Low-threshold supercontinium generation in bulk dielectrics and semiconductors

Abstract

Positive thermo-optic coefficient (dn / dT>0K -1 Control of low-threshold femtosecond supercontinuum generation (fsSCG) in bulk nonlinear materials (BNLM) with a 1000 Hz frequency response is provided by coupling light of a first wavelength output by an fs oscillator at full pulse repetition rate (PRR) into the BNLM. The coupling of light creates a nonlinear lensing of the coupled beam into the BNLM, but is insufficient to provide sufficient optical intensity to reach the threshold of fsSCG. To increase the pulse energy to reach the SCG threshold, light of a second wavelength different from the first wavelength is absorbed into the BNLM to form a thermal lens in the BNLM and assist the nonlinear lensing in generating the SCG.

Description

[Technical Field]

[0001] This disclosure relates to femtosecond supercontinuum generation (SCG) and supercontinuum laser sources. In particular, this disclosure relates to a method and system for generating low-threshold SCG in nonlinear materials (NLMs) of bulk dielectrics and semiconductors by generating a thermal lensing effect along with a nonlinear self-focusing effect. [Background technology]

[0002] SCG is the formation of a wide-band continuous spectrum by the propagation of high-power pulses through a nonlinear medium. In particular, fs-pulse SCG (fsSCG) is attracting attention because it yields an optical spectrum that combines a wide harmonic bandwidth with high spatial and temporal coherence. Therefore, fsSCG is important for many applications, especially for optical frequency combs, arbitrary optical waveform synthesis, and attosecond pulse generation. An optical frequency comb is equivalent to an fs-pulse train and uses a watt-level average power P of 0.1W to 10W and 10 7 Hz~10 10 A relatively high pulse repetition rate (PRR) or frequency f in the Hz range R In other words, low pulse energy W=P av / f R It has a current of 0.1 nJ to 100 nJ and is essential for spectroscopy, detection, microscopy, and imaging.

[0003] The technology for fsSCG in specially designed nonlinear optical fibers and waveguides (such as silicon nitride Si3N4) is well-established. However, the use of fibers and waveguides with restricted geometries comes at the cost of increased complexity of the laser system and reduced overall efficiency. Furthermore, nonlinear fibers and waveguides have inherent limitations regarding SCG power and coherence, and require precise alignment.

[0004] Bulk materials, such as transparent amorphous solids (e.g., silicate and non-silicate optical glasses), crystals (e.g., oxides, fluorides, phosphides), and semiconductors (silicon, germanium, and other Group III-V and Group II-VI materials), also support fsSCG. The advantages of fsSCG in these materials are, in particular, that they are relatively simple, meaning low-cost and flexible, and that peak and average power can be scaled. Laser propagation in these materials is not limited by the cross-sectional shape of the material, mitigating alignment sensitivity. Furthermore, SCG in some bulk materials is characterized by compressing femtosecond input pulses into even shorter output pulses with fewer optical cycles. For example, in Patent Documents 1, 2, and 3 by the applicant (these documents are incorporated collectively in this application by reference), Cr 2+ This describes teaching SCG in random pseudo-phase-matched gain media such as ion-doped polycrystalline zinc sulfide.

[0005] Femtosecond SCG in nonlinear materials is controlled by the nonlinearity of the selected bulk material and the interaction of nonlinear absorption and chromatic dispersion. The physical image of fsSCG can be understood within the framework of filamentation, i.e., the interaction of self-focusing, self-phase modulation, and multiphoton absorption / ionization-induced free electron plasma. The interaction of these physical phenomena gives rise to filaments (dynamic structures with a strong core that can propagate over distances much longer than the typical diffraction length while maintaining a narrow beam size without the need for an external guiding mechanism) (Non-Patent Literature 1). A key consequence of filament formation is very strong nonlinear broadening of the pulse spectrum, i.e., the bandwidth of the output spectrum is much larger than that of the input spectrum. Figures 1a and 1b show a typical setup for fsSCG in bulk material. The presence of filamentation in Figure 1a results in strong broadening, but in its absence, the output spectrum is not broadened, as shown in Figure 1b.

[0006] The initial stage of filament formation is determined by self-focusing, that is, the χ of the medium. (3)Nonlinearity induces 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). The local intensity is high at the center of the beam and low at its edge. Thus, the χ (3) medium with n2 > 0 functions like an intensity-dependent lens. The self-focusing threshold is determined by the critical power P Crit , which is determined by the parameters of the gain medium (nonlinear and linear components of the refractive index, wavelength of the wave coupled to the medium, etc.). The value of P Crit of the gain medium (also referred to as a bulk dielectric, semiconductor, nonlinear material or nonlinear medium (NLM)) is in the range of 0.1 MW to several tens of MW depending on the material.

[0007] FsSCG in a bulk gain medium occurs when the peak power (P Pk ) of the input pulse significantly (usually by more than one order) exceeds P Crit . Thus, based on the above, a standard implementation of fsSCG in a gain NLM is based on an fs laser, with a relatively high multi-MW level peak power (up to 100 MW), a high μJ level pulse energy, and typically operates at a low kHz repetition rate.

[0008] However, many important applications of fsSCG, such as optical frequency combs, require an fs laser that operates at a high multi-MHz rate, i.e., the full repetition rate f R = 10 7 Hz to 10 10 Hz and a low nJ level pulse energy. The peak power level of an nJ fs pulse is usually from sub-MW to less than 10 MW (i.e., P Pk ≤ P Crit ), which is too weak to cause self-focusing in the NLM. Thus, SCG and spectral broadening are either too weak or simply do not occur. This is shown in Fig. 1b.

[0009] Experimental data on fsSCG in bulk NLM raises a number of issues regarding the propagation of few-cycle pulses in bulk NLM. In the operation of an fs oscillator at full PRR, the fs pulse does not reach the desired peak power sufficient to generate fsSCG. In prior art schemes, fsSCG cannot be achieved with existing PRRs. Therefore, an additional mechanism to assist non-linear focusing to induce fsSCG at high PRR must be identified. If such a mechanism and its control method are known, a universal methodology for low-threshold fsSCG in the target NLM can be provided even when operating the fs oscillator at full PRR (relatively high as described above).

[0010] Therefore, it is necessary to provide an improved method for achieving low-threshold fsSCG in the target NLM with nJ-level pulse energy (P Pk ≦P Crit ) and a high multi-MHz pulse repetition rate using known physical processes.

[0011] A laser system configured to execute the improved process is also needed.

Prior Art Documents

Patent Documents

[0012]

Patent Document 1

Patent Document 2

Patent Document 3

Non-Patent Documents

[0013]

Non-Patent Document 1

[0014] The concept of the present invention is based on the synergistic effect resulting from the thermal lens formed on a target NLM as a result of the interaction between light and the NLM, and the nonlinear self-focusing effect. In particular, the thermal lens effectively assists the nonlinear focusing phenomenon when generating a low threshold fsSCG.

[0015] The method disclosed herein provides a positive thermo-optic coefficient (i.e., the temperature derivative of the refractive index dn / dT > 0K) -1 The process involves selecting a desired NLM from a plurality of transparent materials having the following properties, and selecting a wavelength to which an fs pulse train is coupled to the selected NLM. The fs pulse train 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, it does not have enough energy to reach the threshold of the fsSCG because the self-focusing in the NLM is too weak.

[0016] Then, the additional wavelengths obtained by coupling with the auxiliary laser source NLM, or as a result of the nonlinear effect caused by the interaction between the fs pulse and the NLM, are absorbed by the NLM. This absorption is accompanied by thermal dissipation along the cross-section of the fs beam, leading to the formation of a thermal lens. The addition of the thermal lens assists nonlinear self-focusing, resulting in the formation of a filament at the low peak power of the fs pulse.

[0017] The selected NLM may or may not be a gain medium. In other words, the selected NLM does not need to be an optical amplifier. Advanced criteria for a suitable NLM require that it be at least partially transparent (transmissive) at the wavelength of the coupled fs pulse train and have a positive thermo-optic coefficient. The selected NLM may be found in publicly available sources well known to those skilled in the art, or it may be determined experimentally.

[0018] According to one feature of the method disclosed herein, the selected NLM has high second-order nonlinearity and third-order nonlinearity (χ (2) ≠0, χ (3) It is characterized by (≠0). As a result of such nonlinear effects, additional wavelengths are generated in the NLM by three-wave mixing, optical parametric generation, optical rectification, and multiphoton absorption. At least one of these new wavelengths is absorbed by the selected NLM, resulting in the formation of a thermal lens. Another nonlinear effect that generates additional wavelengths is four-wave mixing, which, like the Kerr effect, exhibits third-order nonlinearity (χ²). (3) It arises from (≠0). In addition to the newly generated wavelengths, spectral components that exceed the transparency window (range) of the selected material are also absorbed, contributing to the formation of a thermal lens.

[0019] According to other features, in addition to the fs pulse, a continuous wave (CW) beam is coupled to a selected NLM. The wavelength of the CW beam is selected so that it is absorbed by the NLM, causing thermal dissipation and the formation of a thermal lens. The thermal lens, along with nonlinear focusing, is useful for reaching the low threshold of the SCG.

[0020] According to other features of the method of this disclosure, the selection of a nonlinear material is based on the wavelength of the fs oscillator used in a given system. Conversely, if a nonlinear material and its optical properties are known, the fs oscillator is selected to operate at a wavelength that, in interaction with the known material, gives both nonlinear focusing and other nonlinear effects that result in additional wavelengths known to be absorbed by the NLM to give thermal lensing. Many material properties, such as absorption spectra, are well known in much of the literature.

[0021] Another feature of the method of this disclosure is to determine the formation of a thermal lens. In particular, the spectrum of the input fs pulse is repeatedly measured at the input and output of a selected nonlinear material. The maximum output spectral bandwidth significantly exceeds the input spectral bandwidth, indicating the formation of a sufficiently strong thermal lens and also indicating that the threshold for fsSCG has been reached.

[0022] Further features of the method of this disclosure relate to the optimization of the fsSCG required to achieve the broadest spectrum of the fs pulse at the output of a selected material after a threshold has been reached. The optimization includes controlling and varying 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 the pre-chirpening of the input fs pulse.

[0023] In place of or in combination with some or all of the optimization methods described above, the methods of the present disclosure may include determining the location of a self-focusing point within a selected material and identifying the time distribution of the coupled fs pulse at that location. Preferably, if the fs pulse is pre-chirped, the optimization further includes selecting a material that features a dispersion useful for compressing the pre-chirped pulse, according to features of the other methods. The most efficient optimization is achieved by compressing the pre-chirped pulse at the location of the nonlinear self-focusing into the shortest possible fs pulse.

[0024] Other aspects of this disclosure may include any or a combination of the above-described features and other features relating to an optical system configured to perform the methods of this disclosure. Accordingly, a system of the present invention may include any one of the disclosed features, or some or all of the selected features.

[0025] According to this embodiment, the system of the present disclosure may include an fs oscillator and an optical pump that superimposes multiple output beams in a selected nonlinear material. The optical pump facilitates the formation of a thermal lens. Yet another system does not require an additional light source and consists only of an fs oscillator and a selected NLM. According to the concept of the present invention, the parameters of the fs oscillator and the NLM are selected so that the NLM partially absorbs the fs laser radiation, provides a thermal waveguide, and forms a thermal lens that assists nonlinear focusing when generating a low threshold SCG.

[0026] The features described above and other features of this disclosure will become even more readily apparent from the accompanying drawings. [Brief explanation of the drawing]

[0027] [Figure 1] Figure 1a shows a typical configuration for bulk fsSCG, characterized by filamentation and strong nonlinear broadening when PPk >> PCrit, where PPk is the peak power and PCrit is the critical power. Figure 1b shows a typical configuration for bulk fsSCG, characterized by no filamentation and weak nonlinear broadening when PPk ≤ PCrit. [Figure 2] The spectral bandwidth simulation of a low-threshold SCG is shown as a function of laser gain and the refractive index change imposed by the thermal lens of this disclosure. [Figure 3] Figure 3a shows an exemplary system configured to carry out the method of the present invention. Figure 3b shows another exemplary system configured to carry out the method of the present invention. [Figure 4] Figure 4a shows the simulation-predicted spectra with and without the experimentally measured SCG thermal effect of the present disclosure. Figure 4b shows a simulation of the lateral fluence profile of a prior art nJ pulse. Figure 4c shows the lateral distribution of the nJ pulse in the thermal guide of the present disclosure. [Figure 5] Figure 5a shows the measured spectra of the fs pulse at the input and output of the selected NLM from Figure 3a at relatively low average and peak power, with the output spectrum including the fundamental band (f). Figure 5b shows the measured spectra of the fs pulse at the input and output of the NLM from Figure 3a at higher average and peak power than those in Figure 5a, with the output band including the fundamental band (f) and the long-wave IR (infrared) band (0f) generated in the NLM via optical rectification. Figure 5c shows the measured spectra of the fs pulse at higher average and peak power than those in Figure 5b, with the output spectrum including the intermediate band generated in the NLM via a three-wave mixing chain between the spectral components of the f-band and the 0f-band. [Modes for carrying out the invention]

[0028] The following describes various aspects of one or more embodiments with reference to the accompanying drawings, which are not to scale. The drawings are included to illustrate and further understand the various aspects and embodiments and are incorporated into the specification, forming part of the specification, but do not limit any particular embodiment. The drawings, together with the rest of the specification, are intended to illustrate the principles and operation of the disclosed and claimed aspects and embodiments. With respect to the drawings, identical or substantially identical components shown in multiple drawings are represented by the same number. For clarity, not all components are labeled in all drawings.

[0029] Figure 1a shows a typical configuration for bulk fsSCG, P Pk >>P Crit It is characterized by filamentation and strong nonlinear widening in the equation, where P Pk This is the peak power, P Crit This is critical power.

[0030] Figure 1b shows a typical configuration for bulk fsSCG, P Pk ≤P Crit It is characterized by the absence of filamentation and weak nonlinear widening.

[0031] Figure 2 shows a simulation of the spectral bandwidth of a low-threshold SCG as a function of laser gain and the refractive index change imposed by the thermal lens of this disclosure.

[0032] Figure 3a shows an exemplary system configured to carry out the method of the present invention.

[0033] Figure 3b shows another exemplary system configured to carry out the method of the present invention.

[0034] Figure 4a shows the experimentally measured SCG versus the simulated spectra with and without the thermal effect of this disclosure.

[0035] Figure 4b shows a simulation of the lateral fluence profile of an nJ pulse using the conventional technology.

[0036] Figure 4c shows the lateral distribution of the nJ pulse in the thermal guide according to this disclosure.

[0037] Figure 5a shows the measured spectra of fs pulses at the input and output of the selected NLM from Figure 3a at relatively low average and peak power, with the output spectrum including the fundamental band (f).

[0038] Figure 5b shows the measured spectra of the fs pulse at the input and output of the NLM in Figure 3a at higher average and peak power than those in Figure 5a, where the output band includes the fundamental band (f) and the long-wave IR (infrared) band (0f) generated in the NLM via optical rectification.

[0039] Figure 5c shows the measured spectrum of the fs pulse at higher average and peak power than that of Figure 5b, and the output spectrum includes an intermediate band generated in the NLM via a three-wave mixing chain between the spectral components of the f-band and the spectral components of the 0f-band.

[0040] The subject of this invention relates to an additional optical mechanism that enables the nonlinear focusing of fs pulses to reach the fsSCG threshold, which would not be achievable using nonlinear focusing alone. Insufficient nonlinear focusing results from low pulse energy, i.e., insufficient peak power to generate the strong nonlinear effect that leads to fsSCG. In particular, fs pulses output by fs laser oscillators typically operating at high PRR have insufficient pulse energy and peak power to reach the SCG threshold in the bulk nonlinear material (BNLM) receiving the pulse. A solution to this problem is to generate a thermal lens in the BNLM, as disclosed herein, which, in combination with the nonlinear lens, results in fsSCG. The thermal lens provides additional focusing of the insufficiently nonlinearly focused fs pulse along the longitudinal direction of the BNLM, assisting the nonlinear focusing to reach the fsSCG threshold at full PRR in the 10 MHz to 10 GHz range of the fs oscillator. The SCG threshold achievable with the concept of this invention tends to be less than half the SCG threshold achievable by nonlinear focusing alone.

[0041] Figure 2 illustrates the importance of thermal lensing for generating fsSCG in a BNLM (illustrated as NLM). Figure 2 shows a simulation of the spectral bandwidth (Δν(THz)) of a low-threshold SCG as a function of gain (G) and the refractive index change Δn imposed by the thermal lensing. The lower, middle, and upper arrows represent the qualitative trajectories of the increase in pump power and its effect on the achievable maximum values ​​of gain and Δn in pump laser absorption in low-level, medium-level, and high-level NLMs, respectively. The broadening of the output spectrum with increasing gain is not very pronounced, indicating that laser gain alone (i.e., approximately a fourfold increase in pulse energy and peak power) is insufficient to reach the fsSCG threshold (i.e., achieve strong spectral broadening). However, to some extent, gain contributes to spectral broadening. In contrast, the refractive index change Δn (upper arrow) generates a thermal lens in the medium, which is useful for broadening the output spectrum and thus useful for reaching the fsSCG threshold. In conclusion, the comparison of the curved surfaces indicates that the waveguide formed due to thermal lensing is what significantly enables the desired low threshold SCG. Furthermore, Figure 2 shows that the selected BNLM does not necessarily have to be a laser gain medium to reach the fsSCG threshold; that is, thermal lensing alone (i.e., an increase in Δ at a constant G=1) may be sufficient.

[0042] To overcome the insufficient pulse energy and peak power, i.e., the pulse energy limitation, of the fsSCG in conventional BNLMs, this disclosure teaches how to generate a thermal self-focusing mechanism (also known as a thermal lens) based on the temperature dependence n(T) of the refractive index. The thermal lens assists conventional nonlinear self-focusing and is due to the intensity dependence of the refractive index n(I) = n0 + n2I (Equation 1). The formation of the thermal lens is described in detail below.

[0043] Many BNLMs have a positive refractive index temperature derivative dn / dT > 0K. -1It is characterized by the following. Furthermore, as is known to those skilled in the art, heat dissipation along the axis of a laser beam propagating through an absorbent medium induces a temperature distribution across the beam cross-section, which can be approximated as follows: d 2 T(r) / dr 2 +(1 / r)dT / dr+P h / (κV)=0 (Equation 2) In the formula, P h ΔT is the thermal power dissipated into the medium, κ is the thermal conductivity of the medium, V is the volume of the heat dissipation region, and r is the radial distance of heat dissipation from the beam axis. Therefore, heat dissipation causes a local temperature rise ΔT, which induces the following local change in refractive index: Δn = (dn / dT)ΔT (Equation 3) Therefore, a medium that dissipates heat along the axis of the laser beam functions as a temperature-dependent lens (also known as a thermal lens). Under the influence of a thermal lens, beam propagation in a BNLM can be considered analogous to light propagation in a waveguide, as long as Δn is a fraction of the refractive index n. Thus, the fsSCG method of this disclosure combines to some extent the advantages of bulk and restricted shapes, enabling the generation of superctave coherent spectra at nJ-level pulse energies and high repetition rates, similar to waveguide configurations. At the same time, its spatial and temporal dynamics are similar to those in a bulk medium, characterized by additional focusing, ionization, etc., which are important for the favorable characteristics of the proposed fsSCG method.

[0044] The above provides a roadmap (guideline) for the generation of SCG in BNLMs relating to the concept of this disclosure. Due to the wide selection of BNLMs characterized by third-order nonlinearity, nonlinear focusing is based on the Kerr self-focusing effect exhibited by the formation of nonlinear lenses. Based on the details described above, nonlinear lenses alone are insufficient to increase the intensity of the fs pulse to a level sufficient for the formation of a broad output spectrum (i.e., the fsSCG threshold is not reached). To increase the intensity of the fs pulse, a thermal focusing effect is generated to assist nonlinear focusing. This generation may be by absorbing light of the wavelength of the fs pulse, or other suitable wavelengths absorbed in the BNLM via linear and / or nonlinear absorption mechanisms, thereby generating a thermal lens in the medium according to Equation 1 in the selected BNLM. Linear absorption in bulk dielectrics and semiconductors is a well-known effect. Wavelengths corresponding to linear absorption in specific media can be found in available literature or measured using available instruments. Nonlinear absorption can be achieved by utilizing nonlinear processes such as (1) multiphoton absorption, which is typical for a wide variety of BNLMs, (2) three-wave mixing, or (3) four-wave mixing, which generates a new wavelength that is different from the fundamental wavelength of the fs pulse but can be absorbed by the selected BNLM. Thus, the methodology of this disclosure includes the selection of the operating wavelength of the fs oscillator, and the linearity, absorptivity, and refractiveness (Equation 1) of the BNLM. For three-wave mixing, the selected BNLM has a third-order nonlinearity (χ (3) In addition to ≠0, there is also the second-order nonlinearity (χ²). (2) It is desirable to have a value (≠0). The heat generated by absorption dissipates across the pump beam, creating a refractive index gradient Δn=(dn / dT)ΔT across the pump beam, which is approximately proportional to the absorbed power. Under these conditions, the region along the axis of the laser beam has a higher refractive index than the beam periphery that forms the thermal lens. Ultimately, both the primary nonlinear lens and the thermal lens work together to reach the threshold for filament formation, resulting in fsSCG.

[0045] Figures 3a and 3b respectively illustrate exemplary optical systems configured to realize the concept of the present invention. Each illustrated system includes an fs laser or oscillator that outputs a train of nJ fs pulses having a relatively narrow input spectrum in the full PRR range of 10 MHz to 10 GHz. An upstream lens L or equivalent optical element (e.g., a concave mirror) focuses the fs light into the body of a BNLM, designated as an NLM. The pulse peak power of the nJ fs pulses is below critical power (i.e., P) in the range of sub-MW to 10 MW. Pk ≤P Crit Therefore, the known pulse peak power is only sufficient to generate a weak nonlinear lens. Consequently, the fsSCG threshold is not reached in the selected BNLM. The downstream lens L collimates the light at the output of the NLM.

[0046] Referring particularly to Figure 3a, the optical system further includes a second laser source or pump that can operate in a CW or pulsed manner, outputting light of a second wavelength different from the wavelength of the fs pulse. The femtosecond and CW emissions are superimposed onto a dichroic mirror (DM) by an upstream lens L or equivalent optical element (e.g., a concave mirror) and focused into the BNLM. In this case, optimization of the fsSCG can be achieved by controlling the pump power and / or the beam sizes of both lasers, in addition to the methods discussed below. These parameters can be controlled by incorporating an optical apparatus (OA) including one or more lenses. The pump power can be controlled by numerous methods well known in the art, although the vast majority of laser sources have controllable power.

[0047] For example, the second wavelength is selected so that it is absorbed in the BNLM by the pump. The optical properties (absorption spectrum, etc.) of the BNLM used here are well known in much literature. Typically, the pump outputs a second wavelength of 1.5 μm to 2 μm, but this range is not comprehensive due to the diversity of BNLMs and may shift to some extent, though not significantly, in the opposite spectral direction. Typically, the second wavelength can be coupled in the BNLM and propagate in the same direction as or in the opposite direction to the first wavelength.

[0048] Using other nonlinear processes, new additional wavelengths different from the fs wavelength and second operating wavelength of each laser source can be generated. These new wavelengths, which are neither the first nor the second wavelength, can be absorbed in the BNLM and contribute to the formation of a thermal lens. The generation of new wavelengths in a specifically selected BNLM with second-order nonlinearity (and of course, third-order nonlinearity) is generally referred to as three-wave mixing, but includes a variety of processes disclosed below.

[0049] One process in three-wave mixing involves the generation of second harmonic (SHG) of the fundamental frequency of the fs beam (which itself is not absorbable in the NLM), and the second harmonic is absorbable. This absorption leads to thermal dissipation and subsequent filamentation, resulting in the generation of fsSCG and spectral broadening of the output fs pulse.

[0050] Other processes are known as sum frequency generation and difference frequency generation. In both of these frequency conversions, the wavelengths of the fs laser and the pump laser (neither 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.

[0051] Another type of three-wave mixing is optical rectification. This effect is somewhat similar to difference frequency generation, where 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 absorbable in the BNLM.

[0052] Another process of three-wave mixing is parametric generation, in which the pump wavelength is selected to interact with the BNLM to generate several new wavelengths longer than the initial wavelength of the fs laser, at least one of which is absorbable and creates a thermal lens. One of these new wavelengths is absorbable in the selected BNLM and participates in the formation of the thermal lens.

[0053] As mentioned above, there are many BNLMs that possess cubic nonlinearity and are also characterized by cubic nonlinearity. Generally, these materials exhibit cubic nonlinearity (χ (3) Single-crystal materials and polycrystalline materials having (≠0) second-order nonlinearity (χ (2) The material is selected from the subgroup of BNLM (including BNLM) that has ≠0. Examples of single-crystal materials include oxides (BBO (barium borate)) and phosphides (ZGP). Other examples include birefringent phase-matched materials, pseudo-phase-matched materials, and random pseudo-phase-matched materials, selected from one of the following: PPLN (periodically polarized reversing lithium niobate), PPSLT (periodically polarized reversing stoichiometric lithium tantalate), PPKTP (periodically polarized reversing potassium titanyl phosphate), OP-GaAs (orientation patterned gallium arsenide), OP-GaP (orientation patterned gallium phosphide), polycrystalline ZnS, and polycrystalline ZnSe.

[0054] Figures 4a and 4c show the simulation-predicted spectra versus the experimentally measured nJ-level pulse energy of the SCG in the system of Figure 3a, with and without thermal effects. Figure 4b shows the lateral fluence profile of the pulse without thermal effects (corresponding to WG off in Figure 4a). Figure 4c shows the fluence distribution with a weakly focused thermal waveguide, corresponding to WG on in Figure 4a. The white line represents 1 / e 2 The beam waist is shown, and its initial value is 85 μm.

[0055] Figures 4a to 4c demonstrate that the presence or absence of a thermal waveguide in the medium results in entirely different intensity profiles along the propagation direction. In the absence of a thermal waveguide (Figure 4b), (i) an fs pulse with nJ-level energy propagates roughly like a Gaussian beam, i.e., it has very low nonlinear self-focusing due to the optical Kerr effect, and (ii) the pulse spectrum undergoes very little spectral broadening (also due to the optical Kerr effect). In contrast, Figure 4c shows the presence of a thermal waveguide, which leads to the formation of a thermal lens, and its contribution to the nonlinear lens within the NLM. This results in a dramatic increase in laser intensity within the NLM, followed by an explosive increase in spectral bandwidth, i.e., the generation of supercontinuum (low threshold SCG) at nJ-level energy input pulses.

[0056] Figure 3b shows a system comprising a single fs oscillator (laser) and a bulk nonlinear medium (NLM). The parameters of the fs laser and NLM are selected so that the NLM partially absorbs the fs laser radiation via a linear or nonlinear mechanism. This imposes a thermal waveguide in the NLM having a refractive index change Δn = (dn / dT)ΔT along the axis of the pump beam, as described above. The inventors have named this method self-thermal-waveguiding. Substantially all nonlinear processes disclosed in relation to Figure 3a act on the self-thermal-waveguiding in Figure 3b, and the BNLM is configured to support both three-wave and four-wave processes (e.g., four-wave mixed multiphoton absorption, etc.) and, of course, Kerr nonlinear focusing processes, which are particularly important for the selected BNLM. In contrast to Figure 3a, all of the above-mentioned nonlinear processes are generated at only the first fs wavelength to generate new absorbable wavelengths.

[0057] The experimental results of low-threshold fsSCG in the self-thermal waveguide system shown in Figure 3b are shown in Figures 5a to 5c. The experiment involved PRR (frequency) f R This was performed using a mode-locked Cr:ZnS fs laser at 81 MHz and a ZGP crystal as the BNLM. High second-order nonlinearity (χ (2)A 3mm long ZGP (zinc germanium phosphine) crystal with a ≠0 property was constructed for optical rectification of the input fs pulse.

[0058] ZGP crystals absorb certain spectral components through nonlinear frequency conversion of the input pulse, specifically the SG component of a 1.2 μm input pulse and the long-wave IR (infrared) component of output pulses with wavelengths exceeding 12 μm. These nonlinear absorptions create thermal waveguides within the ZGP medium. The confinement of fs radiation within these thermal waveguides leads to an increase in laser intensity. This increase in laser intensity, in turn, leads to increased nonlinear absorption, more continuous and powerful thermal waveguide formation, and stronger confinement of fs radiation, resulting in filamentation and ultimately SCG. In addition to ZGP, BNLM exhibits high third-order nonlinearity (χ (3) Examples of materials with a ≠0 pH include fluorides (CaF2), sulfides and selenides (ZnS, ZnSe, GaSe), and TM (transition metal): group II-VI semiconductors (e.g., single crystals and polycrystalline Cr:ZnS, Cr:ZnSe, Fe:ZnS, Fe:ZnSe).

[0059] In particular, Figures 5a to 5c show the measured spectra of fs pulses at the input (in) and output (out) of the NLM. The spectra were measured while gradually increasing the pulse energy and the average power of the pulse train. The output spectrum consists of the fundamental band (f), the long-wave IR band (0f) generated in the NLM by optical rectification, and the intermediate band generated in the NLM via a three-wave mixing chain between the spectral components of the f band and the 0f band (shown in Figure 5c).

[0060] Figure 5a corresponds to an input pulse with an energy of 14 nJ (average power of 1.1 W) at the fundamental frequency f. As can be seen, the nonlinear broadening of the output pulse is very low in this scheme. The 16.7% loss in the NLM is thought to be due to linear losses (e.g., linear absorption, incomplete coating of the sample, etc.). Figure 5b corresponds to 32 nJ, resulting in a somewhat wider nonlinear broadening than in Figure 5a. The 19.8% loss shows both linear and nonlinear losses, with the nonlinear loss being due to nonlinear focusing. Figure 5c corresponds to an input pulse with an energy of 46 nJ (average power of 3.8 W). In this scheme, the nonlinear broadening of the output pulse is very strong, with the pulse propagating with a loss of 23.5%, which includes linear and nonlinear losses and corresponds to an additional 0.3 W of thermal dissipation in the NLM. Based on the above, a reliable indicator that the filamentation threshold has been reached is the generation of a thermal lens due to additional nonlinear absorption into the BNLM. Therefore, a 3.3-fold increase in input pulse energy results in a dramatic enhancement of spectral broadening and a low threshold fsSCG, which is simultaneously controlled by nonlinear and thermo-optical effects in the BNLM.

[0061] The low threshold SCG obtained according to this disclosure can be further improved by (i) "correct" pre-chirpening or pre-shaping of the input pulse from the fs laser, (ii) additional laser gain in the NLM, and (iii) optimization of the thermal waveguide parameters (i.e., optimization of the refractive index change Δn along the axis of the pump beam). Improvement (i) can be achieved by selectively inserting an undoped YAG (yttrium aluminum garnet) plate, a ZnSe plate, a mirror with chromatic dispersion, a volume Bragg grating (VBG), or other components between the fs oscillator and the BNLM. All of these components may be parts of the optical apparatus OA shown in Figure 3a and are similarly available in the system of Figure 3b. Of course, it is desirable that the dispersion characteristics of the BNLM be selected to cancel pre-chirpening and compress the fs pulse to the shortest possible pulse width within the BNLM. Improvement (ii) can be achieved by utilizing a BNLM that is both a laser material and a nonlinear material. The additional laser gain G results in an additional increase in intensity within the NLM, i.e., a low threshold SCG with a broader output spectrum, as shown in Figure 4b. An improvement to (iii) is to fine-tune the pump laser absorption within the NLM to obtain a low threshold SCG with an even broader output spectrum. The importance of fine-tuning Δn for the low threshold SCG parameters is shown in Figure 4c, where the shortest fs pulse is obtained at the focal point of the thermal guide within the NLM. Optimization of this disclosure can be achieved through experimentation or through computer simulation.

[0062] The embodiments of this disclosure according to the present invention are not limited to the details of the configuration and arrangement of components given in the above description and shown in the accompanying drawings. These embodiments also envision other embodiments and can be implemented or performed in a variety of ways. Examples of specific embodiments are given for illustrative purposes only and are not limiting. In particular, functions, components, elements, and features described in relation to one or more embodiments are not excluded from similar roles in other embodiments.

[0063] The expressions and terminology used in this Application are for illustrative purposes only and are not limiting. Singular references to examples, embodiments, components, elements, and functions of the Systems and Methods of this Disclosure may also include plural references, and plural references to embodiments, components, elements, and functions of this Disclosure may include singular references only. Whether a reference is singular or plural does not limit the Systems and Methods of this Disclosure, or their components, functions, or elements. The use of terms such as “includes,” “equipment,” “possesses,” and “contains” in this Application includes the matters listed with respect to those terms, their equivalents, and additional matters. The term “or” can be interpreted comprehensively, and matters described using “or” may refer to one, more than, or all of those matters. Furthermore, if there is a discrepancy between the use of terminology in this Application and the use of terminology in references incorporated into this Application, the use of terminology in references incorporated into this Application is supplementary to that of this Application, and in the event of a conflict, the use of terminology in this Application shall prevail.

[0064] While multiple aspects of one or more examples have been described, it should be understood that a variety of changes, modifications, and improvements will readily come to mind for those skilled in the art. For example, the examples of this disclosure can be used in other contexts. Such changes, modifications, and improvements are part of this disclosure and within the scope of the examples of this disclosure. Accordingly, the above description and drawings are merely examples.

Claims

1. Positive thermo-optic coefficient (dn / dT > 0K) －１ A method for controlling femtosecond supercontinium generation (fsSCG) in bulk nonlinear material (BNLM) having ), By coupling light emitted at the first wavelength from an fs oscillator operating at full pulse repetition rate (PRR) into a bulk nonlinear material (BNLM), nonlinear focusing of the fs pulse coupled into the bulk nonlinear material (BNLM) is produced. The method involves forming a thermal lens in the bulk nonlinear material (BNLM) by interacting it with light of a second wavelength, which is absorbable by the bulk nonlinear material (BNLM) and differs from the first wavelength. A method wherein the nonlinear focusing of the fs pulse and the thermal lens together generate an fs supercontinuum at the full pulse repetition rate (PRR) of the fs oscillator.

2. The method according to claim 1, wherein the bulk nonlinear material (BNLM) is selected to have linear absorption, nonlinear absorption, or both linear and nonlinear absorption at the first and second wavelengths, and the first wavelength is selected from the near-infrared to mid-infrared spectrum in the range of 1 μm to 10 μm.

3. The bulk nonlinear material (BNLM) exhibits a third-order nonlinearity (χ （３） It has (≠0) and optionally exhibits second-order nonlinearity (χ²). （２） A selection is made from amorphous materials, single-crystal materials, and polycrystalline materials having (≠ 0), The single crystal material is YAG (yttrium aluminum garnet), BBO (barium borate), ZGP (zinc germanium phosphine), CaF2, ZnS, ZnSe, or GaSe. The method according to claim 1, wherein the amorphous material includes silicate glass or non-silicate glass.

4. The bulk nonlinear material (BNLM) exhibits a second-order nonlinearity (χ （２） The method according to claim 1, wherein a single-crystal material and a polycrystalline material having pseudo-phase matching or random pseudo-phase matching (≠0) is selected, and one or a combination of sum-frequency mixing, difference-frequency mixing, optical parametric generation, and optical rectification is produced, and a material is selected from one of PPLN (periodic polarization reversal lithium niobate), PPSLT (periodic polarization reversal stoichiometric lithium tantalate), PPKTP (periodic polarization reversal potassium titanyl phosphate), OP-GaAs (orientation patterned gallium arsenide), OP-GaP (orientation patterned gallium phosphide), polycrystalline ZnS, and polycrystalline ZnSe.

5. The method according to claim 3, wherein the bulk nonlinear material (BNLM) is selected from single-crystal or polycrystalline transition metal (TM):II-VI semiconductors containing Cr:ZnS, Cr:ZnSe, Fe:ZnS, and Fe:ZnSe.

6. The method according to claim 1, wherein the absorption of the second wavelength induces a radial temperature distribution along the cross-section of light acting as a thermal waveguide, thereby forming the thermal lens.

7. The method according to claim 2, wherein the interaction between the bulk nonlinear material (BNLM) and the first wavelength partially converts the first wavelength to one or more additional wavelengths by multiphoton absorption of the first wavelength, nonlinear three-wave mixing, nonlinear four-wave mixing, or a combination thereof.

8. The method according to claim 1, wherein the interaction between the bulk nonlinear material (BNLM) and the first wavelength and the second wavelength partially converts the first wavelength and the second wavelength into one or more additional wavelengths through nonlinear three-wave mixing or nonlinear four-wave mixing of the first wavelength and the second wavelength, and the first wavelength and the second wavelength propagate in the bulk nonlinear material (BNLM) in the same direction or in opposite directions.

9. The invention further comprises optimizing supercontinium generation (SCG) to achieve the lowest possible energy and peak power of the fs pulse at the input of the bulk nonlinear material (BNLM) and to achieve a wide spectrum of the fs pulse at the output of the bulk nonlinear material (BNLM), Optimizing the supercontinium generation (SCG) is (a) Adjusting the beam size of the first wavelength of light incident on the bulk nonlinear material (BNLM), (b) Adjusting the beam size and average power of the light of the second wavelength, (c) Prechirp the fs pulses positively or negatively upstream of the bulk nonlinear material (BNLM) by inserting an optical element selected from a combination of bulk optical material (YAG, ZnSe) or a volume Bragg grating (VBG) and dispersion mirrors, thereby identifying the optimal time distribution of the fs pulses at the self-focusing position. (d) Compressing the pre-chirped fs pulse by selecting a material-dispersible bulk nonlinear material (BNLM), (e) Identifying the self-focusing location of the pre-chirped fs pulse within the bulk nonlinear material (BNLM), and compressing the pre-chirped fs pulse to the shortest possible pulse width at the identified location, or (f) The method according to claim 1, comprising a selective combination of (a) to (e) above.

10. The method according to claim 1, wherein the bulk nonlinear material (BNLM) is configured as a gain medium or a non-gain medium at the first wavelength.

11. The method according to claim 1, wherein the self-focusing threshold in the presence of the thermal lens is less than or equal to half the threshold in the absence of the thermal lens.

12. An optical system for controlling femtosecond supercontinium generation (fsSCG), An fs oscillator that outputs light having an fs pulse train at a full pulse repetition rate (PRR) in the range of 10 MHz to 10 GHz at the first wavelength, A bulk nonlinear material (BNLM) receiving an fs pulse of pulse energy insufficient to reach the threshold for femtosecond supercontinium generation (fsSCG), The bulk nonlinear material (BNLM) has a positive thermo-optic coefficient (dn / dT > 0K). －１ An optical system having a ) configured to absorb light of a second wavelength different from the first wavelength, wherein the absorbed light induces thermal dissipation across the cross-section of the first wavelength, forming a thermal lens along the longitudinal direction of the bulk nonlinear material (BNLM), and the thermal lens increases the intensity of the nonlinear focused fs pulse of the first wavelength to the threshold of the femtosecond supercontinium generation (fsSCG).

13. The optical system according to claim 12, wherein the bulk nonlinear material (BNLM) is selected to have linear absorption, nonlinear absorption, or both linear and nonlinear absorption at the first and second wavelengths, and the first wavelength is selected from the near-infrared to mid-infrared spectrum in the range of 100 nm to 10 μm.

14. The bulk nonlinear material (BNLM) exhibits a third-order nonlinearity (χ （３） It has (≠0) and optionally exhibits second-order nonlinearity (χ²). （２） A selection is made from amorphous materials, single-crystal materials, and polycrystalline materials having (≠ 0), The single crystal material is YAG (yttrium aluminum garnet), BBO (barium borate), ZGP (zinc germanium phosphine), CaF2, ZnS, ZnSe, or GaSe. The optical system according to claim 12, wherein the amorphous material includes silicate glass or non-silicate glass.

15. The optical system according to claim 12, wherein the bulk nonlinear material (BNLM) is selected from single-crystal and polycrystalline materials having second-order nonlinearity (χ(2) ≠ 0) and having pseudo-phase matching or random pseudo-phase matching, and produces one or a combination of sum-frequency mixing, difference-frequency mixing, optical parametric generation, and optical rectification, and is selected from one of PPLN (periodic polarization reversal lithium niobate), PPSLT (periodic polarization reversal stoichiometric lithium tantalate), PPKTP (periodic polarization reversal potassium titanyl phosphate), OP-GaAs (orientation patterned gallium arsenide), OP-GaP (orientation patterned gallium phosphide), polycrystalline ZnS, and polycrystalline ZnSe.

16. The second-order nonlinearity (χ （２） The optical system according to claim 15, wherein the bulk nonlinear material (BNLM) having ≠0 is selected from single-crystal or polycrystalline birefringent phase-matched material, pseudo-phase-matched material, or random pseudo-phase-matched material, the birefringent phase-matched material is one of LN (lithium niobate), LBO (lithium borate), BBO (barium borate), KTP (potassium titanyl phosphate), ZGP (zinc germanium phosphide), and GaSe, the pseudo-phase-matched material is one of PPLN (periodic polarization reversal lithium niobate), PPSLT (periodic polarization reversal stoichiometric lithium tantalate), PPKTP (periodic polarization reversal potassium titanyl phosphate), OP-GaAs (orientation patterned gallium arsenide), and OP-GaP (orientation patterned gallium phosphide), and the random pseudo-phase-matched material is one of polycrystalline ZnS and polycrystalline ZnSe.

17. The optical system according to claim 16, wherein the bulk nonlinear material (BNLM) is configured for three-wave mixing (TWM) which includes a nonlinear process selected from one or more of the following: second harmonic generation (SHG), sum frequency generation, difference frequency generation, optical rectification, and parametric generation.

18. The amorphous substance includes silicate glass and non-silicate glass, and the single crystal substance includes oxides (YAG, BBO), phosphides (ZGP), fluorides (CaF ２ ), sulfides and selenides (ZnS, ZnSe, GaSe), The optical system according to claim 14, wherein the bulk nonlinear material (BNLM) is selected from transition metal (TM):II-VI semiconductors including single crystal or polycrystalline Cr:ZnS, Cr:ZnSe, Fe:ZnS, and Fe:ZnSe, and is configured to generate the second wavelength by laser interaction between the first wavelength and an additional wavelength, multiphoton absorption, nonlinear three-wave mixing, or nonlinear four-wave mixing, or is configured for multiphoton absorption.

19. The system further comprises an auxiliary laser source that outputs an additional wavelength coupled to the bulk nonlinear material (BNLM), The optical system according to claim 18, wherein the additional wavelength and the first wavelength propagate in the same or opposite directions, the additional wavelength is the second wavelength absorbed in the bulk nonlinear material (BNLM), or pumps the first wavelength, or generates the second wavelength by nonlinear interaction with the bulk nonlinear material (BNLM) and the first wavelength to produce a three-wave mixing, and the auxiliary laser source operates in a continuous wave or pulsed manner.

20. The system further comprises a lens device positioned between the auxiliary laser source and the bulk nonlinear material (BNLM) and configured to control and change the beam size of the additional wavelength light, wherein the auxiliary laser source is configured to control and adjust the average power of the additional wavelength light, or The optical system according to claim 19, wherein the fs oscillator and the bulk nonlinear material (BNLM) are configured to change the beam size of the first wavelength of light.

21. The system further comprises a dispersion element disposed between the fs oscillator and the bulk nonlinear material (BNLM), The dispersion element comprises one or more of the following: an undoped YAG plate, a ZnSe plate, a mirror having chromatic dispersion, and a volume Bragg grid (VBG), and is configured to chirp an fs pulse, and the bulk nonlinear material (BNLM) is configured to have material dispersibility that compresses the pre-chirpened fs pulse. The optical system according to claim 12, wherein the beam sizes of the first wavelength and the second wavelength, and the power of the second wavelength are controlled such that the nonlinear focus and the thermal lens have a common focusing position within the bulk nonlinear material (BNLM).

Images