Patent Application
20220100050
The invention relates to a method for transposing the frequency (frequency-conversion) of an optical signal by mixing a plurality of waves, for example, using four-wave mixing, as well as to a device for implementing such a method.
Molecular spectroscopy applications require the provision of an optical radiation with a wavelength ranging between 2 μm (micrometer) and 6 μm. However, radiation sources that can operate in this spectral range and that have the features required for these applications are very expensive or are not available. It has therefore been proposed that the radiation that is required for such spectroscopic application is produced from a laser source that operates at about 1.55 μm, since such laser sources are available at a low cost by virtue of their mass use for telecommunication applications. The optical signal that is produced by the laser source, the wavelength of which optical signal is approximately 1.55 μm, then undergoes frequency-conversion in order to obtain an optical signal that is useful for the desired application, for example, a useful optical signal that is in the 2 μm-6 μm spectral band. Throughout the present description, the cited wavelengths relate to the free-space propagation of the electromagnetic radiation in vacuum or air. When a considered radiation propagates in one or more waveguide(s), the wavelength value cited for this radiation is that of a radiation with the same frequency as that in the waveguide(s), but which would freely propagate in vacuum or air.
In a known manner, the frequency-conversion of a source optical signal to produce a useful optical signal can be performed using a non-linear mechanism, called four-wave mixing, which may result from an optical Kerr effect. To this end, one or two optical pumping radiation(s) is (are) used to convert two photons of this (these) pumping radiation(s) into a photon of the useful signal and an additional photon of the source signal. The case where the two pump photons belong to one and same monochromatic radiation is called degenerate case, as opposed to a non-degenerate case where the two pump photons have different wavelength values. Such frequency-conversion mechanism is most often implemented within a waveguide, for example, within an optical fiber or an integrated waveguide, by simultaneously injecting the one or the two pumping radiation(s) and the source signal into this waveguide, and extracting the useful signal therefrom.
However, in order to occur, the non-linear four-wave mixing mechanism requires that a relationship, called phase-matching relationship, is met. This phase-matching relationship applies to the propagation constants k that are effective in the waveguide where the four-wave mixing occurs. It is of the following form: k(λpump1)+k(λpump2)−k(λsource)−k(λuseful)+ε=0, where k(λpump1) and k(λpump2) are the propagation constants of the two pumping radiations in the used waveguide, k(λsource) is the propagation constant of the source signal in this same waveguide, and k(λuseful) is the propagation constant of the useful signal also in this same waveguide. ε is a non-linear term, in general very weak, the expression of which is known, and which depends in particular on the power of the pumping radiations. The propagation constants k(λpump1), k(λpump2), k(λsource) and k(λuseful) express the guided nature of the propagation of the pumping radiations, of the source signal and of the useful signal in the waveguide that is used to produce the frequency conversion. In a known manner, each of the pumping radiations, the source signal and the useful signal propagates in the waveguide according to a normal mode thereof, also referred to as eigenmode, and the dependence of the propagation constant k as a function of the wavelength is the dispersion relationship of this normal mode. The value of each of the propagation constants k(λpump1), k(λpump2), k(λsource) and k(λuseful) also depends, in accordance with the normal mode of the waveguide, on parameters of this waveguide, in particular on geometric parameters thereof and on optical parameters of its constituting materials. The values of these parameters of the waveguide then must be selected so that the phase-matching relationship is met for values of λpump1, λpump2 and λsource that are within spectral ranges of the optical sources used to produce the pumping radiations and the source signal, respectively, and for a value of λuseful that is suitable for the desired application for the useful signal. In the particular case of a degenerate pumping radiation, the phase-matching relationship becomes: 2·k(λpump)−k(λsource−k(λuseful)+ε=0, where λpump is the wavelength of the degenerate pumping radiation.
However, the number of parameters of the waveguide that are available is insufficient to allow the phase-matching relationship to be met simultaneously for values of λpump1, λpump2, λsource and λuseful within desired ranges. Then, it has been proposed, in particular in the article entitled “Coupling-length phase matching for nonlinear optical frequency conversion in parallel waveguides”, by Ivan Biaggio, Virginie Coda and Germano Montemezzani, Physics Review A 90, 043816, 2014, for the waveguide that is used to produce the frequency-conversion by four-wave mixing to be coupled to an additional waveguide. This coupling modifies at least some of the propagation constants k(λpump), k(λsource) and k(λuseful). In this way, additional parameters are available for adjusting the propagation constants k(λpump), k(λsource) and k(λuseful) that relate to the waveguide where the frequency-conversion occurs. These additional parameters relate to the additional waveguide and to the coupling that exists between both waveguides. It is thus possible to adjust the values of the parameters of the two coupled waveguides so that the phase-matching relationship is met on average for λpump, λsource and λuseful values that are of interest.
However, in such coupled waveguide system, the source signal, the one or more pumping radiation(s) and the useful signal are each progressively transferred from one waveguide to the other one during their propagation, repeatedly and alternately between both waveguides. Thus, each signal or radiation is alternately contained in one of the waveguides and then in the other one. As a result, the phase-matching relationship is only met transiently during these transfers of signals/radiation(s) between both waveguides. The useful signal then appears transiently and disappears thereafter, repeatedly, during the propagation of the radiations in the waveguides. By adapting the parameters of the system, it becomes possible to avoid each re-decrease of the intensity of the useful signal, so that this intensity increases in a manner that on average is linear in relation to a longitudinal coordinate of the waveguides. However, even by increasing the length of the waveguides, it is still impossible to achieve in this way an intensity of the useful signal that is sufficient for certain applications. Furthermore, when the waveguides are produced using the integrated optical circuit technology that is currently available, and when these waveguides are straight, their length is limited by the maximum size of the integrated optical circuits that is imposed by the tools of the technology that is used. In the current state, this maximum size is a few centimeters. However, bending the waveguides within an integrated optical circuit makes that the phase-matching relationship is no longer met at the bending locations of the waveguides.
Furthermore, splitting devices that are based on a plurality of coupled waveguides are commonly used to distribute between a plurality of outputs a light intensity that is injected at an input of such splitting device. This is a different use, which does not involve four-wave mixing produced by a non-linear effect. Most often, such light intensity splitting device has a waveguide length that is less than 100 μm, and a separation distance between the coupled waveguides that is less than 0.25 μm.
Based on this situation, an object of the present invention is to produce a useful signal by four-wave mixing with an intensity that is higher than in the prior art. In particular, the object of the invention is to produce a useful signal with an intensity that is sufficient for a spectroscopic application.
To achieve this or another object, a first aspect of the invention proposes a new method for frequency-converting a source optical signal in order to produce a useful optical signal, by mixing a plurality of waves as a result of a non-linear interaction between these waves. The method comprises producing, within at least one waveguide, at least one photon of the useful signal from at least one photon of at least one optical pumping radiation. This combination of photons occurs in accordance with a phase-matching relationship, which connects respective propagation constants of the source signal, of each pumping radiation and of the useful signal, with these propagation constants being effective in said at least one waveguide. The invention equally applies when several photons of said at least one pumping radiation that are involved in the wave mixing are degenerate or non-degenerate.
Each waveguide has at least one individual normal mode—or eigenmode—that is effective for each of the source signal, of the at least one pumping radiation and of the useful signal propagating in this waveguide separately from each other waveguide. In addition, each waveguide has at least one individual parameter that modifies an dispersion relationship which is effective for the source signal, each pumping radiation and the useful signal that propagate in this waveguide according to its individual normal mode. Such an individual parameter may be, for example, a geometric parameter of the waveguide.
For the invention, said at least one waveguide comprises at least two waveguides that are arranged so that the individual normal mode of each waveguide is coupled with an individual normal mode of at least one another of the waveguides, for each of the source signal, of each pumping radiation and of the useful signal.
The method comprises simultaneously injecting the source signal and each pumping radiation into at least one of the waveguides, and extracting the useful signal from at least one of these waveguides. Then, since at least some of the individual normal modes of the waveguides are coupled, each of the source signal, of each pumping radiation and of the useful signal that propagates at a location in the waveguides according to the individual normal mode of one of the waveguides has an intensity distribution between several of the waveguides that varies along these waveguides.
Also for the invention, at least one coupling parameter, for example, at least one separation distance between the waveguides, modifies an intensity of the coupling that exists between the individual normal modes of at least two of the waveguides.
Then, according to the invention, respective values of the individual parameters of the waveguides and of said at least one coupling parameter are selected so that the phase-matching relationship is met for at least one set of respective propagation constants of the source signal, of each pumping radiation and of the useful signal, with each of these propagation constants relating to a collective normal mode of all of the waveguides. This collective normal mode, also called super-mode, is effective for the propagation of the source signal, of each pumping radiation or of the useful signal, and is such that the source signal, each pumping radiation or the useful signal that propagates in all of the waveguides according to this collective normal mode has an intensity distribution between the waveguides that is constant along the waveguides.
The invention therefore proposes selecting the values of the parameters of the waveguides and of each coupling parameter so that the phase-matching relationship is met for the propagation constants relating to the collective normal mode(s) of all the waveguides, such that this (these) collective normal mode(s), is (are) used by the source signal, each pumping radiation and the useful signal, as opposed to the propagation constants relating to the individual normal modes of the waveguides. In other words, by way of an example for a four-wave mixing case, the invention replaces the requirement of a phase-matching relationship of the type: kindividual(λpump1)+kindividual(λpump2)−kindividual(λsource)−kindividual(λuseful)+εindividual=0 in the non-degenerate case, or of type: 2·kindividual(λpump)−kindividual(λsource)−kindividual(λuseful)+εindividual=0 in the degenerate case, relating to one or more individual normal mode(s) of the waveguides, with the phase-matching relationship applied to one or more collective normal mode(s) of the waveguides: kcollective(λpump1)+kcollective(λpump2)−kcollective(λsource−kcollective(λuseful)+εcollective=0 in the non-degenerate case, or 2·kcollective(λpump)−kcollective(λsource)−kcollective(λuseful)+εcollective=0 in the degenerate case.
As a result of the invention, in the general case of mixing a plurality of waves, the phase-matching relationship is continually met during the propagation of the source signal, of each pumping radiation and of the useful signal in the waveguides. For this reason, the intensity of the useful signal increases rapidly as a function of the longitudinal coordinate of the waveguides. It can thus reach higher levels, in particular intensity levels that are sufficient for the useful signal to be used in spectroscopy. In the case of four-wave mixing, in particular as produced by a Kerr effect, the intensity of the useful signal increases substantially quadratically as a function of the longitudinal coordinate of the waveguides.
Preferably, the mixing of a plurality of waves that is implemented in the invention may be three-, four-, five- or six-wave mixing. For example, three-wave mixing can result from a non-linear interaction of the second-order dielectric susceptibility type, also called chi-squared effect (x2), and as is particularly produced by a lithium niobate material, in which the waves propagate. Six-wave mixing can result from a non-linear interaction of the plasma effect type.
Particularly advantageous implementations of the invention may correspond to four-wave mixing processes for producing the useful signal. For example, such four-wave mixing can result from a Kerr effect. In this case, a photon of the useful signal is produced with an additional photon of the source signal from two photons of the at least one pumping radiation.
Preferably, irrespective of the number of waves in the mixing arid of the pumping radiations that can be degenerate or non-degenerate as appropriate, the waveguides that are used for the invention may be formed in an integrated optical circuit. They then produce confinement efficiencies for the optical signals and the optical radiations, which are higher than those that can be achieved using optical fiber technology. These waveguides using integrated optical circuit technology then may be curved without causing any losses of intensity that are significant for the normal modes of guided propagation. In this case, the waveguides that are used for the invention may be parallel to each other and arranged side-by-side in at least one portion of the integrated optical circuit. Their meandering or spiral arrangement allows them to be manufactured in integrated optical circuits, the dimensions of which are compatible with the available industrial tools.
Still with reference to waveguides that are part of an integrated optical circuit, at least two of these waveguides may be curved and parallel in a bend that is shared by these at least two waveguides. These waveguides thus have respective curvatures that are different in the bend. In such case, according to an improvement of the invention, at least some of the respective individual parameters of the two waveguides may have values in the bend, such that two parts of at least one and same signal or radiation from among the useful signal, each pumping radiation and the source signal, one of which propagates in any one of the curved waveguides and the other one which propagates in another one of these curved waveguides, according to the individual normal modes thereof, remain in-phase along radial directions each perpendicular to the curved waveguides in the bend. Then, parts of the useful signal, parts of the pumping radiation, or parts of the source signal, which propagate in the curved waveguides, remain in-phase with each other along the bend, exactly or even to the first-order in relation to a longitudinal coordinate of the waveguides in the bend. It is thus possible to fold the waveguides without reducing the efficiency of the multi-wave mixing for producing the useful signal.
Still for implementations of the invention using integrated optical circuit technology, the waveguides may have respective lengths that range between 1 mm (millimeter) and 100 mm, and any two of the waveguides that are neighboring may have a separation distance between them that ranges between 0.125 μm and 3 μm, when this distance is measured perpendicular to the two neighboring waveguides.
According to common variants of the integrated optical circuit technology, each waveguide may be made of a material that is selected from silicon (Si), titanium oxide (TiO2) or silicon nitride (Si3N4), and may be formed on a quartz substrate (SiO2), and thus may be embedded in a silica layer (SiO2) acting as a sheath for each waveguide. In other integrated optical circuit technologies, the substrate and/or the sheath of each waveguide alternatively may be made of any dielectric material that has a refractive index value of less than 2.00 for the wavelengths of the useful signal, of each pumping radiation and of the source signal, including polymer materials or air.
In general, the following additional features may be reproduced for preferred improvements or embodiments of the invention, separately or by combining several of them together:
Also possibly, the invention method may be used to produce a plurality of different useful optical signals, in particular two different useful optical signals, by mixing a plurality of waves resulting from a non-linear interaction between these waves. In this case, the method involves simultaneously producing, within at least one waveguide, at least one photon of each of the useful signals with at least one additional photon of the source signal from at least one photon of the at least one optical pumping radiation, in accordance with a phase-matching relationship, which connects respective propagation constants of the source signal, said at least one pumping radiation and each of the useful signals, that are effective in the at least one waveguide.
A second aspect of the invention proposes an optical device that is suitable for implementing a method according to the first aspect of the invention.
Such a device comprises a plurality of waveguides each having at least one individual normal mode that is effective for optical radiations propagating in this waveguide separately from each other waveguide. Moreover, each waveguide has at least one individual parameter that modifies a dispersion relationship effective for each radiation that propagates in this waveguide according to its individual normal mode.
The waveguides of the device are arranged so that the individual normal mode of each of the waveguides is coupled with an individual normal mode of at least one another of the waveguides. Thus, since at least some of the individual normal modes of the waveguides are coupled, each radiation that propagates at a location in the waveguides according to the individual normal mode of one of these waveguides has an intensity distribution several of the waveguides that varies throughout the waveguides.
For the invention, the device is such that at least one coupling parameter modifies an intensity of the coupling that exists between the individual normal modes of at least two of the waveguides.
Then, according to the invention, respective values of the individual parameters of the waveguides and of said at least one coupling parameter are such that a method according to the first aspect of the invention can be implemented using the device. In other words, these values of the individual parameters of the waveguides and of said at least one coupling parameter are such that the phase-matching relationship of a four-wave mixing process is met for a source signal, at least one pumping radiation and a useful signal that each propagate in the waveguides according to at least one collective normal mode of all of the waveguides of the device.
The features and advantages of the present invention will become more clearly apparent from the following detailed description of non-limiting embodiments, with reference to the appended figures, in which:
For clarity sake, the dimensions of the elements that are shown in these figures correspond neither to actual dimensions nor to actual dimension ratios. In addition, identical reference signs that are indicated in different figures denote elements that are identical or that have identical functions.
Moreover, the invention is described hereafter in the case of four-wave mixing such as that resulting from a Kerr effect, and in the case of a pumping radiation that is degenerate: λpump1=λpump2=λpump using the notations of the general part of the present description. However, a person skilled in the art will be able to apply this description to a case of pumping radiations that are not degenerate without exercising inventive skill, and also to the case of a non-linear interaction that produces a different wave mixing process.
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When the separation distance W is less than or of the order of the evanescent transverse extension of the individual normal mode of at least one of the waveguides 1 and 2, the resulting overlap between the individual normal modes of the two waveguides produces a coupling between these normal modes. This coupling is even more intense when the separation distance W is short. Typically, W may range between 0.125 μm and 3 μm.
Actually, the individual normal modes of the two waveguides 1 and 2 as described until now, and each corresponding to the radiation that is only confined on one of the two waveguides, is no longer a normal mode for the set of both coupled waveguides. Then, radiation which is injected into one of the two waveguides will oscillate from one waveguide to the other during its propagation in the longitudinal direction x. As a result, a non-linear effect, such as the optical Kerr effect, can only occur in an extent that varies substantially periodically with the coordinate x. A radiation that is generated by this non-linear effect then has an average intensity that remains limited. It is possible to locally modify the dispersion relationships of the individual normal modes of the two waveguides 1 and 2 by varying the values of h1, L1, h2, L2 and W as a function of x, so that the radiation that is produced by the non-linear effect accumulates gradually. Its intensity can then increase on average linearly as a function of x. However, such a linear increase in the intensity of the radiation that is generated by the non-linear effect remains insufficient for many applications.
The invention then proposes a new setting of the parameters of each waveguide 1 and 2, and of the coupling parameter, which produces a faster increase in the intensity of the radiation that is produced by the non-linear effect.
According to the invention, the values of h1, L1, h2, L2 and W are selected to meet the phase-matching relationship of the non-linear effect with the propagation constants of the normal modes of all of the coupled waveguides. These normal modes of all of the coupled waveguides have been referred to as collective normal modes of the coupled waveguides. Each propagation constant that is used for the phase-matching relationship is therefore that of one of these collective normal modes.
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The non-linear effect, for example, the optical Kerr effect, which is used to produce a useful optical signal, simultaneously produces a photon of this useful signal and a photon of a source optical signal from two photons of an optical pumping radiation. The source signal and the pumping radiation are injected into the waveguides 1 and 2, or at least into one of them, and when they propagate along the longitudinal coordinate x the intensity of the pumping radiation decreases, whereas those of the source signal and of the useful signal increase. The aim is to achieve a sufficient intensity for the useful signal at x=L, while the intensity of this useful signal is zero at x=0. To ensure that the non-linear effect occurs, a phase-matching relationship has to be verified, which connects the propagation constants of the source signal, of the pumping radiation and of the useful signal. This phase-matching relationship is of the following form: 2·k(λpump)−k(λuseful)−k(λsource)+ε=0, where λpump is the free-space propagation wavelength in vacuum of the pumping radiation, λuseful is the free-space propagation wavelength in vacuum of the useful signal, λsource is the free-space propagation wavelength in vacuum of the source signal, and ε is a low-value non-linear term, the expression of which is known. According to the invention, the values of the propagation constants k(λpump), k(λuseful) and k(λsource) to be introduced into this phase-matching relationship each relate to a collective normal mode of the coupled waveguides. However, this collective normal mode may not be the same between any two from among the source signal, the pumping radiation and the useful signal. Thus, for the case of the two coupled waveguides of [
2·kodd(λpump)−kodd(λuseful)−kodd(λsource)+ε=0;
2·keven(λpump)−kodd(λuseful)−kodd(λsource)+ε=0;
2·kodd(λpump)−keven(λuseful)−keven(λsource)+ε=0;
2·keven(λpump)−keven(λuseful)−keven(λsource)+ε=0;
k
odd(λpump)+keven(λpump)−keven(λuseful)−kodd(λsource)+=0;
k
odd(λpump)+keven(λpump)−kodd(λuseful)−keven(λsource)+ε=0.
In order to produce the useful signal according to the invention, at least one of these relationships is to be met for at least one value of λuseful in the spectral range that is desired for the contemplated application of the useful signal, and for at least one value of λsource and at least one value of λpump that must be adopted. The existence of such a triplet of values λuseful, λsource, λpump is provided by a suitable selection of values for h1, L1, h2, L2 and W that configure each of the kodd(λ) and keven(λ) dispersion relationships, where λ still generically denotes one of the wavelengths λuseful, λsource and λpump. These values of h1, L1, h2, L2 aand W can be found using digital computations, from the kodd(λ, h1, L1, h2, L2, W) and keven(λ, h1, L1, h2, L2, W) functions. According to a possible method for finding a solution, the function f(λsource)=2·kodd(λpump, h1, L, h2, L2, kodd(λuseful, h1, L1, h2, L2, W)−kodd(λsource, h1, L1, h2, L2, W)+ε can be plotted as a function of λsource, with the values of λpump, λuseful, h1, L1, h2, L2 and W being fixed, and a search is undertaken for the existence of a value of λsource corresponding to a radiation emission unit that would be available for the source signal, and for which this function f(λsource) is cancelled. This search is subsequently restarted for other values of λpump, λuseful, h1, L1, h2, L2 and W, and also for each of the combinations of the odd and even collective normal modes between the source signal, the pumping radiation and the useful signal, as cited above for obtaining solutions of several phase-matching relationships that are all possible. Solutions thus can be found whereby λsource ranges between 1.3 μm and 1.8 μm, preferably between 1.5 μm and 1.6 μm. Such values correspond to laser emission sources that are commonly used for telecommunication applications. λpump can range between 1.2 μm and 2.6 μm, preferably between 1.7 μm and 2.1 μm, corresponding to thulium-doped fiber laser emission sources. Finally, λuseful can range between 2 μm and 6 μm, preferably between 2.2 μm and 4.5 μm, in order to be suitable for a molecular spectroscopy application, for example. To this end, a common value equal to 0.22 μm or 0.34 μm can be assigned to the heights h1 and h2 of the waveguides 1 and 2, and the separation distance W can range between 0.125 μm and 3 μm. L1 and L2 can be identical and can range between 0.370 μm and 2.10 μm.
In practice, the equation 2·kodd(λpump, h1, L1, h2, L2, W)−kodd(λuseful, h1, L1, h2, L2, W)−kodd(λsource, h1, L1, h2, L2, W)+ε=0 simply can be replaced with the inequality 2·kodd(λpump, h1, L1, h2, L2, W)−kodd(λuseful, h1, L1, h2, L2, W)−kodd(λsource, h1, L1, h2, L2, W)<π/L, and likewise for each other phase-matching equation, where L still denotes the common length of the two waveguides 1 and 2 along the longitudinal coordinate axis x. Each of these phase-matching inequalities is generically denoted hereafter as Δkcollective<πr/L, to designate all the combinations of the odd and even collective normal modes between the source signal, the pumping radiation and the useful signal. The non-linear term ε then does not need to be computed, and the knowledge of the dispersion relationships of the collective normal modes kodd(λ) and keven(λ) is sufficient.
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Some applications require that the useful signal is made up of a plurality of spectral components, such as, for example, a comb of wavelengths within a spectral range around an average wavelength value λuseful average. Then, if the pumping radiation is monochromatic, the generation of such useful signal requires using a comb of wavelengths for the source signal, around an average wavelength value λsource average. It is then necessary for the phase-matching relationship f(λsource)=0 or Δkcollective<π/L to be verified to the nearest second-order for all the values of λsource in the vicinity of λsource average. To this end, values of λpump, h1, L1, h2, L2 and W must be found, which are such that the partial derivative of the f-function or of Δkcollective with respect to λsource is zero for the values of λsource average and λuseful average, which verify f(λsource_average, λuseful_average)=0 or Δkcollective(λsource_average, λuseful_average)<π/L. Equivalently, the partial derivative of the f-function or of Δkcollective with respect to λuseful is zero for the values of λsource average and λuseful average.
In order to facilitate the manufacture of parallel waveguides in an integrated optical circuit, in particular when the length L is several centimeters, these waveguides may need to be bent in a plane parallel to the substrate, in order to reduce the lateral dimensions of this substrate. For example, the parallel waveguides can form meanders or can be wound on the surface of the substrate of the integrated optical circuit. [
[
It is understood that the invention can be reproduced by modifying secondary aspects of the embodiments that have been described in detail above, while maintaining at least some of the cited advantages. In particular:
| Number | Date | Country | Kind |
|---|---|---|---|
| 19 00450 | Jan 2019 | FR | national |
| Filing Document | Filing Date | Country | Kind |
|---|---|---|---|
| PCT/FR2020/050055 | 1/15/2020 | WO | 00 |
