Patent Application
20180252985
The invention relates to a method and an apparatus for generating a frequency comb. Especially the invention relates to a generation of an optical frequency comb using a laser beam introduced to an optical manipulator.
An optical frequency comb (OFC), that is, coherent broadband light that has a spectrum consisting of many equidistant discrete lines, has become a valuable tool in many research areas, such as time and frequency metrology and molecular spectroscopy. Mode-locking of lasers is the most common method used to generate OFC. Other methods include phase-modulated Fabry-Perot cavities, and optical microresonators. Octave spanning frequency comb generation and mode-locking have recently been demonstrated with such microresonators.
The mode-locked laser example produces in time domain short (femtosecond) laser pulses with a certain repetition frequency frep. The spectrum of the laser is a frequency comb, where the mode spacing is exactly frep, as can be seen in prior art
In the time domain of the left portion of
The microresonator comb is also referred to as Kerr comb, as the comb formation is based on an optical Kerr effect, i.e., third order optical nonlinearity. (Third order nonlinearity=cubic nonlinearity=Kerr nonlinearity=χ(3) nonlinearity). One example of the microresonator comb is described in a publication of EP1988425B1.
The principle of Kerr comb formation in a microresonator is presented in a prior art
The four-wave mixing is one of the many effects that originate from Kerr nonlinearity. The comb formation process typically starts by so-called degenerate FWM, where two pump laser photons are converted to a pair of new photons. This leads to a symmetric sideband generation around the initial pump laser frequency (Process (1) in prior art
The strength of the Kerr nonlinearity (and hence the strength of the FWM process) is proportional to IL×n2, where IL is the laser intensity in the resonator (units W/m2), and n2 is the so-called nonlinear refractive index (a.k.a. Kerr coefficient; units m2/W). (The “total” refractive index is n=n0+IL×n2, where no is the linear refractive index of the material). An OFC can be generated only if IL×n2 is high enough. Just like no, the nonlinear refractive index is a material property and cannot be varied. The value of n2 is relatively small for most materials, which means that IL needs to be very high in order to obtain OFC generation. High enough intensity can be obtained in a high-quality microresonator, which confines the laser field in a very small mode volume.
The non-degenerate FWM can be understood qualitatively as follows: As two laser beams at frequencies ν1 and ν2 propagate in the material, they produce, through the Kerr effect, a nonlinear refractive index, which oscillates at difference frequency Δν=|ν1−ν2|. This oscillating refractive index modulates the phases of the laser fields, leading to new sidebands at frequencies ν1±Δν and ν2±Δν.
The mode spacing of the comb is (roughly) determined by the resonator size.
The frequency difference between the adjacent resonance modes of the microresonator is Δν=c/nL, where c is the speed of light, and n˜n0 is the refractive index of the resonator material. L is the round-trip length of the resonator. For a silica microresonator, a typical optical circumference is nL=1.5×1 mm, leading to a microresonator mode spacing of Δν˜(3×108 m/s)/1.5 mm˜200 GHz. The mode spacing of the frequency comb is approximately the same as the mode spacing of the microresonator.
Dispersion, the variation of refractive index no with wavelength, has an effect on comb formation. Due to the dispersion, the frequency spacing Δν of the microresonator modes is not precisely constant but changes with wavelength. This can potentially lead to a non-equidistant OFC, and will ultimately limit the optical bandwidth of the comb because the comb modes generated by FWM do not anymore overlap with the resonator modes. However, self-phase modulation (SPM) and cross-phase modulation (XPM), which are effects originating from Kerr nonlinearity, can partly compensate for the microresonator dispersion. As a result, generation of an equidistant broadband OFC is possible. Note that as Kerr nonlinearity (n2) is a material property, the dispersion compensation (and hence efficient Kerr comb generation) is only possible at certain wavelengths, depending on the microresonator material used in the experiments.
In the self-phase modulation the phase of a light wave is modified by the wave itself. This originates from the Kerr effect: The refractive index of the material changes by Δn=IL×n2, where IL is again the intensity of the light field. The change in the refractive index leads to a phase change, as the wavelength in the material is λ0/n=λ0/(n0+Δn), with λ0 being the vacuum wavelength.
Cross-phase modulation (XPM) is essentially the same as SPM, but now the phase of light wave A is modified by the intensity of light wave B (and vice versa). Again, this occurs due to Kerr nonlinearity, which is described by the nonlinear refractive index n2.
There are however some disadvantages relating to the known prior art, such as that the Kerr comb generation is generally only possible in the microresonators, whereupon the mode spacing is quite large, which is clear drawback, because especially in gas analysis small mode spacing is needed. In addition, laser intensity required for OFC generation is very high in most materials used for Kerr comb generation. Furthermore the comb mode spacing according to the Kerr com generation cannot be tailored or changed. In addition the Kerr comb generation, as well as OFC generation by mode-locked lasers, is also very difficult or even impossible in mid-infrared wavelengths.
An object of the invention is to alleviate and eliminate the problems relating to the known prior art. Especially the object of the invention is to provide an apparatus and method for frequency comb generation by laser intensity significantly smaller than in known systems. In addition, one object of the invention is to provide a method and apparatus, where nonlinearity can be tailored and the comb mode spacing can be changed or controlled. Also an object is to providing the optical frequency comb generation with significantly smaller laser intensities than in prior art, as well as to generate mid-infrared wavelengths.
The object of the invention can be achieved by the features of independent claims.
The invention relates to an apparatus for frequency comb generation using an optical manipulator according to claim 1. In addition the invention relates to a method for frequency comb generation using an optical manipulator according to claim 22.
According to an embodiment of the invention a frequency comb is generated by using an optical manipulator and a component comprising second order nonlinearities. The optical manipulator is advantageously configured to introduce a laser beam and/or its derivatives in a repetitive (e.g. resonating) manner to the component. The component is configured to interact with said laser beam and/or derivatives of said laser beam and thereby generate frequencies for the frequency comb. The component comprises advantageously optical nonlinear crystal material having second order nonlinearity. The component material may be for example quasi-phase-matched or birefringent phase matched optical nonlinear crystal material. The derivatives of said laser beam are e.g. beams at harmonic frequencies (such as second harmonic frequency) of said laser beam or frequencies of the already generated comb which are reintroduced to the component.
In the invention the third order nonlinearity (Kerr effect) is mimicked by a process called cascaded second order nonlinearity, which is also known as a cascaded quadratic nonlinearity (CQN) or cascaded χ(2) nonlinearity or χ(2):χ(2)-nonlinearity. The second order nonlinear effects occurs in materials that lack inversion symmetry—materials that possess large second order nonlinearity are often referred to as nonlinear crystals.
According to an embodiment the component is configured to apply cascading quadratic nonlinearity process, to which said frequency comb generation is based on. According to an embodiment, the component may have, or is arranged to apply, a phase matching deviated slightly from zero (Δk≠0) in order to perform said frequency comb generation by cascaded quadratic nonlinearity. However, according to an exemplary embodiment the second order nonlinearities at phase matching (Δk=0) may also be enough to provide the frequency comb generation. The invention using the component with the second order nonlinear effects offers huge advantage over the known prior art, such as Kerr nonlinearity, namely the effective third order nonlinearity arising from the cascaded quadratic nonlinearity can be tailored by adjusting Δk, while the prior art “true” Kerr nonlinearity is a fixed material parameter.
The component comprises advantageously quasi-phase-matched optical nonlinear crystal material, such as periodically poled lithium niobate (PPLN), periodically poled lithium tantalite (PPLT), periodically poled potassium titanyl phosphate (PPKTP), lithium niobate doped with metal ions, such as Mg (MgO:PPLN). Alternatively, or in addition to, the component may also comprise birefringently phase-matched nonlinear crystals, such as beta barium borate (BBO), which are suitable for applying cascading quadratic nonlinearity process.
Advantageously the apparatus is configured to produce the frequency comb in the mid-infrared region. This can be achieved directly by using a mid-infrared pump laser for the cascaded quadratic nonlinear effect, or indirectly by using an additional nonlinear crystal material with second order nonlinearity to transfer a comb from e.g. near-infrared to mid-infrared, as is described in this document elsewhere (e.g.
According to an embodiment the optical manipulator may comprise an optical resonator, optical fiber resonator or loop, or microresonator or monolithic or other solid crystal resonator.
According to an embodiment the component is arranged to function as an optical waveguide. In the embodiment the optical manipulator may comprise mirrors, which are arranged around the component, whereupon the mirrors are configured to reflect laser beam and/or its derivatives in a repetitive manner to the component. According to an example the ends of the component are provided with reflective material, such as mirrors, in order to reflect said laser beam wavelength and/or its derivatives in a repetitive manner within said component functioning as a waveguide.
In addition, according to an embodiment, interface materials at the interface of the component and/or the surrounding medium may be selected so to perform a total internal reflection of the laser beam and/or its derivatives and thereby generating the resonator. Still in addition an angle of incidence of the laser beam and/or its derivatives in relation to the inner surface of the component (so inside the component) may be arranged to be as a critical angle for the total internal reflection so that said total internal reflection happens and thus reintroducing the laser beam and/or its derivatives in a repetitive or resonating manner back to the component.
The repetitive manner means that the laser beam and/or its derivatives constructively interferes with itself, beam and/or its derivatives within said component (or optical manipulator) after a round trip thereby generating a resonator of said component.
According to an embodiment the optical manipulator may comprise an optical microresonator, wherein the component material is arranged to interact with the laser beam and/or derivatives of the laser beam and thereby generate frequencies for the frequency comb. The microresonator may be fabricated for example of a second-order nonlinear quasi-phase-matched or birefringent optical crystal, as is discussed elsewhere in this document.
According to an embodiment the optical manipulator comprises at least one first loop, such as an optical fiber resonator loop. The loop may receive the laser beam and/or its derivatives and additionally introduce the received laser beam and/or its derivatives back to the optical manipulator and to said component, thereby forming the resonator. It should be noted that according to an embodiment at least two first loops may be used. When the length of the second first loop is different than the length of the first first loop, an additional comb with a different mode spacing is generated.
Because the mode spacing of the comb is (roughly) determined by the resonator size, the length of the resonator (such as loop or fiber resonator or other structure, where the beam and/or its derivatives travels a certain path, which length can be changed) determines the comb mode spacing Thus the choosing of the length of the resonator, such as the loop, offers easy, inexpensive and effective way to determine the comb mode spacing, and can be chosen according to an intended application of the comb. In addition in this case no mirrors are even needed, as the fiber loop forms the resonator. In contrast to microresonator combs known from prior art, the comb mode spacing according to the current invention can be designed for almost any application. Also small mode spacing of the order of 50 to 500 MHz can be easily obtained, unlike with the prior art Kerr combs, for example. The small mode spacing is needed, e.g. in gas analysis applications.
According to an embodiment the optical manipulator may also comprise at least one sample loop, such as an optical fiber resonator loop. The sample loop may receive the laser beam and/or its derivatives and introduce the received laser beam and/or its derivatives to interact with a sample medium, and thereby form an interacted laser beam derivative, comprising e.g. absorption spectrum. After interacting the sample loop advantageously introduces said interacted laser beam derivative back to the optical manipulator and to said component. The sample medium may be e.g. gas or liquid medium. The sample loop or apparatus may comprise a cavity, to which the sample medium can be led, for example, or portion of the covering material of the loop can be removed in order to arrange the sample medium to be optically contact with the portion of the sample loop and thereby allowing the laser beam and/or its derivatives interact with the sample medium.
It is to be noted that the sample loop can be used for introducing the beam and/or its derivative to interact with the sample medium, even if none of the first loop is used so the use of the first loop is not mandatory. In addition it is to be noted that the structure and properties of the sample loop are advantageously similar than with the first loop, but the sample loop is only modified so that it is able to introduce the beam and/or its derivative to interact with the sample medium.
Spectroscopy of a gas or liquid medium can be done inside or outside of the apparatus. The spectroscopy may be implemented by using e.g. two slightly different combs. The combs may be produced simultaneously by the apparatus thanks to the sample loop or a second first loop. According to an example the length of the sample loop is different than the length of any of the first loop, but may also be same.
According to an embodiment the component may comprise at least two portions, wherein the first portion comprises different structural properties than the second portion. The structural properties relate especially to the property of the second order nonlinearity or phase matching (or both), such as which wavelengths are phase matched and how much phase matching is deviated from zero. By this the first portion is configured to generate the frequency comb with frequencies differing from the frequency comb generated by the second portion, whereupon two different frequency combs can be formed.
Still in addition, the apparatus may also comprise an additional optical devices arranged in connection with the apparatus, such as an optical amplifier configured to amplify the intensity of at least one wavelength transferred by at least one loop or other portion of the apparatus. Alternatively or additionally the apparatus may also comprise an optical filter for filtering desired wavelengths, or amplitude or phase modulator, such as electro-optic modulator for modulating desired wavelengths, as an example.
As discussed elsewhere in this document, the comb mode spacing may be easily changed or controlled by changing the length of the resonator (such as a fiber loop or dimensions of other structure used as a resonator or part of a resonator, for example). Alternatively, or additionally also an electro-optic modulator can be used, at least for fine control of the mode spacing. The length of the resonator can be changed e.g. by mechanical stretching or thermal expansion. In addition the comb mode spacing can be changed or controlled by applying an electric field over the component and thereby changing the refractive index of said component.
As an example, the apparatus can be designed according to an embodiment so that it nominally produces a mode spacing of 100 MHz, for example, when a fine tuning of ˜1 MHz can be achieved e.g. by slightly changing the length of the resonator (such as a fiber loop). It should be noted that these values or ranges are only example and the invention or the scope of the invention is not limited only to those.
The apparatus advantageously comprises also an input for receiving and inputting the laser beam from a laser source, and additionally also an output for outputting the generated frequency comb, as well as other derivatives of the laser beams, such as the absorption spectrum, when one or more sample loops (or other portion of the resonator) are used for sample medium analysis or gathering optically data of the sample medium. The input and/or output may comprise an aperture, an optical fibre, optical waveguide, prism and/or lens, which can be used for guiding the laser beam in and out from the optical manipulator.
One of the basic principles of the method and apparatus for the frequency comb generation is following. At first the inputted laser beam is converted to a second harmonic (SH) wave, and after a short propagation in the component the second harmonic wave (SH) is back-converted to a new beam, which advantageously deviates slightly from the laser beam frequency due to the cascaded quadratic nonlinearity or additionally due to the phase matching deviated (slightly) from zero. It is to be noted that the SH is here only as an example and additionally also other cascaded quadratic nonlinear processes of type “second order nonlinearity” are possible, such as for example a sum frequency generation (SFG), so SFG with back conversion in analogous way as SHG with back conversion depicted above.
To be precise, the comb formation requires that new wavelength components are generated by this back-conversion process. These new components are advantageously in the same wavelength region as the inputted laser beam, but at slightly different wavelengths. Thus effects of the frequency comb essentially similar to those arising from true third-order nonlinearity can be achieved (mimicked).
A nonlinear refractive index n2case of the component used can be approximated as:
where deff is the second-order nonlinear coefficient of the component material, and npump and nshg are the linear refractive indexes at the laser beam and second-harmonic frequencies, respectively, and Δk is a wave-vector mismatch representing said phase matching of the SH process.
According to an advantageous embodiment the nonlinear refractive index n2case is configured to be changeable by changing the value of wave-vector mismatch (Δk). As an example this can be done, e.g. by changing the poling period A of a quasi phase matching component (crystal). Another way to change the wave-vector mismatch (Δk) is via changing temperature of the component (crystal). Therefore, according to the invention, the nonlinear refractive index n2case can be positive or negative value (negative values of n2case can be obtained e.g. by using Δk>0). This is impossible with the prior art “true” Kerr nonlinearity, for which n2 is always positive and depends on the material. This makes it possible to achieve not only positive but also negative SPM, which allows for compensation of both normal and anomalous dispersion, while the SPM arising from the “true” Kerr nonlinearity can only compensate for anomalous dispersion.
According to an embodiment the component (such as the crystal or the optical fiber) may consist of at least two different medium or the component (such as the crystal or the optical fiber) or at least part of it may be doped material. The doping may be implemented by a material that provides laser gain. In that case the component may interact with the laser beam inputted and generate a second wavelength of the inputted beam inside the resonator or optical manipulator. The second wavelength may function as the derivative, and serve as a pump to the cascade nonlinear process, and thereby generate the actual frequencies for the frequency comb.
It is to be noted that the apparatus may comprises a laser source, such as a continuous wave or pulsed pump laser source. Alternative or in addition to, an outer laser source may also be used, whereupon the optical manipulator is optically coupled, for example via the input, with the laser source output so that the laser beam can be introduced to the component as depicted. In addition it is to be noted that the offset frequency of the comb generated or shifted e.g. by portion 1 can be tuned by tuning the frequency or power of the used laser, such as a pump laser.
Further the embodiments of the invention described in this document, where at least one first loop and/or at least one sample loop are used, can be utilized in determining and analysing sample medium, such as gas or liquid samples. There the first frequency comb is advantageously generated by using at least the one first loop, as is depicted elsewhere in this document. However, according to another embodiment the first frequency comb may be generated just by using the component, whereupon the sample loop can be used even without the first loop or other resonator. Additionally at least one second loop is used to receive the laser beam and/or it derivatives, introduce the received laser beam and/or its derivatives to interact with a sample medium, and to form an interacted laser beam derivative comprising an absorption spectrum due do interaction with said sample. In addition interacted laser beam derivative is introduced back to the optical manipulator and again to the component to form a second frequency comb, the frequencies of which deviates from the first frequency comb by Δf.
According to an embodiment the apparatus may also comprise a detector, whereupon the first and second frequency combs are introduced to the detector. On the detector they form a third frequency comb, which is based on a beat signal of said first and second frequency combs on the detector. The beat signal is based on the (small) frequency differences Δf of said first and second frequency combs. According to an embodiment the comb mode spacing of the third frequency comb is Δf. Advantageously the third frequency comb comprises also the absorption spectrum information inherited from said second frequency comb. Most advantageously the frequency range or the comb mode spacing of said third frequency comb 4f is on the range of 1 Hz-1 kHz, in which case the third frequency comb is typically centered at 1 kHz-1 GHz (audio or radio frequencies), which are much easier to measure and analyse accurately than optical frequencies.
The present invention offers clear advantages over the known prior art, which are next discussed. In the current invention it is very convenient that the effective third order nonlinearity arising from the cascaded quadratic nonlinearity of the discussed embodiment can be tailored by adjusting Δk, while the prior art “true” Kerr nonlinearity is a fixed material parameter and cannot be changed. As a result the effective third order nonlinearity (i.e., the value of n2) due to the cascaded quadratic nonlinearity (CQN) can be several orders of magnitude higher according to the current invention than the prior art “true” Kerr nonlinearity of most materials. Therefore, the laser intensity required for optical frequency comb (OFC) generation is significantly smaller in the current invention than in the case of prior art Kerr comb generation. In practice, this means more versatility in the implementation and application of the OFC.
While the prior art Kerr comb generation is only possible in microresonators, the frequency comb according to the invention can be generated in a larger resonator, which allows smaller mode spacing. In addition it does not need to be of that high quality even, which makes simpler implementation and possibility of obtaining a small mode spacing. The small mode spacing is needed e.g. in gas analysis.
In addition to the strength of effective four-wave mixing (FWM), as well as also other effects related to effective prior art Kerr nonlinearity, can be tailored e.g. by adjusting Δk. In particular, self-phase modulation (SPM) and cross-phase modulation (XPM) can be tailored according to the invention to balance resonator dispersion practically at any wavelength within the transparency range of the component, or crystal material. In the prior art “true” Kerr nonlinearity case, SPM and XPM are fixed material parameters, which makes the comb formation possible only at certain wavelengths, depending on material dispersion, which is clear disadvantage. This is one of the reasons why the prior art Kerr comb generation is difficult at mid-infrared wavelengths.
In addition the frequency comb generation according to the invention can be implemented e.g. with a simple continuous-wave (CW) laser without modulators, whereupon the apparatus is simple and inexpensive compared to e.g. mode-locked lasers. It is also possible to operate at any wavelength within the transparency range of the nonlinear crystal material. In particular, the frequency comb according to the invention also works in the mid-infrared region, so especially at wavelengths>3 μm, which is important for example for gas analysis applications, and cannot be accessed by mode-locked lasers. For example the mid-infrared operations with the prior art Kerr combs are challenging e.g. due to material dispersion.
Furthermore the frequency comb can be easily combined with other second-order nonlinear processes, which makes it possible to access e.g. the mid-infrared region with readily available low-cost near-infrared pump lasers, which is not possible with the prior art microresonator Kerr comb systems. Moreover, due to the high effective third-order nonlinearity, smaller laser intensity can be used than in the prior art Kerr combs. For the same reason, the resonator does not need to be of high quality. Together with the possibility to tailor the cascaded quadratic nonlinearity process, these features make versatile low-cost comb generation for a variety of applications possible. Also, the new embodiments based on an optical waveguide or microresonator make the comb generator compact and robust and lead to much higher laser intensity (and hence CQN strength) than in the “free-space” solutions presented. This is because the laser beams involved in the process are confined within a small mode volume by the waveguide/microresonator, while in the free-space solution the beams diverge as they propagate in the crystal.
The invention is explained in this document with reference to the aforementioned embodiments, and several advantages of the invention are demonstrated. It is clear that the invention is not only restricted to these embodiments, but comprises all possible embodiments within the spirit and scope of the inventive thought and the following patent claims. The novel features which are considered as characteristic of the invention are set forth in particular in the appended claims. The invention itself, however, both as to its construction and its method of operation, together with additional objects and advantages thereof, will be best understood from the following description of specific embodiments when read in connection with the accompanying drawings.
The exemplary embodiments of the invention presented in this patent application are not to be interpreted to pose limitations to the applicability of the appended claims. The verb “to comprise” is used in this patent application as an open limitation that does not exclude the existence of also unrecited features. The features recited in depending claims are mutually freely combinable unless otherwise explicitly stated.
Next the invention will be described in greater detail with reference to exemplary embodiments in accordance with the accompanying drawings, in which:
Energy conservation:
hν
SHG
=hν
pump
+hν
pump (1)
Phase matching (momentum conservation):
Δk=kSHG−2kpump=0 (2)
where kx=2πnx/λx is the wavevector, with x denoting the subscripts pump, SHG. The first of these conditions is met by definition. The phase matching condition, on the other hand, is in general not met because npump≠nSHG owing to material dispersion. The physical interpretation of this is such that as the phase velocities (c/nx) of the two waves in the crystal are different, SHG waves generated at different locations in the crystal interfere destructively, and thus no significant output at SHG is generated (see the left panel of
One of the most common techniques of achieving phase matching is quasi phase matching (QPM), where the crystal orientation is periodically inverted such that the phase of the emitted SHG wave is inverted (shifted by 180 deg) after every Lc. Here, Lc=π/(kSHG−2kpump) is the so-called coherence length, i.e. the propagation length in the crystal (so component) after which the SHG field would normally come out of phase relative to the previously emitted field (see the curve 104 in
Δk=kSHG−2kpump−2π/Λ=0 (3)
If the crystal is patterned with a poling period Λ=Lc, then Δk=0 and (quasi) phase matching for efficient SHG is achieved. In this case, the SHG power grows monotonously as the pump laser beam propagates in the crystal (see the curve 105 in
The cascaded quadratic nonlinearity is obtained especially if Δk is slightly detuned from zero. In this case, the pump field is first converted to the second harmonic (SH) wave, but after a short propagation in the crystal the SH-wave is back-converted to the pump frequency due to the phase mismatch (see
where deff is the second-order nonlinear coefficient of the crystal material, and npump and nshg are the linear refractive indexes at the pump and second-harmonic frequencies, respectively.
The cascaded quadratic nonlinearity can produce effects similar to those arising from the prior art “true” third-order nonlinearity. As an example, self-phase modulation arising from cascaded quadratic nonlinearity can be understood as shown in
It's worth mentioning that the growth of comb side modes in the case of cascaded quadratic nonlinearity can also be explained by pure second-order processes, without analogy with Kerr-type four-wave mixing. Even in the case of small phase-mismatch (Δk≠0 but close to zero), there is always some second-harmonic (SH) power produced in the crystal (so crystal component). Therefore, for Δk=0 or for Δk≠0 but close to zero, this SH power can act as a pump for so-called optical parametric oscillation (OPO). This is a second-order nonlinear process essentially inverse to SHG but enhanced by an optical resonator. The original pump at frequency νpump needs to resonate in order this OPO/back-conversion process to take place. The optical bandwidth of the OPO process is relatively large, allowing for back-conversion to frequencies close to, but other than νpump exactly. In this manner, this cascaded process, SHG followed by back-conversion, transfers energy from the pump frequency to the nearby resonator modes, creating a frequency comb that has a mode spacing which is (approximately) equal to the resonator mode spacing. Also the OPO/back-conversion process needs to obey the phase-matching condition, but just like in the case of SHG, Δk doesn't need to be exactly zero. These both processes however become weaker as Δk is detuned away from zero.
In addition it is to be noted that the frequency comb structure is inherited around all derivatives owing to inherent nonlinear mixing processes. For example, the comb around the second harmonic (SH) frequency is produced by SHG and sum-frequency generation (SFG) from the comb modes that are located around the original pump laser frequency (νpump). Also, in the case of
The apparatus 11 illustrated in
A common feature of the implementations illustrated in
The waveguide 115 is advantageously fabricated inside an optical nonlinear crystal component material, which is for example periodically poled lithium niobate (PPLN). In apparatus 12 in
| Number | Date | Country | Kind |
|---|---|---|---|
| 20155655 | Sep 2015 | FI | national |
This application is a U.S national application of PCT-application PCT/FI2016/050627 filed on Sep. 12, 2016 and claiming priority of Finnish application FI 20155655 filed on Sep. 11, 2015, the contents of all of which are incorporated herein by reference.
| Filing Document | Filing Date | Country | Kind |
|---|---|---|---|
| PCT/FI2016/050627 | 9/12/2016 | WO | 00 |
