Abstract
An apparatus for frequency comb generation comprises a component of second order nonlinearity, where the component is configured to interact with a laser beam or derivatives of the laser beam and thereby generate frequencies for the frequency comb. The apparatus comprises advantageously an optical manipulator, which both comprises the component but additionally is configured to introduce the beam or its derivatives in a repetitive or resonating manner to the component. The component is e.g. a monolithic or other solid optical resonator or microresonator comprising optical crystal and having said second order nonlinearity.
Claims
1. An apparatus for frequency comb generation using an optical manipulator, wherein the apparatus comprises: an input for guiding a continuous wave pumped laser beam into the optical manipulator, a component comprising second order nonlinearity, the optical manipulator being configured to introduce said continuous wave pumped laser beam and/or its derivatives in a resonating manner to said component, whereupon the component is configured to interact with said laser beam or derivatives of said laser beam and thereby generate frequencies for the frequency comb, and an output configured to output frequencies of the frequency comb generated by said component, wherein said component comprises at least one first and second portions, wherein a phase matching of the first portion deviates from zero, whereupon the second portion is configured to generate the frequency comb with frequencies differing from said frequency comb generated by said first portion.
2. An apparatus of claim 1, wherein said component comprises quasi-phase-matched optical nonlinear crystal material, comprising periodically poled lithium niobate (PPLN), periodically poled lithium tantalite (PPLT), periodically poled potassium titanyl phosphate (PPKTP), lithium niobate doped with metal ions, or birefringently phase-matched nonlinear crystals.
3. An apparatus of claim 1, whereupon said component is configured to perform cascading quadratic nonlinearity process.
4. An apparatus of claim 1, wherein the phase matching of said component is arranged to deviate from zero.
5. An apparatus of claim 1, wherein the optical manipulator comprises an optical resonator, optical fiber resonator or microresonator or monolithic or other solid crystal resonator.
6. An apparatus of claim 1, wherein the optical manipulator comprises mirrors arranged around the component, whereupon said component functions as a waveguide, and said mirrors are configured to reflect the inputted laser beam or its derivatives in a repetitive manner to said component within said optical manipulator.
7. An apparatus of claim 1, wherein the ends of the component are provided with reflective material in order to reflect said laser beam wavelength or its derivatives in a repetitive manner within said component.
8. An apparatus of claim 1, wherein interface materials at the interface of the component and the surrounding medium are selected to perform a total internal reflection of the laser beam or its derivatives and/or the angle of the laser beam or its derivatives is arranged to be as a critical angle for total internal reflection so that said total internal reflection is configured to reintroduce said laser beam or its derivatives in a repetitive manner within said component functioning as a waveguide.
9. An apparatus of claim 1, wherein the optical manipulator comprises at least one first loop, which is configured to receive said laser beam or its derivatives and additionally configured to introduce said received laser beam or its derivatives back to said optical manipulator and to said component.
10. An apparatus of claim 9, wherein apparatus comprises at least two first loops (118), wherein the length of the second first loop is same or different than the length of the first loop in order to provide the same or a different comb mode spacing.
11. An apparatus of claim 1, wherein the optical manipulator comprises at least one sample loop or resonator, which is configured to receive said laser beam and/or it derivatives, introduce said received laser beam or its derivatives to interact with a sample medium and to form an interacted laser beam derivative, and additionally configured to introduce said interacted laser beam derivative back to said optical manipulator and to said component.
12. An apparatus of claim 11, wherein the length of the sample loop is different than the length of at least one first loop.
13. An apparatus of claim 9, wherein the apparatus comprises an optical amplifier, optical filter, or amplitude or phase modulator, such as electro-optic modulator, arranged in the connection with said optical manipulator or at least one loop.
14. An apparatus of claim 1, wherein the optical manipulator comprises an optical microresonator, wherein said component material is arranged to interact with said laser beam or derivatives of said laser beam and thereby generate frequencies for the frequency comb.
15. An apparatus of claim 9, wherein the apparatus is configured to change or control the comb mode spacing by changing the length of the loop, using an electro-optic modulator, changing the resonator length by mechanical stretching or thermal expansion, or applying an electric field over the component and thereby changing the refractive index of said component.
16. An apparatus of claim 1, wherein said component comprises at least two portions, wherein the first portion comprises different structural properties of said second order nonlinearity, whereupon the second portion is configured to generate the frequency comb with frequencies differing from said frequency comb generated by said first portion.
17. An apparatus of claim 1, wherein said input and/or output comprises an aperture, an optical fibre, optical waveguide, prism or lens for guiding a laser beam in and out from the optical manipulator.
18. An apparatus of claim 1, wherein said apparatus is first configured to convert the inputted laser beam to a second harmonic wave, and after a propagation in the component to back-convert said second harmonic wave to a new beam deviating from the laser beam frequency due to the cascaded quadratic nonlinearity in order to produce effects of the frequency comb essentially similar to those arising from true third-order nonlinearity.
19. An apparatus of claim 1, wherein the apparatus is configured to produce said frequency comb in the mid-infrared region.
20. An apparatus of claim 1, wherein the apparatus comprises a laser source, comprising a continuous wave or pulsed pump laser source.
21. An apparatus of claim 1, wherein the component comprises at least two different medium, comprising doping material, and is configured to interact with the laser beam inputted to said component and generate a second wavelength of said inputted beam, wherein said second wavelength is configured to function as said derivative or a pump wave and generate the frequencies for the frequency comb.
22. A method for frequency comb generation, wherein the method comprises: introducing a continuous wave pumped laser beam or its derivatives to a component in a resonating manner, where said component comprises second order nonlinearity, where said component interacts with said continuous wave pumped laser beam or derivatives of said laser beam and thereby generates frequencies for the frequency comb, and outputting frequencies of the frequency comb generated by said component, wherein said component comprises at least one first and second portions, wherein a phase matching of the first portion deviates from zero, whereupon the first portion generates the frequency comb with frequencies differing from said frequency comb generated by said second portion.
23. A method of claim 22, wherein said component performs cascading quadratic nonlinearity process.
24. A method of claim 22, wherein the phase matching of said component deviates from zero.
Description
BRIEF DESCRIPTION OF THE DRAWINGS
[0056] Next the invention will be described in greater detail with reference to exemplary embodiments in accordance with the accompanying drawings, in which:
[0057] FIG. 1 illustrates, in time and frequency domains, a prior art optical frequency comb generation based on a mode-locked laser,
[0058] FIG. 2 illustrates the principle of the prior art microresonator Kerr comb generation,
[0059] FIG. 3 illustrates a principle of phase matching and mismatching,
[0060] FIG. 4 illustrates a principle of self-phase modulation originating from a cascaded quadratic process,
[0061] FIGS. 5A-5C illustrate principle of optical frequency comb generation by cascaded quadratic nonlinearity process according to an advantageous embodiment of the invention,
[0062] FIGS. 6A-6D illustrate examples of a cascaded quadratic nonlinearity (CQN) comb generation in a singly-resonant OPO advantageous embodiment of the invention,
[0063] FIGS. 7A-B illustrate a principle of an implementation of an optical frequency comb generation based on cascaded quadratic nonlinearity according to an advantageous embodiment of the invention,
[0064] FIGS. 8-9 illustrate examples of a comb generation using a solid component based on an optical waveguide according to an advantageous embodiment of the invention,
[0065] FIG. 10 illustrates another example of the comb generation according to an advantageous embodiment of the invention,
[0066] FIG. 11 illustrates still another example of the comb generation according to an advantageous embodiment of the invention, and
[0067] FIGS. 12-13 illustrate still another example of the comb generation according to an advantageous embodiment of the invention.
DETAILED DESCRIPTION
[0068] FIGS. 1-2 illustrate a prior art and are discussed earlier in this document.
[0069] FIG. 3 illustrates a principle of second harmonic generation without quasi-phase matching (left panel) and with quasi-phase mismatching (right panel). The second harmonic generation (SHG), or frequency doubling, is a typical example of a second order nonlinear process. In SHG, a laser beam (pump laser beam, a.k.a. fundamental beam, whose frequency is .sub.pump=c/.sub.pump, where .sub.pump is the laser wavelength) 103 is passed through a nonlinear crystal. In this process, two pump photons are converted into a photon that has twice the energy of a pump photon. The pump laser beam can be efficiently converted into the second harmonic frequency (.sub.SHG=2.sub.p) if the following conditions are met:
Energy conservation:
h.sub.SHG=h.sub.pump+h.sub.pump(1)
Phase matching (momentum conservation):
k=k.sub.SHG2k.sub.pump=0(2)
where k.sub.x=2n.sub.x/.sub.x 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 n.sub.pumpn.sub.SHG owing to material dispersion. The physical interpretation of this is such that as the phase velocities (c/n.sub.x) 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 FIG. 3). The left panel illustrates the phase-mismatched situation (k0) SHG, where there is not significant output power at frequency .sub.SHG. The right panel illustrates the phase-matched (k=0) SHG process, where the power at frequency .sub.SHG grows monotonically at the expense of pump power as the pump laser beam propagates in the crystal.
[0070] 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 L.sub.c. Here, L.sub.c=/(k.sub.SHG2k.sub.pump) 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 FIG. 3). In practice, QPM can be achieved by periodical poling of the crystal material using an electric field that permanently inverts the crystal polarity. The poling period (QPM period), which is denoted by A, is typically 5-50 m, depending on the crystal material, wavelengths, and on the type of interaction. In case of QPM, the phase-matching condition for SHG becomes:
k=k.sub.SHG2k.sub.pump2/=0(3)
[0071] If the crystal is patterned with a poling period =L.sub.c, then k=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 FIG. 3). Note, however, that the crystal can also be designed for other values of , which makes it possible to tailor the value of phase-mismatch, k.
[0072] The cascaded quadratic nonlinearity is obtained especially if k 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 FIG. 3). The term cascaded here refers to the fact that this process is a cascade of two second order nonlinear processes: SHG and back conversion. The back conversion process is also referred to as downconversion (as the frequency is halved), or optical parametric conversion. This kind of cascaded process results in physical phenomena, that essentially mimic those originating from the third order (the prior art Kerr nonlinearity). This can be described in terms of effective nonlinear refractive index, which is defined as:
[00002]
[0073] where d.sub.eff is the second-order nonlinear coefficient of the crystal material, and n.sub.pump and n.sub.shg are the linear refractive indexes at the pump and second-harmonic frequencies, respectively.
[0074] 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 FIG. 4, which illustrates a principle of self-phase modulation originating from a cascaded quadratic process, where self-phase modulation is followed by back-conversion. The line 106 describes the fundamental (pump) field, and the 107 line denotes the field at SH frequency. Owing to phase-mismatch (k0), the generated SH wave is converted back to the fundamental frequency after a propagation of approximately half a coherence length. Because the pump wave and second harmonic wave propagate with different velocities in the crystal (so component), the back-converted wave acquires a phase difference relative to the original pump field. As a result, also the total field (original+regenerated) at .sub.pump is phase-shifted. This corresponds to the prior art true self-phase modulation.
[0075] FIGS. 5A, 5B illustrate principle of optical frequency comb generation by cascaded quadratic nonlinearity process according to an advantageous embodiment of the invention, where it can be seen that owing to the capability of cascaded quadratic nonlinearity to mimic third-order nonlinearities, such as FWM and SPM, optical frequency comb generation with effects similar to Kerr comb generation may be possible. The process is pumped with a laser at frequency .sub.pump. Phase-mismatched second harmonic generation (SHG) produces light at frequency .sub.shg. Back-conversion of this light generates a comb around .sub.pump.
[0076] 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 (k0 but close to zero), there is always some second-harmonic (SH) power produced in the crystal (so crystal component). Therefore, for k=0 or for k0 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 .sub.pump 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 .sub.pump 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, k doesn't need to be exactly zero. These both processes however become weaker as k is detuned away from zero.
[0077] FIG. 6 illustrates a basic principle of optical frequency comb generation by the cascaded quadratic nonlinearity using the apparatus with an additional second-order nonlinear crystal component 114 presented in FIG. 7b. The upper panel of FIG. 5B shows the OPO process that takes place in the additional nonlinear crystal component 114. Either the signal beam or idler beam (or both) resonate in the optical manipulator (resonator) formed by the mirrors. The OFC is produced around the resonant wavelength (in this example around .sub.s), if the cascaded quadratic nonlinearity process in first crystal component 110 is designed accordingly. This process, shown in the lower panel of FIG. 5B is identical to that shown in FIG. 5A. Due to other nonlinear mixing processes, the comb structure is copied also to other wavelengths involved, such as the idler.
[0078] 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 (.sub.pump). Also, in the case of FIG. 6, SFG between the idler and signal waves copies the comb around frequency .sub.p. as can be seen in FIG. 6A-6D.
[0079] FIGS. 6A-6D illustrates additionally cascaded quadratic nonlinearity (CQN) comb generation in a singly-resonant OPO. In FIG. 6A Signal and idler photons are generated from the pump photons (1/.sub.p=1/.sub.s+1/.sub.i, where .sub.p, s, and i are the wavelengths of the pump, signal, and idler beams, respectively. The signal wave resonates in the OPO cavity. In Figs. B) and C), cascaded quadratic nonlinearities lead to comb formation (SFG=sum frequency generation). In Fig D) the comb structure is transferred to the idler wave by difference frequency generation (DFG). Back conversion of the signal and idler combs also creates a weak comb structure in the depleted pump wave.
[0080] FIGS. 7A-7B illustrate a principle of an implementation of an optical frequency comb generation based on cascaded quadratic nonlinearity according to an advantageous embodiment of the invention. The components of the cascaded quadratic nonlinearity based frequency comb generator apparatus 10, 11 illustrated in FIGS. 7A-7B are an input 109 for a laser beam that supplies energy for the cascaded quadratic nonlinearity process at frequency .sub.pump, the second-order nonlinear crystal component 110 that produces the cascaded quadratic nonlinearity process, and the optical manipulator 111 (a.k.a. optical cavity) functioning as the resonator and formed by mirrors 112 or other reflecting devices. In addition the apparatus also comprises an output 108 for outputting the generated frequency comb. The pump wave resonates in the resonator, and the comb mode spacing is roughly determined by the resonator mode spacing. Also, the resonator is used for the efficient back-conversion process (OPO) to take place (FIG. 5A).
[0081] FIG. 7A illustrates an exemplary implementation (apparatus 10) of an optical frequency comb based on cascaded quadratic nonlinearity. The cascaded quadratic nonlinearity crystal component 110 is placed inside an optical manipulator 111 (functioning as a resonator) comprising four mirrors 112. Any number of mirrors is possible so to provide the resonator. FIG. 7B illustrates another exemplary implementation (apparatus 11), where the cascaded quadratic nonlinearity pump laser beam 113 is produced inside the manipulator 111 using another nonlinear process, namely optical parametric oscillation (OPO).
[0082] The apparatus 11 illustrated in FIG. 7B is otherwise similar to that 10 shown in FIG. 7A, but an additional second-order nonlinear crystal component 114 is placed in the optical manipulator 111. This component 114 is used for optical parametric oscillation (OPO), which is fundamentally similar to the back-conversion process illustrated in FIG. 5A. However, these two shouldn't be confused, namely there are also some differences. According to an embodiment the additional OPO is phase-matched such that a pump laser beam at frequency .sub.p produces two new beams: so-called signal (.sub.s, which now equals to .sub.pump of the cascaded quadratic nonlinearity process) and idler (.sub.i), see FIG. 5B. As usual, energy is conserved in the process: .sub.p=.sub.s+.sub.i. The purpose of this additional process is two-fold: [0083] (1) The pump beam (.sub.pump) for the cascaded quadratic nonlinearity process is now produced inside the optical manipulator (resonator), in the additional crystal component 114. This simplifies the experimental implementation, since coupling of a high-power external pump beam to the resonator, as in the right panel of FIG. 7, is not always so trivial. [0084] (2) The additional OPO works as a wavelength converter. Good and inexpensive pump lasers are readily available at near-infrared, but not at mid-infrared, which is an important wavelength range for many applications. The OPO converts light of the pump laser to the signal and idler frequencies, the latter of which typically lies in the mid-infrared region. In addition the optical frequency comb structure generated by cascaded quadratic nonlinearity around the signal frequency (.sub.s) is inherently transferred to the mid-infrared region, around .sub.i. This occurs due to another second-order process, difference frequency generation (DFG), in the additional crystal component 114. The DFG process obeys the same phase-matching condition as the OPO process .sub.p=.sub.s+.sub.i and the comb at .sub.s mixes with .sub.p, producing a comb at .sub.i.
[0085] A common feature of the implementations illustrated in FIGS. 7A-7B is that they are based on a free-space optical manipulator 111 (resonator), where the resonator comprises separate mirrors 112, and the laser beam(s) propagate in free space between the mirrors. The apparatuses of FIGS. 7A, 7B and 8-9 may also comprise a laser source 121, but also auxiliary laser sources may be used. FIGS. 8-9 illustrate another examples (apparatus 12, 13) of a comb generation using a monolithic or other solid component based on an optical waveguide 115 according to an advantageous embodiment of the invention, where the resonator is formed around the second-order nonlinear material without any free-space propagation. The monolithic or other solid structure used in the apparatuses 12, 13 of FIGS. 8-9 makes the setup more compact, robust, as well as simpler and easier to use and assemble. Also, many embodiments of the monolithic or other solid structure lead to a higher laser intensity I.sub.L inside the resonator (optical manipulator), which enhances the cascaded quadratic nonlinearity effect, hence making the comb generation possible with low-power lasers, allowing thus cost efficiency and low power consumption.
[0086] 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 FIG. 8, the resonator is formed by coating the crystal component ends with reflecting material 116 such that they 116 reflect the light at comb wavelength. Another possibility is to place mirrors in contact with the waveguide ends. Light is typically coupled in and out either in free space, or using optical fibers 117, but also other guiding devices can be used, as is described in this document elsewhere. In apparatus 13 in FIG. 9, the waveguide 115 (crystal component) is part of a fiber-optic resonator. In this embodiment no mirrors are needed, as a fiber loop 118 forms a resonator, so introduces the beam derivatives 103A in a repetitive or resonating manner to the component 115. The length of the resonator (loop 118) determines the comb mode spacing, and can be chosen according to the intended application of the comb, as is described in this document elsewhere.
[0087] FIG. 10 illustrates another example (apparatus 14) of the comb generation according to an advantageous embodiment of the invention, where additional components 119, 124, such as the sample (auxiliary) optical loop 119 can be integrated in to the apparatus. The sample optical loop 119 can be used for example to sample medium analysis, as is described elsewhere in this document. Additionally, or alternatively, the additional components 119, 124 may comprise also optical amplifiers, gas cells, or filters or the like. Also, the resonator can have several parallel branches that can have different lengths. As a result, several combs with different mode spacings can be generated with a single apparatus, which offers clear advantages over the prior art solutions.
[0088] FIG. 11 illustrates still another example of the comb generation (apparatus 17) according to an advantageous embodiment of the invention, where the structure essentially similar as in FIG. 7A (or FIG. 7B) is modified by applying additional semi-transparent reflectors 112A between the original reflectors 112 and 112B, and thereby providing two parallel resonators with different lengths. According to an embodiment a sample to be determined may be inserted for example in the area of 112C, if this example is used for sample analysis (optional feature).
[0089] FIGS. 12-13 illustrate still another example (apparatus 15, 16) of the comb generation according to an advantageous embodiment of the invention by using the monolithic or other solid structure. In FIG. 12 the comb is generated in a microresonator 120 fabricated of a nonlinear quasi-phase-matched optical crystal. The apparatus and method can also be used to transfer the frequency comb to a different wavelength region than the original pump laser wavelength. For example, a mid-infrared comb can be generated using a low-cost near-infrared pump laser, as is depicted in FIG. 13, where the process is the same as that described in FIG. 6, and can also be implemented, e.g., in the embodiments of FIGS. 8 and 9. The quasi phase matching (QPM) structure responsible for the OPO wavelength conversion can be integrated in the same device with the QPM-structure responsible for the cascaded quadratic nonlinearity process, which is impossible with the conventional prior art Kerr combs. This can be achieved with the invention by doping 123 the component material with suitable doping medium or using two differently configured sections in the second order nonlinear medium (123A, 123B) in the microresonator component 120.
