Patent ID: 12259635

DETAILED DESCRIPTION

The present disclosure relates generally to the field of quantum operations. More specifically, the present disclosure provides systems and methods for generating a coherent laser light.

Embodiments of the present disclosure are described in detail with reference to the drawings wherein like reference numerals identify similar or identical elements.

Although the present disclosure will be described in terms of specific examples, it will be readily apparent to those skilled in this art that various modifications, rearrangements, and substitutions may be made without departing from the spirit of the present disclosure. The scope of the present disclosure is defined by the claims appended hereto.

For purposes of promoting an understanding of the principles of the present disclosure, reference will now be made to exemplary embodiments illustrated in the drawings, and specific language will be used to describe the same. It will nevertheless be understood that no limitation of the scope of the present disclosure is thereby intended. Any alterations and further modifications of the novel features illustrated herein, and any additional applications of the principles of the present disclosure as illustrated herein, which would occur to one skilled in the relevant art and having possession of this disclosure, are to be considered within the scope of the present disclosure.

Optical parametric oscillation (OPO) is distinguished by its wavelength access, that is, the ability to flexibly generate coherent light at wavelengths that are dramatically different from the pump laser (e.g., input laser) and, in principle, bounded solely by energy conservation between the input pump field and the output signal (e.g., idler) fields. As integrated photonics advances toward many applications in quantum information science, metrology, and sensing, microchip OPO devices can provide a path for accessing relevant wavelengths using lasers. OPOs based on the third-order (χ(3)) optical non-linearity are of particular interest, as χ(3)is naturally available in silicon photonics. Apart from wavelength access, conversion efficiency and output power are critical to real-world applications, and to date, no χ(3)OPO device has been able to simultaneously realize high performance with respect to all three metrics of wavelength access, conversion efficiency, and output power. The disclosed technology demonstrates a microresonator photonics OPO device with unprecedented performance, approaching that of fiber-based and tabletop technologies. The disclosed microresonator OPO device produces output signal and idler fields widely separated in frequency from each other (>150 THz) and from the pump and exhibits a pump-to-idler conversion efficiency up to 29% with a corresponding output idler power of >18 mW on-chip. Underpinning this performance is the suppression of competitive nonlinear processes that would otherwise saturate parametric gain and the strong overcoupling of the output light while maintaining a high overall cavity quality factor. The disclosed technology may be readily applied to existing silicon photonics platforms with heterogeneously integrated pump lasers, enabling flexible coherent light generation across a broad range of wavelengths.

Referring toFIGS.1and2, a diagram of an example system10and device100for generating a coherent laser light using hybrid-mode optical parametric oscillation (hOPO), is shown. The device100is configured for on-chip coherent light generation via the third order (χ(3)) non-linearity. The device100has the benefit of enabling broad spectral coverage with small device footprints at a low pump power.

The system10may include a light source102(e.g., pump) configured to pump a first color laser light and a device100configured to generate a coherent second color light (i.e., signal) and a coherent third color light (i.e., idler). The device100generally includes a waveguide110, and a microring resonator130(e.g., a microresonator) configured to generate a coherent second color light and the coherent second color light in response to the first color laser light. The coherent second color light is a different color than the first color laser light. The coherent third color light is a different color than the first color laser light. The coherent second color light is a different color than the third color laser light. The waveguide110is configured to couple the light source102to the microring resonator130. The waveguide110may be comprised of, for example, silicon nitride and/or silicon oxynitride, or other such suitable materials.

The term hybrid-mode-family as used herein includes different mode families. The demonstrated hOPO devices have a threshold power of about 10 mW and show unprecedented robustness against geometric variation (up to 500 nm change in ring width), pump frequency tuning (about 1:1 ratio of the output signal, and idler tuning to the input pump tuning), and temperature tuning (across a temperature range of 40° C.). By operating in a regime in which the pump band is in a regime of large normal dispersion, hOPO is particularly promising for realizing high conversion efficiency from pump to signal, as most competing four-wave mixing mediated processes are suppressed. In aspects, an hOPO on-chip conversion efficiency of about eight percent, and with signal power as high as about five mW may be achieved.

The microring resonator130generally includes a layer132comprised of silicon nitride (Si3N4) and a substrate134comprised of silicon dioxide (SiO2). It is contemplated that other suitable materials may be used for the substrate134and for the layer132. For example, the layer132material may include sapphire, quartz, MgF2or any material with a similar refractive index. The layer132includes a ring width (RW) which can be configured for tuning the microring resonator130, a ring radius (RR), and a height (H). The microring resonator130may include a cladding136comprised of air. The cladding136may be disposed on a first side of the layer132. The microring resonator130includes a plurality of modes selected from different families of modes. The modes are typically either transverse-electric-like (TE) or transverse-magnetic-like (TM). For hOPO, the phase and frequency match the azimuthal modes of the microring resonator130to different transverse spatial mode families of the microring resonator130. In aspects, the microring resonator130may further include a layer of silicon (Si) disposed on a second side of the substrate134. The microring resonator130may further include a heater139configured for thermal management of the microring resonator130.

The device100uses ring widths, for example, with an aspect ratio of RW:H of about 8.7:1. The device100has its first four modes (sorted by decreasing effective modal index) as transverse electric1(TE1), transverse electric2(TE2), transverse magnetic1(TM1), and transverse electric3(TE3), as shown inFIG.8. Lower-order modes have higher effective modal indices because of better confinement to the Si3N4core. TM1appears after TE2because the microring aspect ratio of about 8.7:1 is much larger than the aspect ratios typically used in single-mode-family OPO or Kerr frequency comb generation in air-clad systems, which are usually between about 1.5:1 and about 3:1. The ring has a large normal dispersion (D) across the entire spectral range under consideration (top panel ofFIG.6). The compensation of the effective modal indices (i.e., phase-matching) is not achieved by a fine dispersion design as in the sOPO case, but rather by the difference of the effective modal indices of the two-mode families at either the idler or signal position. For example, the second panel ofFIG.6illustrates a case in which phase-matching is achieved by using higher-index (H), higher-index (H), and lower-index (L) modes for idler, pump, and signal (frequencies ordered from low to high). In terms of frequency mismatch Δv, the matching of the effective modal indices (dashed line) is equivalent to matching a dashed line that is shifted in the normal dispersion regime (where Δv<0), with the shift related to the effective modal index difference of the signal mode in this case. As a result, this hOPO scheme will likely be free of many noise processes (e.g., those labeled as II and III as described earlier), and the main potential competitive process remaining is the adjacent signal and idler modes of the same configuration (i.e., HHL), illustrated by process I shown in the bottom panel ofFIG.6.

The device100utilizes high-performance χ(3)OPO on a silicon microchip. By suppressing competing nonlinear processes that would otherwise saturate parametric gain and by strongly overcoupling the output mode while retaining high overall Q, a wide spectral separation between the participating modes (signal-idler separation of greater than about 150 THz), a high conversion efficiency (up to about 29%) is simultaneously realized, and useful output power (up to about 21 mW), a compelling combination of properties that have not previously been simultaneously achieved in on-chip OPO. The disclosed technology enables the use of OPO in silicon photonics to address many requirements for deployable laser technologies in scientific applications, particularly in light of recent progress on heterogeneous integration of III-V lasers and silicon nonlinear photonics.

In a χ(3)OPO, pump photons at vpare converted to up-shifted signal photons (vs, with vs>vp) and down-shifted idler photons (vi, with vi<vp) that satisfy energy conservation (2vp=vs+vi). Appreciable conversion efficiency requires phase-matching so that 2βp=βi+βiwhere βp,s,i,is the propagation constant for the pump, signal, and idler modes, respectively. In microring resonators, which have periodic boundary conditions, this phase relationship can be recast as 2mp=ms+miwhere mp,s,idenotes the azimuthal mode order of the pump, signal, and idler modes, respectively. Finally, OPO has a power threshold, meaning that the cavity modes must have sufficiently low loss rates (high loaded Q) that can be exceeded by the available parametric gain. While phase and frequency-matching and high-Q are baseline requirements for OPO, additional requirements are imposed if high-performance OPO is to be achieved. First, it is necessary to suppress competitive nonlinear processes that, for example, divert pump energy to the creation of frequency components other than the targeted signal and idler frequencies (FIG.4). In addition, to maximize the conversion efficiency for the output field of interest, the pump injection into the microring and output extraction from the microring is optimized.

The conversion efficiency for the signal (or idler) is dependent on the coupling regime (e.g., overcoupled/undercoupled) of both the signal (or idler) and the pump. As a starting point, a simplified three-mode model in which only the pump, signal, and idler modes are allowed to interact, from which the system's maximum conversion efficiency, ηmaxs,i≡Ns,i/Npcan be derived is considered. Here, Npis the flux of pump photons at the input of the waveguide110and Ns,iis flux of signal or idler photons at the output of the waveguide110. The maximum conversion efficiency, ηmaxs,i, will occur when the Kerr-shifted modes are perfectly phase-matched and frequency-matched and can be written in terms of the coupling parameter Kp,s,iof each resonance as:

ηs,imax=12⁢Kp⁢Ks,i(Kp+1)⁢(Ks,i+1),(Eqn.1)

where Kp,s,i=κ(p,s,i),ext/κ(p,s,i),intand κ(p,s,i),(ext,int)is the extrinsic (waveguide coupling) or intrinsic loss rate for the pump mode, signal mode, or idler mode. Eqn. 1 shows that ηmaxs,iin a χ(3)OPO increases to a maximum value of 0.5 as Kp,s,iincreases without bound. However, strongly overcoupling the resonator decreases the total Q≡v/(κext+κint) of the corresponding cavity mode(s), yielding a less efficient nonlinear enhancement. Strongly overcoupling the resonator may translate into very high threshold powers, which may be unsupportable by compact pump lasers. Therefore, efficient OPO generation via overcoupling uses a resonator with very high intrinsic Qintab out v/κintas a starting point. Si3N4microring resonators, suitable for nonlinear photonics and created by mass-production fabrication techniques, can yield intrinsic Qint>107, suggesting that strong overcoupling can be reached while maintaining high overall Q.

In practice, the saturation of OPO usually occurs before ηmaxs,iis reached, especially when imposing the additional requirement of achieving ηmaxs,iwith high output power. In OPO, the frequency mismatch Δv=—2vp+vs+vibetween the cold-cavity resonances is compensated by their Kerr shifts, which are pump-power dependent quantities, so that there is a limited range of input powers for which Δv will be small enough for high conversion efficiency to be achieved. Thermo-refractive shifts will typically also play a role, and in widely-separated OPO the wavelength-dependence of the thermo-refractive shifts also becomes meaningful. However, because dispersion is influenced by device100geometry, these effects can be addressed by choosing a geometry that targets Δv>0 compatible with the input power range of interest.

A more significant challenge comes from parasitic nonlinear processes that deplete the gain of the desired OPO process. Competitive parasitic nonlinear processes in the device100are a consequence of a device's100many azimuthal spatial modes and can be worsened by the presence of higher-order transverse spatial modes (including those of a different polarization). As a result, in widely-separated OPO, there can be hundreds of modes that exist between the pump and targeted signal (or idler) mode, which can be populated by processes such as modulational instability and subsequent Kerr comb formation. These processes are detrimental to system efficiency as they divert pump photons away from the targeted three-mode OPO process. The natural way to limit close-to-pump parasitic nonlinear processes is to situate the pump in the normal dispersion regime so that Kerr shifts lead to a larger amount of frequency mismatch for nearby signal-idler pairs. However, normal dispersion around the pump (i.e., Δv<0) must be balanced by sufficient higher-order dispersion for the widely-separated signal-idler pair of interest to be frequency matched so that Δv is about 0. However, the amount of normal dispersion near the pump is also important, as cross-phase modulation involving the widely-separated signal and idler modes can result in nonlinear conversion to unwanted spectral channels near the pump if the amount of normal dispersion is insufficient. Thus, a dichotomy arises: strong normal dispersion suppresses parasitic processes, but strong normal dispersion makes the frequency matching and phase matching conditions challenging to satisfy.

This problem is circumvented through the use of hybrid-mode OPO (hOPO), in which phase and frequency matches azimuthal modes from different transverse spatial mode families. hOPO makes it possible for each of the pump, signal, and idler bands to have strong normal dispersion, thereby suppressing competitive processes while maintaining phase and frequency matching for the targeted modes. Hence, through careful design of the resonator's dispersion, it is possible to isolate the hOPO, taking the many-mode system to the limit where the system behaves like the modeled three-mode system, where high output power and high conversion efficiency are simultaneously accessible without sacrificing wavelength access.

Referring toFIG.3, a flow diagram for operation800for generating a coherent laser light in accordance with aspects of the present disclosure is shown. Although the blocks ofFIG.8are shown in a particular order, the blocks or steps need not all be performed in the illustrated order, and certain blocks can be performed in another order. The operation ofFIG.8will be described below, and such operation may be performed by the device100ofFIG.1. These variations are contemplated to be within the scope of the present disclosure.

Initially, at block302a light source102of device100pumps a first color laser light. Next at block304the light source102is coupled to a waveguide110of device100.

Next, at block306a microring resonator130of device100is coupled to the light source102via the waveguide110. The microring resonator130includes a layer132comprised of silicon nitride, the layer132includes a first side and a second side; a substrate134comprised of silicon dioxide disposed on the second side of the layer132; and a cladding136comprised of air disposed on the first side of the layer132. The layer132includes a ring width (RW) and a height (H).

Next at block308, the microring resonator130generates a coherent second color light and a coherent third color light based on hybrid-mode optical parametric oscillation. In aspects, the microring resonator130may be designed by selecting a pump mode of the light source from a higher-effective-index mode, selecting a signal mode from a lower-effective-index mode; and matching of effective modal indices based on a difference of the higher-effective-index and the lower-effective-index at a wavelength of a signal wave.

Referring toFIG.5a graph of a single-mode-family OPO (sOPO) is shown. The pump operates at a near-to-zero but still normal dispersion (the top panel), and the effective modal indices have to be matched for idler, pump, and signal according to the equation ns/ns+ni/ni=2np/np (dashed line in the second panel) for modes with zero frequency mismatch (third panel) Δv=ns+ni−2np=0. Such sOPO can have three competitive processes, the process in the designed configuration but with adjacent signal and idler modes also exhibiting OPO (I), close-band OPO (II) or frequency comb generation, and cluster comb generation where many closely-spaced parametric sidebands surround the targeted signal and/or idler modes (III).

Referring toFIG.6a graph of the hOPO device100where two different mode families are used is shown. The pump mode is chosen from the higher-effective-index mode (H), which exhibits normal dispersion across the entire spectral range under consideration. The signal can be from the lower-effective-index mode (L). The matching of effective modal indices (i.e., phase-matching) in this case depends on the difference of H and L modal indices at the signal wavelength rather than the dispersion of a single mode family (H or L) as in sOPO (FIG.5). Equivalently, the frequency matching line is shifted downward, due to the difference of effective indices of these two modes at the signal frequency, as shown in the third panel. This configuration is termed HHL, indicating a higher-index (H) or lower-index (L) mode family from which each of the signal mode, pump mode, and/or idler mode (in this order) is taken. Because the pump mode is in a more strongly normal dispersion region than in sOPO, most competitive processes will be excluded, and only process I is expected to potentially be present.

Referring toFIG.7, a graph of other hOPO configurations is shown. The hOPO can operate in many other configurations. First, as shown in the top panel, the lower-index mode family (L) can have anomalous dispersion for idler and pump frequencies, with the higher-index mode being normal for all three frequencies; moreover, the dispersion of H and/or L can be shifted up and down. Second, besides the MIL scheme, LHH (or LHL) can also be used as shown in the second panel. Moreover, when two modes are adjacent to each other and similar in effective modal indices, these two modes can exhibit either a direct crossing (third panel) or an anticrossing (bottom panel).

From the perspective of hOPO, these two cases (direct crossing and anticrossing) are not particularly different as long as the participating modes (i.e., those whose effective modal indices enable phase-matching for frequency-matched modes) are situated away from the crossing/anticrossing point. In the mode anticrossing case, an additional benefit is that the mode overlap is guaranteed because of mode hybridization. In other hOPO cases (without mode hybridization), adequate spatial mode overlap for modes from differing families is required, similar to other nonlinear mixing processes using different families, for example, χ(2)OPO and second-/third-harmonic generation.

Referring toFIG.8, a diagram illustrating the dominant electric field components of the TE1, TE2, TM1, and TE3modes of the device100ofFIG.1is shown. The dominant electric field components of the TE1, TE2, TM1, and TE3modes are shown at about 390 THz (769 nm) in an exemplary device100with ring radius RR of about 28 μm, ring width RW of about 2.8 μm, and ring thickness H of about 323 nm are with the effective modal indices sorted from high to low.

Referring toFIG.9, a diagram that illustrates the dispersion, the effective modal index, and the frequency mismatch to support hOPO is shown. The top panel shows the dispersion parameter for the higher branch (H curve), which hybridizes TM1and TE3modes in a microring with RW=about 2.8 μm and H=about 323 nm. The dispersion around 390 THz is about −1860 ps/(nm·km). In comparison, the dispersion for the TE1mode (dashed line) in such a device is about −830 ps/(nm·km), and the dispersion around the pump mode in sOPO13 (dashed line, RW=about 825 nm) is very close to zero dispersion, i.e., greater than about −100 ps/(nm·km). The middle panel shows the effective modal indices of the higher and lower branches, which hybridize TM1and TE3modes. The curves exhibit an anti-crossing at about 368 THz, where the higher branch (H) shifts from TE3to TM1, and the lower branch (L) shifts from TM1to TE3, with frequency increased from about 340 THz to about 435 THz. The bottom panel shows the frequency mismatch (Δv) in all four possible configurations when the pump is at 390 THz and from the H branch. The four configurations are labeled based on the chosen families for the idler, pump, and signal modes, and are LHL, HHL, LHH, and HHH. Choosing the pump from the H branch ensures that it is in the normal dispersion regime, as shown in the curve for HHH. The only configuration that supports the frequency matching needed for OPO is LHH, with the idler frequency of about 370 THz and the signal frequency of about 410 THz.

FIG.10shows a graph that illustrates the optical spectra as the pump frequency (Vp) of the device ofFIG.1is tuned from about 387 THz to about 392 THz. On the y axis, 0 dB is referenced to 1 mW, i.e., dBm.

FIG.11shows a graph that illustrates tuning the pump from shorter wavelength to longer wavelength, to follow the triangular shape of thermal bistability. The physics of hOPO suggests that hOPO should be very robust to device dispersion. As described earlier, the underlying reason is that phase-matching is realized by considering the difference in effective modal index between two mode families at one frequency (signal or idler) instead of through fine balancing of higher-order dispersion in one mode family. A consequence of this is that a change to device dimensions over a wide range should only lead to a small change of signal and idler frequencies, as long as the pump mode device is still in the normal dispersion regime. In aspects, the hOPO output tunes as a function of ring width (RW) variation, pump detuning, and temperature tuning, as illustrated inFIGS.1,2, and11.

FIG.12is a graph that illustrates the ring width (RW) of the device ofFIG.1being changed from about 2.5 μm to about 3.0 μm. InFIG.12hOPO is very robust with respect to RW, with the output spectrum remaining consistent with the signal and idler frequencies remaining in the same frequency bands when varying RW from about 2.5 μm to about 3.0 The signal, pump, and idler frequencies are plotted in diamonds, circles, and squares inFIG.12, and the simulated results are plotted as solid lines. The experimental results and the theoretical predictions agree well, with a slight deviation of about 5 THz on the RW=about 3 μm side, which is likely due to imprecise knowledge of the fabricated geometry due to nanofabrication uncertainty.FIG.13is a graph that illustrates pump light frequency (Vp) vs. signal light frequency (Vs) when the pump light frequency is varied. In the device with RW of about 2.6 when the pump laser is coupled into the cavity with its frequency varying from about 386.8 THz (right) to about 386.5 THz (left), the signal light and the idler light are tuned to about 0.3 THz and about 0.2 THz, respectively, in a continuous fashion. The microscope images on the right show the signal light scattered by the microring surface roughness, where the scattered light is brighter (from top to bottom), as the pump laser is coupled deeper into the cavity. The pump light and idler light are filtered out by a short-pass filter.FIG.14illustrates Vs, Vp, and Vi as the temperature is varied. The hOPO output is found to be stable across this temperature range of about 40° C.

FIG.15is a graph illustrating the optical spectra of the device ofFIG.1. A relatively flat output optical spectrum from a hOPO device100pumped at about 389.1 THz in the RW of about 3 μm device. Signal and idler outputs are within about −3.5 dB of the pump output. On the y-axis, 0 dB is referenced to 1 mW, i.e., dBm. A power dependence study with the pump frequency fixed.

The robustness of hOPO also indicates that it should be capable of reaching higher power output for signal and idler, particularly considering its dispersion naturally restricts competitive nonlinear processes. To date, the sOPO typically show about −10 dB to about −20 dB lower output power at the signal and idler than at the pump. When signal and idler are very widely separated, the signal output power level is typically further decreased, likely because of coupling (as the high-frequency signal tends to be undercoupled in microring-waveguide geometries if the pump is critically-coupled). Besides coupling, the low output power is mainly due to competitive processes, which limit the OPO conversion efficiency when the power is significantly above the threshold. Therefore, hOPO behaves better than sOPO because hOPO has much fewer competitive processes than sOPO.

An example of such performance for a RW of about 3 μm device pumped at about 389.1 THz. This hOPO can exhibit a very flat output spectrum, as shown inFIG.15, where signal and idler outputs are both within about −3.5 dB of the pump output. Next, the pump power may be changed while fixing the pump frequency and calculate the conversion efficiencies (for signal and idler) and output powers (for pump, idler, signal) in the waveguides.

FIG.16is a graph illustrating the signal-to-pump output ratio and idler-to-pump output ratio of the device ofFIG.1. The ratio inFIG.16is collected from the optical spectra ofFIG.15. Examining first the output spectra, the idler and signal are up to about −3.0 dB and about −3.4 dB away from the pump, respectively, inFIG.16.

FIG.17is a graph illustrating the signal to pump output and idler to pump output efficiencies and the pump output power, signal output power, and idler output power for the device ofFIG.1. Next, the on-chip conversion efficiency is up to about 8±2% and about 7±2% for idler and signal, respectively, in the top panel ofFIG.17. The output power is up to about 5±1 mW and about 4.6±0.9 mW for idler and signal, respectively, in the bottom panel ofFIG.17. The metrics of flatness of the output spectrum, conversion efficiency, and output power are likely optimized at slightly different regions of parameter space.

FIG.18shows a graph illustrating another example of an hOPO device with a TM1-TE2anti-crossing. In this case, the hOPO device100has a thickness of H=about 385 nm and a ring width of RW=about 2.3 μm. As shown in the top panel ofFIG.18, the simulation suggests that TE2and TM1modes have an anti-crossing around 420 THz, below which TE2is the higher-index (H) branch and TM1is the lower-index (L) branch. The H branch exhibits large normal dispersion across the spectral range of interest, as shown in the inset. As shown in the bottom panel, the frequency mismatch (Δv) calculated from the simulation confirms that the H branch has a normal dispersion as the HRH curve (blue) is below zero. Out of the four cases with the H mode as the pump, the only case supporting OPO is HHL (red). Such hOPO exists for three consecutive pump modes from about 386 THz to about 388 THz, as shown inFIG.19. In the 386 THz case (the top panel), the signal is around the mode anti-crossing of 420 THz; in the other two cases, the signals are at frequencies below the anti-crossing point. Because the signal is in the L branch in the MIL configuration, the signal should be about equally split into TM1and TE2in the top panel, and be more dominantly composed of TM1rather than TE2in the two other two panels. In other words, the mode anti-crossing does not seem necessary for hOPO to exist.

In aspects, the device100may be fabricated through a photonic damascene process. The device100may include a microring resonator130with a layer132(FIG.1) that may have a height (H) of about 890 nm thick that is fully silicon dioxide (SiO2)-clad silicon nitride (Si3N4) with outer radius of about 23 μm and a ring width (RW) of about 3 μm.FIG.20shows a typical cross-section of a microring, which has an inverted trapezoidal shape, with a sidewall angle of about 16 degrees as a result of the reflow step within the damascene process.

The frequency mismatch Δv for phase-matched sets of the signal mode, the idler mode, and the pump mode may be measured as shown inFIG.20. Δv is plotted as a function of the relative mode number μ, indexed with respect to a pump band mode at about 308 THz. Two cases may be considered, the targeted process in which the idler and pump are from the fundamental transverse electric (TE0) mode family, and the signal is from the fundamental transverse magnetic mode (TM0) family, and one in which all three modes are from the TE0mode family, i.e., the more typical single mode family case. In the TE0-TE0-TM0hOPO scheme, Δv of about 0 at frequencies near about 390 THz and about 226 THz, indicating that the OPO signal and idler pair may be anticipated near these frequencies for an appropriate level of pump laser detuning and Kerr nonlinear shifts to compensate for any non-zero frequency mismatch. In contrast, Δv<0 at all frequencies for the TE0-TE0-TE0case, indicating that the widely separated process of interest will not occur for this set of modes. These results confirm that the pump is situated in a regime of normal dispersion, which is explicitly validated through the evaluation of the dispersion parameter D for the TE0and TM0mode families, where

D=-c2⁢π⁢λ2⁢∂2β∂v2.D<0
for the TE0family, not only in the pump band but also in the idler band (as well as the signal band). In addition, D<0 for the TM0family in the signal band. As discussed above, this normal dispersion throughout the entire frequency range between the signal and idler, and in particular surrounding the pump, should suppress many potentially competing nonlinear processes.

The resonator-waveguide coupling is critical for a high-performance OPO. Conversion efficiency and output power of the idler generated near about 1300 nm. ηmaxidepends on the coupling parameter for the pump Kpand for the idler Ki, with greater efficiency being achieved with increased Kiand Kp. Additionally, to maintain an acceptable threshold power and because the extraction of the signal is not focused on, small Ksmay be targeted. Using a straight waveguide that is at a gap and tangent to the ring naturally leads to variation in resonator-waveguide coupling across broad spectral ranges, since the modal overlap between ring and waveguide modes depends on the evanescent decay lengths of each mode, which itself depends on wavelength. As a result, long wavelength modes tend to be overcoupled and short wavelength modes tend to be undercoupled, so that Ki>Kp>Ksas desired, provided that intrinsic quality factors remain high throughout.

Referring toFIG.21, an example layout and side cutaway of the device100ofFIG.1is shown.

Referring toFIG.22, coupling parameters Ki, Kp, and Ksis shown for a series of devices100in which the resonator-waveguide gap is varied between about 200 nm and about 500 nm. An increase in Ki,p,swith decreasing gap is shown inFIG.22, where Ki>Kp>Ks. Specific gap values may be chosen to target the high-performance overcoupled regime. For example,FIG.20shows the cavity mode transmission spectra at a gap of 300 nm. Of note are the high intrinsic quality factors achieved, e.g., Qintabout {5.2×106, 6.1×106, 3.5×106} for the signal, pump, and idler bands, respectively. This enables significant overcoupling to be achieved (Ki≳10, Kp≳1) while maintaining high overall Q s. In comparison to other works utilizing resonators of a similar cross-section and size (i.e., an FSR of 1 THz), the intrinsic Qs observed are somewhat higher. This is likely a consequence of the relatively wide approximately 3 μm ring widths that are used, which limits the interaction of the optical field with the sidewalls. The ability to use such wide rings is a benefit of the hOPO scheme.

The disclosed technology has the benefit of enabling a high-performance on-chip microresonator optical parametric oscillation that produces>about 15 mW of output power at conversion efficiencies of >about 25%, without compromising on the span of the output signal and idler frequencies (>about 150 THz signal-idler separation). Simultaneously realizing these three features in an on-chip OPO represents a significant advance in the realization of flexible wavelength access for lasers. Furthermore, its development on a platform compatible with silicon photonics makes the device100well suited for wide-scale deployment outside of laboratory settings. The disclosed technology may use combined coupling engineering and flexible frequency matching techniques, such as the hybrid mode-matching scheme used in this work (or recently implemented photonic crystal microring approaches), to enable high-performance OPO across different wavelength bands, including the visible and mid-infrared.

Certain embodiments of the present disclosure may include some, all, or none of the above advantages and/or one or more other advantages readily apparent to those skilled in the art from the drawings, descriptions, and claims included herein. Moreover, while specific advantages have been enumerated above, the various embodiments of the present disclosure may include all, some, or none of the enumerated advantages and/or other advantages not specifically enumerated above.

The embodiments disclosed herein are examples of the disclosure and may be embodied in various forms. For instance, although certain embodiments herein are described as separate embodiments, each of the embodiments herein may be combined with one or more of the other embodiments herein. Specific structural and functional details disclosed herein are not to be interpreted as limiting, but as a basis for the claims and as a representative basis for teaching one skilled in the art to variously employ the present disclosure in virtually any appropriately detailed structure. Like reference numerals may refer to similar or identical elements throughout the description of the figures.

The phrases “in an embodiment,” “in embodiments,” “in various embodiments,” “in some embodiments,” or “in other embodiments” may each refer to one or more of the same or different example embodiments provided in the present disclosure. A phrase in the form “A or B” means “(A), (B), or (A and B).” A phrase in the form “at least one of A, B, or C” means “(A); (B); (C); (A and B); (A and C); (B and C); or (A, B, and C).”

It should be understood that the foregoing description is only illustrative of the present disclosure. Various alternatives and modifications can be devised by those skilled in the art without departing from the disclosure. Accordingly, the present disclosure is intended to embrace all such alternatives, modifications, and variances. The embodiments described with reference to the attached drawing figures are presented only to demonstrate certain examples of the disclosure. Other elements, steps, methods, and techniques that are insubstantially different from those described above and/or in the appended claims are also intended to be within the scope of the disclosure.