Generating optical pulses via a soliton state of an optical microresonator coupled with a chip based semiconductor laser

Abstract

A light pulse source and method for generating repetitive optical pulses are described. The light pulse source includes a continuous wave cw laser device, an optical waveguide optically coupled with the laser device, an optical microresonator, and a tuning device. The optical microresonator coupling cw laser light via the waveguide into the microresonator, which, may include, a light field in a soliton state with soliton shaped pulses coupled out of the microresonator for providing the repetitive optical pulses. The laser device includes a chip based semiconductor laser, the microresonator and/or the waveguide may reflect an optical feedback portion of light back to the semiconductor laser, which may provide self-injection locking relative to a resonance frequency of the microresonator. The tuning device is arranged for tuning at least one of a driving current and a temperature of the semiconductor laser such that the microresonator may provide the soliton state.

Claims

1. A light pulse source, being adapted for generating repetitive optical pulses, comprising: a continuous wave laser device being arranged for providing continuous wave laser light, an optical waveguide being optically coupled with the continuous wave laser device, an optical microresonator being made of a resonator material, which has a third order (Kerr) nonlinearity and an anomalous resonator dispersion, wherein the continuous wave laser device and the optical microresonator are arranged on a common chip substrate device for coupling the continuous wave laser light via the optical waveguide into the optical microresonator, which is configured to include, at a predetermined output frequency of the continuous wave laser device, a light field in a soliton state, so that soliton shaped pulses are coupled out of the optical microresonator for providing the repetitive optical pulses, and a tuning device being arranged for adjusting the output frequency of the continuous wave laser device, wherein the continuous wave laser device comprises a chip based semiconductor laser, at least one of the optical microresonator and the optical waveguide is adapted for back-reflecting an optical feedback portion of light to the semiconductor laser, which is configured for getting self injection locking relative to a resonance frequency of the optical microresonator by the effect of the optical feedback portion, and the tuning device is arranged for tuning at least one of a driving current and a temperature of the semiconductor laser such that the optical microresonator is configured for providing the soliton state.

2. The light pulse source according to claim 1, wherein the semiconductor laser has a linewidth in a range from 10 cm.sup.−1 to 500 cm.sup.−1.

3. The light pulse source according to claim 1, wherein the semiconductor laser comprises a single-mode laser diode.

4. The light pulse source according to claim 1, wherein the semiconductor laser comprises a multi-frequency laser diode.

5. The light pulse source according to claim 1, wherein the common chip substrate device comprises an integral chip substrate carrying both of the semiconductor laser and the optical microresonator.

6. The light pulse source according to claim 1, wherein the common chip substrate device comprises a hybrid chip substrate with a first chip carrying the semiconductor laser and a second chip carrying the optical microresonator, wherein the first and second chips are bonded to each other.

7. The light pulse source according to claim 1, wherein the tuning device is arranged for setting a first operation condition of the semiconductor laser, wherein self injection locking between the semiconductor laser and the optical microresonator is provided, and a second operation condition of the semiconductor laser, wherein the soliton state of the light field in the optical microresonator is provided.

8. The light pulse source according to claim 7, further comprising a sensor device being arranged for detecting the first and second operation conditions of the semiconductor laser.

9. The light pulse source according to claim 8, wherein the sensor device is arranged for monitoring an output power of the optical microresonator.

10. The light pulse source according to claim 1, wherein the optical waveguide does not include a frequency filter section.

11. The light pulse source according to claim 1, wherein the tuning device is arranged for controlling the temperature of the semiconductor laser, wherein the tuning device includes a heating element being arranged for setting a temperature of a continuous wave laser device carrying a section of the chip substrate device.

12. The light pulse source according to claim 1, wherein at least one of the optical microresonator and the optical waveguide at an output side of the optical microresonator includes a reflective structure being configured for reflecting the optical feedback portion of light back to the semiconductor laser.

13. The light pulse source according to claim 12, wherein the reflective structure comprises at least one of a grating or an indentation structure created at the at least one of the optical microresonator and the optical waveguide.

14. A light pulse generation method, which includes generating repetitive optical pulses, comprising the steps of: creating continuous wave laser light with a continuous wave laser device, optically coupling the continuous wave laser light via an optical waveguide into an optical microresonator being made of a resonator material, which has a third order (Kerr) nonlinearity and an anomalous resonator dispersion, wherein the continuous wave laser device and the optical microresonator are arranged on a common chip substrate, adjusting the output frequency of the continuous wave laser device such that, at a predetermined output frequency of the continuous wave laser device, the optical microresonator creates a light field in a soliton state, and coupling soliton shaped pulses out of the optical microresonator for providing the repetitive optical pulses, wherein the continuous wave laser device comprises a chip based semiconductor laser, an optical feedback portion of light is back-reflected from at least one of the optical microresonator and the optical waveguide to the semiconductor laser, the semiconductor laser gets self injection locking relative to a resonance frequency of the optical microresonator by the effect of the optical feedback portion, and the adjusting step includes tuning at least one of a driving current and a temperature of the semiconductor laser such that the optical microresonator creates the light field in the soliton state.

15. The light pulse generation method according to claim 14, wherein the continuous wave laser light is created with a linewidth in a range from 10 cm.sup.−1 to 500 cm.sup.−1.

16. The light pulse generation method according to claim 14, wherein the continuous wave laser light comprises single-mode laser light.

17. The light pulse generation method according to claim 16, wherein the continuous wave laser light comprises single-mode laser light with a linewidth in a range from 100 kHz to 5 MHz.

18. The light pulse generation method according to claim 14, wherein the continuous wave laser light comprises multi-frequency laser light.

19. The light pulse generation method according to claim 14, wherein the adjusting step includes setting a first operation condition of the semiconductor laser, wherein self injection locking between the semiconductor laser and the optical microresonator is provided, and a second operation condition of the semiconductor laser, wherein the soliton state of the light field in the optical microresonator is provided.

20. The light pulse generation method according to claim 19, further comprising a step of detecting the first and second operation conditions of the semiconductor laser.

21. The light pulse generation method according to claim 20, wherein the detecting step includes monitoring an output power of the optical microresonator.

22. The light pulse generation method according to claim 14, wherein the step of optically coupling the continuous wave laser light via the optical waveguide into the optical microresonator does not include frequency filtering in a section of the optical waveguide.

23. The light pulse generation method according to claim 14, wherein the adjusting step includes controlling the temperature of the semiconductor laser by setting a temperature of a continuous wave laser device carrying section of the chip substrate device with a heating element.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Further details and advantages of the invention are described in the following with reference to the attached drawings, which schematically show in:

(2) FIG. 1: features of preferred embodiments of a light pulse source according to the invention;

(3) FIG. 2: variants of coupling a semiconductor laser via an optical waveguide or photonic wire bonding with an optical microresonator;

(4) FIG. 3: vertically coupling a semiconductor laser output to an optical waveguide;

(5) FIG. 4: an illustration of manufacturing a hybrid chip substrate embodiment of the invention;

(6) FIG. 5: further optional features of a light pulse source according to the invention; and

(7) FIGS. 6 to 8: results of experimental tests and numerical simulations of the inventive creation of repetitive optical pulses.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

(8) Preferred embodiments of the invention are described in the following with particular reference to the structure of the inventive light pulse source and in particular the features of coupling a chip based semiconductor laser with the optical microresonator and operating a tuning device, which is used for achieving the soliton state of the optical microresonator. Exemplary reference is made to the use of one circular microresonator made of a Si.sub.3N.sub.4. It is emphasized that the invention is not restricted to this particular type of an optical microresonator, but rather possible with other resonators being made of e.g. CaF.sub.2, BaF.sub.2, SiN, AlN, SiO.sub.2 or Si and/or having a linear resonator configuration, e. g. comprising a linear waveguide with corrugation at both ends, to form a Fabry Perot resonator. Furthermore, multiple light pulse sources of the invention can be combined, depending on the application of the invention, e. g. for simultaneous generation of multiple frequency combs with different spectral characteristics. Details of manufacturing the optical microresonator and waveguides as well as operating e.g. a cw laser or a monitoring device are not described as far as they are known per se from conventional techniques.

(9) Light Pulse Source

(10) According to the schematic, enlarged illustration of FIG. 1, the light pulse source 100 comprises a cw laser device 10, an optical waveguide 20 being optically coupled with the cw laser device 10, and an optical microresonator 30 on a common chip substrate device 40. Furthermore, the light pulse source 100 comprises a tuning device 50 for adjusting the output frequency of the cw laser device 10 and optionally a sensor device 60 for monitoring an output of the light pulse source 100. The sensor device 60 comprises at least one photodiode 61. Due to the compact structure of combining the cw laser device 10 and the optical microresonator 30 on the common chip substrate device 40, the light pulse source 100 has a volume of less than about 1 ccm only.

(11) The cw laser device 10 comprises a chip based semiconductor laser 11, in particular a multi-frequency Fabry-Perot-resonator based laser diode, like e. g. an Indium Phosphide (III-V) multiple longitudinal mode laser diode chip, creating cw laser light 2. The laser diode is e. g. an InGaAsP/InP multiple quantum well laser diode (manufacturer: SemiNex and Q-photonics). The semiconductor laser 11 has a laser carrier chip 41, which is a first section of the chip substrate device 40. The laser carrier chip 41 provides a carrier substrate and a heat sink. For tuning an output frequency of the semiconductor laser 11, the laser carrier chip 41 optionally includes a heating element 53, like a resistive heater, thermally coupled with the semiconductor laser 11 and electrically coupled with the tuning device 50.

(12) The optical waveguide 20 is a linear waveguide with a first end 21 being optically coupled with the output of the semiconductor laser 11, e. g. by a direct contact of waveguide and laser facets. The optical waveguide 20 is made of e. g. Si.sub.3N.sub.4, AlN, or SiO.sub.2, and it is arranged on a resonator carrier chip 42, which is a second section of the chip substrate device 40. The resonator carrier chip 42 is made of e. g. Si.sub.3N.sub.4. The optical waveguide 20 serves as both of an input waveguide (first waveguide section 22) carrying light fields of the cw laser light 2 to the optical microresonator 30 and an output waveguide (second waveguide section 23) carrying soliton shaped optical pulses 1 coupled out of the optical microresonator 30. The second waveguide section 22 can be coupled at a second end 24 of the optical waveguide 20 with another coupling waveguide 25 and/or the sensor device 60.

(13) The optical microresonator 30 is made of a resonator material, which has a third order (Kerr) nonlinearity and an anomalous resonator dispersion, e. g. Si.sub.3N.sub.4. The optical microresonator 30 has a high resonator quality Q.sub.0 with Q.sub.0>1×10.sup.7. With an example, the optical microresonator 30 is a photonic chip-scale Si.sub.3N.sub.4 microresonator as described in [7]. The optical microresonator 30 is arranged on the resonator carrier chip 42, such that optical coupling with the optical waveguide 20 via evanescent light fields through a lateral waveguide surface is obtained.

(14) The laser carrier chip 41 is made of InP, and it is directly butt-coupled to a resonator carrier chip 42 carrying the optical microresonator 30. The butt-coupling scheme (see also FIG. 4) gives an overall insertion loss of about 6 dB (diode-chip-lensed fiber), with a double inverse tapered structure for the light input/output coupling [38]. When the frequency of the light emitted from the semiconductor laser 11 coincides with a high-Q resonance of the optical microresonator 30, laser self-injection locking takes place as described below. This process (see also [29]) occurs due to reflecting an optical feedback portion 3 of light back to the semiconductor laser 11 (see dotted line in FIG. 1), which is obtained e. g. bulk and surface Rayleigh scattering in the optical microresonator 30 or reflective structures 31 within the optical microresonator 30 (see FIGS. 1, 2 and 4) or in the second waveguide section 23. The optical feedback portion 3 of light is injected back into the semiconductor laser 11, thus providing a frequency selective optical feedback to the semiconductor laser 11, leading to single-frequency operation and a significant reduction of the laser linewidth. The reflective structures 31 may comprise at least one grating and/or corrugation structure being adapted for a back reflection into specific mode of the semiconductor laser 11.

(15) The tuning device 50 includes a driving current control 51 of the semiconductor laser 11 and/or a temperature control 52 connected with the heating element 53. The control units are configured for implementing the adjusting procedure such that the optical microresonator 30 is capable of providing the soliton state as described below. To this end, they can be connected with the sensor device 60.

(16) The semiconductor laser 11 and the optical microresonator 30 are arranged on the common chip substrate device 40 for coupling the cw laser light 2 via the optical waveguide 20 into the optical microresonator 30. The substrate device 40 may comprises the laser carrier chip 41 and the resonator carrier chip 42 (hybrid embodiment, e. g. FIG. 1) or a common single carrier chip 43 (e. g. FIG. 2).

(17) FIG. 2 additionally shows variants of coupling the semiconductor laser 11 with the optical waveguide 20, including a heterogeneous integration (FIG. 2A) or a hybrid integration using photonic wire bonding coupling (FIG. 2B). With the heterogeneous integration, an output fibre 12 of the semiconductor laser 11 is optically coupled with the optical waveguide 20. For photonic wire bonding coupling, an optical fibre is arranged between the output facet 13 of the semiconductor laser 11 and the first end 21 of the optical waveguide 20. In both cases, the optical fibre can be a wave guiding section that is made of dielectric material e.g. SiN or SiO.sub.2.

(18) Another variant of coupling the semiconductor laser 11 with the optical waveguide 20 is shown with the cross-sectional view of a single chip substrate device 40 in FIG. 3. With this embodiment, a vertical coupling, i. e. coupling with a coupling direction deviating from the longitudinal resonator extension of the semiconductor laser 11, is provided. The semiconductor laser 11, e. g. the InP based laser diode, and the optical waveguide 20, made of e. g. Si.sub.3N.sub.4, are embedded in the common chip substrate device 40, made of e. g. a SiO.sub.2 bulk 44 on a Si substrate 45. A lateral surface of the optical waveguide 20 is optically coupled with the semiconductor laser 11.

(19) For the hybrid embodiment, butt coupling can be obtained by gluing together the laser carrier chip 41 and the resonator carrier chip 42, as shown in FIG. 4. In practical manufacturing, drops 46 of an optically transparent glue, like an optical epoxy resin, are provided and the laser carrier chip 41 is pressed against the resonator carrier chip 43 (see arrow).

(20) By using e. g. the high-Q photonic chip-scale Si.sub.3N.sub.4 microresonator 30, preferably manufactured using the photonic Damascene reflow process [26, 27] (see further details below), in conjunction with the multiple-longitudinal-mode (multi-frequency) Fabry-Perot InP laser diode chip, self-injection locking [28, 29] is observed in a regime where solitons are formed concurrently. Such self-injection locking with concurrent soliton formation has been demonstrated for bulk ultrahigh-Q crystalline MgF.sub.2 resonators [13, 30]. The inventors observed that the current tuning of the laser diode induces transitions from the injection-locking-based single-longitudinal-mode lasing (×1000 fold reduction of linewidth), to Kerr frequency combs, breather soliton formation, followed by stable multiple and single DKS formation in the integrated microresonator. Heterodyne measurements (described below) demonstrate the low-noise nature of the generated soliton states. Such electrically-driven photonic chip-based soliton microcomb created according to the invention, provide a solution for integrated, unprecedentedly compact optical comb sources suitable for high volume applications.

(21) Manufacturing the Light Pulse Source

(22) The photonic integrated Si.sub.3N.sub.4 chip, including the optical microresonator 30 on the resonator carrier chip 42, is fabricated by using the photonic Damascene reflow process. Preferably, a plurality of chips are manufactured simultaneously. Waveguide and resonator patterns are defined by deep-UV stepper lithography and transferred to a SiO.sub.2 preform via dry etching. A preform reflow step is used to reduce the waveguide sidewall roughness caused by dry etching [26, 36, 37], allowing for smooth waveguides and leading to high-Q factors for the microresonator. Chemical mechanical polishing (CMP) allows precise control of the waveguide height to 750±20 nm, measured over the full 4-inch (about 10 cm) wafer scale. No top cladding is deposited onto the Si.sub.3N.sub.4 waveguide. The precise dimension control by both the lithography (mainly in the waveguide width) and CMP (in the height) enables samples of the same design to have the identical geometry at different positions on the wafer.

(23) The optical microresonator 30 is coupled to the optical waveguide 20 on the resonator carrier chip 42 through evanescent light fields. CW light 2 is coupled onto the Si.sub.3N.sub.4 chip via double inverse nanotapers [38] on the optical waveguides at both of the input and output facets, i.e. from the semiconductor laser 11 (laser diode chip) to the optical microresonator 30 (microresonator chip) and from the optical microresonator 30 to a lensed fiber which collects soliton shaped pulses 1 (the comb spectrum), as schematically shown in FIG. 2A. In addition, the optical waveguide's geometry is designed to achieve a high coupling ideality with reduced parasitic losses [39].

(24) Microresonator Dispersion

(25) The microresonator dispersion can be extracted by measuring the transmission spectrum, which is calibrated by a standard optical frequency comb [40, 41]. The dispersion of the optical microresonator 30 is represented in terms of resonant frequency deviation with respect to a linear grid, namely:

(26) $D_{\mathrm{int}}={\omega }_{\mu }-\left({\omega }_0+\mu D_1\right)=\underset{m\ge 2}{.Math.}\frac{{\mu }^m{D}_m}{m!}$
where ω.sub.μ are the physical resonant frequencies of the microresonator. A central resonance (to which the laser is injection locked) is given the index μ=0. D.sub.1=2π×FSR is the repetition frequency. The second order element D.sub.2 is the group velocity dispersion (GVD) of the microresonator and D.sub.2>0 represents the anomalous GVD.

(27) Each resonance can be fitted using the model based on coupled mode theory [42, 43] from the transmission spectrum. The resonance linewidth reflects the total loss rate (κ) of the microresonator, which consists of both the intrinsic loss rate (κ.sub.0) and the external coupling rate κ.sub.ex, i.e. κ=κ.sub.0+κ.sub.ex. To extract the intrinsic Q-factor (Q.sub.0), highly under-coupled microresonators are measured, i.e. κ.sub.ex.fwdarw.0.

(28) In practical implementations, three sets of optical microresonators 30 have been tested which differ in terms of FSRs: ˜1 THz, ˜150 GHz, and <100 GHz. The tests are described below with reference to FIGS. 6 to 8. The microresonator corresponding to results shown in FIG. 6 has: Q.sub.0≈6×10.sup.6, FSR=1.02 THz, D.sub.2/2π≈188 MHz, for fundamental TE mode. The microresonator width is 1.53 μm. The microresonator corresponding to results shown in FIG. 7 has: Q.sub.0≈6.5×10.sup.6, FSR=149 GHz, D.sub.2/2π≈3.90 MHz (fundamental TE mode), the microresonator width is 1.58 μm. The microresonators corresponding to results shown in FIG. 8 have: Q.sub.0≈8.2×10.sup.6, (for FIG. 4(d)) FSR=88.6 GHz, D.sub.2/2π≈1.10 MHz (fundamental TE mode), the microresonator width is 1.58 μm; (for FIG. 8E) FSR=92.4 GHz, D.sub.2/2π≈1.56 MHz (fundamental TE mode), the microresonator width is 1.58 μm.

(29) Such high Q-factors have already enabled direct soliton comb generation in microresonators without amplification of the seed laser [27]. The threshold power for parametric oscillation can be as low as sub-milli-Watt (critical coupled), which is calculated as:

(30) $P_{\mathrm{th}}=\frac{{\kappa }^2{n}^2{V}_{\mathrm{eff}}}{4\omega {\mathrm{cn}}_2}$

(31) where n is the refractive index, V.sub.eff indicates the effective modal volume, ω is the angular frequency of light, c the speed of light in vacuum, and n.sub.2 is the nonlinear refractive index. For Si.sub.3N.sub.4 microresonators with FSR ˜1 THz (n≈1.9, V.sub.eff≈1.5×10.sup.−16 μm.sup.3, and n.sub.2≈2.4×10.sup.−19 m.sup.2/W). Hence, the threshold power is as low as P.sub.th≈0.62 mW.

(32) As an example, multiple DKS in the microresonator with FSR ˜92.4 GHz are generated when applying a current of about 280 mA to the diode chip, corresponding to an optical output power of about 50 mW. The output power is measured as about 11 mW, collected by using a lensed fiber at the output chip facet 24, indicating a coupling efficiency of about 22% (overall insertion loss −6.6 dB). The optical power in the optical waveguide 20 is estimated to be about 23.5 mW, which has been demonstrated sufficient to excite DKS in high-Q Si.sub.3N.sub.4microresonators [27].

(33) Light Pulse Generation Method and Practical Characterization of the Light Pulse Source

(34) Features of the light pulse generation method and results of experimental tests, obtained with an embodiment of the light pulse source 100 as shown in FIG. 5 are described in the following with reference to FIGS. 6 to 8.

(35) The light pulse source 100 of FIG. 5 comprises the cw laser device 10, the optical waveguide 20 and the optical microresonator 30 on the common chip substrate device 40, the tuning device 50 and the sensor device 60 with a first photodiode 61 as shown in FIG. 1. Furthermore, in particular for the tests of the source or for monitoring a source in operation, a monitoring device 70 is provided, including optical spectral analyzer 71, an oscilloscope 72 and/or an electrical-signal spectral analyzer 73. The optical spectral analyzer 71 is provided for characterizing the output pulses 1 in the optical domain, while the electrical-signal spectral analyzer 73 is provided for characterizing a beating signal by a heterodyne measurement of the output pulses 1 and the output of a reference laser 80, e. g. Toptica CTL1550, short-time linewidth of about 10 kHz, in the radio frequency (RF) domain. With the electrical-signal spectral analyzer 73, the coherence of the output pulses 2 can be monitored by employing a heterodyne beatnote measurement to a selected comb tooth with the narrow-linewidth reference laser 80. Furthermore, the tuning device 50 is connected with an arbitrary function generator 54 for setting adjustment procedures.

(36) The heterodyne measurement is used to assess the coherence of the generated soliton shaped pulses 1, as its line shape reveals the frequency noise spectral density with respect to the reference laser 80. In fact, the frequency noise may consist of both the white noise (resulting in a Lorentzian line shape) and the flicker noise (corresponding to a Gaussian line shape). Therefore, the Voigt profile [44] can be employed to fit the beat signal, which represents the convolution of the Lorentzian (L(f)) and the Gaussian (G(f)) line shapes, i.e.:

(37) $G\left(f;\sigma \right)=\frac{{\exp }^{-f^2/2{\sigma }^2}}{\sigma \sqrt{2\pi }},L\left(f;\psi \right)=\frac{\gamma }{\pi \left(f^2+{\psi }^2\right)}$$V\left(f\right)={\int }_{-\infty }^{+\infty }G\left(f^{\prime };\sigma \right)L\left(f-f^{\prime };,\psi \right){\mathrm{df}}^{\prime }$
where f indicates the frequency shift with respect to the center of the beat signal, in the radio frequency domain, and σ and ψ scale the linewidth. To initiate the fitting it is assumed that, on the wings of the beat profile, the signal is mostly contributed by the white noise that determines the intantaneous linewidth described by ψ. In contrast, around the center of the beat profile, the signal is also contributed by flicker noise depending on e.g. the acquisition time of the ESA, as well as the stability of current or temperature controller. This part of noise is scaled by σ. The full width at half maximum (FWHM) of the Gaussian line shape is then Δf.sub.G=2σ and Δf.sub.L=2ψ for the Lorentzian.

(38) FIG. 6 illustrates the generation of an electrically pumped soliton microcomb via laser-injection-locked soliton formation. FIG. 6A shows a transmission spectrum of a Si.sub.3N.sub.4 microresonator 30 of 1.02 THz FSR (featuring two sets of resonances: the fundamental transverse electric (TE) mode family (marked by circles) and one high-order TE mode family). FIG. 6B shows the laser spectrum of the multi-frequency semiconductor laser 11, in particular laser diode, (corresponding to state i in FIG. 6F). FIG. 6C shows measured and fitted heterodyne beat signal between the free running semiconductor laser 11 and the narrow-linewidth reference laser 80 (showing 60 MHz linewidth). FIG. 6D shows in the top panel (state ii in FIG. 6F) spectra of single-longitudinal-mode that is injection-locked to a selected resonance of the microresonator, and in the bottom panel (state iii in FIG. 6F) the spectrum of the Kerr frequency comb that stems from the laser injection locking. The inset of FIG. 6D shows one resonance of the fundamental TE mode showing mode splitting due to backscattering, with the estimated 118 MHz coupling strength between the forward and backward propagating modes. FIG. 6E shows a heterodyne beat signal between the injection-locked semiconductor laser 11 and the reference laser 80. The measured beat signal is fitted with Voigt profile with full width at half maximum (FWHM) ˜186 kHz (cf. details below).

(39) FIG. 6F shows a typical transmitted power trace measured at the chip output facet 24, by current modulation imposed on the semiconductor laser 11, in which different states are marked: (i) Noisy, multi-frequency lasing without injection locking; (ii) Laser injection locking to a microresonator resonance, and simultaneous formation of low-noise single-longitudinal-mode lasing; (iii) formation of Kerr frequency comb. State (i) is a first phase of setting a first operation condition of the semiconductor laser, wherein the self injection locking between the semiconductor laser and the optical microresonator is obtained, while state (ii) is a second phase of setting a second operation condition of the semiconductor laser, wherein the soliton state of the light field in the optical microresonator is created.

(40) An advantageous feature of the invention is to match the optical power requirement for soliton generation in the optical microresonator 30 to that of the semiconductor laser 11. This is achieved by employing the high-Q Si.sub.3N.sub.4 microresonator with high-Q factors (Q.sub.0>1×10.sup.7) across the entire L band (see above). The Fabry-Perot laser diode of the semiconductor laser 11 is centered at 1530 nm, and its emission spectrum without self-injection locking is shown in FIG. 6B. The mode spacing is 35 GHz, determined by the Fabry-Perot cavity length. The overall maximum optical output power is about 100 mW when applying a current of about 350 mA to the laser diode. The electrical power consumed by the laser diode is less than 1 W. FIG. 6C shows the heterodyne beatnote of the free running laser diode mode with the reference laser 70, revealing both a Gaussian linewidth of 60 MHz and an estimated short-time linewidth of 2 MHz.

(41) The inventors first studied self-injection locking of the semiconductor laser 11 to the photonic chip-based microresonator 30. This is achieved by tuning the current of the semiconductor laser 11, which not only changes the optical output power, but also shifts the lasing frequency via the carrier dispersion effect. Initially, the semiconductor laser 11 operates multi-frequency [FIG. 6B, a regime where none of the high-Q microresonator modes is frequency-matched with the multimode laser emission of the diode. By shifting the lasing frequency of the diode via current tuning, it is observed that the initially multi-frequency emission spectrum switches to single mode operation, indicative of self-injection locking. FIG. 6D demonstrates that the lasing frequency coincides with a selected resonance of the microresonator 30, and it is also observed that injection locking occurs for several resonances. All resonances, which give rise to the laser self-injection locking, feature mode splitting as a result of backscattering (cf. the inset in FIG. 6D). The backcoupling rate for the measured resonance, extracted from its mode-splitting profile, is γ/2π=118 MHz (see above). The presence of this back-coupling leads to an amplitude reflection coefficient (r) from the passive microresonator 30 on resonance:

(42) $r=\frac{2\mathrm{\eta \Gamma }}{1+{\Gamma }^2}$
where η=κ.sub.ex/κ characterizes coupling efficiency (κ=κ.sub.0+κ.sub.ex, with η=½ corresponding to critical coupling, and η≈1 corresponding to strong overcoupling), and Γ=γ/κ is the normalized mode coupling parameter that describes the visibility of the resonance split. According to [32], this reflection can initiate self-injection locking, and give rise to a narrow linewidth of:

(43) $\mathrm{\delta \omega }\approx {\mathrm{\delta \omega }}_{\mathrm{free}}\frac{Q_{\mathrm{LD}}^2}{Q^2}\frac{1}{16r^2\left(1+{\alpha }_{ℊ}^2\right)}$
where Q=ω/κ is the microresonator quality factor, ω/2π is the light frequency, δω.sub.free/2π is the linewidth of the free running laser. The phase-amplitude coupling factor α.sub.g is the linewidth enhancement factor, given by the ratio of the variation of the real refractive index to the imaginary refractive index of the laser diode active region in response to a carrier density fluctuation [33] and takes typical values from 1.6 to 7.

(44) The InGaAsP/InP multiple quantum well laser diode has α.sub.g=2.5. The laser diode quality factor Q.sub.LD can be estimated as

(45) $Q_{\mathrm{LD}}\approx \frac{{\mathrm{\omega \tau }}_d{R}_o}{1-R_o^2},$
where R.sub.o is the amplitude reflection coefficient of the output laser mirrors, and τ.sub.d is the laser cavity round trip. The reflection coefficient is a parameter of the laser diode and is given by the laser diode manufacturer as R.sub.0=√{square root over (0.15)} as well as α.sub.g=2.5. Other experimentally determined parameters are κ/2π≈110 MHz, γ/2π≈118 MHz, η≈0.64, Γ≈1, and τ.sub.d=1/FSR.sub.diode=1/(35 GHz)=28.6 ps. The theoretical estimation for the narrowed linewidth is δω/2π˜0.1 kHz.

(46) The inventors compared these theoretical estimates of the self-injection locked linewidth to experiments. The linewidth of the self-injection-locked single-longitudinal-mode laser is measured by the heterodyne measurement as shown in FIG. 6E. The line shape is fitted with a Voigt profile, which represents a convolution of Lorentzian and Gaussian line shape (see above, description of heterodyne detection), yielding a Gaussian contribution to the linewidth of 186 kHz. The estimated Lorentzian contribution amounts to 0.7 kHz, describing the wings of the measured beatnote. Self-injection locking leads to a narrowing of the white noise of the laser diode [32]. Therefore, this value should be compared with the Lorentzian contribution in the Voigt profile (i.e. 0.7 kHz) corresponding to a more than 1000-fold reduction in the linewidth.

(47) Injection locking occurs also in the case where the laser cavity and microresonator are detuned from each other, and as outlined below, is preferred to generate dissipative Kerr solitons using self-injection locking. The locking range is defined as the frequency range over which the laser diode emission self-injection locks to the high-Q microresonator resonance and follows the expression [32]:

(48) ${\mathrm{\Delta \omega }}_{\mathrm{lock}}\approx r\sqrt{1+{\alpha }_{ℊ}^2}\frac{\omega }{Q_{\mathrm{LD}}}$

(49) The theoretically estimated locking range exceeds Δω.sub.lock/2π≈30 GHz.

(50) To tune the self-injection-locked laser frequency into the regime where Kerr combs (and DKS) are formed, the inventors preferably use “injection pulling”, which pulls the lasing frequency away from the high-Q resonance used for the self-injection locking. Injection pulling is a result of slight phase difference between the laser emission and its feedback, leading to imperfect locking [32]. Importantly, this effect is obtainable by tuning the current or temperature of the laser diode, allowing the laser frequency to be changed concurrently with the self-injection locking, providing thereby a frequency scan over the resonance, as used for DKS formation [6].

(51) FIG. 6F shows the optical output power (transmission) trace as a function of the current tuning, where self-injection locking is deterministically observed. An initial chaotic power trace (state (i)) in FIG. 6F is switched to a step-like pattern (state (ii) in FIG. 6F, the centre marked region). The average output power reduces during the switching since the self-injection leads to single-longitudinal-mode operation, with enhanced power being coupled into the high-Q resonance of the Si.sub.3N.sub.4 microresonator 30. Most significantly, upon further tuning the current, a second step-like pattern in the power trace is observed (state (iii) in FIG. 6F, the right marked region), corresponding to the formation of a (low noise) Kerr frequency comb. Indeed, at high optical power levels (typically setting the current to be ˜300 mA), Kerr comb generation was observed upon tuning the current, as shown in FIG. 6D. This phenomenon is supported by the high Q-factor of the microresonator 30, allowing sub-mW threshold power for parametric oscillations (see above).

(52) The inventors have shown that self-injection locking can also be observed in devices with an electronically detectable mode spacing (149 GHz, and <100 GHz), and critically if it can also enable operation in a regime where DKS are formed concurrently. FIG. 7 shows the evolution of Kerr frequency comb in the regime of laser self-injection locking, from noisy state in the operation regime of modulation instability (FIG. 7A), via a so called breathing state (FIG. 7B), eventually to a low-noise state (FIG. 7C) showing the formation of a DKS in the microresonator, where the spectrum is a hyperbolic secant envelope (solid line showing the fitting of the spectral envelope). Each inset shows the low-frequency radio frequency (RF) spectrum corresponding to each state. The current imposed to the diode is initially set ˜300 mA and the increase to evoke the transitions is within 1 mA. The Si.sub.3N.sub.4microresonator in this measurement has an FSR of 149 GHz.

(53) With further details, FIG. 7A shows the self-injection locked Kerr comb generation in the optical microresonator 30 with an FSR of 149 GHz. Significantly, not only were Kerr combs observed but also switching into the DKS regime [6]. Upon self-injection locking, and via current tuning, a Kerr comb is firstly excited in a low-coherence state, as evidenced by the noise in the low-frequency RF spectrum (inset in FIG. 7A). For such low repetition rates the amplitude noise is still a valid indicator of the frequency comb's coherence, in contrast to terahertz mode spacing resonators where the noise can be located at high RF frequencies (>1 GHz) [34]. Importantly, upon increasing the current to the diode further, which leads to a laser detuning increase by injection pulling, the low-coherence comb state is turned into an intermediate oscillatory state. That can be identified as a breather DKS (FIG. 7B) [35], where the soliton exhibits periodic oscillations. The RF spectrum shows the breathing frequency at ˜490 MHz exhibiting harmonics, see inset in FIG. 7B. Such soliton breathing dynamics, i.e. breather DKS, have been studied previously [35], and in particular the breathing frequency depends on the laser detuning. The observation of a DKS breathing state demonstrates that the injection pulling enables operation in the effectively red detuned regime, required for soliton generation.

(54) Further increasing the laser current, a transition to a low-noise comb state is observed, demonstrating the formation of stable DKS as shown in FIG. 7C. The spectral envelope of the frequency comb exhibits a secant-squared profile, corresponding to a single soliton circulating in the resonator, with the breathing oscillations absent from the RF spectrum (inset in FIG. 7C). This transition, which is induced here by current and/or temperature tuning only, has been achieved in previous work by tuning the laser over the resonance from the blue to the effectively red detuned side [6]. Most significantly, to corroborate operation in the soliton state, the coherence is verified via the heterodyne beatnote measurement [2]. The heterodyne beatnote of a soliton comb tooth with the reference laser 80 is shown in FIG. 8C. The measured heterodyne beatnote linewidth is comparable to that of the injection-locked laser FIG. 6D, i.e. the Gaussian linewidth is 201 kHz and the estimated short-time Lorentzian linewidth (that describes the wings of the beatnote only) is 1 kHz. These values indicate no degradation of the coherence during the process of soliton comb generation via laser self-injection locking.

(55) Moreover, formation of soliton shaped pulses via laser self-injection locking was also observed in Si.sub.3N.sub.4 microresonators with FSRs below 100 GHz, an electronically detectable repetition rate, where due to the high Q-factors (Q.sub.0˜8×10.sup.6) enabled by the photonic Damascene reflow process, soliton combs could still be generated [27]. This is described in the following with reference to FIG. 8. FIG. 8A shows measured and fitted dispersion curves in a Si.sub.3N.sub.4microresonator (cross-section 1.58×0.75 μm.sup.2), which has the FSR=92.4 GHz, and the second order dispersion element indicating the anomalous group velocity, D.sub.2/2π≈1.56 MHz. FIG. 8B shows a histogram of resonance linewidths that are about 110 MHz, corresponding to a loaded Q-factor of about 1.8×10.sup.6. FIG. 8C shows a heterodyne beat signal between the sideband of soliton Kerr frequency comb and the reference laser 80. The measured beat signal is fitted with the Voigt profile. FIGS. 8D and 8E illustrate multiple dissipative solitons formed in Si.sub.3N.sub.4microresonators, in the breathing state (FIG. 8D) as well as in the low-noise stable soliton state (FIG. 8E), the fitting of the spectrum envelope (solid lines) further shows the relative position of solitons circulating in the microring cavity (schematic insets). The low-frequency RF spectra corresponding to breather solitons are also shown as insets. Spectra in FIGS. 8D and 8E are generated in Si.sub.3N.sub.4 microresonators with a free spectral range (FSR) of 88 GHz and 92 GHz, respectively.

(56) With further details, the parabolic dispersion profile of FIG. 8A shows quadratic contribution from an anomalous group velocity dispersion (GVD) to be: D.sub.2/2π≈1.56 MHz, centered at a wavelength ˜1540 nm. The loaded resonance linewidth κ/2π is ca. 110 MHz (FIG. 8B), corresponding to an over-coupled regime of the microresonator (the intrinsic loss rate is κ.sub.0/2π<30 MHz).

(57) In these type of microresonators, multiple dissipative solitons are observed, shown in FIGS. 8D and 8E, not only in the breathing state but in the low-noise stable soliton state as well. The spectral envelope reveals a multi-soliton state as a result of interfering Fourier components of the solitons. By fitting these spectral envelopes (as outlined below), the number of solitons can be resolved and their relative positions can be estimated, illustrated as insets in FIGS. 8D and 8E. The overall transmitted optical power, consisting of both the comb power and the residual pump power, is measured ˜11 mW (see above).

(58) Dissipative Kerr soliton comb spectral fitting is provided on the basis of the following considerations. It is known that N identical solitons circulating in the resonator produce a spectral interference on the single soliton spectrum [6, 7]:

(59) $S^{\left(N\right)}\left(\mu \right)=S^{\left(1\right)}\left(\mu \right)(N+2\underset{j\ne l}{.Math.}\cos \left(\mu \left({\varphi }_j-{\varphi }_l\right)\right)$
Here φ.sub.i∈[0,2π] is the position of the i-th pulse along the cavity roundtrip, μ is the comb mode index relative to the pump laser frequency and S.sup.(1)(μ) is the spectral envelope of a single soliton following an approximate secant hyperbolic squared:

(60) $S^{\left(1\right)}\approx {A\mathrm{sech}}^2\left(\frac{\mu -{\mu }_c}{\mathrm{\Delta \mu }}\right)$
where A is the power of the comb lines near the pump and Δμ is the spectral width of the comb (in unit of comb lines) and μ.sub.c is the central mode of the soliton (to account for soliton recoil or self frequency shift). Knowing the comb repetition rate f.sub.r, the spectral width (or pulse duration) can be retrieved: Δf=f.sub.rΔμ.

(61) The spectral envelope of the single or multiple soliton states are fitted using the following procedure: First, the peaks {tilde over (S)}(μ) constituting the frequency comb are detected and labeled with their relative mode index from the pump μ, and the pump mode is rejected. The number of solitons N is estimated by taking the inverse Fourier transform of this spectrum, which yields the autocorrelation of the intracavity waveform, and detecting its peaks [7]. The set of fitting parameters {A,Δμ,μ.sub.c,φ.sub.i|i∈2,N} is defined accordingly (the position of one soliton is arbitraly set to zero) and the above expression for S.sup.(N)(μ) is fitted to the experimental points {tilde over (S)}(μ). When N solitons are perfectly equi-spaced, the repetition is multiplied by N and the single soliton expression can be fitted on every N line.

(62) The features of the invention disclosed in the above description, the drawings and the claims can be of significance both individually as well as in combination or sub-combination for the realization of the invention in its various embodiments. The invention is not restricted to the preferred embodiments described above. Rather a plurality of variants and derivatives is possible which also use the inventive concept and therefore fall within the scope of protection. In addition, the invention also claims protection for the subject and features of the subclaims independently of the features and claims to which they refer.