Patent Application
20160266466
The present disclosure relates generally to waveguides, and, more particularly, to waveguides formed in a gas, such as air, and systems and methods for forming and using such waveguides.
Long range filamentation of intense femtosecond laser pulses in gases is an area of increasing interest, as it combines exciting potential applications with fundamental nonlinear optical physics. As shown in
It remains a significant limitation that femtosecond filamentation cannot deliver high average power over long distances in a single tight spatial mode. This is due to the fact that for laser pulses having a peak power on the order of several Pcr, the beam will collapse into multiple filaments with shot-to-shot variation in their transverse location. For Pcr˜5-10 GW, this means that single filament formation requires pulses of order ˜1 mJ. For a 1 kHz pulse repetition rate laser, this represents only 1 W of average power.
Systems, methods, and devices for generating a waveguide structure in a gas, such as air, are disclosed herein. In some embodiments, a plurality of laser pulses is nonlinearly absorbed by a gas to generate respective spatially elongated heated gas volumes transversely spaced apart from each other. Transient density variations caused by the spatially elongated heated gas volumes provide a refractive index profile capable of guiding electromagnetic radiation through the gas. For example, the waveguide structure in the gas is disposed between the spatially elongated heated gas volumes and results from interaction between acoustic waves generated by the spatially elongated heated gas volumes or from a non-uniform thermal gas profile caused by the spatially elongated heated gas volumes. The nonlinear absorption can be repeated at regular intervals to renew the waveguide in the gas, thereby allowing for the guiding of high average power radiation (e.g., on the order of megawatts) that is well below self-focusing or stimulated Raman scattering thresholds. In other embodiments, a single spatially elongated heated gas volume is used as a waveguide by appropriate timing between the guided radiation and the laser pulse forming the heated gas volume. The spatially elongated heated gas volumes can be generated using remote focusing of sub-picosecond laser pulses and/or multiple sub-picosecond filaments.
In one or more embodiments, a method comprises directing a plurality of propagating laser pulses through a gas. Each of the propagating pulses can be formed from the same laser beam or from separate laser beams. The propagating pulses are nonlinearly absorbed by the gas to generate respective spatially elongated heated gas volumes transversely spaced apart from each other. The directing is such that a waveguide is formed in the gas at a location between the heated gas volumes and such that each laser pulse has or is concentrated to have an intensity causing the nonlinear absorption thereof by the gas.
In one or more embodiments, a system comprises at least one laser and an optical system. The at least one laser generates sub-picosecond laser pulses. The optical system can direct the pulses from the at least one laser through a gas such that each laser pulse has or is concentrated to have an intensity causing nonlinear absorption by the gas so as to generate respective spatially elongated heated gas volumes transversely spaced apart from each other.
In one or more embodiments, a waveguide is formed by directing a plurality of propagating sub-picosecond laser pulses through a gas. The pulses can be nonlinearly absorbed by the gas to generate respective spatially elongated heated gas volumes transversely spaced from each other. The waveguide can comprise a core region of the gas and an outer region of the gas (e.g., an annular region). The outer region of the gas can surround the core region and can have a density less than that of the core region. The waveguide can be formed by interaction between acoustic waves generated by the spatially elongated heated gas volumes or by a non-uniform thermal gas profile caused by the spatially elongated heated gas volumes.
In one or more embodiments, a method can comprise generating a first spatially elongated heated volume in a gas by nonlinear absorption of at least one laser pulse. The method can further include using a non-uniform density profile in the gas as a waveguide for electromagnetic radiation. The density profile can be caused, at least in part, by the first spatially elongated heated volume.
Objects and advantages of embodiments of the disclosed subject matter will become apparent from the following description when considered in conjunction with the accompanying drawings.
Embodiments will hereinafter be described with reference to the accompanying drawings, which have not necessarily been drawn to scale. Where applicable, some features may not be illustrated to assist in the illustration and description of underlying features or have been exaggerated in order to assist in their illustration and description. Throughout the figures, like reference numerals denote like elements.
Systems, methods, and devices for generating a waveguide structure in a gas, such as air, are disclosed herein. One or more short laser pulses (e.g., less than 1 ps), each having or being concentrated to have a sufficiently high intensity, are directed through and nonlinearly absorbed by a gas (i.e., different from linear absorption since it is proportional to the higher orders of the intensity rather than the first order) to form one or more spatially elongated heated gas volumes. The resulting one or more heated gas volumes can cause transient density variations in the gas that provide a refractive index profile capable of guiding electromagnetic radiation through the gas. The one or more short laser pulses can be in the form of remotely focused sub-picosecond laser pulses and/or sub-picosecond filaments.
In some embodiments, a plurality of laser pulses is simultaneously directed through the gas to generate respective spatially elongated heated gas volumes spaced apart from each other. The resulting waveguide structure (based on an induced refractive index profile between the heated gas volumes) results from interaction between acoustic waves generated by the laser pulse absorption or from a non-uniform thermal gas profile (or non-uniform density profile) caused by the spatially elongated heated gas volumes. The nonlinear absorption can be repeated at regular intervals to renew the waveguide in the gas, thereby allowing for the guiding of high average power radiation (e.g., on the order of megawatts) that is well below self-focusing or stimulated Raman scattering thresholds.
In other embodiments, each spatially elongated heated gas volume itself can be used as a waveguide. Referring to
The timing between injection of the guided radiation and the laser pulse 204 forming the heated gas volume 206 can be controlled to take advantage of a short (e.g., less than 1 μs in air) temporal window 212 following the laser pulse where the positive density crest of a single cycle acoustic wave 208 launched by the absorption of the laser pulse is used to guide light. After this window, the density hole (e.g., the inner region 214) formed by the heated gas volume 206 acts to defocus any light that may be injected along the direction of propagation 202. For example, a second pulse can be directed through the heated gas volume at a time, ti, after the laser pulse 204 is first directed or absorbed by the gas, where
w0 is a spot size of the second pulse, and cs is the speed of sound in the gas.
The laser pulse 204 can be in the form of a remotely focused sub-picosecond laser pulse and/or a sub-picosecond filament. For example, a system for remote focusing and scanning of laser pulses is shown in
The optical system 306 can further scan the focal volume 310 to different locations in the gas over time, for example, by moving the focal volume 310 along a scanning direction 314 to form a spatially elongated heated gas volume 316. Although shown as a substantially straight volume 316 in
In another example, a system for producing a heated gas volume via filamentation is shown in
The intensity of the filament 408 can exceed, for example, 1012 W/cm2, although other intensity values capable of causing nonlinear absorption of the filament may also be possible. Unique to sub-picosecond filaments 408 is their extended high intensity propagation over many Rayleigh lengths and their ultrafast nonlinear absorption in the gas, stored in plasma and atomic and molecular excitation, which creates an axially extended impulsive pressure source to drive gas hydrodynamics. The nonlinear absorption of the filament 408 by the gas as it propagates along direction 412 forms a spatially elongated heated gas volume 416 in its wake and substantially aligned with the direction of propagation 412 (i.e., the direction of elongation of the gas volume 416 is the same as the direction of propagation 412 of the filament 408).
As noted above, the spatially elongated heated gas volume 316 in
For example, in a single femtosecond filament in air at standard conditions, energy is absorbed through ionization and two-photon excitation of rotational states. For typical pulse durations of ˜40-100 fs, approximately 25 mJ/cm3 is deposited over the ˜50 μm radius filament core by plasma generation and molecular rotational excitation. The hydrodynamic response of air to this pressure impulse leads, over a ˜100 ns timescale, to the formation of an outgoing, single cycle cylindrical acoustic wave, which leaves behind a region of hot air and a corresponding density depression. The density depression or “hole” then decays by thermal diffusion over milliseconds. The refractive index profile enabling air waveguiding is related to the change in density Δn/(n0˜1)=Δρ/ρ0, where Δn is the change in refractive index, n0−1=2.8×10−4 is the index of refraction of air at ambient density ρ0, and Δρ is the change in density.
The effect of the long timescale gas density hole left by a pulse or sequence of pulses is to reduce the index of refraction near the center of the beam seen by the next pulse in the sequence. This will have a defocusing effect (i.e., a negative lens) on the pulse.
Although a single spatially elongated heated gas volume eventually results in a beam-defocusing gas-density hole, a guiding structure can be formed in the gas using judicious placement of more than one spatially elongated heated gas volumes. Inspection of the time-varying density profiles resulting from nonlinear absorption of a sub-picosecond laser pulse shows that there are two regimes in the gas dynamical evolution that can enable guiding of secondary electromagnetic radiation. Acoustic guiding (also referred to herein as the “acoustic regime,” “acoustic guiding regime,” or an “acoustic waveguide”) can occur over a short timescale interval (e.g., on the order of 1 μs in air) and works by confining electromagnetic radiation in the enhanced density peak resulting from collision of acoustic waves from multiple heated gas volumes transversely spaced from each other (i.e., spaced from each other in a transverse direction perpendicular to, or at least crossing, the direction of elongation of the heated gas volumes). Thermal guiding (also referred to herein as the “thermal regime,” “thermal guiding regime,” or a “thermal waveguide”) can occur over a relatively larger timescale interval (e.g., on the order of 1 ms in air) and works by confining electromagnetic radiation in a core of near ambient gas density surrounded by a cladding region or moat of diffusively merged density holes formed by the multiple heated gas volumes.
Referring to
The colliding acoustic waves (e.g., 208a, 208b in
For example, the array of elongated heated gas volumes may be formed by remotely focusing and scanning sub-picosecond laser pulses through the gas. An example of such a system is shown in
Each successive pulse can have a center bandwidth shifted further to one end of the light spectrum than the previous pulse (e.g., successive pulses having increasingly red-centered bandwidths). The pulse to pulse bandwidth adjustment can be performed, for example, with a spatial light modulator (not shown). For example, for a blue to red shift, successive pulses diffract off diffraction grating 712 at increasing angles, as schematically illustrated by rays 705 for pulse 704 and rays 707 for pulse 706 in
Although generation of only a single spatially elongated heated gas volume is discussed with respect to the system illustrated in
In another example, the array of elongated heated gas volumes may be formed by scanning a beam collapse location for successively generated filaments. An example of such a system is shown in
Successive short pulses separated by the time τ1 can be increasingly positively chirped, for example. For example, pulse 754 may be more negatively chirped while pulse 756 may be more positively chirped. The pulse to pulse chirp adjustment can be performed, for example, using a spatial light modulator. Pulse 754 collapses from beam shape 766 at point 770 to form a first filament 776 while pulse 756 collapses from beam shape 764 at point 768 to form a second filament 774. Because of the change in the chirping, the beam collapse point 768 for the second pulse 756 is closer to the source 752 than the beam collapse point 770 for the first pulse 754. Thus, successive pulses collapse and form filaments increasingly closer to the source 752, as illustrated by arrow 772, thereby creating a concatenated sequence of shorter filaments forming a longer filament. In other words, the first pulse in the sequence would collapse farthest from the source 752 while the last pulse in the sequence would collapse closest to the source 752. Thus, shorter lengths of filaments, created by a sequence of pulses, can be used to form a longer filament. The timing sequence may also be reversed such that the sequence of concatenations moves away from the source 752 (i.e., the propagation direction 762 and the concatenated sequence direction 772 can be the same).
As the filaments 774, 776 are nonlinearly absorbed by the gas, an elongated heated gas volume is generated, with a direction of elongation being the same as the direction of propagation 762. Although generation of only a single spatially elongated heated gas volume is discussed with respect to the system illustrated in
In another example, the array of elongated heated gas volumes may be formed by an array of filaments, for example, an array of four filaments that are spaced apart from each other in a plane perpendicular to their direction of propagation. Each filament generates an elongated heated gas volume 206 in its wake, as illustrated in
Injection and guiding experiments were performed using the experimental setup illustrated in
An exemplary effect of a 4-filament structure on the gas dynamics is shown in
A second, longer lasting and significantly more robust thermal regime is achieved tens of microseconds later, well after the sound waves have propagated far from the filaments. In the thermal regime, the gas is in pressure equilibrium. As illustrated in panels (c) and (d) of
In both the acoustic and thermal regimes, the diameter of the air waveguide “core” was approximately half the filament lobe spacing. An end mode image from injection and guiding of a low energy λ=532 nm pulse in the acoustic waveguide produced from a 10 cm long 4-filament is shown in
In a tested embodiment, best coupling into the acoustic waveguide occurred at an injection delay of ˜200 ns and f/#>100, with a peak guided efficiency of 13%. Efficient guiding in the acoustic regime took place over an injection delay interval of only ˜100 ns, consistent with the time for a sound wave to cross the waveguide core region, a/cs˜100 ns, where 2a=75 μm and cs˜3.4×104 cm/s is the speed of sound in air. Proper balancing with respect to energy and transverse position of the 4-filament lobes allowed for the superposition of acoustic waves to form a well-defined air waveguide core. These values for the acoustic regime are with respect to a tested embodiment and should not be considered as limiting of embodiments of the disclosed subject matter since features and values may depend on various conditions and system configurations.
By comparison, the thermal guides in the tested embodiment were far more robust, stable, and long-lived. Results from the thermal guide produced by a 70 cm long 4-filament are also shown in
Guiding efficiency versus injected pulse delay is plotted in
Although an array of four spatially elongated heated gas volumes 206a-206d has been discussed above with respect to
In each of
In any of these examples or other disclosed embodiments, a waveguide structure in the gas can be formed in a manner similar to the waveguide structure formed by an array of four spatially elongated heated gas volumes described above, for example, by remote focusing of multiple sub-picosecond laser pulses or by using a corresponding array of filaments. For example,
For example, in a multifilament acoustic guide, each of the filaments, equidistant from a common center, launches a single cycle acoustic wave. The interference maximum produced when the waves meet on axis can last τ˜a/cs<1 μs, where α is the elongated heated volume diameter, which sets the acoustic wavelength, and cs is the speed of sound in the gas. Panels (c) and (d) of
Row (a) of
Embodiments of the disclosed subject matter can be used to guide electromagnetic radiation from a source, for example, for conveying radiation to a remote location or for conveying radiation from a remote location. For example, the source of electromagnetic radiation and the optical system configured to generate the waveguide can be co-located, e.g., at an originating end of the waveguide. In another example, the source of electromagnetic radiation and the optical system configured to generate the waveguide can be remote from each other, e.g., with the source at an end of the waveguide opposite to the originating end, for remote detection.
For example,
The optical system 2106 focuses the multiple laser pulses such that each has a peak power greater than
where λ is the wavelength of each laser pulse, and n0 and n2 are the linear and nonlinear indices of refraction of the gas, respectively, so as to form the array of filaments 2110. As explained above, the filaments 2110 are nonlinearly absorbed by the gas as they propagate through the gas, leaving spatially elongated heated gas volumes 2120 in their wake, with the direction of elongation (and the corresponding guiding direction 2122 of the waveguide) following (e.g., substantially parallel to, or at least locally parallel when the waveguide is curved) the direction of propagation 2112 of the filaments 2110. As is apparent from
A control system 2104 can control operation of the laser source 2102, the secondary radiation source 2108, and/or the optical system 2106. In particular, the control system 2104 can regulate the timing between the filaments 2110 and the secondary radiation 2118 to take advantage of the desired waveguiding regime. For example, the control system controls the time delay, ti, between the filaments and the injected pulse such that 0<ti≦D/cs to take advantage of the acoustic waveguiding regime. Because of the longer lifetime of the thermal waveguiding regime, it may be preferable in embodiments for the control system to control the time delay, ti, such that D/cs<ti<R2/4α. Alternatively or additionally, the time delay between the filaments and the injected secondary radiation can be controlled via optical system components, for example, by introducing a very long path length delay.
The optical system 2206 focuses the multiple laser pulses such that each has a sufficient intensity to cause nonlinear absorption of the laser pulse by the gas. For example, each laser pulse can be concentrated to have an intensity of at least 1012 W/cm2, although other intensity values capable of nonlinear absorption of a laser pulse may also be possible. Following the scanned focal volumes 2210, spatially elongated heated gas volumes 2220 are formed, with the direction of elongation (and the corresponding guiding direction 2222 of the waveguide) following (e.g., substantially parallel to, or at least locally parallel when the waveguide is curved) the direction of scanning 2212 (and crossing the direction of propagation 2224). As is apparent from
A control system 2204 can control operation of the laser source 2202, the secondary radiation source 2208, and/or the optical system 2206. In particular, the control system 2204 can regulate the timing between the focal volume scanning and the secondary radiation 2218 to take advantage of the desired waveguiding regime, for example, as described above with respect to
Although the setup illustrated in
In optical stand-off detection techniques, spectroscopic or other light-based quantitative information is collected from a distance. Such schemes can include, but are not limited to, light detection and ranging (LIDAR) and laser-induced breakdown spectroscopy (LIBS). In LIDAR, the signal is induced by a laser pulse, either by reflection or backscattering from distant surfaces or atmospheric constituents. In remote LIBS, laser breakdown of a distant target is accompanied by isotropic emission of characteristic atomic and ionic species. Embodiments of the disclosed subject matter include using a waveguide generated by the nonlinear absorption of a laser pulse (either via scanning a focus as described above with respect to
As explained above, the filaments 2310 are nonlinearly absorbed by the gas as they propagate through the gas, leaving spatially elongated heated gas volumes 2320 in their wake, with the direction of elongation following (e.g., substantially parallel to, or at least locally parallel when the waveguide is curved) the direction of propagation 2312 of the filaments 2310. The waveguide in the gas generated by the array of filaments 2310 can be used to guide radiation 2318 from secondary source 2322 at one end of the waveguide to an opposite originating end of the waveguide, for example, where optical system 2306 or different optical components (not shown) direct radiation 2318 to a detector 2308. The guided radiation 2318 from source 2322 may primarily employ the thermal waveguiding regime 2316, although either waveguiding regime is possible depending on waveguide length and radiation timing. In addition, the direction of propagation 2324 of the filaments 2310 and the direction of propagation of the secondary radiation 2318 may be opposite to each other. Thus, the generated waveguide in the gas can act as an efficient standoff lens.
The signal collection properties of the waveguides were tested using an isotropic, wide bandwidth optical source containing both continuum and spectral line emission, produced by tight focusing at f/10 of a 6 ns, 532 nm, 100 mJ pulse from a laser 2402 (e.g., a frequency-doubled Nd:YAG laser) to generate a breakdown spark 2404 in air. The air spark laser 2402 and the filament laser 2408 were synchronized with RMS jitter<10 ns. The delay between the spark and the filament structure was varied to probe the time-evolving collection efficiency of the air waveguides. The air spark and filament beams cross at an angle of 22°, so that the spark has a projected length of ˜500 μm transverse to the air waveguide. As depicted in
The collected signal appeared on the CCD image as a guided spot with a diameter characteristic of the air waveguide diameter, as shown in
Embodiments of the disclosed subject matter can combine guiding aspects, for example, as discussed above with respect to
As discussed above, the acoustic and thermal waveguide regimes are formed in the gas only temporarily following the nonlinear absorption of the sub-picosecond laser pulses. However, the waveguide may be renewed or recreated by repeating the directing of laser pulses at a sufficiently high repetition rate to maintain the guiding thermal gas density profile between the spatial locations of the elongated heated gas profiles. For example, as shown in
For example, based on a single filament diameter of ˜100 μm, an electron density of ˜3×1016 cm−3, ionization energy of ˜10 eV per electron, and 5 meV of heating per air molecule, approximately 0.5 mJ is needed per meter of each filament. With a femtosecond laser system of a few hundred millijoules pulse energy, waveguides hundreds of meters long are possible. Because the disclosed waveguides operating in the thermal formation regime can have long lifetimes (e.g., on the order of milliseconds in air) and a core-to-cladding refractive index difference of a few percent (e.g., at least 1-2%), the waveguides can be used to guide very high average powers that are well below the self-focusing and ionization thresholds.
With regard to thermal blooming from molecular and aerosol absorption in the atmosphere, the deposited laser energy which can raise the local gas temperature by a fraction η of ambient is given by PgΔt/A=1.5ηα−1p, where Pg is the guided laser power, Δt is the pulse duration, α is the absorption coefficient, A is the waveguide core cross sectional area, and p is the ambient pressure. Thermal blooming competes with guiding when η is approximately equal to the relative gas density difference between the core and cladding. The index (and density) difference between the core and cladding can be of the order of ˜2% at millisecond timescales. Taking η=0.02, p=1 atm, and α=2×10−8 cm−1, gives PgΔt/A<˜1.5×105 J/cm2 as the energy flux limit for thermal blooming. For example, for a 1.5 mm diameter air waveguide core formed from an azimuthal array of filaments, the limiting energy is PgΔt˜2.7 kJ. If a high power laser is pulsed for Δt˜2 ms, consistent with the lifetime of the 10 Hz-generated thermal waveguides, the peak average power can be 1.3 MW.
In such environments, air heating by the filament array itself could help dissipate the aerosols before the high power beam is injected, raising the thermal blooming threshold and also reducing aerosol scattering. An air waveguide even more robust against thermal blooming and capable of quasi-continuous operation may be possible using a kHz repetition rate filamenting laser. The cumulative effect of filamenting pulses arriving faster than the density hole can dissipate can lead to steady state hole depths of order ˜10%.
Referring to
If a single volume is selected at 2804, the process proceeds to 2806 where a sub-picosecond laser pulse having or concentrated to have a sufficient intensity (e.g., >1012 W/cm2) to cause nonlinear absorption is directed through the gas at an initial time, t=0, e.g., as a filament or by remote focusing and scanning of the laser pulse. As described above, the sub-picosecond laser pulse is nonlinearly absorbed by the gas and generates a spatially elongated heated gas volume (e.g., elongated in a direction following the filament propagation direction or in a direction following the scanning of the focal volume). The process then proceeds to 2808 where the secondary radiation (e.g., light) is conveyed by the resulting waveguide (e.g., co-axial with the single elongated heated gas volume) at a time, ti, after the laser pulse is first directed or absorbed by the gas, where
w0 is a spot size of the second pulse, and cs is the speed of sound in the gas. For example, ti can be less than 1 μs. When the secondary radiation originates from a same location as the laser pulse of 2806, the timing may be with respect to when the laser pulse is first directed or with respect to a time of the nonlinear absorption of the laser pulse. When the secondary radiation originates from a location different than the laser pulse of 2806 (e.g., in a remote detection setup), the timing may be with respect to a time of the nonlinear absorption of the laser pulse. The process then proceeds to 2810, where it is determined if the process should be repeated. If repetition is desired, the process proceeds to the beginning at 2804; otherwise, the process may terminate at 2812.
If the multiple volume option is selected at 2804, the process proceeds to 2814 where multiple sub-picosecond laser pulses having or concentrated to have a sufficient intensity (e.g., >1012 W/cm2) to cause nonlinear absorption are simultaneously directed through the gas at an initial time, t=0, e.g., as an array of filaments or by remote focusing and scanning of multiple laser pulses. As described above, the sub-picosecond laser pulses are nonlinearly absorbed by the gas and generate multiple spatially elongated heated gas volumes (e.g., elongated in a direction following the filament propagation direction or in a direction following the scanning of the focal volume). The process then proceeds to 2816, where the desired waveguide regime is selected. If the acoustic regime is selected, the process proceeds to 2818, where the secondary radiation (e.g., light) is conveyed by the resulting waveguide (e.g., co-axial with the single elongated heated gas volume) at a time given by 0<ti≦D/cs, where D is the average transverse spacing between the elongated heated gas volumes (i.e., between the filaments, see
If the thermal regime is selected at 2816, the process proceeds to 2820 where the secondary radiation (e.g., light) is conveyed by the resulting waveguide (e.g., co-axial with the single elongated heated gas volume) at a time given by D/cs<ti<R2/4α, where α is the thermal diffusivity of the gas and R is a transverse length scale of a thermal gas density profile resulting from the spatially elongated heated gas volumes. For simple array configurations, for example, as illustrated in
In embodiments, the repetition rate may be high enough to maintain the desired thermal gas density profile. For example, the repetition rate can be greater than 4α/R2 where α is the thermal diffusivity of the gas and R is a transverse length scale of the thermal gas density profile.
Embodiments of the disclosed waveguides and methods can be used for guiding light or other electromagnetic radiation through a gas in a number of applications. For example, the disclosed waveguides can be used to concentrate heater beams for remote atmospheric lasing schemes or for inducing characteristic emission for standoff detection of chemical compounds, as described above. In another example, the disclosed waveguides can be used for remote detection. In many remote detection applications, the collection of fluorescence or other light emission over large distances may be desired, but very little of the isotropically emitted fluorescence or other light emission reaches the detector at a distance. The disclosed waveguides can be used as an effective collection lens, thereby enhancing the detected signal. In another example, the disclosed waveguides could be used in atmospheric laser communication. In still another example, the disclosed waveguides could be used to deliver high power (e.g., >1 MW) over short distances (e.g., <1 m) or over long distances (e.g., >1 m) as part of a laser weapon or optical propulsion system. In yet another example, the disclosed waveguides could be used to enhance and control the propagation of an injected ultrashort filamenting laser pulse. Potential applications for both transmission and collection using the disclosed waveguides include directed energy, lightning control, atmospheric lasing, light detection and ranging (LIDAR), laser-induced breakdown spectroscopy (LIBS), and versions of resonance-enhanced multiphoton ionization (REMPI) spectroscopy. Other examples would be readily apparent to one of ordinary skill in the art.
Various details regarding theory, simulations, and experimental results not explicitly recited herein can be found in one or more of the following publications, which are hereby incorporated by reference herein in their entireties and constitute part of the disclosed subject matter: (1) Cheng et al., “The Effect of Long Timescale Gas Dynamics on Femtosecond Filamentation,” Optics Express, February 2013, 21(4): pp. 4740-51; (2) Jhajj et al., “Demonstration of Long-Lived High-Power Optical Waveguides in Air,” Physical Review X, February 2014, 4:11027; (3) Rosenthal et al., “Collection of Remote Optical Signals by Air Waveguides,” Optica, July 2014, 1(1): pp. 5-9; (4) Jhajj et al., “Optical Mode Structure of the Air Waveguide,” Optics Letters, November 2014, 39(21): pp. 6312-15; (5) Wahlstrand et al., “Direct Imaging of the Acoustic Waves Generated by Femtosecond Filaments in Air,” Optics Letters, March 2014, 39(5): pp. 1290-93.
In one or more first embodiments, a method comprises directing a plurality of propagating laser pulses through a gas. Each of the propagating pulses is formed from the same laser beam or from separate laser beams. The propagating pulses are nonlinearly absorbed by the gas to generate respective spatially elongated heated gas volumes transversely spaced apart from each other. The directing is such that a waveguide is formed in the gas at a location between the heated gas volumes and such that each laser pulse has or is concentrated to have an intensity causing the nonlinear absorption thereof by the gas.
In the first embodiments or any other of the disclosed embodiments, each laser pulse has an intensity of at least 1012 W/cm2 when nonlinearly absorbed by the gas.
In the first embodiments or any other of the disclosed embodiments, the directing the plurality of propagating laser pulses comprises phase-shifting a beam profile of a laser pulse.
In the first embodiments or any other of the disclosed embodiments, the plurality of laser pulses is generated simultaneously. For example, the plurality of laser pulses may be formed and/or directed at an identical time or within 10% of a pulse width of the respective pulses.
In the first embodiments or any other of the disclosed embodiments, the waveguide is formed by interaction between acoustic waves generated from the spatially elongated heated gas volumes, or by a non-uniform thermal gas density profile caused by the spatially elongated heated gas volumes.
In the first embodiments or any other of the disclosed embodiments, the spatially elongated heated gas volumes are on the periphery of the waveguide. For example, the heated gas volumes can surround or at least partially surround a core region of the waveguide, as viewed along a direction of elongation of the gas volumes.
In the first embodiments or any other of the disclosed embodiments, the directing comprises focusing the laser pulses to respective focal volumes, and scanning the focal volumes through the gas to form the spatially elongated heated gas volume. The waveguide extends along a direction of the scanning. The direction of the scanning can be straight or curved.
In the first embodiments or any other of the disclosed embodiments, the scanning comprises phase shifting and/or spectrum shifting laser beams producing said laser pulses to change locations of the corresponding focal volumes.
In the first embodiments or any other of the disclosed embodiments, the laser pulses have a peak power greater than Pcr and form a plurality of filaments. The waveguide extends along a direction of propagation of the filaments. Pcr satisfies the equation:
where λ is the wavelength of each laser pulse, and n0 and n2 are the linear and nonlinear indices of refraction of the gas, respectively. For example, the wavelength can be 800 nm, around 800 nm (e.g., within 10% of 800 nm), or any other wavelength or wavelength range. For example, Pcr can be at least 5 GW.
In the first embodiments or any other of the disclosed embodiments, lines of propagation of the filaments are on the periphery of the waveguide. For example, the filaments can surround or at least partially surround a core region of the waveguide, or bound an inner region of the waveguide.
In the first embodiments or any other of the disclosed embodiments, the plurality of filaments comprises an array of filaments generated using a phase-shifting optical system. For example, the phase-shifting optical system can comprise one or more half-pellicles or a spatial phase front shifter acting in either reflection mode (e.g., as a segmented stepped mirror) or transmission mode (e.g., as a transparent phase plate). Alternatively or additionally, the phase-shifting optical system can comprise a spatial light modulator acting as a spatial phase front shifter in either reflection mode or transmission mode.
In the first embodiments or any other of the disclosed embodiments, each laser pulse is less than or equal to 1 ps. For example, the laser pulse can be less than 200 fs or on the order 100 fs.
In the first embodiments or any other of the disclosed embodiments, the method further comprises repeating the directing a plurality of propagating laser pulses at a repetition rate that maintains a thermal gas density profile of the waveguide. The repetition rate can be greater than 4α/R2, where α is the thermal diffusivity of the gas and R is a transverse length scale of the thermal gas density profile. For example, the repetition rate can be greater than or equal to 500 Hz, for example, 1 kHz.
In the first embodiments or any other of the disclosed embodiments, the method further comprises at a time, ti, after the directing a plurality of propagating laser pulses or after nonlinear absorption of the propagating laser pulses, injecting electromagnetic radiation from a secondary source into the waveguide formed in the gas.
In the first embodiments or any other of the disclosed embodiments, the time, of the injecting can satisfy either 0<ti<D/cs, where D is the average transverse spacing between the elongated heated gas volumes and cs is the speed of sound in the gas, or D/cs<ti<R2/4α, where α is the thermal diffusivity of the gas and R is a transverse length scale of a thermal gas density profile of the waveguide. For example, R can be equal to or approximately equal to (e.g., within 10% of) D. For example, the time, ti, can be less than 1 μs or between 10 μs and 3 ms, inclusive. For example, the waveguide can have a lifetime of at least 500 μs.
In the first embodiments or any other of the disclosed embodiments, the method further comprises guiding electromagnetic radiation from a source thereof using said waveguide.
In the first embodiments or any other of the disclosed embodiments, the waveguide has a length along a direction of elongation of the heated gas volumes that is at least 1 m, for example, at least tens or hundreds of meters.
In the first embodiments or any other of the disclosed embodiments, the waveguide can convey electromagnetic radiation having a peak average power of at least 1 MW.
In the first embodiments or any other of the disclosed embodiments, the laser pulses are directed at discrete times, i.e., not continuously.
In the first embodiments or any other of the disclosed embodiments, the electromagnetic radiation (e.g., light) guided by the waveguide can be separated in space and/or time from the laser pulses forming the waveguide.
In one or more second embodiments, a system comprises at least one laser that generates sub-picosecond laser pulses, and an optical system that directs the pulses from the at least one laser through a gas such that each laser pulse has or is concentrated to have an intensity causing nonlinear absorption by the gas so as to generate respective spatially elongated heated gas volumes transversely spaced apart from each other.
In the second embodiments or any other of the disclosed embodiments, the laser pulses can have an intensity of at least 1012 W/cm2 when nonlinearly absorbed by the gas.
In the second embodiments or any other of the disclosed embodiments, the at least one laser is constructed to generate pulses at a repetition rate greater than 4α/R2 so as to maintain a thermal gas density profile resulting from the spatially elongated heated gas volumes, where α is the thermal diffusivity of the gas and R is a transverse length scale of the thermal gas density profile. For example, R can be equal to or approximately equal (e.g., within 10%) to D.
In the second embodiments or any other of the disclosed embodiments, the system further comprises at least a control system for controlling the at least one laser and/or the optical system.
In the second embodiments or any other of the disclosed embodiments, the system further comprises a control system and a secondary source of electromagnetic radiation. The control system controls a time delay, ti, between the laser pulses from the at least one laser and injection of electromagnetic radiation from said secondary source.
In the second embodiments or any other of the disclosed embodiments, the control system controls the time delay, ti, such that either 0<ti<D/cs, where D is the average transverse spacing between the elongated heated gas volumes and cs is the speed of sound in the gas, or D/cs<ti<R2/4α, where α is the thermal diffusivity of the gas and R is a transverse length scale of a thermal gas density profile resulting from the spatially elongated heated gas volumes is satisfied. For example, R can be equal to or approximately equal (e.g., within 10%) to D.
In the second embodiments or any other of the disclosed embodiments, the system further comprises a waveguide formed in the gas at a location between the spatially elongated heated gas volumes. The spatially elongated heated gas volumes are on the periphery of said waveguide.
In the second embodiments or any other of the disclosed embodiments, the waveguide comprises an enhanced density peak in the gas resulting from collision of acoustic waves generated by the spatially elongated heated gas volumes, and/or a lower density annular region of gas surrounding a higher density core region of gas caused by thermal diffusion in the gas resulting from (and/or including) the spatially elongated heated gas volumes.
In the second embodiments or any other of the disclosed embodiments, the waveguide has a length along a direction of elongation of the heated gas volumes of at least 1 m.
In the second embodiments or any other of the disclosed embodiments, the system further comprises a secondary source of electromagnetic radiation configured to inject electromagnetic radiation into said waveguide and/or a detector configured to detect electromagnetic radiation guided by said waveguide.
In the second embodiments or any other of the disclosed embodiments, the optical system comprises a spectrum-shifting apparatus and/or a phase-shifting apparatus. The phase-shifting apparatus can be constructed to phase shift segments of a near field phase front of the laser pulse with respect to other segments thereof.
In the second embodiments or any other of the disclosed embodiments, the phase-shifting apparatus comprises a half-pellicle and/or a spatial phase front shifter acting either in reflection mode (e.g., as a segmented stepped mirror) or in transmission mode (e.g., as a transparent phase plate) and/or a spatial light modulator acting as a spatial phase front shifter in either reflection mode or transmission mode.
In one or more third embodiments, a waveguide comprises a core region of gas, and an outer region of gas surrounding the core region. The outer region has a density less than that of the core region. The waveguide is formed by directing a plurality of propagating sub-picosecond laser pulses through the gas. The pulses are nonlinearly absorbed by the gas to generate respective spatially elongated heated gas volumes transversely spaced from each other. The waveguide is formed by interaction between acoustic waves generated by the spatially elongated heated gas volumes and/or by a non-uniform thermal gas profile caused by the spatially elongated heated gas volumes.
In the third embodiments or any other of the disclosed embodiments, the outer region of gas is a substantially annular region.
In the third embodiments or any other of the disclosed embodiments, the spatially elongated heated gas volumes are on the periphery of the waveguide.
In the third embodiments or any other of the disclosed embodiments, the waveguide is capable of guiding electromagnetic radiation having a peak average power of at least 1 MW over at least 1 m.
In the third embodiments or any other of the disclosed embodiments, the waveguide is curved along at least a portion of its length and/or is straight along at least a portion of its length.
In one or more fourth embodiments, a method comprises generating a first spatially elongated heated volume in a gas by nonlinear absorption of at least one laser pulse, and using a non-uniform density profile in the gas as a waveguide for electromagnetic radiation. The density profile is caused, at least in part, by the first spatially elongated heated volume.
In one or more fourth embodiments or any other of the disclosed embodiments, each laser pulse has an intensity of at least 1012 W/cm2 when nonlinearly absorbed by the gas.
In one or more fourth embodiments or any other of the disclosed embodiments, the using as a waveguide comprises injecting the electromagnetic radiation into the waveguide so as to be guided thereby.
In the fourth embodiments or any other of the disclosed embodiments, the generating comprises focusing each laser pulse to a focal volume and scanning the focal volumes through the gas to form the first spatially elongated heated volume.
In the fourth embodiments or any other of the disclosed embodiments, the scanning comprises phase shifting and/or spectrum shifting a laser beam producing each laser pulse to change a location of the focal volume.
In the fourth embodiments or any other of the disclosed embodiments, the generating comprises directing a sub-picosecond laser pulse through the gas along a first direction of propagation to form the first spatially elongated heated volume, and the using a non-uniform density profile comprises injecting a further pulse following the sub-picosecond laser pulse along the first direction of propagation at a time, ti, after said directing or after nonlinear absorption of the laser pulse, where
w0 is a spot size of the injected second pulse, and cs is the speed of sound in the gas. For example, the injecting may occur on the order of 1 μs after said directing or after the nonlinear absorption of the laser pulse, e.g., 0.1 μs, 1.0 μs, or 10 μs, inclusive, or any time period between 0.1 μs and 10 μs after the directing or nonlinear absorption, depending on gas density and gas type, among other things.
In the fourth embodiments or any other of the disclosed embodiments, the sub-picosecond laser pulse has a peak power greater than Pcr and forms a filament along the first direction of propagation, the waveguide extending along the first direction of propagation and following the filament, where
λ is the wavelength of the laser pulse, and η0 and η2 are the linear and nonlinear indices of refraction of the gas, respectively.
In the fourth embodiments or any other of the disclosed embodiments, the method further comprises simultaneously with the generating the first spatially elongated heated volume, generating at least a second spatially elongated heated volume in the gas using nonlinear absorption of at least one second laser pulse. The second spatially elongated heated volume is transversely spaced from the first spatially elongated heated volume. The non-uniform density profile in the gas is caused, at least in part, by the first and second spatially elongated heated volumes. The waveguide is formed in the gas between the first and second spatially elongated heated volumes.
In the fourth embodiments or any other of the disclosed embodiments, each second laser pulse has an intensity of at least 1012 W/cm2 when nonlinearly absorbed by the gas.
It will be appreciated that the disclosed modules, processes, or systems associated with forming or use of the waveguide in air may be implemented in hardware, hardware programmed by software, software instruction stored on a non-transitory computer readable medium or a combination of the above. For example, any of the methods or processes disclosed herein can be implemented, for example, using a processor configured to execute a sequence of programmed instructions stored on a non-transitory computer readable medium, which processor and/or computer readable medium may be part of a system configured to form or use said waveguide in air. For example, the processor can include, but is not limited to, a personal computer or workstation or other such computing system that includes a processor, microprocessor, microcontroller device, or is comprised of control logic including integrated circuits such as, for example, an Application Specific Integrated Circuit (ASIC). The instructions can be compiled from source code instructions provided in accordance with a programming language such as Java, C++, C#.net or the like. The instructions can also comprise code and data objects provided in accordance with, for example, the Visual Basic™ language, LabVIEW, or another structured or object-oriented programming language. The sequence of programmed instructions and data associated therewith can be stored in a non-transitory computer-readable medium such as a computer memory or storage device which may be any suitable memory apparatus, such as, but not limited to read-only memory (ROM), programmable read-only memory (PROM), electrically erasable programmable read-only memory (EEPROM), random-access memory (RAM), flash memory, disk drive and the like.
Furthermore, any of the methods or processes disclosed herein can be implemented as a single processor or as a distributed processor, which single or distributed processor may be part of a system configured to form or use said waveguide in air. Further, it should be appreciated that the steps mentioned herein may be performed on a single or distributed processor (single and/or multi-core). Also, any of the methods or processes described in the various figures of and for embodiments herein may be distributed across multiple computers or systems or may be co-located in a single processor or system. Exemplary structural embodiment alternatives suitable for implementing any of the methods or processes described herein are provided below.
Any of the methods or processes described above can be implemented as a programmed general purpose computer, an electronic device programmed with microcode, a hard-wired analog logic circuit, software stored on a computer-readable medium or signal, an optical computing device, a networked system of electronic and/or optical devices, a special purpose computing device, an integrated circuit device, a semiconductor chip, and a software module or object stored on a computer-readable medium or signal, for example, any of which may be part of a system configured to form or use said waveguide in air.
Embodiments of the methods, processes, and systems (or their sub-components or modules), may be implemented on a general-purpose computer, a special-purpose computer, a programmed microprocessor or microcontroller and peripheral integrated circuit element, an ASIC or other integrated circuit, a digital signal processor, a hardwired electronic or logic circuit such as a discrete element circuit, a programmed logic circuit such as a programmable logic device (PLD), programmable logic array (PLA), field-programmable gate array (FPGA), programmable array logic (PAL) device, or the like. In general, any process capable of implementing the functions or steps described herein can be used to implement embodiments of the methods, systems, or computer program products (i.e., software program stored on a non-transitory computer readable medium).
Furthermore, embodiments of the disclosed methods, processes, or systems may be readily implemented, fully or partially, in software using, for example, object or object-oriented software development environments that provide portable source code that can be used on a variety of computer platforms. Alternatively, embodiments of the disclosed methods, processes, or systems can be implemented partially or fully in hardware using, for example, standard logic circuits or a very-large-scale integration (VLSI) design. Other hardware or software can be used to implement embodiments depending on the speed and/or efficiency requirements of the systems, the particular function, and/or particular software or hardware system, microprocessor, or microcomputer being utilized. Embodiments of the disclosed methods, processes, or systems can be implemented in hardware and/or software using any known or later developed systems or structures, devices and/or software by those of ordinary skill in the art from the function description provided herein and with knowledge of high power laser systems and/or computer programming arts.
Furthermore, the foregoing descriptions apply, in some cases, to examples generated in a laboratory, but these examples can be extended to production techniques. For example, where quantities, techniques, time scales, and amplitudes apply to the laboratory examples, they should not be understood as limiting. In addition, although specific wavelengths, frequencies, powers, intensities, optical components and/or materials have been disclosed herein, other wavelengths, frequencies, powers, intensities, optical components and/or materials may also be employed according to one or more contemplated embodiments.
Features of the disclosed embodiments may be combined, rearranged, omitted, etc., within the scope of the invention to produce additional embodiments. Furthermore, certain features may sometimes be used to advantage without a corresponding use of other features.
It is thus apparent that there is provided in accordance with the present disclosure, waveguides and systems and methods for forming and using such waveguides. Many alternatives, modifications, and variations are enabled by the present disclosure. While specific embodiments have been shown and described in detail to illustrate the application of the principles of the present invention, it will be understood that the invention may be embodied otherwise without departing from such principles. Accordingly, Applicants intend to embrace all such alternatives, modifications, equivalents, and variations that are within the spirit and scope of the present invention.
The present application claims the benefit of U.S. Provisional Application No. 61/901,186, filed Nov. 7, 2013, which is hereby incorporated by reference herein in its entirety.
This invention was made with government support under FA95501310044 awarded by the Air Force Office of Scientific Research (AFOSR). The government has certain rights in the invention.
| Filing Document | Filing Date | Country | Kind |
|---|---|---|---|
| PCT/US14/64480 | 11/7/2014 | WO | 00 |
| Number | Date | Country | |
|---|---|---|---|
| 61901186 | Nov 2013 | US |
