15 controls the backward or forward laser tuning controller 7 to tune until a single soliton remains in the optical resonator based on determined soliton removals using the processed signal 11.

(30) The processor 15 is configured to control the laser tuning controller 7 to backward tune the laser light from the second wavelength to the third wavelength to remove solely one soliton of the generated multiple solitons based on signal 11 to provide a plurality of solitons that comprises one less soliton than that of the initially generated multiple solitons or to provide a single soliton in the optical resonator 3.

(31) The processor 15 is configured to control the laser tuning controller 7 to backward tune the laser light from the third wavelength to lower wavelengths to remove solitons of the plurality of solitons one-by-one by processing the signal 11 to identify each soliton extinction in order to provide a single soliton in the optical resonator 3.

(32) The processor 15 is configured to control the laser tuning controller 7 to adiabatically backward tune the laser light. The processor 15 can also control the laser tuning controller 7 to backward tune the laser light at a tuning speed that is slower than a thermal relaxation rate of the solitons.

(33) The apparatus includes a memory containing a routine or algorithm permitting to processor 15 to operate as indicated above. However, the soliton generation method disclosed herein can alternatively be carried out without such a commanding processor by an apparatus user.

(34) The principles of microresonator frequency comb generation and the formation of dissipative Kerr solitons (DKS) are shown in FIG. 1b. CW laser light is coupled to a high-Q optical resonator 3, where modulation instability (MI) and cascaded four-wave-mixing processes lead to the formation of a broadband frequency comb.

(35) Two exemplary microresonator platforms 3: Si.sub.3N.sub.4 on-chip ring microresonators (FIG. 2) and MgF.sub.2 crystalline resonators (FIG. 3) are disclosed herein.

(36) The Si.sub.3N.sub.4 microresonator (FIG. 2) was fabricated using the Photonic Damascene process described in reference [38] listed below and fully incorporated herein by reference. The microresonator has FSR of 100 GHz. A single mode filtering section was added to the micro-rings in order to suppress high-order modes (see reference [39] fully incorporated herein by reference). The Si.sub.3N.sub.4 microresonator can also be fabricated using the process described in US patent application US2016/0327743 fully incorporated herein by reference.

(37) The dispersion parameters of the microresonators are measured using the frequency comb assisted laser spectroscopy method (as set out in reference [40]): D.sub.2/2=12 MHz, D.sub.3/2=O (1 kHz) (where the resonance frequencies near .sub.0 are expressed in a series .sub.=.sub.0+.sub.i1D.sub.i.sup.i/i!, where iN, is the mode number). Pumped resonance is at 1553.4 nm. Tuning speed for soft excitation is 1 nm/s. Pump power is 2-3 W on a chip.

(38) The MgF.sub.2 crystalline resonator (FIG. 3) was fabricated by diamond turning of a cylinder blank and subsequent hand polishing to achieve high Q

(39) $\left(\mathrm{linewidt}h\frac{}{2}=100\mathrm{kHz}\right).$

(40) The diameter of 5 mm yields a FSR D.sub.1/2=14 GHz. The dispersion parameters at the pump wavelength of 1553 nm are: D.sub.2/2=1.9 kHz, D.sub.3/2=O (1 Hz). The pump laser (fiber laser, wavelength 1553 nm; short-term linewidth 10 kHz) is amplified to 250 mW. The relative laser frequency is monitored by counting the heterodyne beat between the pump laser and a reference laser stabilized to an ultra-stable cavity. The light is evanescently coupled to a WGM with a tapered optical fiber.

(41) The laser tuning technique was developed as an effective method to the formation of dissipative Kerr solitons, in which the CW pump laser 5 is tuned (from short to long wavelengths) over the cavity resonance, referred to as the forward tuning. Initially, the CW pump is in the blue detuned regime. The cavity resonance is shifted due to the slow thermal and fast Kerr nonlinearity of the microresonator, resulting in a self-locking of the cavity resonance to the pump laser 5. In this regime the Kerr comb formation can be observed. The mechanism results in a triangular trace in the generated comb light, over the pump frequency detuning. When the pump is tuned over the cavity resonance, it enters the effectively red-detuned regime where multiple dissipative Kerr solitons (i.e. multiple-solitons) can be formed. The soliton state is accompanied with a step-like power trace in the generated comb light, where the step height corresponds to the number of solitons (N) inside the resonator.

(42) Transitions to states with lower number of solitons may also occur and the power trace will exhibit a characteristic steps. Eventually, by stopping the pump laser 5 tuning at a step while ensuring the thermal equilibrium in the resonator, stable multiple-soliton and even single soliton states can be accessed (FIG. 4). This forward tuning method was applied in MgF.sub.2, Si.sub.3N.sub.4 and silica resonators 3 for single dissipative Kerr soliton generation.

(43) Remarkably, an additional laser tuning towards shorter wavelengths (backward tuning) provides a way to reliably access the single soliton state starting from an arbitrary multiple soliton state. The result of this backward tuning sequence, shown in FIG. 6 and FIG. 7, allows for successive extinction of intracavity solitons (soliton switching) down to the single soliton state (N.fwdarw.N1.fwdarw. . . . .fwdarw.1).

(44) FIG. 7 shows one trace of the generated light of the Si.sub.3N.sub.4 microresonator 3, where switching from seven solitons to the single soliton is observed. Strikingly, the power trace of the generated comb light reveals a regular staircase pattern with equal stair length and height. The exact soliton number in each step can be precisely inferred from the step height. The pattern is almost identical over multiple experimental runs (using the same tuning speed and pump power) regardless of the initial soliton number N. Each transition between multiple-soliton states occurs with the extinction of preferably one soliton at a time, which is confirmed by the relative positions of the intracavity solitons that are retrieved from the optical spectrum as shown in FIGS. 8 to 10.

(45) The backward tuning process should preferably be adiabatic to induce the successive reduction of the soliton number: the thermal equilibrium is required at each multiple-soliton state. This is satisfied by choosing a tuning speed much slower than the thermal relaxation rate that depends on the effective mode volume and the thermal diffusivity of a microresonator 3. For the Si.sub.3N.sub.4 microresonator 3, the exemplary backward tuning speed is chosen 40 MHz/s, while the exemplary forward tuning speed is 100 GHz/s. In this way, all soliton states (N) are deterministically accessible. In contrast to the robust backward tuning that enables successive extinction of intracavity solitons, the forward tuning in Si.sub.3N.sub.4 microresonators 3 leads to collective extinction of solitons.

(46) The backward tuning was also carried out in MgF.sub.2 crystalline microresonators 3, where the successive soliton switching to the single soliton state is also achieved. In contrast to the Si.sub.3N.sub.4 platform, the single soliton state can directly be accessed with the forward tuning in MgF.sub.2 microresonators 3. However, this requires fine adjustments on the coupling, the pump power and the tuning speed. The backward tuning, on the other hand, is much more robust and significantly facilitates the generation of single soliton states for crystalline resonators 3.

(47) The soliton switching in both Si.sub.3N.sub.4 and crystalline MgF.sub.2 resonator 3, proves that the backward tuning represents a universal approach to the generation of a single soliton state in microresonators, provided that the thermal locking can be achieved.

(48) Dissipative Kerr solitons in microresonators represent stable and self-reinforcing intracavity light patterns resulting from double balance between pump and cavity losses, as well as chromatic dispersion and Kerr nonlinearity of the resonator. The key parameter of such soliton state is the effective laser frequency detuning that determines both the amplitude and the duration of soliton pulses.

(49) This detuning is defined as 2.sub.eff=.sub.0.sub.p, where .sub.0 indicates the frequency of a cavity resonance and .sub.p is the pump laser frequency. The pump frequency can be precisely controlled, but the resonance frequency is thermally shifted from the initial cold cavity resonance frequency .sub.0, making it a priori not possible to evaluate the effective detuning.

(50) On the other hand, the absolute detuning 2=.sub.0.sub.p can be introduced and measured as the position of the pump frequency relative to the fixed cold cavity resonance. It has been shown that solitons are supported within a certain range of the effective detuning, when the pump is effectively-red detuned (.sub.p<.sub.0), which is here referred to as the soliton existence range for a given constant input power.

(51) According to another aspect of the present disclosure, a non-destructive soliton probing scheme and apparatus has been developed that allows to track the effective detuning and extract the soliton number N of microresonator frequency combs. An exemplary apparatus setup 17 is presented in FIG. 11a and schematically shown in FIG. 11b.

(52) As shown in FIG. 11b, the apparatus may include the elements of the apparatus 1 (illustrated in FIG. 1a) and additionally include a phase modulator 19 for modulating the pumping laser light to non-destructively probe soliton generation in the optical resonator 3 and also include a modulation response analyzer 21 for receiving an optical response signal 23 outputted by the optical resonator 3 and for determining a modulation response signal 25 to non-destructively probe soliton generation in the optical resonator 3. The modulation response signal 25 represents the response of the optical resonator 3 to the phase modulation of the pumping laser light.

(53) The processor 15 is configured to determine, from the modulation response signal 25 provided by the modulation response analyzer 21 to the processor 15, the effective pump detuning value representing the detuning (during pumping) of the pump laser wavelength from a cavity resonance wavelength of the optical resonator 3. This is done for example by determining the C-resonance in the modulation response signal 25 (see FIG. 12) as detailed further below. To maintain a soliton state in the optical resonator 3, the processor 15 is further configured to monitor the effective pump detuning value and to adjust the measured effective pump detuning value by controlling the laser tuning controller 7 to tune the pump laser wavelength. This allows the effective pump detuning value to be adjusted to a value or to within a range that permits to maintain the soliton state in the optical resonator 3.

(54) The processor 15 can be configured to monitor the evolution of the modulation response signal 25 or the effective pump detuning value while carrying out backward tuning via the controller 7 to determine the extinction of a single soliton state in the optical resonator 3. Successive single soliton state extinctions can be determined and the laser tuning controller 7 can be controlled to stop tuning when a desired number of solitons or a single soliton is determined to be present in the optical resonator 3. The processor 15 can be further configured to then monitor the effective pump detuning value and to control the laser tuning controller 7 to tune the pump laser wavelength to maintain the multiple solitons or the single soliton state in the optical resonator 3.

(55) The apparatus 17 includes a memory containing a routine or algorithm permitting to processor 15 to operate as indicated above. However, the soliton generation method disclosed herein can alternatively be carried out without such a commanding processor by an apparatus user.

(56) FIG. 11a shows further details of one possible exemplary embodiment of the apparatus 17. It is to be noted that not all the shown elements are necessary in the apparatus 17 to carry out the present invention. The Si.sub.3N.sub.4 resonator 3 is pumped with a CW laser light from an external-cavity diode laser 5 amplified by an erbium-doped fiber amplifier 27 (EDFA) to 3 to 5 W. The CW pump 5 is coupled to the on-chip resonator 3 using lensed fibers 29 with coupling losses of 2.5-3 dB per facet.

(57) The Si.sub.3N.sub.4 resonator 3 includes a substantially circular or ring SiN waveguide section and a SiO.sub.2 cladding as shown in FIG. 2. The SiN microresonator studied has a waveguide height of 0.8 m and a nominal width of 1.5 m. The waveguide section includes a tapered section where the taper waist ranges from 0.5 m to the nominal width and the taper length is fixed to be 180 m.

(58) For soliton probing measurements, a 10 GHz electro-optical phase modulator (EOM) 19 is placed before the EDFA 27 with additional polarization controller 31 for adjusting input polarization. The pump frequency wavelength in the pump backward tuning is measured by a wave-meter 33 with resolution of 50 MHz. For the long sweeps, an arbitrary function generator 35 is used.

(59) The output signal from the chip 3 is split in several paths among the optical spectrum analyzer OSA (for the measurements of combs spectra), the oscilloscope OSC (for the measurements of generated light by filtering out the pump with FBG) and a vector network analyzer (VNA) receiver 21 (for the measurements of and modulation response).

(60) As shown in the exemplary set-up of FIG. 11a, the apparatus 17 employs the pump laser 5, whose frequency is phase modulated using a phase modulator 19 and a vector network analyzer (VNA), that produces weak optical sidebands with sweeping frequency (v) in the range 5 kHz-4.5 GHz, which probe the state of the microresonator system 3. The complex modulation response 25 to such probes is measured and determined by the modulation response analyzer 21 which is the VNA.

(61) This non-destructive probing method is based on the measurement of the frequency-dependent S21 parameter of the optical resonator. The input signal of the system in this case is presented by the RF-modulation of the CW-pump (before entering the resonator), and the output signal is the modulation response of transmitted optical intensity measured with the high-speed photodiode. A 2-port vector network analyzer (VNA) is, for example, used in the S21 measurement regime, where port-1 was connected to the EOM (phase modulator), to provide a phase modulation of the CW pump, and the transmitted optical intensity was detected with a 25-GHz photodiode connected to port-2 of the VNA for the measurements of the modulation response.

(62) This probing method enables to identify different stages in the generation of frequency comb, including the soliton formation, see FIG. 12. First (FIG. 12-I), when the pump is in the blue-detuned regime (.sub.p>.sub.0), away from the cavity resonance, the modulation response 23 on the VNA 21 shows a Lorenzian-like resonance profile that corresponds to the cavity resonance with the peak position indicating |.sub.eff|. Second (FIG. 12-II), when (forward) tuning the pump frequency into the cavity resonance, where the frequency comb in the chaotic MI regime is observed, the modulation response shows an asymmetric profile with the peak position being fixed, indicating the thermal and Kerr locking of the cavity resonance to the pump frequency. Third (FIG. 12-III), when the frequency comb is in the soliton state, with the pump laser tuned in the soliton existence range in the red-detuned regime, the modulation response shows unexpectedly a double-resonance feature. Finally (FIG. 12-IV), when the pump frequency is tuned out of the soliton existence range where no comb is observed, the modulation response shows again a single, Lorenzian-like resonance similar to the first stage.

(63) The double-resonance response that is observed in the presence of soliton states can be attributed to the superposition of weak continuous background and intense soliton pulses. Due to different intensities each component induces a different Kerr shift to the cavity resonance which we can discriminate by the modulation probing. Since the pump is far detuned from the cavity resonance, the high-frequency peak in the modulation response corresponds to the cavity resonance that is slightly shifted by the CW component (C-resonance). The peak position in this way indicates the effective detuning. On the other hand, the resonance shifted by solitons appears as the low-frequency peak (S-resonance). The position of the S-resonance is nearly fixed as it depends on the intensity of individual soliton, while the magnitude is related to the number of solitons (N).

(64) The non-destructive soliton probing was applied to both Si.sub.3N.sub.4 and MgF.sub.2 microresonators. The double-resonance response is observed in both platforms when having soliton state frequency combs, and was investigated with different soliton number N and pump detunings, see FIG. 13 to 16. The response is qualitatively similar for both platforms. The peak position of the -resonance varies with the pump frequency (FIGS. 13 and 15), while the S-resonance frequency is practically fixed as predicted. The peak height of the S-resonance linearly depends on the soliton number N (FIGS. 14 and 16). A theoretical analysis of the non-destructive soliton probing scheme confirms the double-resonance response of a soliton state (see FIGS. 17 and 18).

(65) The response of dissipative Kerr solitons to weak amplitude pump modulation was previously numerically investigated. While two peaks in the response were also numerically observed in that work (and attributed conceptually to Feshbach and relaxation oscillations in the presence of third order dispersion), the present results reveal the underlying physical origin of the soliton probing scheme, not requiring higher order dispersion. Moreover, phase modulation provides higher contrast of the modulation response.

(66) As a way to extract the effective pump detuning .sub.eff, the probing technique enables to precisely track the process of microresonator frequency comb generation. In a soliton state, thermal drifts of the cavity resonance originating from various external sources may cause variations of .sub.eff. Based on the modulation response 25, the effective detuning can be monitored and adjusted (e.g. by tuning the pump frequency) in order to maintain the soliton state within the soliton existence range. In practice, feedback-locking of .sub.eff is possible, which allows for long-term operation of a soliton state in a microresonator 3.

(67) Transitions of soliton states in the laser backward tuning by applying the non-destructive soliton probing in Si.sub.3N.sub.4 microresonators are shown in FIGS. 19 to 20. Forward tuning is first employed in order to generate a multiple soliton state with N=6, and then slow backward tuning is performed. The power trace of the generated light in the microresonator 3 again shows the staircase pattern in the backward tuning, which corresponds to successive soliton switching from N=6 to the single soliton state (FIG. 19). The VNA traces are simultaneously recorded and continuously stacked in order to monitor the evolution of the modulation response during the process (see FIG. 19).

(68) The results reveal a relationship between the evolution of modulation response 25 and the soliton switching. Within each soliton step, the C-resonance shifts towards the S-resonance due to the decrease of the effective detuning when the laser is tuned backward. When the two resonances overlap, the amplitude of S-resonance is significantly enhanced, leading to a high-intensity single-peak profile (FIG. 19). The phenomenon is also confirmed by the theory. The next moment after having such a response, soliton switching occurs, which results in the power drop in the generated light trace as one soliton is extinct (N.fwdarw.N1).

(69) After the switching, the -resonance abruptly separates from the S-resonance. Meantime, while still being Kerr locked, the S-resonance intensity is reduced to a lower level than the previous state, since the number of solitons is reduced by one. In the absence of solitons (N=0), the S-resonance equally is absent in the modulation response, but the -resonance is still present and captured (FIG. 19).

(70) The same measurement was carried out in MgF.sub.2 resonators, see FIG. 20. Similar switching dynamics as in Si.sub.3N.sub.4 microresonators are observed: (1) the power trace shows staircase profile of successive soliton switching; (2) the backward tuning shifts the VNA -resonance towards the S-resonance; (3) soliton switching occurs with the overlap of - and S-resonances and the enhancement of the S-resonance intensity. However, there are several details which differ between Si.sub.3N.sub.4 and MgF.sub.2 platforms. First, the optical quality factor Q of MgF.sub.2 crystalline resonators (10.sup.9) is three order of magnitude higher than for Si.sub.3N.sub.4 micro-rings (10.sup.6). The - and S-resonances in the modulation response of crystalline resonator are better resolved as a result of the narrower linewidth. The laser tuning range in Si.sub.3N.sub.4 microresonators is O (1 GHz), while that in MgF.sub.2 resonators is O (1 MHz). Second, after each soliton switching the MgF.sub.2 resonator shows slower recoil of the -resonance than the Si.sub.3N.sub.4 microresonator. This is attributed to the distinct thermal relaxation of the two platforms. The MgF.sub.2 resonator has a larger effective mode volume and physical size than the chip-scale Si.sub.3N.sub.4 micro-ring resonators such that the thermal relaxation time is longer. In the evolution of the modulation response of the MgF.sub.2 resonator (FIG. 3(f)), the recoil of the -resonance leaves curved trajectory while it is very abrupt in the Si.sub.3N.sub.4 microresonator.

(71) The non-destructive soliton probing scheme combined with the backward tuning allows an understanding of the soliton switching dynamics in microresonators. The modulation response clearly predicts the switching and therefore provides a convenient tool to control the soliton states and induce switching on demand. In devices, one can perform deterministic switching by tuning the pump frequency, while monitoring the effective laser frequency detuning revealed by the VNA response.

(72) The successive soliton switching in backward tuning is attributed to the thermal nonlinearity of optical microresonators. Due to material absorption, the intracavity energy of a soliton state thermally shifts the cavity resonance via thermal expansion and thermal change of the refractive index: .sub.0=.sub.0.sub.T, where .sub.T is the thermally induced resonance shift which is approximately (neglecting cross term) proportional to the energy of intracavity field:
.sub.T(N)E.sub.C+N.Math.E.sub.S(1)
where E.sub.C is the energy of the component, E.sub.S is the energy of one soliton and N the number of solitons. Thus, the effective detuning can be expressed as 2.sub.eff=.sub.0.sub.T.sub.p.

(73) Physically, the soliton switching occurs when the laser backward tuning reduces the detuning to the bifurcation point of the system. This boundary value can be identified from the VNA trace and is represented by the position of the S-resonance. After the switching, one soliton is extinct which decreases the energy in the cavity, and thereby reduces the thermal shift .sub.T. This spontaneously stabilizes the system in a new soliton state, by effectively increasing the effective detuning. The process is reflected in the evolution of the modulation response (see FIG. 19) as a separation of - and S-resonance after the switching. It should be also noted that the recoiled -resonance frequency is similar after each switching event, because the resonator loses approximately similar amount of energy. Overall, the thermal nonlinearity lifts the degeneracy of soliton states with respect to the pump frequency.

(74) The pump backward tuning enables deterministic and successive soliton switching, opening access to soliton states N, N1, . . . , 1. It is therefore possible to experimentally explore the soliton existence range in terms of the absolute and the effective detuning in each state, which to the inventors best knowledge has never been directly experimentally measured for cavity solitons of any kind. In terms of effective detuning, we express the soliton existence range as .sub.s<.sub.eff<.sub.max. The lower boundary .sub.s is identified in the backward soliton switching: it corresponds to the frequency where the -resonance and the fixed S-resonance overlap. In the studied Si.sub.3N.sub.4 microresonator under chosen pumping conditions this quantity is measured as .sub.s0.78 GHz. The upper detuning boundary .sub.max of the soliton existence range can be explored for each soliton state when the pump laser is tuned forward until the soliton comb disappears. Based on the theory and standard LLE simulations, this detuning is expected to be identical for all states corresponding to different number of solitons (see FIG. 24), as the boundary of the energy balance of dissipative Kerr solitons. In experiments under the same pumping conditions such maximum effective detuning .sub.max is found for all soliton states as 2.0 GHz, yet no clear feature in the modulation response enables to predict this maximum boundary.

(75) FIG. 21 displays a one-trace mapping of six steps of soliton states in Si.sub.3N.sub.4 microresonator as a function of the absolute pump frequency (wavelength) (i.e. the absolute detuning ). For each soliton step, we first tune the pump forward approaching the maximum detuning (.fwdarw..sub.max), and then tune backward towards the soliton switching point (.fwdarw..sub.s) where the soliton state is switched from N to N1. Since the thermally induced cavity resonance shift is included in the absolute frequency detuning, we observe that the soliton existence range in the absolute detuning is increasingly offset for a larger number of soliton. This creates the staircase pattern of the generated light and enables successive soliton switching. However, if the generated light trace is plotted with respect to the effective laser detuning (.sub.eff) as done in FIG. 22, it appears that all the soliton steps are stacked vertically within the range .sub.s<.sub.eff<.sub.max, which corresponds to the expected theoretical diagram when the thermal effect is neglected.

(76) We performed numerical simulations based on both LLE and coupled mode equations with the additional thermal relaxation equation included which verify that the deterministic soliton switching is enabled by the thermal nonlinearity of the microresonator (FIGS. 23 and 24). By including the thermal effects into numerical simulations, we are able to reproduce the staircase power trace, corresponding to the successive reduction of the soliton number in the backward pump tuning (cf. red curve in FIG. 23). Analytical power traces of soliton steps (black dashed lines) indicate soliton existence ranges for multiple-soliton states with different N. They reveal a displacement of the soliton existence range between different soliton states (qualitatively similar to the measured in FIG. 21) as a consequence of the thermal nonlinearity.

(77) When the thermal effects in simulations are switched off, soliton steps are well aligned and the soliton existence range is again degenerate with respect to the soliton number (N), see FIG. 24. No soliton switching is therefore observed in the backward tuning. Numerical simulation also revealed the soliton breather states that is considered as an intermediate state between the chaotic MI operation regime and the stable soliton state. In the breather state, the soliton pulse peak power and the pulse duration, as well as the average intacavity energy, will experience periodical oscillations. This induces thermal perturbations to the cavity resonance and initiates the soliton switching.

(78) The inventors experimentally, numerically and analytically demonstrate the discovery that soliton states in a microresonator are not detuning degenerate, and can be individually addressed by laser detuning. This effect is platform independent and can be used in a laser backward tuning process to achieve a successive reduction of the soliton number (N.fwdarw.N1.fwdarw. . . . .fwdarw.1).

(79) This deterministic switching is enabled by the thermal nonlinearity of the microresonator and provides a route to obtain a single soliton state from an arbitrary multiple soliton state.

(80) A non-destructive soliton probing technique enables to track the thermal impact of external perturbations of the system on its stability. The technique also allows to lock the soliton state against the impact of these perturbations and gives clear insights of soliton dynamics inside the cavity.

(81) Combining this technique with the laser backward tuning allows for deterministic soliton switching and makes accessible any target multiple-soliton state in a predictable way. The results are in good agreement with analytical treatment of the soliton comb including thermal effects as well as numerical simulations, and can be applied to all Kerr nonlinear microresonators.

(82) While the invention has been disclosed with reference to certain preferred embodiments, numerous modifications, alterations, and changes to the described embodiments, and equivalents thereof, are possible without departing from the sphere and scope of the invention. Accordingly, it is intended that the invention not be limited to the described embodiments, and be given the broadest reasonable interpretation in accordance with the language of the appended claims.

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