Low-threshold supercontinuum generation in bulk dielectrics and semiconductors

Abstract

Control is provided by coupling the light of the first wavelength output by the fs oscillator in a full-pulse repetitive PRR to the bulk nonlinear material (BNLM), which has a positive thermo-optic coefficient (dn / dT > 0 K). ‑1 The low-threshold femtosecond supercontinuum (fs SCG) in the BNLM. Optical coupling in the BNLM creates a nonlinear lensing of the coupled beam, which is insufficient to provide sufficient light intensity to reach the fs SCG threshold. To increase the pulse energy and reach the SCG threshold, a second wavelength of light, different from the first wavelength, is absorbed in the BNLM to form a thermal lensing within the BNLM, which assists the nonlinear lensing in generating the SCG.

Description

Technical Field

[0001] This disclosure relates to methods for generating femtosecond supercontinuum (SCG) and supercontinuum laser sources. Specifically, this disclosure relates to methods and systems for generating low-threshold SCG in bulk dielectrics and nonlinear semiconductor materials (NLMs) by generating thermal lensing effects and nonlinear self-focusing effects. Background Technology

[0002] The SCG (Special Frequency Comb) forms a wide continuous spectrum by propagating high-power pulses through a nonlinear medium. The SCG with fs pulses (fs SCG) is particularly noteworthy because it produces a spectrum that combines a wide superoctave bandwidth with high spatial and temporal coherence. Therefore, fs SCG is crucial for many important applications, especially including the generation of optical frequency combs, arbitrary optical waveform synthesis, and attosecond pulse generation. An optical frequency comb (which is equivalent to an fs pulse sequence) has a watt-level average power P between 0.1 and 10 W and a relatively high pulse repetition rate (PRR) or frequency f. R The range is 10 7 Hz and 10 10 Between Hz, and therefore low pulse energy W=P av / f R =0.1-100nJ) is essential for spectroscopy, sensing, microscopy and imaging.

[0003] The technology for SCG in specially designed optical nonlinear fibers and waveguides (e.g., silicon nitride (Si3N4)) is well-established. However, the use of fibers and waveguides characterized by constrained geometries comes at the cost of increased complexity and reduced overall efficiency of the laser system. Furthermore, nonlinear fibers and waveguides inherently limit the power and coherence of SCG and require precise alignment.

[0004] Bulk materials, including, for example, transparent amorphous solids (e.g., silicate and non-silicate optical glasses), crystals (e.g., oxides, fluorides, phosphides), and semiconductors (silicon, germanium, and other III-V and II-VI materials), also support fsSCG. The advantages of fs SCG in these materials include, in particular, relative simplicity and therefore low cost, flexibility, and the possibility of scaling peak and average power. In these materials, laser propagation is not limited by the material's cross-sectional profile, which allows for relaxed alignment sensitivity. Furthermore, SCGs in some bulk materials are characterized by compressing femtosecond input pulses into even shorter output pulses (comprising only a few optical cycles). For example, USPP 2021 / 0124236 and USP 10,216,063, 10,216,063, and 10,483,709 (all co-owned with the subject application and incorporated herein by reference in their entirety) teach that random quasi-phase-matched gain media (such as those doped with Cr)2+ SCG in polycrystalline zinc sulfide (ionic).

[0005] Femtosecond SCGs in nonlinear media are governed by the interactions between nonlinearity, nonlinear absorption, and dispersion of the chosen bulk material. The physical picture of fs-SCGs can be understood within the framework of filamentation: self-focusing, self-phase modulation, and the interaction between multiphoton absorption / ionization-induced free electron plasmas. The interactions between these physical phenomena lead to the formation of a filament, “a dynamic structure with an intense core that is able to propagate over extended distances much larger than the typical diffraction length while keeping a narrow beam size without the help of any external guiding mechanism” (A. Couairon and A. Mysyrowicz, Femtosecond filamentation in transparent media, Phys. Rep. 441, 47-190 (2007)). A significant consequence of filament formation is the very strong nonlinear broadening of the pulse spectrum, i.e., the bandwidth of the output spectrum is much larger than the bandwidth of the input spectrum. Figure 1A and Figure 1B The standard settings for fsSCG in bulk materials are shown. Figure 1A The presence of mesofilamentization leads to strong broadening, but if mesofilamentization is absent, such as Figure 1B As shown, the output spectrum is not broadened.

[0006] The initial stage of filament formation is controlled by self-focusing: the χ of the medium (3) Nonlinearity causes an intensity-dependent refractive index: n(I) = n0 + n2I, where I is the intensity, n0 is the linear refractive index, and n2 is the nonlinear refractive index. Local intensity is higher at the beam center and lower at its edges. Therefore, χ with n2 > 0... (3) The bulk medium acts as an intensity-dependent lens. The self-focusing threshold is determined by the critical power P. Crit To define the critical power P Crit This is further defined by the parameters of the gain medium, including the nonlinear and linear components of the refractive index and the wavelength coupled into the medium. The P in the gain medium (bulk dielectric and semiconductor, also known as a nonlinear material or medium (NLM)) Crit The value ranges from 0.1 MW to tens of MW, depending on the material.

[0007] If the peak power of the input pulse (P) Pk Significantly exceeding P Crit (Typically by an order of magnitude or more), then fs-SCG occurs in the bulk gain medium. Therefore, based on the foregoing, the standard implementation of fs-SCG in gain NLM is based on an fs laser with relatively high multi-MW peak power (up to 100MW) and correspondingly high μJ pulse energy, which typically operates at a low kHz repetition rate.

[0008] However, many important applications of fs-SCG (including optical frequency comb generation) require high multi-MHz rates (i.e., at the full repetition rate f of a mode-locked oscillator). R =10 7 -10 10 fs lasers operating at Hz and low nJ pulse energies. The peak power level of nJ fs pulses is typically in the sub-MW to less than 10MW (i.e., P2). Pk ≤P Crit The spectral broadening is too weak to cause self-focusing in NLM. Therefore, SCG and spectral broadening are either too weak or do not occur at all. Figure 1B This situation is illustrated in the image.

[0009] Experimental data associated with fs SCG in a volume NLM raise several questions regarding the propagation of several-period pulses within the volume NLM. Operation of the fs oscillator with full PRR does not allow the fs pulse to reach the desired peak power sufficient to generate the fs SCG. Acceptable prior art schematics fail to achieve the fs SCG under existing PRR conditions. Therefore, additional mechanisms should be identified that contribute to nonlinear focusing to induce fs SCG at high PRR. Understanding and controlling these mechanisms will provide a general approach for low-threshold fs SCG in NLMs of interest, although the full PRR, as described, is high and relative when the fs oscillator is operated with full PRR.

[0010] Therefore, it is necessary to utilize known physical processes to provide nJ-level pulse energies (P0) in the NLM of interest. Pk ≤P Crit An improved method for achieving low threshold fs-SCG with high multi-MHz pulse repetition rate.

[0011] Another requirement is a laser system configured to perform improved processes. Summary of the Invention

[0012] The present invention is based on the cumulative effect generated by the nonlinear self-focusing effect and the thermal lensing formed in the NLM of interest due to the interaction between light and the NLM disclosed herein. Specifically, the thermal lensing effectively helps linear focusing phenomena to produce low-threshold fs SCG.

[0013] The disclosed method includes obtaining values ​​from the thermo-optic coefficient with a positive thermo-optic coefficient (i.e., the temperature derivative of the refractive index or dn / dT > 0 K). -1 The desired NLM is selected from a set of transparent materials whose wavelengths are coupled to the fs pulse sequence. The fs pulse sequence is output by an fs oscillator operating at full PRR in the range of 10 MHz to 10 GHz, and when coupled to the NLM, there is not enough energy to reach the threshold of fs SCG because the self-focusing in the NLM is too weak.

[0014] Then, one or more additional wavelengths, obtained either by coupling to the NLM of the auxiliary laser source or due to nonlinear effects caused by the interaction between the fs pulse and the NLM, are absorbed by the NLM. This absorption is accompanied by heat dissipation along the cross-section of the fs beam, which leads to the formation of a thermal lens. The addition of the thermal lens aids in nonlinear self-focusing and thus results in the formation of a filament that reduces the peak power of the fs pulse.

[0015] The selected NLM may or may not be a gain medium. In other words, the selected NLM does not have to be an optical amplifier. Standards for suitable NLMs require that they be at least partially transparent at the wavelength of the coupled fs pulse sequence and have a positive thermo-optical coefficient. The selected NLM can be found in publicly accessible resources that are well known to those skilled in the art or determined experimentally.

[0016] According to a characteristic of the disclosed method, the selected NLM has high second-order nonlinearity and third-order nonlinearity (χ, respectively). (2) ≠0 and χ (3) The characteristics of ≠0). Additional wavelengths are generated in the NLM due to nonlinear effects such as three-wave mixing, optical parameter generation, optical rectification, and multiphoton absorption. At least one of these new wavelengths is absorbed in the selected NLM, leading to the formation of a thermal lens. Another nonlinear effect leading to the generation of additional wavelengths can include four-wave mixing, similar to the Kerr effect, where four-wave mixing is caused by a third-order nonlinearity (χ). (3) (≠0) causes this. In addition to the newly generated wavelengths, those spectral components located outside the transparent window of the selected material are also absorbed, thus contributing to the formation of the thermal lens.

[0017] According to another feature, in addition to the fs pulse, a continuous wavelength (CW) beam is coupled into a selected NLM. The wavelength of the CW beam is selected so that it is absorbed in the NLM, resulting in the dissipation and formation of a thermal lens, which, combined with nonlinear focusing, helps to achieve a low threshold for the SCG.

[0018] According to another feature of the disclosed method, the selection of the nonlinear material is based on the wavelength of the fs oscillator used in a given schematic. Conversely, if the nonlinear material and its optical properties are known, the fs oscillator is selected to operate at the wavelength that interacts with the known material to provide both a nonlinear focusing effect and some other nonlinear effects responsible for the known additional wavelengths to be absorbed in the NLM to provide thermal lensing. Many material properties, including the absorption spectrum, are well documented.

[0019] Another feature of the disclosed method includes determining the formation of a thermal lens. Specifically, the spectrum of the input fs pulse is repeatedly measured at the input and output of the selected nonlinear material. A maximum output spectral bandwidth that significantly exceeds the input spectral bandwidth indicates the formation of a sufficiently strong thermal lens and indicates that the threshold of fs SCG has been reached.

[0020] Another feature of the disclosed method involves optimizing the fs SCG necessary to achieve the widest spectrum of the fs pulse at the output of the selected material after a threshold has been reached. This optimization includes controllably changing the initial size of the input beam spot and / or the average power of the coupled fs pulse and / or the average power of the auxiliary laser source, and / or pre-chirping the input fs pulse.

[0021] Alternatively, or in combination with selective or all of the above-described optimization techniques, the disclosed method may include determining the location of a self-focal point within a selected material and identifying the temporal distribution of the coupled fs pulse at that location. Preferably, if the fs pulse is pre-chirped, the optimization, according to yet another method feature, includes selecting a material characterized by its ability to compress the dispersion of the pre-chirped pulse. The most efficient optimization occurs by compressing the pre-chirped pulse into the shortest possible fs pulse at the location of the nonlinear self-focalization.

[0022] Other aspects of this disclosure relate to optical schematic diagrams configured to perform the disclosed methods, which may include any of the above and other features or combinations thereof. Therefore, schematic diagrams of the invention may include any of the disclosed features or a combination of selective or all of the disclosed features.

[0023] According to this aspect, the disclosed schematic diagram may include an fs oscillator and an optical pump having a corresponding output beam to be superimposed within a selected nonlinear material. The optical pump facilitates the formation of a thermal lens. Another schematic diagram does not require an additional light source and is configured only with an fs oscillator and a selected NLM. According to the concept of the invention, the parameters of the fs oscillator and NLM are selected such that the NLM partially absorbs the fs laser radiation, which applies thermal waveguide and forms a thermal lens that helps nonlinearly focus to produce a low-threshold CG. Attached Figure Description

[0024] The above and other features of the disclosed aspects will become more apparent from the following figures, in which:

[0025] Figure 1A The standard settings of the fs-SCG are shown, characterized by P Pk >>P Crit The filamentation and strong nonlinear broadening at time, where Ppk is the peak power and Pcrt is the critical power.

[0026] Figure 1B The standard settings of the fs-SCG are shown, characterized by P Pk ≤P Crit There is no filamentation or weak nonlinear broadening at that time.

[0027] Figure 2 The simulated spectral bandwidth of the low-threshold SCG is shown as a function of laser gain (g) and the refractive index change imposed by the disclosed thermal lens.

[0028] Figure 3A This is an exemplary schematic diagram configured to perform the method of the present invention.

[0029] Figure 3B This is another exemplary schematic diagram configured to perform the method of the present invention.

[0030] Figure 4A The spectrum of SCG is shown by experimental measurement versus simulation prediction with or without the disclosed thermal effects.

[0031] Figure 4B The simulated transverse flux distribution of an nJ pulse based on known techniques is shown.

[0032] Figure 4C The lateral distribution of thermal conductance of the nJ pulse according to this disclosure is shown.

[0033] Figure 5A This shows the results at relatively low average and peak power levels. Figure 3A The measured spectra of the fs pulses at the input and output of the selected NLM correspond to the corresponding blue and red curves; where the output spectrum includes the baseband (f).

[0034] Figure 5B It shows that in greater than Figure 5A Average power and peak power at average power and peak power Figure 3A The measured spectrum of the fs pulse at the input and output of the NLM, wherein the output band includes the baseband (f) and the long-wave IR band (Of) generated in the NLM via optical rectification.

[0035] Figure 5C It shows that at higher Figure 5A Average power and peak power at average power and peak power Figure 3A The measured spectrum of the fs pulse at the input and output of the NLM, wherein the output spectrum includes the intermediate frequency band generated in the NLM via a series of three-wave mixing between spectral components from the f band and the of band. Attached Figure Description

[0037] At least one embodiment will be discussed below with reference to the accompanying drawings, which are not intended to be drawn to scale. These drawings are included to provide illustration and further understanding of the aspects and embodiments, and are incorporated into and constitute a part of this specification, but are not intended to be a definition of limitation on any particular embodiment. The drawings, together with the remainder of the specification, serve to illustrate the principles and operation of the described and claimed aspects and embodiments. In the drawings, each identical or substantially identical component shown in the various figures is indicated by the same numerals. For clarity, not every component may be labeled in every figure. In the drawings:

[0038] Figure 1A The standard settings of the fs-SCG are shown, characterized by P Pk >>P Crit The filamentation and strong nonlinear broadening at time, where Ppk is the peak power and Pcrt is the critical power.

[0039] Figure 1B The standard settings of the fs-SCG are shown, characterized by P Pk ≤P Crit There is no filamentation or weak nonlinear broadening at that time.

[0040] Figure 2 The simulated spectral bandwidth of the low-threshold SCG is shown as a function of laser gain (g) and the refractive index change imposed by the disclosed thermal lens.

[0041] Figure 3A This is an exemplary schematic diagram configured to perform the method of the present invention.

[0042] Figure 3B This is another exemplary schematic diagram configured to perform the method of the present invention.

[0043] Figure 4A The spectrum of SCG is shown by experimental measurement versus simulation prediction with or without the disclosed thermal effects.

[0044] Figure 4B The simulated transverse flux distribution of an nJ pulse based on known techniques is shown.

[0045] Figure 4C The lateral distribution of thermal conductance of the nJ pulse according to this disclosure is shown.

[0046] Figure 5A This shows the results at relatively low average and peak power levels. Figure 3A The measured spectra of the fs pulses at the input and output of the selected NLM correspond to the corresponding blue and red curves; where the output spectrum includes the baseband (f).

[0047] Figure 5B It shows that in greater than Figure 5A Average power and peak power at average power and peak power Figure 3A The measured spectrum of the fs pulse at the input and output of the NLM, wherein the output band includes the baseband (f) and the long-wave IR band (Of) generated in the NLM via optical rectification.

[0048] Figure 5C It shows that at higher Figure 5A Average power and peak power at average power and peak power Figure 3A The measured spectrum of the fs pulse at the input and output of the NLM, wherein the output spectrum includes the intermediate frequency band generated in the NLM via a series of three-wave mixing between spectral components from the f band and the of band. Detailed Implementation

[0049] The subject of this invention relates to an additional optical mechanism that, together with nonlinear focusing of the fs pulse, allows the attainment of the fsSCG threshold, which would be impossible using nonlinear focusing alone. Insufficient nonlinear focusing occurs due to low pulse energy and therefore insufficient peak power to generate the strong nonlinear effect that leads to fs SCG. Specifically, fs laser oscillators typically operate with high PRR, outputting fs pulses where the pulse energy and peak power are insufficient to reach the SCG threshold in the BNLM receiving these pulses. As disclosed herein, the solution to this problem is to generate a thermal lens in the BNLM that, in combination with the nonlinear lens, results in fs SCG. The thermal lens provides additional focusing for fs pulses that are insufficiently nonlinearly focused along the length of the BNLM and helps nonlinear focusing reach the fs SCG threshold at full PRR in the range of the fs oscillator between 10 MHz and 10 GHz. The SCG threshold achieved according to the inventive concept tends to be reduced by half the SCG threshold achievable by nonlinear focusing alone.

[0050] Figure 2 The importance of thermal lenses for generating fs SCG in BNLM (labeled as NLM) is shown. Specifically, Figure 2The simulated spectral bandwidth of the low-threshold SCG (Δv(THz)) is shown as a function of gain (G) and the refractive index change Δn imposed by the thermal lens. The red, purple, and green arrows indicate the qualitative trajectory of increasing pump power and its effect on the maximum achievable values ​​of gain and Δn at low, medium, and high levels of pump laser absorption in the NLM, respectively. With increasing gain, the broadening of the output spectrum is somewhat negligible, indicating that the laser gain alone (i.e., an increase of approximately 4-fold in pulse energy and peak power) is insufficient to reach the fs SCG threshold (i.e., to achieve strong spectral broadening). While the gain does contribute to spectral broadening to some extent, the refractive index change Δn (green arrow) resulting from the thermal lens in the medium contributes to the broadening of the output spectrum, thus reaching the fs SCG threshold. In summary, the comparison of the blue and red curves clearly demonstrates that it is precisely due to the waveguide formed by the thermal lens that the desired low-threshold SCG is largely achieved. Figure 2 It also shows that, in order to achieve the fs SCG threshold, the selected BNLM does not necessarily have to be a laser gain medium: a thermal lens alone (i.e., increasing Δn at a constant G = 1) may be sufficient.

[0051] To overcome the insufficient pulse energy and peak power of conventional fs-SCG in BNLM and the resulting pulse energy limitation, this disclosure teaches how to generate a temperature-dependent thermal self-focusing mechanism (also known as thermal lensing) based on the refractive index n(T). Thermal lensing aids conventional nonlinear self-focusing caused by the intensity dependence of the refractive index n(I) = n0 + n2I (Equation 1). The formation of thermal lensing is further illustrated below.

[0052] Many BNLMs are characterized by a positive temperature derivative of the refractive index, dn / dT > 0 K. -1 As is known to those skilled in the art, the heat dissipation along the axis of a laser beam propagating through an absorbing medium causes the temperature distribution T(r) across the beam cross section, which can be approximated as...

[0053]

[0054] Among them, P h Let denoted as κ be the heat dissipation power in the medium, κ be the thermal conductivity of the medium, V be the volume of the heat dissipation region, and r be the radial distance of the heat dissipation from the beam axis. Therefore, heat dissipation produces a local temperature increase ΔT, which in turn causes a local change in the refractive index.

[0055]

[0056] Therefore, the medium with heat dissipation along the laser beam axis acts as a temperature-dependent lens, also known as a thermal lens. Under the influence of the thermal lens, beam propagation in a BNLM can be analogous to light propagation in a waveguide, provided Δn is a fraction of the refractive index n. Thus, the disclosed fs-SCG method combines the advantages of both bulk and confined geometry to some extent. Similar to a waveguide-based setup, it allows for the generation of superoctave coherent spectra at nJ-level pulse energies and high repetition rates. Simultaneously, the spatial and temporal dynamics are analogous to those in a bulk medium, and are characterized by additional focusing, ionization, etc., which are central to the advantageous properties of the proposed fs-SCG scheme.

[0057] The foregoing provides a roadmap for generating fs SCG in a BNLM according to the present invention. Due to the wide selection range of BNLMs characterized by third-order nonlinearity, nonlinear focusing is based on the Kerr self-focusing effect exhibited by the formation of a nonlinear lens. Based on the details discussed above, a nonlinear lens alone is insufficient to increase the intensity of the fs pulse to a level sufficient to form a wide output spectrum (i.e., the fs SCG threshold is not reached). To increase the intensity of the fs pulse, a thermal focusing effect is generated to aid nonlinear focusing. This can be generated by light absorbing the wavelength of the fs pulse or any other suitable wavelength of light absorbed in the BNLM via any linear and / or nonlinear absorption mechanism, and thus, in the selected BLNM, a thermal lens is generated in the medium according to Equation 1. Linear absorption in bulk dielectrics and semiconductors is a well-known effect. The wavelength corresponding to linear absorption in a particular medium can be found in available literature or measured using available equipment. Nonlinear absorption can be achieved by utilizing nonlinear processes such as: (1) typical multiphoton absorption, practically used in various BNLMs; (2) three-wave mixing; and (3) four-wave mixing to generate a new wavelength that differs from the fundamental wavelength of the fs pulse but can be absorbed by the selected BNLM. Therefore, the methods described herein involve selecting the linearity and absorption refractive index (Ex 1) of the BNLM and the operating wavelength of the fs oscillator. For three-wave mixing, the selected BNLM, in addition to having a third-order nonlinearity (χ... (3) In addition to ≠0, it should also have second-order nonlinearity (χ). (2) (≠0). The heat generated by absorption is dissipated on the pump beam, resulting in a refractive index gradient Δn = (dn / dT)ΔT on the pump beam, which is approximately proportional to the absorption power. Under these conditions, the region along the laser beam axis has a higher refractive index than the region surrounding the beam that forms the thermal lens. Finally, the primary nonlinear lens and the thermal lens cooperate to reach the filament formation threshold, resulting in fs SCG.

[0058] Figure 3A and Figure 3BVarious exemplary optical schematics configured to implement the inventive concept are shown. Each schematic shown includes an fs laser or oscillator with a full PRR output fs nJ pulse sequence ranging from 10 MHz to 10 GHz, the fs nJ pulse sequence having a relatively narrow input spectrum. An upstream lens L or equivalent optical component (e.g., a concave mirror) focuses the fs light into the body of a BNLM (labeled NLM). The peak power of the nJ fs pulse is below a critical power (i.e., P0). Pk ≤P Crit The pulse peak power varies from sub-MW to 10MW. Therefore, the known pulse peak power is only sufficient to produce a weakly nonlinear lens. Thus, the fs SCG threshold in the selected BNLM is not reached. The downstream lens L collimates the light at the output of the NLM.

[0059] For details, please refer to the following: Figure 3A The optical schematic also includes a second laser source or pump, which can operate in CW or pulsed mode to output light of a second wavelength different from the fs pulse. The femtosecond and CW radiations are superimposed on a dichroic mirror (DM) and focused in a BNLM by various upstream lenses L or equivalent optical components (e.g., concave mirrors). Here, optimization of the fs SCG can be achieved by controlling the pump power and / or the beam size of the two lasers, as well as other methods discussed below. These parameters can be controlled by incorporating an optical arrangement OA comprising one or more lenses. The pump power can be controlled using a variety of methods well known in the art (the vast majority of laser sources have controllable power).

[0060] For example, a second wavelength is chosen to pump the BNLM so that it is absorbed in the BNLM. The optical properties (including the absorption spectrum) of the BNLM used here are well documented. Typically, a second wavelength of 1.5 to 2 μm is pumped out, but this range is not exclusive due to the wide variety of BNLMs and can be slightly, rather than extensively, shifted in the opposite spectral direction. Technically, the second wavelength can be coupled into the BNLM to propagate in the same or opposite direction as the first wavelength.

[0061] Other nonlinear processes can be used to generate new additional wavelengths that differ from the fs and second operating wavelength of the individual laser sources. These new wavelengths, instead of the first and second wavelengths, can be absorbed in the BNLM and thus contribute to the formation of thermal lenses. Generating new wavelengths in a specially selected BNLM with second-order (and of course third-order) nonlinearity is often referred to as three-wave mixing, but it includes the various processes disclosed below.

[0062] One process in three-wave mixing involves the generation of the second harmonic (SHG) of the fundamental frequency of the fs beam, which is not absorbable in the NLM itself, but its second harmonic is absorbable in the NLM. This absorption leads to heat dissipation and eventual filamentation, resulting in the generation of the fsSCG and spectral broadening of the output fs pulse.

[0063] Another process is called sum-frequency or difference-frequency generation. In both types of frequency conversion, the wavelengths of the individual fs and pump lasers (none of which are absorbable) interact with each other and with the BNLM to generate a third wavelength within the absorption spectrum of the selected BNLM.

[0064] Another type of three-wave mixing is optical rectification. This effect is somewhat similar to difference generation, because the interaction between the fs laser and the BNLM generates a new wavelength that is longer than the first wavelength of the fs laser and is absorbable in the BNLM.

[0065] Another process in three-wave mixing is parameter generation, where a pump wavelength is selected to interact with the BNLM to generate new wavelengths that are longer than the initial wavelength of the fs laser, and at least one of these new wavelengths is absorbable to produce thermal lenses. One of these new wavelengths is absorbable in the selected BNLM to participate in the formation of the thermal lens.

[0066] As mentioned above, there are many BNLMs exhibiting third-order nonlinearity (which also exhibit second-order nonlinearity characteristics). Typically, these materials can be selected from those with third-order nonlinearity (χ²). (3) Single-crystal and polycrystalline materials with ≠ 0, including those exhibiting second-order nonlinearity (χ²) (2) BDLM subgroups with ≠0. Single-crystal materials include oxides (BBO), phosphides (ZGP), etc. In addition, quasi-phase-matched materials or random quasi-phase-matched materials are selected from one of PPLN, PPSLT, OP-GaAs, OP-GaP, polycrystalline ZnS, and polycrystalline ZnSe.

[0067] Figures 4A to 4C Showing whether or not Figure 3A The thermal effect shown in the schematic diagram is compared with the simulated spectrum by experimentally measured SCG nJ-level pulse energy. Figure 4B The transverse flux distribution of the pulse without any thermal effects is shown (corresponding to) Figure 4A (The blue line in the middle). Figure 4B It shows the corresponding Figure 4A The red line represents the flux distribution of the weakly focused thermal waveguide. The white line indicates the 1 / e² beam waist, with an initial value of 85 μm.

[0068] Figures 4A to 4CThis illustrates how the absence and presence of thermal waveguides in a medium lead to drastically different intensity distributions along the propagation direction. In the absence of thermal waveguides ( Figure 4B In the case of (i) an fs pulse with energy on the order of nJ, it propagates more or less like a Gaussian beam, i.e., it has very low nonlinear self-focusing due to the optical Kerr effect; (ii) the pulse spectrum undergoes a very small amount of spectral broadening (also due to the optical Kerr effect). In contrast, Figure 4C The presence of the thermal waveguide is shown to lead to the formation of thermal lenses and their contribution to the nonlinear lenses within the NLM. This, in turn, results in a dramatic increase in laser intensity within the NLM, followed by an explosive increase in spectral bandwidth, i.e., the generation of a supercontinuum at nJ-level energies (low-threshold SCG) of the input pulse.

[0069] Figure 3B A schematic diagram is shown, comprising a single fs oscillator (laser) and a bulk nonlinear medium (NLM). The parameters of the fs laser and the NLM are chosen such that the NLM partially absorbs the fs laser radiation via some linear or nonlinear mechanism. This, in turn, applies a thermal waveguide in the NLM, which has a refractive index change Δn = (dn / dT)ΔT along the axis of the pump beam, as described above. The inventors refer to this schematic diagram as a self-heating waveguide. In fact, refer to... Figure 3A All publicly disclosed nonlinear processes are in Figure 3B It plays a role in self-heating waveguides, where the BNLM is configured to support three-wave and four-wave processes (e.g., four-wave mixing multiphoton absorption, and of course, Kerr nonlinear focusing processes), which is particularly important for the selected BNLM. Figure 3A Conversely, only the first fs wavelength generates all the aforementioned nonlinear processes, resulting in the generation of new absorbable wavelengths.

[0070] Figures 5A to 5C The image shows a... Figure 3B Experimental realization of a low-threshold fs-SCG with a self-heating waveguide schematic diagram. Here, the experiment uses PRR (frequency) f R A mode-locked Cr:ZnSfs laser with a frequency of 81 MHz was used, and the laser was operated using a ZGP crystal as a BNLM. It exhibits high second-order nonlinearity (χ²). (2) A 3mm long ZGP (zinc germanium phosphate) crystal (≠0) is configured for optical rectification of the input fs pulse.

[0071] ZGP crystals absorb some spectral components resulting from the nonlinear frequency conversion of the input pulse. Specifically, it absorbs the SH of the 1.2 μm input pulse and the long-wavelength IR components of the output pulse with wavelengths above 12 μm. These nonlinear absorptions create a thermal waveguide in the ZGP medium. The confinement of fs radiation in the thermal waveguide leads to increased laser intensity. The increased laser intensity, in turn, leads to increased nonlinear absorption and a continuously stronger thermal waveguide and stronger confinement of fs radiation, resulting in filamentation and ultimately SCG. Besides ZGP, BNLMs can include fluoride (CaF2) or sulfide and selenide (ZnS, ZnSe, GaSe) and TM:II-VI semiconductors, which can have high third-order nonlinearity (χ²). (3) Single and polycrystalline Cr:ZnS, Cr:ZnSe, Fe:ZnS, Fe:ZnSe (≠0)

[0072] Specifically, Figures 5A to 5C The measured spectra of the fs pulse at the input (blue curve) and output (red curve) of the NLM are shown. This spectrum was measured as the average power of the pulse sequence and pulse energy gradually increased. The output spectrum includes the baseband (f), the long-wavelength IR band (0f) generated in the NLM via optical rectification, and the intermediate band generated in the NLM via a series of three-wave mixing between the spectral components from the f and 0f bands, as shown. Figure 5C As shown.

[0073] Figure 5A This corresponds to 14 nJ of energy (1.1 W average power) of the input pulse at the fundamental frequency f. It can be seen that the nonlinear broadening of the output pulse is very low in this case. Due to factors such as linear absorption and imperfect coating of the sample, the 16.7% loss in the NLM can be considered a linear loss. Figure 5B Corresponding to the ratio Figure 5A The nonlinear broadening is slightly wider at 32nJ. 19.8% of the loss indicates both linear and nonlinear loss, with the latter being due to nonlinear focusing. Figure 5C This corresponds to an input pulse energy of 46 nJ (3.8 W average power). In this case, the nonlinear broadening of the output pulse is very strong, and the pulse propagates with a loss of 23.5% (including both linear and nonlinear losses corresponding to the additional 0.3 W heat dissipation in the NLM). Based on the foregoing, the reliable indication that the filamentation threshold has been reached is due to thermal lensing caused by the additional nonlinear absorption in the BNLM. Therefore, increasing the input pulse energy by 3.3 times results in a significant enhancement of the spectral broadening and leads to a low threshold fs-SCG, which is simultaneously controlled by nonlinear and thermo-optical effects in the BNLM.

[0074] The low-threshold SCG obtained according to this disclosure can be further improved by: (i) "correct" pre-chirping and pre-shaping of the input pulse from the fs laser, (ii) additional laser gain (G) in the NLM, and (iii) optimization of the parameters of the thermal waveguide (i.e., optimization of the refractive index variation Δn at the axis of the pump beam). Improvement (i) can be achieved by selectively inserting undoped YAG plates, ZnSe plates, dispersive mirrors, volume Bragg gratings (VBGs), and other components between the fs oscillator and the BNLM. All these components can be, for example, Figure 3A The optical arrangement OA shown is part of the optical arrangement OA, and can also be used in the same way. Figure 3B A schematic diagram. Of course, the dispersion characteristics of the BLNM should be selected to eliminate pre-chirp and compress the fs pulse to the shortest possible duration within the BLNM. Improvement (ii) involves utilizing a BNML, which is both a laser and a nonlinear material. The additional laser gain G results in an additional increase in intensity within the NLM, and thus leads to a low-threshold SCG with a wider output spectrum, such as... Figure 4B As shown. Improvement (iii) includes fine-tuning the pump laser absorption within the NLM, resulting in a low-threshold SCG with even a wider output spectrum. Figure 4C The text illustrates the importance of fine-tuning Δn for parameters of low-threshold SCG. Figure 4C The shortest fs pulse is obtained at the focal point of thermal conduction in the NLM. The disclosed optimization can be achieved experimentally or through computer simulation.

[0075] The aspects of the invention disclosed herein are not limited to their application to the details of the construction and arrangement of the components set forth in the following description or shown in the accompanying drawings. These aspects are open to other embodiments and can be practiced or performed in various ways. Examples of specific implementations are provided herein for illustrative purposes only and are not intended to be restrictive. Specifically, actions, components, elements, and features discussed in connection with any one or more embodiments are not intended to exclude similar roles in any other embodiment.

[0076] Furthermore, the wording and terminology used herein are for descriptive purposes and should not be considered limiting. Any reference to examples, embodiments, components, elements, or actions of systems and methods mentioned herein in the singular may also cover embodiments including the plural, and any plural reference to any embodiment, component, element, or action herein may also cover embodiments including only the singular. References in either the singular or plural form are not intended to limit the currently disclosed systems or methods, their components, actions, or elements. The terms “comprising,” “including,” “having,” “containing,” “involving,” and variations thereof, as used herein, are intended to cover items listed thereafter and their equivalents, as well as additional items. References to “or” may be interpreted inclusively, such that any term described using “or” may refer to a single, more than one, or any of all the terms described. Furthermore, in the event of any inconsistency between the use of terminology in this document and in documents incorporated herein by reference, the usage of terminology in the incorporated reference shall supplement the usage of terminology in this document; in the case of irreconcilable inconsistencies, the usage of terminology in this document shall prevail.

[0077] Having described several aspects of at least one example, it should be understood that various changes, modifications, and improvements will readily occur to those skilled in the art. For example, the examples disclosed herein can also be used in other contexts. Such changes, modifications, and improvements are intended to be part of this disclosure and are intended to fall within the scope of the examples discussed herein. Therefore, the foregoing description and figures are merely illustrative.

Claims

1. A method for generating femtosecond fs supercontinuum in a volumetric nonlinear material BNLM, wherein the BNLM has a positive thermo-optical coefficient dn / dT > 0 K. –1 ,include: The light of a first wavelength emitted by the fs pulse oscillator is coupled into the BNLM, thereby generating nonlinear focusing of the coupled fs pulse in the BNLM, wherein the fs pulse oscillator operates at a full pulse repetition rate (PRR). The BNLM provides an interaction with light of a second wavelength different from the first wavelength and capable of being absorbed by the BNLM, thereby forming a thermal lens in the BNLM. The nonlinear focusing of the fs pulse and the thermal lens cumulatively generate the fs supercontinuum with the full pulse repetition rate PRR of the fs pulse oscillator.

2. The method according to claim 1, wherein, The BNLM is selected to have linear absorption, nonlinear absorption, or both linear and nonlinear absorption at the first wavelength and the second wavelength, with the first wavelength length selected from a near-IR to mid-IR spectral range extending between 1µm and 10µm.

3. The method according to claim 1, wherein, The BNLM is selected from those with third-order nonlinearity χ. （3） Amorphous materials, single-crystal materials, and polycrystalline materials with a crystal structure ≠ 0 The single crystal material is YAG, BBO, ZGP, CaF2, ZnS, ZnSe, or GaSe, and the amorphous material includes silicate and non-silicate glasses.

4. The method according to claim 3, wherein, The BNLM is selected from those with second-order nonlinearity χ. （2） A single or polycrystalline material that is ≠0, quasi-phase matched or randomly quasi-phase matched, which realizes one of sum-frequency mixing, difference-frequency mixing, optical parameter generation or optical rectification or a combination thereof, and is selected from PPLN, PPSLT, PPKTP, OP-GaAs, OP-GaP, polycrystalline ZnS and polycrystalline ZnSe.

5. The method according to claim 3, wherein, The BNLM is selected from TM:II-VI semiconductors, which include single-crystal and polycrystalline Cr:ZnS, Cr:ZnSe, Fe:ZnS, and Fe:ZnSe.

6. The method according to claim 1, wherein, The absorption of the second wavelength causes a radial temperature distribution along the cross section of the light, which acts as a thermal conductor, thereby forming the thermal lens.

7. The method according to claim 2, wherein, The interaction between the BNLM and the first wavelength includes: partially converting the first wavelength into at least one or more additional wavelengths during multiphoton absorption or nonlinear three-wave or four-wave mixing or a combination thereof at the first wavelength.

8. The method according to claim 1, wherein, The interaction between the BNLM, the first wavelength, and the second wavelength includes: partially converting the first wavelength and the second wavelength into at least one or more additional wavelengths during nonlinear three-wave mixing and four-wave mixing of the first wavelength and the second wavelength, wherein the first wavelength and the second wavelength propagate in the same direction or in opposite directions in the BNLM.

9. The method of claim 1, further comprising optimizing the supercontinuum generation to achieve the widest spectrum of the fs pulse at the output of the BNLM with the lowest energy and peak power of the fs pulse at the input of the BNLM, wherein, Optimization of supercontinuum generation includes: (a) Adjust the beam size of the first wavelength of light incident on the BNLM, (b) Adjust the average power and beam size of the second wavelength of light. (c) When inserting an optical element selected from bulk optical materials or a combination of a VBG and a dispersive mirror, identify the optimal time distribution of the fs pulse at the self-focusing position, thereby performing positive or negative pre-chirping on the fs pulse upstream of the BNLM. (d) Select the BNLM to have material dispersion, thereby compressing the pre-chirped fs pulse, or (e) Identify the self-focusing position of the pre-chirped fs pulse within the BNLM, and compress the pre-chirped fs pulse to the shortest pulse duration within the identified position, or (f) Selective combinations of (a) to (e).

10. The method according to claim 9, wherein, The bulk optical material includes YAG or ZnSe.

11. The method according to claim 1, wherein, The BNLM is configured as either a gain medium or a non-gain medium at a first wavelength.

12. The method according to claim 1, wherein, The self-focusing threshold with the thermal lens present is at least half lower than the threshold without the thermal lens.

13. An optical structure for controlling the generation of femtosecond fs supercontinuum, comprising: An fs oscillator outputs light of a first wavelength with a series of fs pulses at a full pulse repetition rate (PRR), the PRR ranging from 10 MHz to 10 GHz; and A bulk nonlinear material BNLM receives an fs pulse with pulse energy that causes local nonlinear focusing, but the pulse energy is insufficient to reach the threshold for generating the fs supercontinuum. BNLM has a positive thermo-optical coefficient dn / dT>0 K –1 It is configured to absorb light of a second wavelength different from the first wavelength, the absorbed light causing heat dissipation through a cross section of the first wavelength, the heat dissipation forming a thermal lens along the length of the BNLM, wherein the thermal lens increases the intensity of the nonlinearly focused fs pulse of the first wavelength to the threshold of the fs supercontinuum generation.

14. The optical structure according to claim 13, wherein, The BNLM is selected to have linear absorption, nonlinear absorption, or linear and nonlinear absorption at the first wavelength and the additional wavelength, with the first wavelength length selected from a near-IR to mid-IR spectral range extending between several hundred nanometers and 10 µm.

15. The optical structure according to claim 13, wherein, The BNLM is selected from those with third-order nonlinearity χ. （3） Amorphous materials, single-crystal materials, and polycrystalline materials ≠ 0, with selected BNLMs exhibiting third-order nonlinearity including those exhibiting second-order nonlinearity χ. （2） Subgroups of BNLM that are not equal to 0.

16. The optical structure according to claim 15, wherein, Each of the BNLMs in the subgroup having the second-order nonlinearity is selected from single-crystal or polycrystalline materials including birefringent phase-matching materials, quasi-phase-matching materials, or random quasi-phase-matching materials. The birefringent phase-matching material is one of LN, LBO, BBO, KTP, ZGP, and GaSe. The quasi-phase-matching material is one of PPLN, PPSLT, PPKTP, OP-GaAs, and OP-GaP. The random quasi-phase-matching material is one of polycrystalline ZnS or polycrystalline ZnSe.

17. The optical structure according to claim 16, wherein, Each of the BNLMs is configured for three-wave mixing (TWM), which includes a nonlinear process selected from one or a combination of second harmonic generation (SHG), sum and difference frequency generation, optical rectification, and parameter generation.

18. The optical structure according to claim 15, wherein, The amorphous material includes silicate glass and non-silicate glass, and the single crystal material includes oxides, phosphides, fluorides, sulfides, or selenides, wherein the oxide includes YAG or BBO, the phosphide includes ZGP, the fluoride includes CaF2, the sulfide includes ZnS, and the selenide includes ZnSe or GaSe. The BNLM is selected from TM:II-VI semiconductors, which include single-crystal and polycrystalline Cr:ZnS, Cr:ZnSe, Fe:ZnS, and Fe:ZnSe that are configured for laser interaction, three-wave mixing, and four-wave mixing to generate the second wavelength and multiphoton absorption.

19. The optical structure of claim 18, further comprising an auxiliary laser source, the auxiliary laser source outputting an additional wavelength coupled to the BNLM such that the additional wavelength propagates in the same direction or in the opposite direction to the first wavelength, the additional wavelength being a second wavelength absorbed in the BNLM, or pumping the first wavelength or nonlinearly interacting with the BNLM and the first wavelength to provide the three-wave mixing, thereby generating the second wavelength, wherein, The auxiliary laser source operates in either continuous wave or pulse mode.

20. The optical structure of claim 19, further comprising a lens arrangement located between the auxiliary laser source and the BNLM and configured to controllably change the beam size of light of an additional wavelength, wherein, The auxiliary laser source is configured to controllably adjust the average power of the light at the additional wavelength; or The lens arrangement is located between the fs oscillator and the BNLM and is configured to change the beam size of the light of the first wavelength.

21. The optical structure of claim 13, further comprising a dispersive element located between the fs oscillator and the BNLM and comprising one or more of an undoped YAG plate, a ZnSe plate, a dispersive mirror, and a volume Bragg grating (VBG), to apply chirp to the fs pulse, wherein the BNLM is configured with material dispersive properties to compress the pre-chirped fs pulse. The beam size of the first wavelength and the second wavelength, as well as the power of the second wavelength, are controlled so that the nonlinear focusing and the thermal lens have a common focal position within the BNLM.

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