GB2478775A

GB2478775A - Methods and systems for converting or amplifying

Info

Publication number: GB2478775A
Application number: GB1004533A
Authority: GB
Inventors: Nathalie Vermeulen; John Edward Sipe; Hugo Jean Arthur Thienpont
Original assignee: Vrije Universiteit Brussel VUB; Universite Libre de Bruxelles ULB
Current assignee: Vrije Universiteit Brussel VUB; Universite Libre de Bruxelles ULB
Priority date: 2010-03-18
Filing date: 2010-03-18
Publication date: 2011-09-21
Also published as: GB201004533D0

Abstract

A system for Raman conversion, parametric conversion, or parametric amplification using quasi-phase-matched Raman-resonant four-wave-mixing or using quasi-phasematched Kerr-induced four-wave-mixing is described. The system comprises a first radiation source for providing a pump radiation beam, a second radiation source for providing a signal radiation beam, and a ring structure for receiving the pump radiation beam and the signal radiation beam, wherein a waveguiding portion of the ring structure is made of uniform material and wherein the radius of the ring structure is selected taking into account the spatial variation of the Raman susceptibility or the spatial variation of the Kerr susceptibility along the ring structure as experienced by radiation travelling along the ring structure for obtaining quasiphase-matched Raman-resonant four-wave-mixing or for obtaining quasi-phasematched Kerr-induced four-wave-mixing. The system also comprises an outcoupling waveguide for coupling out an idler radiation beam generated in the ring structure. The uniform medium may be a (100) grown silicon on insulator waveguide. TE or TM output may be selected by selecting TE or TM input.

Description

Methods and systems for converting or amplifying

Field of the invention

The present invention relates to the field of optics. More particularly, the present invention relates to methods and systems for Raman converters, parametric converters and parametric amplifiers with cavity enhancement and with quasi-phase-matching.

Background of the invention

Over the past several decades there has been growing interest in the development of devices based on third-order nonlinear effects such as Raman-resonant four-wave-mixing and Kerr-induced four-wave-mixing. Raman-resonant four-wave-mixing is a light-matter interaction that is perfectly resonant or almost perfectly resonant with a characteristic energy level of the material such as a vibrational energy level and that is used in Raman converters. Kerr-induced four-wave-mixing is a light-matter interaction that is not resonant with a material level and that is used in parametric converters and parametric amplifiers. Both processes involve three radiation beams.

Kerr-induced four-wave-mixing involves a pump radiation beam at frequency, a signal radiation beam at frequency w, and an idler radiation beam at frequency o.k.

Raman-resonant four-wave-mixing involves a pump radiation beam at frequency w, a Stokes radiation beam at frequency that is lower than the pump frequency, and an anti-Stokes radiation beam at frequency üafltj stokes that is higher than the pump frequency. One also uses the terms signal and idler for the Stokes and anti-Stokes radiation beams, respectively, or vice versa, and uses w5 and o to denote their frequencies. Due to the wavelength versatility offered by Raman-resonant four-wave-mixing and Kerr-induced four-wave-mixing, these processes feature a multitude of application possibilities in different domains. In particular Raman converters, parametric converters and parametric amplifiers based on silicon have attracted much attention because of their potential for application in optical communication systems.

Basically, Raman-resonant four-wave-mixing and Kerr-induced four-wave-mixing are interactions between two pump photons, one signal photon and one idler photon, and the frequencies of these photons a,, w and o satisfy the relation --= 0. For Raman-resonant four-wave-mixing in silicon we have in addition that -2,rx 15.6 THz, which is the Raman shift of silicon. The efficiency of Raman-resonant four-wave-mixing and Kerr-induced four-wave-mixing depends on the pump intensity and on the processes' phase mismatch. The linear part Akjjnea. of their phase mismatch is given by Ak1. = 2k -k -k1 where k{psa}=U){psaXfl{p5a)IC with are wave numbers with n{psa}representing the effective indices of the pump, signal and idler waves, respectively. One can also write Akiinear as Akiinear = _fl2(Aw)2 where fl2 =d2k/dol is the Group velocity dispersion (GVD) at the pump wavelength, fl4 =dk/do is the fourth-order dispersion at the pump wavelength, and Ao is the frequency difference between the pump and signal waves. In many cases, one can use the approximation Akjnear=fl2(AtD)2. The total phase mismatch for Raman-resonant four-wave-mixing and for Kerr-induced four-wave-mixing also contains a nonlinear part that is function of the pump intensity, but since we will consider here linear phase mismatches that are mostly much larger than the nonlinear part of the phase mismatch, the latter can be neglected in the remaining part of this text.

Despite their tremendous application potentialities, the silicon Raman converters demonstrated so far showed some important drawbacks. Due to their one-dimensional single-pass structure, the only way to achieve sufficiently high pump powers in the converters for obtaining efficient Raman-resonant four-wave-mixing was by using pulsed high-power pump sources as demonstrated by Koonath and co-workers. Furthermore, fabricating silicon waveguides that feature perfect phase matching for Raman-resonant four-wave-mixing turned out to be quite challenging.

Thus, a new approach is needed for establishing efficient Raman-resonant four-wave-mixing that takes place in a silicon structure which is easy to fabricate and that does not require high pump input powers.

Regarding silicon-based parametric converters and silicon-based parametric amplifiers, Lipson and co-workers have demonstrated that it is possible to have efficient Kerr-induced four-wave-mixing through phase matching, at least for signal and idler wavelengths relatively close to the pump wavelength. For a pump wavelength situated near the point of zero GVD (/2 = 0), phase-matched Kerr-induced four-wave-mixing could be established over a bandwidth of 200nm in the near-infrared telecom domain for a propagation distance of 1 cm. When using the same approach in the mid-infrared, the bandwidth for phase-matched Kerr-induced four-wave-mixing could be extended to l000nm as Lin and co-worker showed.

However, if one wants to establish Kerr-induced four-wave-mixing where both the pump-signal frequency difference Ao. and the absolute value of the GVD parameter are large, then one should use a technique different from phase matching. This is confirmed by phase-matched Kerr-induced four-wave-mixing experiments performed by Turner and co-workers in a silicon ring resonator that featured a large value for /32 These experiments showed that due to the ring resonator the pump input powers could be kept very low, but at the same time the large value for /2 reduced the maximal Ao. value for which efficient phase-matched Kerr-induced four-wave-mixing could be obtained. Also, if one aims at realizing a silicon-based source that, by changing just one parameter, can generate radiation at different wavelengths spread over the entire transparency region of the silicon material, then one should use a technique different from phase matching. The development of such discretely-tunable silicon-based sources would represent an important step in the search for low-cost, compact, room-temperature light sources tunable in the near-and mid-infrared. Such devices are still scarce nowadays but highly desirable for many applications, ranging from telecommunications and industrial process control, to environmental monitoring and biomedical analysis.

One suggestion has been to use the technique of quasi-phase-matched Raman- resonant four-wave-mixing and to use the technique of quasi-phase-matched Kerr-induced four-wave-mixing.

In the traditional quasi-phase-matching approach for Raman-resonant four-wave-mixing as introduced by Bespalov and Konorov, the Raman characteristics of the medium are periodically adjusted to obtain alternating Raman-active and Raman-passive layers so that the initial phase relation between the waves involved in the Raman-resonant four-wave-mixing process is periodically restored. The approach to obtain quasi-phase-matching for Raman-resonant four-wave-mixing via periodically adapting the Raman characteristics of the medium is however quite complex.

A traditional concept of quasi-phase-matched Kerr-induced four-wave-mixing has been introduced by Kim and co-workers for fiber-optic parametric amplifiers. Hereby, the four-wave-mixing-induced parametric gain, which in non-phase-matched configurations would oscillate due to the varying phase relation among the waves, is enhanced by stopping the parametric amplification at each maximum gain point and by introducing at that point an additional phase shift that restores the phase relation between the waves to its initial condition. In the approach of Kim and co-workers, the restoring phase shift is introduced by inserting sections of highly dispersive fiber in the Kerr-nonlinear fiber, so that the parametric amplifier essentially becomes a composition of two different types of fiber. This is also a rather complex approach.

Summary of the invention

It is an object of embodiments of the present invention to provide efficient methods and systems for four-wave mixing, such as for example Raman-resonant four-wave-mixing and/or Kerr-induced four-wave-mixing. It is an advantage of at least some embodiments of the present invention that efficient four wave mixing, e.g. Raman-resonant four-wave-mixing and/or efficient Kerr-induced four-wave-mixing, can be obtained at wavelengths suitable for use in telecommunication.

It is an advantage of at least some embodiments of the present invention that efficient ring silicon Raman converters, efficient ring silicon parametric converters, and efficient ring silicon parametric amplifiers are provided as well as corresponding methods.

It is an advantage of at least some embodiments according to the present invention that methods and systems are provided that allow obtaining relatively high efficiencies using cavity-enhanced quasi-phase-matched Raman-resonant four-wave- mixing and/or using cavity-enhanced quasi-phase-matched Kerr-induced four-wave-mixing in a silicon resonator.

It is an advantage of embodiments according to the present invention that cavity- enhanced quasi-phase-matched Raman-resonant four-wave-mixing and cavity-enhanced quasi-phase-matched Kerr-induced four-wave-mixing in a silicon ring resonator can provide both a small effective phase mismatch and a high pump intensity, resulting in a boost of the Raman-resonant four-wave-mixing efficiency and br of the Kerr-induced four-wave-mixing efficiency. The latter is especially advantageous for those cases where phase-matched Kerr-induced four-wave-mixing performs badly, i.e. in the cases where the group velocity dispersion at the pump wavelength is large and/or the frequency difference between the pump and the signal is large.

It is an advantage of at least some embodiments according to the present invention that suitable conditions for quasi-phase-matched Raman-resonant four-wave-mixing and for quasi-phase-matched Kerr-induced four-wave-mixing are obtained in a uniform medium. More particularly it is an advantage that the obtained system and method is relatively simple and does e.g. not require active periodical adaptation of the Raman properties or the Kerr properties of a medium.

It is an advantage of at least some embodiments of the present invention that discretely-tunable silicon-based sources could be provided, resulting in a low-cost, compact, room-temperature light sources tunable in the near-and mid-infrared. Such devices are still scarce nowadays but highly desirable for many applications, ranging from telecommunications and industrial process control, to environmental monitoring and biomedical analysis.

It is an advantage of at least some embodiments according to the present invention that a high pump intensity in the Raman converter, in the parametric converter, and in the parametric amplifier does not need to be provided using a high-power pump, but that the pump is resonantly enhanced in the medium for obtaining a sufficiently high pump power. Alternatively or in addition thereto, the signal input power, and the idler power also can be resonantly enhanced, resulting in high intensities being achieved. In other words also the signal input power initially inputted does not need to be a high signal input power pump.

The above objective is accomplished by a method and device according to the present invention.

The present invention relates to a system for conversion or amplification using quasi-phase matched four-wave-mixing, the system comprising a first radiation source for providing a pump radiation beam, a second radiation source for providing a signal radiation beam, and a bent structure for receiving the pump radiation beam and the signal radiation beam, wherein a waveguiding portion of the bent structure is made of a uniform material, e.g. a uniform Raman-active or uniform Kerr-nonlinear material, and wherein the dimensions of the bent structure are selected taking into account the spatial variation of the susceptibility along the bent structure as experienced by radiation travelling along the bent structure for obtaining quasi-phase-matched four-wave-mixing, and an outcoupling waveguide for coupling out an idler radiation beam generated in the bent structure. It is an advantage of embodiments according to the present invention that quasi-phase matching conditions can be achieved.

The system for conversion or amplification may be a system for Raman conversion, parametric conversion or parametric amplification. It is an advantage of embodiments according to the present invention that the structure may be closed, allowing to establish cavity enhancement. In at least some embodiments according to the present invention, the closed structure may be a ring structure, such as for example a circular ring, an elliptical ring, a rectangular ring, etc. It is an advantage of at least some embodiments according to the present invention that a relatively simple system can be obtained allowing quasi-phase-matched four wave mixing, e.g. quasi-phase-matched Raman-resonant four-wave-mixing or quasi-phase-matched Kerr-induced four-wave-mixing. It is an advantage that no active alteration of the Raman properties of the structure and/or no active alteration of the Kerr properties of the structure are required for accurate operation.

The bent structure may be a ring structure.

The ring structure may be circular, and the radius R of the ring structure may be determined substantially inverse proportional with the linear phase mismatch for four-wave mixing. The radius R thereby may be defined as the distance from the center of the circle to the central axis in the ring waveguide. The linear phase mismatch thereby may be defined by the following equation Akijnear =-fl2(Aw)2 expressing the linear phase mismatch as function of the pump-signal frequency difference Ao.The radius R of the circular ring structure may be determined by the relation R = s,with s being a factor equal to +1 or -1, and Akiinear being linear phase mismatch for Raman-resonant four-wave-mixing or being the linear phase mismatch for Kerr-induced four-wave-mixing. The phase relation can be expressed as Zkijnear = 82 (Aw) fl4 (Aw)4 with Ao.

corresponding to the pump-signal frequency difference.

The system furthermore may be adapted to provide a pump radiation beam with wavenumber k and a signal radiation beam with wavenumber k and result in an idler radiation beam with wavenumber k, so that at least one of these beams is at ring resonance and as such at least one of these beams' wavenumbers yields, when multiplying with R, an integer number.

The system may comprise a heating and/or cooling means and a temperature controller for controlling the temperature so that at least one of the pump radiation, the signal radiation and the idler radiation is at ring resonance.

The uniform medium may be a Raman-active medium, and the process may be a quasi-phase-matched Raman-resonant four-wave-mixing process.

The uniform medium may be a Kerr-nonlinear material and the process may be a quasi-phase-matched Kerr-nonlinear four-wave-mixing-process.

It is an advantage of at least some embodiments according to the present invention that quasi-phase matched Raman-resonant four-wave-mixing and/or quasi-phase-matched Kerr-four-wave mixing in a uniform medium such as a silicon ring can be obtained since it does not require special techniques to periodically adapt the Raman characteristics of the medium and/or the Kerr characteristics of the medium.

The uniform medium may be a crystalline material. The uniform medium may be (100) grown silicon.

It is an advantage of embodiments according to the present invention that Raman-resonant four-wave-mixing and/or Kerr-induced four-wave mixing can be established for wavelengths suitable for e.g. telecommunication.

The (100) grown silicon may be a silicon on insulator waveguide.

It is an advantage of at least some embodiments according to the present invention that an easily manufacturable system can be used for obtaining Raman converters, parametric converters or parametric amplifiers.

A controller may be provided for tuning the system with respect to an output wavelength, an output power or an obtained bandwidth.

The system may be adapted for selecting a TE or TM output by selecting respectively a TE or TM input. It is an advantage of embodiments according to the present invention that the polarization of the output is the same as the polarization of the input of the Raman converter, of the parametric converter, and of the parametric amplifier, and thus that no additional polarization filter is required for obtaining a particular polarized output.

The present invention also relates to a method for obtaining conversion or amplification, using quasi-phase-matched four-wave-mixing, the method comprising receiving a pump radiation beam and a signal radiation beam in a bent structure, a waveguiding portion of the bent structure being made of a uniform Raman-active or uniform Kerr-nonlinear material and the dimensions of the bent structure being selected for obtaining quasi-phase-matched four-wave-mixing, obtaining an idler radiation beam by interaction of the pump radiation beam and the signal radiation beam and coupling out an idler radiation beam from the bent structure. Conversion or amplification may be any of Raman conversion, parametric conversion or parametric amplification. The four-wave-mixing process may be a Raman-resonant four-wave-mixing process or a Kerr-induced four-wave-mixing process.

The bent structure may be a ring structure, where the pump radiation beam and the signal radiation beam are guided in the ring structure, whereby the ring structure is circular and has a radius R determined substantially inverse proportional with a linear phase mismatch for quasi-phase-matched Raman-resonant four-wave-mixing or quasi-phase-matched Kerr-induced four-wave-mixing.

The pump radiation beam and the signal radiation beam may be guided in a circular ring structure having a radius fulfilling the relation R=s Akjinear with s being a factor equal to +1 or -1, and Akiinear being the linear phase mismatch for Raman-resonant four-wave-mixing or being the linear phase mismatch for Kerr-induced four-wave-mixing.

The method may comprise guiding the radiation beams in the ring structure and obtaining ring resonance for at least one of the different radiation beams.

The method may comprise adjusting the in-and/or outcoupling efficiency for adjusting the cavity-enhancement of the radiation beams inside the ring structure.

The method may comprise tuning the system with respect to an output wavelength, an output power or an obtained bandwidth.

The present invention also relates to a method for designing a converter or amplifier using quasi-phase-matched four-wave-mixing, the converter or amplifier using a pump radiation beam and a signal radiation beam, the method comprising selecting a bent structure or a bent structure suitable for quasi-phase-matched four-wave-mixing comprising selecting a uniform material for a waveguiding portion of the bent structure and selecting dimensions of the bent structure taking into account the spatial variation of the Raman susceptibility or the Kerr susceptibility along the structure as experienced by radiation travelling along the bent structure.

The present invention also relates to a computer program product for, when executed on a computer, performing a method and/or controlling a system as described above. The present invention also relates to a data carrier carrying such a computer program product or to the transmission of such a computer program product over a wide or local area network.

Particular and preferred aspects of the invention are set out in the accompanying independent and dependent claims. Features from the dependent claims may be combined with features of the independent claims and with features of other dependent claims as appropriate and not merely as explicitly set out in the claims.

These and other aspects of the invention will be apparent from and elucidated with reference to the embodiment(s) described hereinafter.

Brief description of the drawings

Fig. 1 illustrates a schematic representation of a Raman converter, a parametric converter or a parametric amplifier based on a (100) grown silicon ring, according to an embodiment of the present invention.

Fig. 2 illustrates (a) pump, (b) signal, (c) idler intensities in a Raman ring converter with the intensity values at a distance of 0mm (2.1mm) corresponding to A32(A42) in Fig. 1, as can be obtained in an embodiment according to the present invention.

The solid and dashed lines are valid for zero and non-zero losses, respectively.

FIG. 3 illustrates (a) pump, (b) signal, (c) idler intensities in a parametric ring converter with = 1.6 lim with the intensity values at a distance of Ohm (157 hm) ii corresponding to A32(A4) in Fig. 1, as can be obtained in an embodiment according to the present invention.

Fig. 4 illustrates (a) pump, (b) signal, (c) idler intensities in a parametric ring converter with = 1.8 Iim with the intensity values at a distance of Oiim (157 iim) corresponding to 1A312(1A412) in Fig. 1, as can be obtained in an embodiment according to the present invention.

FIG. 5 illustrates a computing system as can be used in embodiments of the present invention for performing a method of resonating or amplifying.

Detailed description of illustrative embodiments

The present invention will be described with respect to particular embodiments and with reference to certain drawings but the invention is not limited thereto but only by the claims. Furthermore, the terms first, second, third and the like in the description and in the claims, are used for distinguishing between similar elements and not necessarily for describing a sequence, either temporally, spatially, in ranking or in any other manner. It is to be understood that the terms so used are interchangeable under appropriate circumstances and that the embodiments of the invention described herein are capable of operation in other sequences than described or illustrated herein.

It is to be noticed that the term "comprising", used in the claims, should not be interpreted as being restricted to the means listed thereafter; it does not exclude other elements or steps. It is thus to be interpreted as specifying the presence of the stated features, integers, steps or components as referred to, but does not preclude the presence or addition of one or more other features, integers, steps or components, or groups thereof. Thus, the scope of the expression "a device comprising means A and B" should not be limited to devices consisting only of components A and B. It means that with respect to the present invention, the only relevant components of the device are A and B. Reference throughout this specification to "one embodiment" or "an embodiment" means that a particular feature, structure or characteristic described in connection with the embodiment is included in at least one embodiment of the present invention. Thus, appearances of the phrases "in one embodiment" or "in an embodiment" in various places throughout this specification are not necessarily all referring to the same embodiment, but may. Furthermore, the particular features, structures or characteristics may be combined in any suitable manner, as would be apparent to one of ordinary skill in the art from this disclosure, in one or more embodiments.

Furthermore, while some embodiments described herein include some but not other features included in other embodiments, combinations of features of different embodiments are meant to be within the scope of the invention, and form different embodiments, as would be understood by those in the art. For example, in the following claims, any of the claimed embodiments can be used in any combination.

In the description provided herein, numerous specific details are set forth. However, it is understood that embodiments of the invention may be practiced without these specific details. In other instances, well-known methods, structures and techniques have not been shown in detail in order not to obscure an understanding of this

description.

Where in embodiments of the present invention reference is made to a uniform Raman-active material, reference is made to a material or medium wherein the Raman susceptibility has a non-zero value.

Where in embodiments of the present invention reference is made to a uniform Kerr-nonlinear material or medium, reference is made to a material or medium wherein the Kerr susceptibility has a non-zero value.

Where in embodiments according to the present invention reference is made to a quasi-phase-matched process, such as for example Raman-resonant four-wave-mixing or Kerr-induced four-wave-mixing, reference is made to a process where the phase-mismatch-induced change in phase relation between the waves involved in the process is fully or partially compensated at several points along the propagation distance. When the value of the phase mismatch is small, or when the product of the phase mismatch and the propagation distance D has an absolute value smaller than pi (Ak* D < pr), the process is called phase-matched. A process is not referred to as phase-matched or quasi-phase-matched in case none of the above approaches apply.

In a first aspect, the present invention relates to methods and systems for performing conversion or amplification using quasi-phase-matched four-wave-mixing processes.

Such four-wave-mixing processes encompass Raman-resonant four-wave-mixing as well as Kerr-induced four-wave-mixing. The methods and systems for performing conversion or amplification may be methods and systems for performing Raman conversion, for performing parametric conversion or for performing parametric amplification. The system according to embodiments of the present invention comprises a first radiation source for providing a pump radiation beam and a second radiation source for providing a signal radiation beam. The system furthermore comprises a bent structure for receiving the pump radiation beam and the signal radiation beam, wherein a waveguide portion of the bent structure is made of uniform material. With uniform material there is meant that the material is uniform Raman-active and/or uniform Kerr-nonlinear material. Nevertheless, due to the curvature of the structure, radiation travelling through the bent structure will not see a uniform Raman susceptibility and/or Kerr susceptibility, but will see a variation therein. More particularly, as the material is uniform in a laboratory reference system fixed to the system, a variation in Raman susceptibility and/or Kerr susceptibility is present felt by the radiation travelling through the bent structure, depending on the polarization of the radiation and the orientation of the principle crystal axes of the silicon material. According to embodiments of the present invention, the dimensions of the bent structure are selected taking into account the spatial variation of the susceptibility along the bent structure as experienced by the radiation travelling along the bent structure so that quasi-phase-matched four-wave-mixing is obtained. The bent structure thus may be any structure allowing to curve the propagation direction of the radiation, such that a variation in susceptibility is felt. In advantageous embodiments, the bent structure may be a closed structure, such as for example a ring structure. Such ring structure may be a circular ring, an elliptical ring, a rectangular ring and the properties of the closed structure may be selected such that at least one of the radiation beams is enhanced. As indicated, the typical dimensions of the bent structure are selected so that quasi-phase-matching is obtained. The typical dimension, such as for example the average length of the waveguide part of the bent structure is in a range between 1 Iim and 10 cm. The structure may be made in a plurality of ways. It may be processed on a substrate, it may be fabricated using different techniques such as CMOS technology, electron beam lithography, photolithography, low-pressure chemical vapour deposition (LPCVD), plasma enhanced chemical vapour deposition (PECVD), thermal oxidation, reactive-ion etching and focused ion beam.

In some embodiments according to the present invention, a closed loop structure is used and the structure is adapted for enhancing at least one and advantageously a plurality or more advantageously all of the radiation beams in the closed loop structure. The system furthermore comprises an outcoupling waveguide for coupling out an idler radiation beam generated in the bent structure.

The material used may be any type of material providing a uniform material, i.e. a uniform Raman-active and/or uniform Kerr-nonlinear material. One example of a material that could be used is for example silicon. Other materials having the same crystal structure typically also can be used. Further examples of materials that can be used are silicon nitride (SiN) and crystalline materials belonging to the m3m point-symmetry group. In one particular example, the material may be silicon on insulator material, i.e. SOl.

As indicated above, the system comprises a first and second radiation sources for generating a pump radiation beam and a signal radiation beam. Such radiation sources typically may be lasers, although embodiments of the present invention are not limited thereto. The type of lasers selected may depend on the application. Some examples of lasers that could be used are semiconductor lasers, solid-state lasers, fiber lasers, gas lasers The required output power and wavelength of e.g. the pump laser depends on the output that one wants to obtain, e.g. of the output power one expect from the converter or amplifier.

In some embodiments, the system also may comprise a controller for controlling the system, e.g. the first radiation source and the second radiation source, and environmental conditions of the system, so as to be able to slightly tune the system.

In one embodiment, a heating and/or cooling means, e.g. heater and/or cooler, may be present for controlling the temperature of the system and in this way also properties of the system. In an advantageous embodiment, the controller may be adapted so that defined conditions for obtaining cavity-enhanced quasi-phase-matched four-wave-mixing, such as a well-controlled temperature, are maintained in the system. Such a controller may operate in an automated and/or automatic way.

The controller may be implementing predetermined rules or a predetermined algorithm for controlling the system, or it may be adapted for using a neural network for controlling the system. The controller may comprise a memory for storing data and a processor for performing the steps as required for controlling. The controller may be computer implemented. Whereas in the present aspect, the controller is described as a component of the system, in one aspect, the present invention also relates to a controller as such for performing a method of controlling a system for operating in quasi-phase-matched four-wave-mixing conditions.

In some embodiments, the system also may comprise a feedback system, providing parameters for checking whether the appropriate conditions are fulfilled and for reporting corresponding information. Such information may for example be transferred to the controller and used by the controller for adjusting or correcting the conditions.

In some embodiments, the resonator or amplifier is adapted for providing a given polarization mode. It thereby is an advantage that no filter means is required for obtaining the polarization mode, as the polarization mode is not altered by the structure.

By way of illustration and for the ease of explanation, embodiments of the present invention not being limited thereto, some features and aspects will now further be described with reference quasi-phase matching for Raman-resonant four-wave-mixing and for Kerr-induced four-wave-mixing in a circular ring structure. The latter provides, without embodiments of the present invention being bound by theory, a possible explanation of the features of the obtained structures.

Quasi-phase-matching for Raman-resonant four-wave-mixing and quasi-phase-matching for Kerr-induced four-wave-mixing is discussed in a (100) grown ring-shaped silicon-on-insulator (SOl) waveguide. A system according to such embodiments is illustrated by way of example in FIG. 1. The material used has a uniform Raman-active medium for the Raman-resonant four-wave-mixing process and a uniform Kerr-nonlinear medium for Kerr-induced four-wave-mixing process, with respect to a laboratory reference system coupled to the system. However, as TE-polarized pump, signal, and idler waves propagate along the ring, with their polarization always perpendicular to their local direction of propagation, the fourth rank Raman tensor and the fourth rank Kerr tensor, that are uniform in the laboratory frame, are position dependent in a reference frame defined by the direction of propagation and the polarization. This leads to a spatial periodic variation of the Raman susceptibility and of the Kerr susceptibility around the ring, and this variation can be used to design a ring with quasi-phase-matched Raman-resonant four-wave-mixing or a ring with quasi-phase-matched Kerr-induced four-wave-mixing. Taking into account that the variation of the Raman susceptibility and of the Kerr susceptibility as experienced by the TE-polarized fields in the (100) grown silicon ring is proportional to cos2 (20) with 8 defined as in Fig. 1, the condition for quasi-phase-matched Raman-resonant four- wave-mixing in the ring or the condition for quasi-phase-matched Kerr-induced four-wave-mixing in the ring is given by Akiinear = (1) where s = ±1 and R is the ring radius in case of a circular ring. Important to know is that even if this quasi-phase-matching condition is not exactly fulfilled, for example due to small deviations of R, the quasi-phase-matching efficiency will still be high.

We also remark that essentially this approach can also be used for any other Raman- active medium with the same crystal symmetry as silicon and for any other Kerr-nonlinear medium with the same crystal symmetry as silicon.

In addition to achieving quasi-phase-matching, we want to design the ring so that the all waves involved in the Raman-resonant four-wave-mixing process and in the Kerr-induced four-wave-mixing process are resonantly enhanced in the ring; this will lead to high intensities in the ring even for low intensity input waves. Complete resonant enhancement occurs when the values of k{1}R correspond to integer numbers. We remark that if k13R and kR have integer values and if in addition the quasi-phase-matching condition expressed above is fulfilled, then k1R will also correspond to an integer number. We also note that in most cases the free spectral range of the ring will be quite small, so that a small temperature tuning will suffice to guarantee that the pump and signal waves, and automatically also the idler wave, are at ring resonances. Using temperature tuning, one can also compensate for phase-shifting phenomena that might occur in the silicon medium, such as self-and cross-phase modulation.

By way of illustration, embodiments of the present invention not being limited thereto, the present invention now will be further illustrated with reference to particular embodiments, illustrating some features and advantages of embodiments according to the present invention. Without wishing to be bound by theory, a mathematical suggestion of how the principles of embodiments of the present invention could be explained also is provided.

In a first particular embodiment, reference is made to a quasi-phase-matched Raman-resonant four-wave-mixing system based on a silicon ring resonator. The system of the example shown thereby is not only adapted for quasi-phase-matched four-wave-mixing, but also illustrates that advantageously use can be made of cavity enhancement effects.

It is assumed that the Raman converter is fed by a TE-polarized pump input and a TE-polarized signal input, with a frequency difference corresponding to the exact Raman resonance: w1 =1.22x10'5 rad/s (2 = 1.55 iim), o5 =1.12x10'5 rad/s (2 = 1.686 urn). This leads to a generated idler wave with frequency o = 1.32x10'5 rad/s (A = 1.434 1rn). The system may have a structure as illustrated in FIG. 1. Such a structure may for example be based on both the ring and the channel being silicon nanowires with an oblong core so that TM fields spontaneously generated in the ring are fully coupled out after each roundtrip, and cannot build up in the ring. Without restricting the general validity of the results, focus is made on quasi-continuous-wave operation.

Assuming that k/l 1 (for k,l=p,s,i) and that Kerr-induced four-wave mixing in silicon is negligible at the considered working point of exact Rarnan resonance, the equations expressing the steady-state spatial variation of the slowly-varying pump, signal and idler field amplitudes A(C),A(C),A1(C) in the SOl ring Rarnan converter are given by A (Jig 2 _ä--=__?__E_p(8)[AjL A Ap -2fA, (2) =-p(O) [A2 A (3) = _-Lp(o) [A2 A1 +A;A:el j_ A1, (4) where =RG, p(G)=4cos2(26) and A{1} is normalized such that A{PSII corresponds to intensity. The terms containing express the Rarnan-resonant four-wave-mixing interaction, and the terms proportional to A{PS}A{SP} and A{1} A{1} describe two accompanying Rarnan processes. The coefficient is the Rarnan gain constant of silicon, equal to 20x109 crn/W, and describe the optical losses in the SOl waveguide. The latter receive contributions from linear propagation losses, two-photon absorption (TPA) and TPA-induced free carrier absorption. At the entry point of light into the ring from the channel one has = 0 (see Fig. 1). Coupling from the channel to the ring is described in the usual way, (AJ2(aJ A1 LA13JLiK1 a1JA14exp(ik1L)J' with j=p,s,i, with the positions of the fields (1)-(4) indicated in FIG. 1, and with L=2rR. One can consider real-valued coupling constants cr7,ic1 that satisfy the relation a2 + K12 = 1.

One now can solve numerically equations (2) to (5) for the Raman converter example introduced in the previous paragraph, with I = 4x101° W/m2, = 1x108 W/m2, Akiinear = -122 cm' (corresponding to a dispersion parameter of -1000 ps/(nm*km) at 2). waveguide modal area A = 0.09 tm2, ic = iç = = 0.22 and 7{p,s,a} =0. When implementing the value for Akijnear in the quasi-phase-matching condition with s = -1, one obtains that quasi-phase-matching is obtained for a ring radius R=328 Iim, which corresponds to a ring circumference of 2.1 mm. The solid lines in FIG. 2 parts (a)-(c) show the steady-state distributions along the ring of the pump, signal and idler intensities, respectively. Using equation (5), one finds from FIG. 2(c) that I = 2.4x109 W/m2. The signal-to-idler conversion efficiency thus is larger than unity. For comparison, a one-dimensional perfectly phase-matched Raman converter with equal length would yield I' 9.4x103 W/m2. The enhancement factor i/i for the ring converter with no losses thus equals 0.3x106, which is very large.

Further considerations are made, whereby losses are taken into account. The dashed curves in Fig. 2 are the simulation results including a linear waveguide loss a=1 dB/cm, a two-photon absorption coefficient /3= 0.5x10" m/W, a free carrier absorption efficiency 0= 6x10'°, and an effective free carrier lifetime 1eff = 0.3 ns.

The enhancement factor i[/i for the ring converter with losses included equals 1.8x104, which is still a large value.

In conclusion, the idler output intensity of a cavity-enhanced quasi-phase-matched silicon ring Raman converter can easily become i04 times larger than that of a one-dimensional perfectly phase-matched Raman converter of equal length. Taking into account the quadratic dependence of the latter's output on the pump input, this also implies that the ring Raman converter needs a 102 times smaller pump input intensity than the one-dimensional Raman converter to produce the same idler output. Furthermore, signal-to-idler conversion efficiencies larger than unity can be obtained using relatively low pump input intensities. These improvements in conversion performance substantially expand the practical applicability of Raman converters in different application domains.

In a second particular embodiment, reference is made to a quasi-phase-matched Kerr-induced four-wave-mixing system based on a silicon ring resonator. The system of the example shown thereby is not only adapted for quasi-phase-matched four-wave-mixing, but also illustrates that advantageously use can be made of cavity enhancement effects. As mentioned above, the condition for quasiphase-matched Kerr-induced four-wave-mixing (FWM) in the ring is given by Akiinear =s-, (1) where s = ±1 and R is the ring radius in case of a circular ring. Taking into account that Akijear -/2 one finds that, for a given value of R, this quasi-phase-matching condition can be fulfilled for different combinations of /2 and Ao. Thus, for a ring resonator with a ring radius R and with a properly designed, non-constant dispersion profile, one can convert via quasi-phase-matched Kerr-induced FWM a fixed signal frequency a to various idler frequencies o spread over the near-and mid-infrared range, by changing only the pump frequency w. Finally, if R is chosen to be small to keep the device compact, one finds that L\W can be large also if /32 is large.

As also mentioned above, the quasi-phase-matching condition expressed above complies with the condition for having the pump field, the signal field and the idler field at ring resonances. The fact that efficient quasi-phase-matching can be combined with cavity enhancement for all three fields in the ring resonator is an important advantage, since for phase-matched Kerr-induced FWM one can obtain cavity enhancement for all three fields only if the pump wavelength is close to the point of zero GVD. Otherwise one has phase-matched Kerr-induced FWM in a doubly-resonant condition rather than in a triply-resonant condition. It also can be remarked that, for quasi-phase-matched Kerr-induced FWM based on Kerr susceptibility variations as is considered in this embodiment, the recovery of the phase relation between the waves after each period of the susceptibility variation is not as complete as when highly-dispersive elements are introduced. This is because the amplitude of the varying part of the Kerr susceptibility is relatively small compared to the amplitude of the constant term of the Kerr susceptibility. Therefore, this quasi-phase- matching technique will in itself be considerably less efficient than the quasi-phase-matching using highly dispersive elements and the phase matching technique used in other structures. However, since it can be combined with cavity enhancement for all three fields also if the GVD at the pump wavelength has a large absolute value and/or the frequency difference between the pump and signal is large, the quasi-phase-matching approach based on Kerr susceptibility variations can in those circumstances establish Kerr-induced FWM efficiencies that are relatively high compared to the efficiencies achieved with phase-matched Kerr-induced FWM.

As an example, one can consider a parametric converter that relies on cavity-enhanced quasi-phase-matched Kerr-induced FWM in a SOl ring as shown by way of example in FIG. 1 and that is fed by a TE-polarized pump input and a TE-polarized signal input. Without restricting the general validity of the results, focus is made on (quasi-)continuous-wave operation. Assuming that k/l 1 (for k,l=p,s,i), the equations expressing the steady-state spatial variation of the slowly-varying pump, signal and idler field amplitudes A(c),A(c).A1(fl in the parametric converter are given by = iy(e)[A 2 2A 2 2A1 2 A + 2iy(6)AAA1e" -FA, (6) = ir(e)[A + 2A + 2Aj21As +i7(6)AAe"' -FA, (7) = j(6) [A12 + 2A13 2 2As2 A1 + ir(e)AA;e1M1rC -F1A1. (8) where = RO, = n (0.88 + 0.l2cos2 (26)) (U)/c) is the effective nonlinearity, n is the Kerr-nonlinear refractive index along the [011] direction, and A{J)SI} is normalized such that A{?7SiI corresponds to intensity. Since both n2 is linearly proportional to the Kerr susceptibility, one obtains that n2 and along with it y feature the same spatial variation along the ring as the Kerr susceptibility. The first terms containing the square brackets at the right hand side of Eqs. (6)-(8) correspond to Kerr-induced self-and cross-phase modulation, and the terms containing e'"express the actual Kerr-induced FWM interaction. The coefficients represent the optical losses in the SOl waveguide. In general, the latter receive contributions from linear propagation losses, two-photon absorption (TPA) and TPA-induced free carrier absorption. At the entry point of light into the ring from the channel we one has e=O(see FIG. 1). Coupling from the channel to the ring is described in the usual way, (AJ2(aJ iK. A11 LA13 J LiK1 aJ A14exp(ik1L)J' with j=p,s,i, with the positions of the fields (1)-(4) indicated in FIG. 1, and with L=2rR. One can consider real-valued coupling constants cr7,ic1 that satisfy the relation a12 + K12 = 1.

One now can numerically solve Eqs. (6)-(9) for a parametric converter with the following parameter values: = 1.6 Iim, 2 = 1.3 lim, 2. = 2.08 Iim, Akiinear = 1606 cm' (corresponding to a dispersion parameter of 1600 ps/(nm*km) at 2). n2° = 6.5x 1018 m2/w, I = 6x10'° W/m2, I = 1x108 W/m2, I = 0 W/m2, waveguide modal area A= 0.09 pm2, linear waveguide loss a= 0.9 dB/cm, two-photon absorption coefficient /3=O.7x10" m/W, free carrier absorption efficiency 0= 6x10'°, effective free carrier lifetime reff = 0.1 ns, ic = 0.14, ic = 0.10, and i = 0.17. When implementing the value for Akijnear in the quasi-phase-matching condition with s=+1, one obtains that quasi-phase-matching is obtained for a ring radius R = 25 Iim, which corresponds to a ring circumference of 157 lim. FIG. 3 parts (a)-(c) show the steady-state distributions along the ring of the pump, signal and idler intensities, respectively. Using Eq. (9) one can derive from FIG. 3 part (c) that = 5x104 W/m2. This corresponds to a signal-to-idler conversion efficiency of -33 dB.

Taking into account that this conversion efficiency is of the same order of magnitude as the conversion efficiencies for phase-matched Kerr-induced FWM in a silicon ring with the same dispersion parameter but with much smaller pump-signal frequency differences, one finds that this quasi-phase-matched cavity-enhancement converter has a relatively good performance.

To demonstrate that also efficiencies higher than -33 dB could be reached, one now can consider a parametric converter pumped at a pump wavelength where the nonlinear refractive index is larger than in the previous case. More specifically, we consider a parametric converter with the following parameter values: 2 = 1.8 im, = 1.43 lim, 2. = 2.43 lim, Ak1. = 1606 cm' (corresponding to a dispersion parameter of 1600 ps/(nm*km) at 2 as in the previous case), n2° = 12x 1018 m2/vv, two-photon absorption coefficient /3=0.5x10" m/W, and free carrier absorption efficiency 0= (1.8/1.55)2x6x10'°. For all other parameters, the same values are taken as in the previous case. FIG. 4 parts (a)-(c) show the steady-state distributions along the ring of the pump, signal and idler intensities, respectively, as obtained by numerically solving Eqs. (6)-(8) for this converter. Using Eq. (9) one can derive from FIG. 4 part (c) that I((ff = 1.2x105 W/m2. This corresponds to a signal-to-idler conversion efficiency of -29 dB.

As a general conclusion, one can say that especially in those cases where phase-matched Kerr-induced FWM performs poorly, i.e., in the cases where the GVD at the pump wavelength is large and/or the frequency difference between pump and signal is large, one can obtain relatively high efficiencies using cavity-enhanced quasi-phase-matched Kerr-induced FWM in a silicon resonator.

Whereas the above aspect has been mainly described with reference to system features, as indicated it also relates to a method for obtaining conversion or amplification, using quasi-phase-matched four-wave-mixing. Such a method comprises receiving a pump radiation beam and a signal radiation beam in a bent structure, a waveguiding portion of the bent structure being made of a uniform Raman-active or uniform Kerr-nonlinear material and the dimensions of the bent structure being selected for obtaining quasi-phase-matched four-wave-mixing. The method also comprises obtaining an idler radiation beam by interaction of the pump radiation beam and the signal radiation beam using at least one quasi-phase-matched four-wave-mixing process such as for example a Raman-resonant or Kerr-induced four-wave-mixing process. The method furthermore encloses coupling out an idler radiation beam from the bent structure. Other or more detailed method steps may be present, expressing the functionality of components of the system as described above.

In one aspect, the present invention also relates to a method for designing a converter or amplifier using quasi-phase-matched four-wave-mixing. The converter or amplifier thereby may be using a pump radiation beam and a signal radiation beam.

The method for designing comprises selecting a bent structure or a bent structure suitable for quasi-phase-matched four-wave-mixing, comprising selecting a uniform material for a waveguiding portion of the bent structure, and selecting dimensions of the bent structure taking into account the spatial variation of the Raman susceptibility or the Kerr susceptibility along the structure as experienced by radiation travelling along the bent structure. The dimensions of the bent structure are selected such that quasi-phase-matched four-wave-mixing is obtained. The method for designing furthermore may be adapted so that the structure provides cavity enhancement for at least one of the radiation beams that will travel in the system, i.e. for which the system is designed, preferably more or all of the radiation beams are cavity enhanced.

In a further aspect, the above described methods for designing or controlling a system for resonating or amplifying using quasi-phase-matched four-wave-mixing or e.g. the controller may be at least partly implemented in a processing system 500 such as shown in Fig. 5. Fig. 5 shows one configuration of processing system 500 that includes at least one programmable processor 503 coupled to a memory subsystem 505 that includes at least one form of memory, e.g., RAM, ROM, and so forth. It is to be noted that the processor 503 or processors may be a general purpose, or a special purpose processor, and may be for inclusion in a device, e.g., a chip that has other components that perform other functions. Thus, one or more aspects of the present invention can be implemented in digital electronic circuitry, or in computer hardware, firmware, software, or in combinations of them. For example, the determination of test pulse properties may be a computer implemented step. The processing system may include a storage subsystem 507 that has at least one disk drive and/or CD-ROM drive and/or DVD drive. In some implementations, a display system, a keyboard, and a pointing device may be included as part of a user interface subsystem 509 to provide for a user to manually input information. Ports for inputting and outputting data also may be included. More elements such as network connections, interfaces to various devices, and so forth, may be included, but are not illustrated in Fig. 5. The memory of the memory subsystem 505 may at some time hold part or all (in either case shown as 501) of a set of instructions that when executed on the processing system 500 implement the steps of the method embodiments described herein. A bus 513 may be provided for connecting the components. Thus, while a processing system 500 such as shown in Fig. 5 is prior art, a system that includes the instructions to implement aspects of the methods for controlling resonating and/or converting and/or amplifying using a quasi-phase matched four-wave-mixing process is not prior art, and therefore Fig. 5 is not labeled as prior art.

The present invention also includes a computer program product which provides the functionality of any of the methods according to the present invention when executed on a computing device. Such computer program product can be tangibly embodied in a carrier medium carrying machine-readable code for execution by a programmable processor. The present invention thus relates to a carrier medium carrying a computer program product that, when executed on computing means, provides instructions for executing any of the methods as described above. The term "carrier medium" refers to any medium that participates in providing instructions to a processor for execution. Such a medium may take many forms, including but not limited to, non-volatile media, and transmission media. Non-volatile media includes, for example, optical or magnetic disks, such as a storage device which is part of mass storage. Common forms of computer readable media include, a CD-ROM, a DVD, a flexible disk or floppy disk, a tape, a memory chip or cartridge or any other medium from which a computer can read. Various forms of computer readable media may be involved in carrying one or more sequences of one or more instructions to a processor for execution. The computer program product can also be transmitted via a carrier wave in a network, such as a LAN, a WAN or the Internet. Transmission media can take the form of acoustic or light waves, such as those generated during radio wave and infrared data communications. Transmission media include coaxial cables, copper wire and fibre optics, including the wires that comprise a bus within a computer.

It is to be understood that although preferred embodiments, specific constructions and configurations, as well as materials, have been discussed herein for devices according to the present invention, various changes or modifications in form and detail may be made without departing from the scope and spirit of this invention.

For example, any formulas given above are merely representative of procedures that may be used. Functionality may be added or deleted from the block diagrams and operations may be interchanged among functional blocks. Steps may be added or deleted to methods described within the scope of the present invention.

Claims

Claims 1.-A system for conversion or amplification using quasi-phase matched four-wave-mixing, the system comprising -a first radiation source for providing a pump radiation beam, -a second radiation source for providing a signal radiation beam, and -a bent structure for receiving the pump radiation beam and the signal radiation beam, wherein a waveguiding portion of the bent structure is made of a uniform Raman-active or uniform Kerr-nonlinear material and wherein the dimensions of the bent structure are selected taking into account the spatial variation of the susceptibility along the bent structure as experienced by radiation travelling along the bent structure for obtaining quasi-phase-matched four-wave-mixing -an outcoupling waveguide for coupling out an idler radiation beam generated in the bent structure.
2. A system according to claim 1, wherein the bent structure is a ring structure.
3. A system according to claim 2, wherein the ring structure is circular, and where the radius R of the ring structure is determined substantially inverse proportional with the linear phase mismatch for four-wave-mixing.
4. A system according to claim 3, wherein the radius R of the circular ring structure is determined by the relation R=s with s being a factor equal to +1 or -1 and Akiinear being the linear phase mismatch for Raman-resonant four-wave-mixing or being the linear phase mismatch for Kerr-induced four-wave-mixing.
5. A system according to any of the previous claims, the system furthermore being adapted to provide a pump radiation beam with wavenumber k and a signal radiation beam with wavenumber k and result in an idler radiation beam with wavenumber k1, so that at least one of these beams is at ring resonance and as such at least one of these beams' wavenumbers yields, when multiplying with R, an integer number.
6. A system according to claim 4, wherein the system comprises a heating and/or cooling means and a temperature controller for controlling the temperature so that at least one of the pump radiation, the signal radiation and the idler radiation is at ring resonance.
7. A system according to any of the previous claims, wherein the uniform medium is a Raman-active medium, and wherein the process is a quasi-phase-matched Raman-resonant four-wave-mixing process.
8. A system according to any of the previous claims, wherein the uniform medium is a Kerr-nonlinear material ad wherein the process is a quasi-phase-matched Kerr-induced four-wave-mixing process.
9. A system according to any of the previous claims, wherein the uniform medium is a crystalline material.
10. A system according to any of the previous claims, wherein the uniform medium is (100) grown silicon.
11. A system according to claim 9, wherein the (100) grown silicon is a silicon on insulator waveguide.
12. A system according to any of the previous claims, wherein furthermore a controller is provided for tuning the system with respect to an output wavelength, an output power or an obtained bandwidth.
13. A system according to any of the previous claims, wherein the system is adapted for selecting a TE or TM output by selecting respectively a TE or TM input.
14. A method for obtaining conversion or amplification, using quasi-phase-matched four-wave-mixing, the method comprising -receiving a pump radiation beam and a signal radiation beam in a bent structure, a waveguiding portion of the bent structure being made of a uniform Raman-active or uniform Kerr-nonlinear material and the dimensions of the bent structure being selected for obtaining quasi-phase-matched four-wave-mixing, -obtaining an idler radiation beam by interaction of the pump radiation beam and the signal radiation beam -coupling out an idler radiation beam from the bent structure.
15. A method according to claim 14, wherein the bent structure is a ring structure, where the pump radiation beam and the signal radiation beam are guided in the ring structure, whereby the ring structure is circular and has a radius R determined substantially inverse proportional with a linear phase mismatch for quasi-phase-matched Raman-resonant four-wave-mixing or quasi-phase-matched Kerr-induced four-wave-mixing.
16. A method according to claim 15, wherein the pump radiation beam and the signal radiation beam are guided in a circular ring structure having a radius fulfilling the relation R=s with s being a factor equal to +1 or -1, Akiinear being the linear phase mismatch for Raman-resonant four-wave-mixing or being the linear phase mismatch for Kerr-induced four-wave-mixing.
17. A method according to any of claims 14 to 16, the method comprising guiding the radiation beams in the ring structure and obtaining ring resonance for at least one of the different radiation beams.
18. A method according to any of claims 14 to 17, wherein the method comprises adjusting the in-and/or outcoupling efficiency for adjusting the cavity-enhancement of the radiation beams inside the ring structure.
19. A method according to any of claims 14 to 18, the method comprising tuning the system with respect to an output wavelength, an output power or an obtained bandwidth.
20. A method for designing a converter or amplifier using quasi-phase-matched four-wave-mixing, the converter or amplifier using a pump radiation beam and a signal radiation beam, the method comprising selecting a bent structure or a bent structure suitable for quasi-phase-matched four-wave-mixing comprising selecting a uniform Raman-active material or a uniform Kerr-nonlinear material for a waveguiding portion of the bent structure and selecting dimensions of the bent structure taking into account the spatial variation of the Raman susceptibility or the Kerr susceptibility along the structure as experienced by radiation travelling along the bent structure.