Non-colinear phase-matched frequency mixing

Abstract

A laser apparatus with non-colinear phase-matched frequency mixing includes a nonlinear crystal from which the output laser beam is generated from a non-colinear phase-matched frequency mixing of a first input laser beam and a second input laser beam. The output laser beam undergoes a walk-off in the walk-off plane. The second input laser beam is lower power than the first input laser beam. The first input laser beam is directed to align its Poynting vector more closely with the output beam Poynting vector than colinear phase matching would. To achieve good spatial overlap in this phase matching scheme, the second input laser beam is stretched in the walk-off plane so that it has a larger lateral size in the walk-off plane than the first input laser beam. This non-colinear phase matching scheme makes it possible to achieve improved beam quality of the output beam.

Description

[Technical Field]

[0001] (Cross-reference of related applications) This application claims priority and interest in U.S. Nonprovisional Patent Application No. 17 / 975,475, filed on 27 October 2022, the disclosure of which is incorporated herein by reference in its entirety.

[0002] (Technical field of invention) This invention relates to walk-off compensation in nonlinear frequency conversion processes where spatial beam overlap is greatly affected by walk-off, such as in sum-frequency mixing in ultraviolet light, where long propagation paths through nonlinear crystals are often required to achieve the desired output power. In particular, this invention relates to the effect of walk-off on the beam quality of a frequency-converted beam. [Background technology]

[0003] (Discussion of background technology) Ultraviolet (UV) laser radiation has a variety of applications. High-power UV laser radiation is used, for example, in photolithography, laser machining, and ophthalmic surgery, while medium-power UV laser radiation has other applications such as semiconductor inspection, flow cytometry, and confocal microscopy. In microscopy and semiconductor inspection, the short wavelengths of UV laser radiation allow for the detection of features smaller than those detectable using visible light radiation.

[0004] In many situations, solid-state lasers are a preferred laser source architecture. However, to date, no solid-state laser has been able to directly generate UV laser radiation with high or moderate power. Instead, high and moderate power UV laser radiation is generated from solid-state lasers by frequency conversion of longer wavelength laser radiation generated within a solid-state laser gain medium. For example, neodymium-doped yttrium aluminum garnet (Nd:YAG) and neodymium-doped yttrium orthovanadate (Nd:YVO4) crystals very effectively generate both continuous-wave and pulsed laser radiation with a wavelength of 1,064 nm, forming the basis of many commonly used UV solid-state laser systems. Multi-stage sum-frequency generation in nonlinear crystals is used to convert 1,064 nm laser radiation into ultraviolet laser radiation. Frequency doubling of the 1,064 nm laser radiation generates a second harmonic at 532 nm, and then sum-frequency mixing of the 532 nm laser radiation and the 1,064 nm laser radiation generates a third harmonic at 355 nm. In an alternative approach, two frequency-duplicating steps convert the 1064nm laser radiation into the fourth harmonic at 266nm. The sum-frequency mixing of the 266nm laser radiation and the 1064nm laser radiation generates the fifth harmonic at 213nm.

[0005] Efficient frequency mixing in a nonlinear crystal relies on a frequency-converted output laser beam and phase-matched (one or more) input laser beams. As the input and output laser beams propagate through the nonlinear crystal, the frequency-converted laser radiation generated at each spatial location constructively interferes with the frequency-converted laser radiation generated at preceding spatial locations. This is not a simple task because the refractive index of the nonlinear crystal varies with wavelength.

[0006] Critical phase matching, also known as "angle-phase matching," is the preferred phase matching technique in many scenarios, and sometimes the only viable one. Critical phase matching utilizes a birefringent nonlinear crystal and leverages the polarization dependence of the refractive index of this birefringent nonlinear crystal. Critical phase matching is generally performed using linearly polarized beams and is most easily understood in the context of uniaxial birefringent crystals. A uniaxial crystal has an optical axis and is characterized by its ordinary refractive index and extraordinary refractive index. For any given laser beam, the optical axis of the uniaxial crystal and the wave vector of the laser beam both define the principal plane. A beam is called an "ordinary" beam when its polarization is perpendicular to the principal plane, and an "extraordinary" beam when its polarization is parallel to the principal plane. An ordinary beam is always subject to an ordinary refractive index. On the other hand, an extraordinary beam is subject to a refractive index that is within the range between the ordinary and extraordinary refractive indexes, and the value of the refractive index depends on the angle between the wave vector and the optical axis. In critical phase matching, the interacting laser beams include both ordinary and extraordinary beams. Phase matching is achieved with a specific orientation of the optical axis of the nonlinear crystal relative to the wave vector of the input beam, given a suitable combination of crystalline material and temperature, and wavelength and polarization direction of the input beam.

[0007] Critical phase matching is performed in most cases using colinear beams. However, one or two of the interacting laser beams may undergo walk-off, meaning that the Poynting vector of each such beam becomes a non-zero angle with respect to the beam's wave vector. In a uniaxial crystal, the extraordinary beam undergoes walk-off, and the walk-off angle depends on the difference between the ordinary and extraordinary refractive indices, and the angle between the wave vector and the optical axis. Walk-off affects the spatial overlap between the interacting beams and limits the effective interaction length. This is particularly problematic when a long interaction length is required to achieve the desired output power. Such situations may necessitate walk-off compensation.

[0008] In a simple walk-off compensation scheme, the input beam size is increased to maintain better spatial beam overlap in the presence of walk-off. This scheme is generally only useful when sufficient input power is available, which is often not the case. Another walk-off compensation scheme utilizes a pair of non-linear crystals, a bi-crystal, i.e., imposing equal amounts of walk-off, but oriented such that the walk-off in the second crystal is opposite to that in the first crystal. The bi-crystal scheme reduces the scale of walk-off by half. Non-collinear phase matching provides another method for walk-off compensation. When the constraint on the parallel input beam wave vectors is relaxed, instead, emphasis can be placed on Poynting vector alignment. However, even in non-collinear phase matching, it is generally not possible to align the Poynting vectors of all the interacting beams. The optimal configuration usually compromises between optimizing the spatial overlap between the input beams and optimizing the spatial overlap between the input and output beams.

Summary of the Invention

Means for Solving the Problems

[0009] What is disclosed herein is a frequency mixing technique that utilizes non-collinear critical phase matching in conjunction with different beam sizes in the walk-off plane to reduce the impact of walk-off and generate an output laser beam with high beam quality. The input beams are arranged such that the region of spatial overlap between the input beams is better aligned with the Poynting vector of the output beam than in the case of collinear phase matching, and one of the input beams is extended laterally in the walk-off dimension to expand the length of this region of spatial overlap between the input beams. In one scenario, this frequency mixing technique can optimize the output beam quality without compromising the output power as compared to conventional collinear phase matching and frequency mixing based on circular input beams.

[0010] For example, in order to generate a 213 nm continuous wave laser beam, consider the problem of sum frequency mixing of a 1064 nm continuous wave laser beam and a 266 nm continuous wave laser beam. Here, the 266 nm beam is the product of a fourth harmonic generation process applied to the 1,064 nm beam. This typically limits the 266 nm input power to 2 watts (W) or less. Maximizing the output power thus necessarily involves maximizing the conversion of the 266 nm power to the 213 nm output beam. For this purpose, the 1064 nm input power is set high enough to substantially deplete the 266 nm beam, and the non-linear crystal is long enough to allow this depletion to occur. Using collinear type I phase matching sum frequency mixing of the ordinary 1064 nm beam and the 266 nm beam, the extraordinary 213 nm radiation generated undergoes walk-off, resulting in an elongated output beam shape. The problem of walk-off is exacerbated by the gradual depletion of the 266 nm power through the length of the non-linear crystal, further degrading the output beam quality.

[0011] Applying this frequency mixing technique to an example of type I sum frequency mixing of an ordinary 1064 nm beam and a 266 nm beam, the 1064 nm wave vector is oriented such that it is parallel (or at least has a low non-parallelism) to the 213 nm Poynting vector. When perfectly parallel, the effect of walk-off on the output beam quality is eliminated. The 266 nm beam is shaped to be elongated in the walk-off dimension, ensuring good spatial overlap between the non-collinear 266 nm beam and the 1,064 nm beam. While the depletion of the 266 nm beam is a problem in the collinear phase matching scheme, this frequency mixing technique uses this depletion to its advantage. When the 1064 nm beam passes through the more diffused 266 nm beam, the high power of the 1064 nm ensures an effective conversion of the 266 nm power to the 213 nm output beam. We have found that this frequency mixing technique can achieve the same 213 nm power as the collinear phase matching scheme, or even a 213 nm power with a very improved beam quality.

[0012] The applicability of this frequency mixing technique is not limited to the 213nm generation example. More generally, the technique is applicable to sum and difference frequency mixing processes that undergo substantial walk-off, which would cause the frequency-converted output beam to have an elongated beam shape in the walk-off dimension in a colinear phase-matching scheme. This frequency mixing technique is also not limited to type I phase matching with an ordinary input beam. In the more general case, beam quality is improved by the Poynting vector of the first input beam of two input beams that are parallel to (or at least less disparallel than in a colinear scheme) the Poynting vector of the output beam, while the second input beam has a larger lateral size in the walk-off plane, ensuring good spatial overlap between the two input beams. For example, the second input beam may have an oval lateral intensity distribution. This technique is particularly advantageous in scenarios where one input beam is very high power and the other input beam is substantially depleted, such as during frequency mixing between a relatively weak ultraviolet input beam and a higher power infrared or visible light input beam. These scenarios not only result in maximum beam degradation in a colinear phase-matching scheme, but the beam quality improvements provided by this technique can also be achieved in these scenarios with little to no cost to output power, or even with further increases in output power.

[0013] In one aspect, a laser apparatus with non-colinearly phase-matched frequency mixing includes a first laser source configured to generate a first input laser beam, a second laser source configured to generate a second input laser beam, and a nonlinear crystal arranged to generate an output laser beam from a non-colinearly phase-matched frequency mixing of the first and second input laser beams. The output laser beam undergoes a walk-off in the walk-off plane within the nonlinear crystal. The wave vectors of the first and second input laser beams are non-colinear and intersect within the nonlinear crystal. The second input laser beam has a lower output than the first input laser beam within the nonlinear crystal. Within the first nonlinear crystal, the angle between the Poynting vector of the first input laser beam and the Poynting vector of the output laser beam is smaller than the angle between the Poynting vector of the second input laser beam and the Poynting vector of the output laser beam. The second input laser beam has a larger lateral size than the first input laser beam in the walk-off plane within the nonlinear crystal.

[0014] In another aspect, a method for non-colinearly phase-matched frequency mixing of laser beams includes (a) generating first and second input laser beams, and (b) directing the first and second input laser beams into a nonlinear crystal, thereby (i) the wave vectors of the first and second input laser beams are non-colinear and intersect within the nonlinear crystal, and (ii) the first and second wave vectors cooperate with the orientation of the nonlinear crystal to promote non-colinearly phase-matched frequency mixing of the first and second input laser beams, resulting in the generation of an output laser beam. The output laser beam undergoes a walk-off in the walk-off plane within the nonlinear crystal. The first input laser beam has higher power than the second input laser beam. The lateral size of the second input laser beam exceeds the corresponding lateral size of the first input laser beam in the walk-off plane. In the first nonlinear crystal, the angle between the Poynting vector of the first input laser beam and the Poynting vector of the output laser beam is smaller than the angle between the Poynting vector of the second input laser beam and the Poynting vector of the output laser beam. [Brief explanation of the drawing]

[0015] The accompanying drawings, incorporated herein and constituting part thereof, schematically illustrate preferred embodiments of the present invention and serve to illustrate the principles of the present invention together with the general description given above and the detailed description of preferred embodiments given below.

[0016] [Figure 1] Figure 1 illustrates a laser apparatus with non-colinear type I phase-matched sum-frequency mixing of two input laser beams within a nonlinear crystal, according to one embodiment. The sum-frequency mixing of the input beams generates an output beam that undergoes walk-off within the nonlinear crystal. The frequency mixing technique utilizes non-colinear critical phase matching, and one of the input beams has an oval shape.

[0017] [Figure 2]Figure 2 is a phase alignment diagram for fully walk-off compensated non-colinear phase alignment in a nonlinear crystal of the apparatus of Figure 1, according to one embodiment.

[0018] [Figure 3] Figure 3 shows an exemplary lateral intensity distribution of the input beam at the input surface of the nonlinear crystal in the apparatus shown in Figure 1.

[0019] [Figure 4] Figure 4 shows, instead, the beam propagation in the nonlinear crystal of the apparatus in Figure 1 when conventional colinear phase matching is used.

[0020] [Figure 5] Figure 5 shows a phase matching diagram for the collinearly phase-matched sum-frequency mixing process in Figure 4.

[0021] [Figure 6] Figure 6 is a phase alignment diagram relating to fully or partially walk-off compensated non-colinear phase alignment in a nonlinear crystal of the apparatus of Figure 1, according to one embodiment.

[0022] [Figure 7] Figure 7 is a data plot illustrating the exemplary performance of the apparatus from Figure 1, modified to operate with two circular input beams and applied to the generation of a 213 nm continuous wave laser beam from a sum-frequency mixture of a 1064 nm continuous wave laser beam and a 266 nm continuous wave laser beam, and comparing the performance with that achieved using colinear phase matching of the circular input beams.

[0023] [Figure 8] Figures 8, 9, and 10 are data plots illustrating the exemplary performance of the apparatus in Figure 1 applied to the generation of a 213 nm continuous wave laser beam from a sum-frequency mixture of a 1064 nm continuous wave laser beam and a 266 nm continuous wave laser beam, with respect to different individual widths of the 266 nm beam in the walk-off dimension, and comparing the performance with that achieved using colinear phase matching. [Figure 9]Figures 8, 9, and 10 are data plots illustrating the exemplary performance of the apparatus in Figure 1 applied to the generation of a 213 nm continuous wave laser beam from a sum-frequency mixture of a 1064 nm continuous wave laser beam and a 266 nm continuous wave laser beam, with respect to different individual widths of the 266 nm beam in the walk-off dimension, and comparing the performance with that achieved using colinear phase matching. [Figure 10] Figures 8, 9, and 10 are data plots illustrating the exemplary performance of the apparatus in Figure 1 applied to the generation of a 213 nm continuous wave laser beam from a sum-frequency mixture of a 1064 nm continuous wave laser beam and a 266 nm continuous wave laser beam, with respect to different individual widths of the 266 nm beam in the walk-off dimension, and comparing the performance with that achieved using colinear phase matching.

[0024] [Figure 11] Figure 11 illustrates a laser apparatus with non-colinear type I phase-matched sum-frequency mixing of two input laser beams, preceding a frequency conversion process that, according to one embodiment, essentially generates one of two input laser beams having an oval flat-top lateral intensity distribution as a result of a walk-off.

[0025] [Figure 12] Figure 12 is a phase matching diagram for a non-colinear type II phase-matched difference frequency generation in a positive uniaxial nonlinear crystal according to one embodiment, where one input beam is a longer wavelength extraordinary light beam, another input beam is a shorter wavelength ordinary light beam, and the output beam is an extraordinary light beam.

[0026] [Figure 13] Figure 13 is a phase matching diagram for a non-colinear type I phase-matched difference frequency generation in a negative uniaxial nonlinear crystal according to one embodiment, where both input beams are anomalous light beams and the output beam is an ordinary light beam. [Modes for carrying out the invention]

[0027] (Detailed description of the invention) Referring here to drawings where similar components are designated by similar numbers, Figure 1 illustrates a single laser apparatus 100 with non-colinear type I phase-matched sum-frequency mixing of two input laser beams 160 and 170 within a nonlinear crystal 130. The sum-frequency mixing of input beams 160 and 170 generates an output beam 180 that undergoes a walk-off within the nonlinear crystal 130. To generate an output beam 180 with high beam quality, the frequency mixing technique of apparatus 100 utilizes an oval-shaped input beam 170 to maintain good spatial overlap between input beams 160 and 170, in conjunction with (a) non-colinear critical phase matching to compensate for the walk-off within the output beam 180. Apparatus 100 includes two laser sources 110 and 120 and a nonlinear crystal 130. Although not shown in Figure 1, apparatus 100 may further include optical components for steering, focusing and / or shaping the input beams 160 and 170.

[0028] Laser source 110 generates input beam 160, and laser source 120 generates input beam 170. The wavelength λ1 of input beam 160 exceeds the wavelength λ2 of input beam 170, and the output of input beam 160 exceeds the output of input beam 170. Input beams 160 and 170 can be infrared, visible light, or ultraviolet. In a certain scenario where the frequency mixing technique of apparatus 100 is found to be very advantageous, input beam 160 is near-infrared and input beam 170 is ultraviolet. In this specification, “near-infrared” refers to a wavelength range between 750 and 1400 nm. “Ultraviolet” refers to a wavelength range between 10 and 400 nm, although in this specification, an ultraviolet beam has wavelengths in the range between 100 and 400 nm, more typically 200 and 280 nm, etc. Input beams 160 and 170 are incident on the input surface 132 of the nonlinear crystal 130. The input beams 160 and 170 propagate in the xz plane of the right-handed Cartesian coordinate system 198 and intersect within the nonlinear crystal 130 (in this specification, any reference to the x, y, and z axes, dimensions, directions, planes, etc., refers to coordinate system 198). The sum-frequency mixing of the input beams 160 and 170 is performed at the wavelength

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[0029] The angle between the input beams 160 and 170 within the nonlinear crystal 130 is exaggerated in Figure 1 for clarity. Typically, the propagation directions of the input beams 160 and 170 are within a few degrees of parallel to each other, and the input beams 160 and 170 generally propagate along the z-direction. The planes 132 and 134 are at opposite ends of the nonlinear crystal 130 in the z-dimension. The planes 132 and 134 are typically planar.

[0030] The input beams 160 and 170 can be collimated or focused within the nonlinear crystal 130. In one example, the input beams 160 and 170 are collimated pulsed laser beams. In another example, the input beams 160 and 170 are continuous wave beams, which are focused within the nonlinear crystal 130 to achieve a desired conversion efficiency.

[0031] The optimal material selection for the nonlinear crystal 130 depends on several factors, including the wavelengths of the input beams 160 and 170, as well as the wavelength of the output beam 180. If the output beam 180 is ultraviolet, the possible material choices for the nonlinear crystal 130 are KH2PO4 (KDP), LiB3O5 (LBO), β-BaB2O4 (BBO), and CSLiB6O 10 This includes (CLBO), KBe2BO3F2(KBBF), and derivatives of KBBF. The following discussion assumes that the nonlinear crystal 130 is a uniaxial crystal with a crystal axis C. The discussion can be easily extended to a biaxial crystal. The crystal axis C is in the xz plane. The input beams 160 and 170 propagate as ordinary beams within the nonlinear crystal 130, and the output beam 180 is an extraordinary beam. Their polarizations are shown in Figure 1.

[0032] Figure 2 is a phase matching diagram 200 relating to fully walk-off compensated non-colinear phase matching within the nonlinear crystal 130 of the apparatus 100. The input beam 160 has a wave vector k1 and a Poynting vector S1, and the input beam 170 has a wave vector k2 and a Poynting vector S2 (Poynting vectors S1 and S2 are not shown in Figure 2). The output beam 180 has a wave vector k3 and a Poynting vector S3. Since the input beams 160 and 170 are ordinary beams, S1 is parallel to k1 and S2 is parallel to k2. The output beam 180 undergoes a walk-off in the xz plane. Since the beam propagation inside the nonlinear crystal 130 is usually within a few degrees of parallel to the z axis, the walk-off is substantially parallel to the x axis, and the x dimension is also called the walk-off dimension. The Poynting vector S3 has a walk-off angle θ with respect to the wave vector k3. WO (For clarity of illustration, angles are shown relatively large in Figure 2. In most realistic examples, all angles are much smaller than those depicted. For example, the walk-off angle is typically less than 100 milliradians (mrad)).

[0033] Non-colinear phase matching is defined as the angle θ between the wave vector k1 of input beam 160 and the wave vector k2 of input beam 170. 12 The range, and the phase matching angle θ between the crystal axis C and the wave vector k3 of the output beam 180. PM This is achievable with respect to the corresponding range. However, in order to ensure parallel energy flow between the input beam 160 and the output beam 180, the angle θ PM The angle θ is the angle between the wave vector k1 of the input beam 160 and the wave vector k3 of the output beam 180. 13 The walk-off angle θ WO It is selected so that it is equal to . With this configuration, the Poynting vector S1 of the input beam 160 is parallel to the Poynting vector S3 of the output beam 180, while the Poynting vector S2 of the input beam 170 is at a non-zero angle with respect to the Poynting vector S3 of the output beam 180.

[0034] When the device 100 operates according to the fully walk-off compensated scheme in Figure 2, the energy of the sum-frequency radiation generated along the propagation path of the input beam 160 in the nonlinear crystal 130 propagates in the same direction as the input beam 160. This is the scenario depicted in Figure 1. For example, consider the three positions 188 shown in Figure 1. All three positions 188 are in the same lateral position of the input beam 160, but are offset longitudinally from each other along the propagation direction of the input beam 160. The sum-frequency radiation generated at all three positions 188 contributes to the same lateral position of the output beam 180. This alignment eliminates walk-off induced distortion in the lateral intensity distribution of the output beam 180.

[0035] Figure 3 shows the input surface 132 of a nonlinear crystal 130 having exemplary transverse intensity distributions 360 for input beam 160 and 370 for input beam 170 superimposed thereon. For convenience, Figure 3 depicts a scenario where the input surface 132 is parallel to the xy plane and input beams 160 and 170 are incident on the input surface 132 in substantially perpendicular incidence. To maximize spatial overlap between the non-colinear input beams 160 and 170, the transverse intensity distribution 370 for input beam 170 is oval. Each of the transverse intensity distributions 360 and 370 is approximately 1 / e of the corresponding input beam. 2 This is shown as an envelope. The input beam 160 may be a Gaussian or nearly Gaussian beam with a circular cross-section, for example, as shown in Figure 3. The input beam 170 may be an elliptical Gaussian beam (or nearly Gaussian) with an elliptical principal axis parallel to the xz plane. Alternatively, the oval transverse intensity distribution of the input beam 170 may have a nearly supergaussian or flat-top profile in the xz plane.

[0036] The transverse intensity distribution 370 is elongated in the walk-off plane compared to the direction orthogonal to the walk-off plane and has a significantly larger range in the walk-off dimension than the transverse intensity distribution 360 of the input beam 160. In other words, the input beam 170 is relatively wide in the walk-off dimension and the input beam 160 is relatively narrow. As seen in FIG. 1, the larger width of the input beam 170 in the walk-off dimension extends the interaction length between the input beams 160 and 170. In one example, the 1 / e 2 x-axis width w x2 of the input beam 170 is 75% or more than 75% greater than the 1 / e 2 x-axis width w x1 of the input beam 160. The 1 / e 2 y-axis widths w y1 and w y2 of the input beams 160 and 170 may be similar to each other or different, as shown in FIG. 3.

[0037] FIG. 3 is schematic and the above discussion is readily generalized for other orientations of the input plane 132 and the corresponding angles of incidence of the input beams 160 and 170. More generally, the input beams 160 and 170 are incident on the input plane 132 at their respective angles of incidence that result in input beams 160 and 170 propagating substantially along the z-axis inside the non-linear crystal 130. In this more general scenario, w x1 and w x2 are replaced with the respective transverse dimensions of the input beams 160 and 170 orthogonal to the y-axis.

[0038] FIG. 4, instead, shows the beam propagation inside the non-linear crystal 130 when conventional collinear phase matching is utilized. In this case, two similarly sized circular Gaussian input beams 460 and 470 co-propagate through the non-linear crystal 130. Using collinear type I phase matching, the sum frequency mixing of the input beams 460 and 470 generates an output beam 480.

[0039] Figure 5 shows a colinear phase-matched diagram 500 relating to the colinearly phase-matched sum-frequency mixing process in Figure 4. Beams 460, 470, and 480 have parallel wave vectors k1, k2, and k3. The colinear phase-matching is the phase-matching angle θ between the wave vector k3 of output beam 180 and the crystal axis C. PM This is achieved in the following case. The Poynting vector S3 of the output beam 480 is the walk-off angle θ with respect to the wave vector k3. WO It is located there. The energy flow of output beam 480 is therefore moved away from the region of spatial overlap between input beams 460 and 470 by a non-zero angle (walk-off angle θ). WO It propagates in ).

[0040] Consider three locations 488 (shown in Figure 4) that are in the same lateral location as the input beam 460 but are offset longitudinally from each other along the propagation direction of the input beam 460. The sum-frequency radiation generated at the different locations 488 will not overlap. The output beam 480 is therefore significantly wider in the walk-off dimension than the input beams 460 and 470. The output beam 480 emerges from the nonlinear crystal 130 with separate non-Gaussian intensity profiles 484X, each with a walk-off dimension. When the depletion of the input beams 460 and 470 is negligible, the lateral intensity distribution of the output beam 480 has a nearly flat-top profile in the walk-off dimension. However, in the example depicted in Figure 4, the input beam 460 is sufficiently powerful to cause substantial depletion of the input beam 470. Therefore, the intensity profile 484X is instead extended in a non-uniform scheme. The beam quality of the output beam 480 is substantially degraded compared to the input beams 460 and 470.

[0041] In contrast, in the non-colinear phase matching scheme in apparatus 100 (Figure 1-3), the beam quality of the output beam 180 can be similar to that of the input beam 160. As shown in Figure 1, the narrower input beam 160 passes through the wider input beam 170 inside the nonlinear crystal 130. The width and propagation direction of the narrower input beam 160 essentially define the region of spatial overlap between input beams 160 and 170. In the fully walk-off compensated scenario shown in Figure 1, the orientation of the region of spatial overlap between input beams 160 and 170 is parallel to the Poynting vector S3 of the output beam 180, preventing walk-off induced distortion of the lateral intensity distribution of the output beam 180 despite the different propagation directions of the input beam 170.

[0042] Figure 1 depicts an embodiment in which the input beams 160 and 170 are Gaussian, having Gaussian intensity profiles 162X and 172X, respectively, in the xz plane. In a fully walk-off compensated scenario in which the input beam 160 and output beam 180 have parallel energy flow within the nonlinear crystal 130, the output beam 180 has a Gaussian intensity profile 184X in the walk-off dimension. The Gaussian intensity profile 184X of the output beam 180 is similar to the Gaussian intensity profile 162X of the input beam 160. The output beam 180 does not suffer the beam quality degradation that plagues the colinear phase matching schemes in Figures 4 and 5.

[0043] Furthermore, depletion of either input beam 160 or 170 does not adversely affect the beam quality of output beam 180. In contrast, apparatus 100 is particularly advantageous when input beam 160 is sufficiently powerful to cause substantial depletion of input beam 170, for example, when the output of input beam 170 is up to 10% or up to 1% of the output of input beam 160 (in this specification, the term “substantial depletion” may mean a reduction of at least 25% of the power). Consider each individual x-axis section of input beam 170 (one x-axis section 378X is shown in Figure 3). Due to the non-collinear arrangement of input beams 160 and 170, the interaction length between input beam 160 and each individual x-axis section of input beam 170 is relatively short. Therefore, when the input beam 160 is sufficiently high power to cause substantial depletion of the input beam 170, for example, when the input beam 170 is a relatively weak ultraviolet laser beam while the input beam 160 is higher power than a near-infrared or visible light laser beam, the power of the input beam 170 is most effectively converted to the output beam 180. The input beam 160 can be generated by a high-power laser system such as a fiber laser. Alternatively, a high-power input beam 160 can be achieved by placing a nonlinear crystal 130 inside a resonant enhancement cavity or inside a laser resonator. In such scenarios, the beam quality improvement provided by the apparatus 100 can be achieved with little or no loss in overall frequency conversion efficiency compared to an apparatus implementing a conventional colinear phase matching scheme. In some cases, the overall frequency conversion efficiency is actually improved.

[0044] The nonlinear crystal 130 has a length of 130L in the z-dimension. Compared to the depicted transverse envelopes of the input beams 160 and 170, the length 130L is, in most cases, much larger than the length shown in Figure 1. For example, the length 130L can exceed 20 millimeters (mm) or 20 mm, while the transverse envelopes of the input beams 160 and 170 can be as small as a fraction of a millimeter. To avoid unwanted laser beam propagation inside the nonlinear crystal 130, the input beams 160 and 170 can overlap on both the input surface 132 and the output surface 134. In an implementation where input beams 160 and 170 overlap in this manner, the output of output beam 180 can be maximized when the lateral centers of input beams 160 and 170 intersect or are near the center of the nonlinear crystal 130, for example, in the middle third of the propagation path of input beam 170 between planes 132 and 134 (i.e., at a distance of no more than one-sixth of the total propagation distance from the center point).

[0045] The fully walk-off compensated phase matching scheme shown in Figure 2 and discussed above represents the optimal case as far as output beam quality is concerned. In some scenarios, it may be sufficient, or even preferable, to merely reduce, rather than eliminate, the angle between the Poynting vectors of input beam 160 and output beam 180. This is applicable, for example, when a longer interaction length between each x-axis section of input beam 160 and input beam 170 is required to achieve the desired frequency conversion efficiency.

[0046] Figure 6 is a phase matching diagram 600 relating to fully or partially walk-off compensated non-colinear phase matching in the nonlinear crystal 130 of the apparatus 100. Phase matching diagram 200 in Figure 2 is a special case of phase matching diagram 600. In phase matching diagram 600, the wave vectors of input beams 160 and 170 are angled away from each other in a manner that reduces the angle between the Poynting vectors of input beam 160 and output beam 180 compared to colinear phase matching. The wave vector k1 of input beam 160 (along with its parallel Poynting vector S1) is angled away from the wave vector k3 of output beam 180 in the direction toward the Poynting vector S3 of output beam 180. The wave vector k1 of input beam 160 is at a non-zero angle θ with respect to the wave vector k2 of input beam 170 (and its parallel Poynting vector S2). 12 The wave vector k2 of the input beam 170 (along with its parallel Poynting vector S2) is angled away from the Poynting vector S3 of the output beam 180. The angle θ between the wave vector k1 of the input beam 160 and the wave vector k3 of the output beam 180. 13 is, angle θ 12 It is an increasing function of the angle θ. 12 When θ increases from zero, 13 The walk-off angle θ WO The angle θ is equal to the point where the energy flow of the input beam 160 and the output beam 180 is parallel and the point is fully walk-off compensated. 13 This is increased to reduce the angle between the energy flow of the input beam 160 and the output beam 180.

[0047] In some scenarios, the output beam quality is affected by the angle θ. 13 When it is initially increased from zero, it improves dramatically, and thereafter the improvement gradually slows down. In one embodiment, the device 100, therefore, the angle θ 13 However, for example, the walk-off angle θ WOIt is configured to operate at at least 50% of the value and provides output beam quality that is nearly as good as that using the fully walk-off compensated scheme in Figure 2.

[0048] Figures 7, 8, 9, and 10 are data plots illustrating the exemplary modeled performance of apparatus 100 when applied to the generation of a 213 nm continuous wave laser beam from a sum-frequency mixture of a 1064 nm continuous wave laser beam and a 266 nm continuous wave laser beam. In this example, input beam 160 has a wavelength of 1064 nm and an output of 1.0 kilowatt (kW), input beam 170 has a wavelength of 266 nm and an output of 1 W, and the nonlinear crystal 130 is a BBO crystal with a length of 6 mm 130 L. Input beams 160 and 170 are Gaussian and intersect at the center of the nonlinear crystal 130. Each of Figures 7-10 shows the beam quality coefficient in the x dimension affected by walk-off.

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[0049] For comparative purposes, the data shown in each of Figures 7-10 are compared with conventional colinear phase-matched (θ 12The data in Figure 7 includes data related to (=0), and the data is acquired using a circular input beam 170, not an oval one. Each of Figures 7-10 includes Figure 790, which shows the shape of the lateral intensity distribution of the 1064 nm input beam and the 266 nm input beam. Both input beams are circular in Figure 7, and when incident on the nonlinear crystal 130, they have a 1 / e of 70 micrometers (μm). 2 It has a diameter. In Figure 8-10, the input beam 170 is elliptical and becomes increasingly oval throughout the series of data plots, while the input beam 160 is 1 / e of 70 μm. 2 It remains circular with a diameter.

[0050] As shown in Figure 7, a conventional colinear phase matching (θ) with a circular input beam 12 =0) represents an output power of 128 milliwatts (mW) and a beam quality factor of 1.73.

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[0051] As is evident from Figure 8-10, higher output power is achieved when non-colinear phase matching is performed using the oval input beam 170. In the case of Figure 8, 1 / e of the input beam 170 2The width is increased to 140 mm in the walk-off dimension (and decreased to 35 μm in the orthogonal dimension). Using this oval shape, an output power of at least 128 mW is maintained, but θ 12 When the beam quality coefficient is 50 mrad, the beam quality coefficient is less than 1.05.

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[0052] Figure 11 illustrates a laser apparatus 1100 with non-colinear type I phase-matched sum-frequency mixing of two input laser beams, preceding another frequency conversion process that essentially generates one of two input laser beams having an oval flat-top lateral intensity distribution as a result of walk-off. Apparatus 1100 is an embodiment of apparatus 100 in which source 120 generates input beam 170 in the frequency conversion process. Apparatus 1100 includes source 110, nonlinear crystal 130, source 1120, and nonlinear crystal 1130. Source 1120 and nonlinear crystal 1130 form an embodiment of source 120 of apparatus 100.

[0053] Source 1120 generates a laser beam 1150, which undergoes a colinearly phase-matched frequency conversion within a nonlinear crystal 1130 to produce a frequency-converted laser beam 1170. In the example described, the laser beam 1150 is frequency-multiplied within the nonlinear crystal 1130, and the laser beam 1150 propagates within the nonlinear crystal 1130 as an ordinary beam. The laser beam 1150 may be a Gaussian beam with a circular cross-section. The frequency-converted beam 1170 is an example of the input beam 170, which undergoes sum-frequency mixing with the input beam 160 within a nonlinear crystal 130 in the embodiment discussed above with reference to apparatus 100.

[0054] One embodiment of the apparatus 1100 further includes an imaging module 1140, for example, one or more imaging lenses, for imaging the frequency-converted beam 1170 from nonlinear crystal 1130 to nonlinear crystal 130. The imaging module 1140 is useful in scenarios where the input beams to the continuous-wave nonlinear crystals 1130 and 130 are focused within each crystal, for example, when the apparatus 1100 is operated with a continuous-wave beam. In scenarios where the input beam is collimated instead, for example, when the input beam is pulsed, the imaging module 1140 may be a telescope relaying the frequency-converted beam 1170 from nonlinear crystal 1130 to nonlinear crystal 130. The imaging module 1140 can magnify or reduce the frequency-converted beam 1170 between the nonlinear crystals 1130 and 130.

[0055] The frequency-converted beam 1170 is an extraordinary light beam within the nonlinear crystal 1130 and therefore undergoes a walk-off. This walk-off causes the lateral intensity distribution of the frequency-converted beam 1170 to be stretched in the walk-off dimension for the nonlinear crystal 1130. The frequency-converting process within the nonlinear crystal 1130 is carried out without significant depletion of the input beam such that the lateral intensity distribution of the frequency-converted beam 1170 has at least a nearly flat-top (or supergaussian) profile 1172X in the walk-off dimension for the nonlinear crystal 1130. The apparatus 1100 thereby conveniently benefits from the walk-off within the nonlinear crystal 1130 and generates the frequency-converted beam 1170 using the oval lateral intensity distribution required in the sum-frequency mixing process within the nonlinear crystal 130.

[0056] In the example depicted in Figure 11, the apparatus 1100 includes a half-wave plate 1142 that rotates the polarization of the frequency-converted beam 1170 between the nonlinear crystals 1130 and 130, so that the frequency-converted beam 1170 propagates through the nonlinear crystal 130 as an ordinary beam. Alternatively, the nonlinear crystals 1130 and 130 may be positioned perpendicular to each other, or the polarization of the frequency-converted beam 1170 may be rotated in a different manner.

[0057] In one embodiment, source 1120 is a frequency-multiplied Nd:YAG (or Nd:YVO4) laser that generates a laser beam 1150 having a wavelength of 532 nm, and nonlinear crystal 1130 is a barium betaborate (BBO) crystal that frequency-multiplies the 532 nm beam using colinear type I phase matching to generate a frequency-converted beam 1170 having a wavelength of 266 nm. In this embodiment, source 110 may be another Nd:YAG (or Nd:YVO4) laser that generates an input beam 160 having a wavelength of 1064 nm, and nonlinear crystal 130 may be a BBO crystal that generates a 213 nm output beam 180 from sum-frequency mixing of the 266 nm input beam and the 1064 nm input beam.

[0058] The lateral intensity distribution of the frequency-converted beam 1170 has a profile 1172X in the walk-off dimension for the nonlinear crystal 1130 when it emerges from the nonlinear crystal 1130. The intensity profile 1172X has a width of 1170W. At the input surface 132 of the nonlinear crystal 130, the lateral intensity distribution of the frequency-converted beam 1170 has a profile 1174X in the walk-off dimension for the nonlinear crystal 130. In the example depicted in Figure 11, the imaging module 1140 is a 1:1 imager that images the size and shape of the frequency-converted beam 1170 from nonlinear crystal 1130 to nonlinear crystal 130 such that the intensity profile 1174X also has a width of 1170W. Alternatively, the frequency-converted beam 1170 may be enlarged or reduced between the nonlinear crystals 1130 and 130 by the imaging module 1140, in which case the shape of the intensity profile 1174X would be similar to the shape of the intensity profile 1172X, but with a different width. The length 1130L of the nonlinear crystal 1130 can be set to achieve a width 1170W of the frequency-converted beam 1170, which results in a frequency-converted beam 1170 having a desired corresponding width within the nonlinear crystal 130.

[0059] In the above discussion of apparatus 100 and its embodiments, the wavelength of input beam 160 exceeds the wavelength of input beam 170. Apparatus 100 and its embodiments may instead be operated using an opposite relationship between the input beam wavelengths, or further, using input beams 160 and 170 of the same wavelength.

[0060] The device 100 can also be operated using the output of input beam 170, which exceeds the output of input beam 160, or using input beams 160 and 170, which have similar outputs. However, such a modified output relationship between input beams 160 and 170 is not very advantageous from the standpoint of optimizing frequency conversion efficiency.

[0061] The apparatus 100 and its embodiments may be modified to perform other types of sum-frequency or difference-frequency mixing other than type I sum-frequency mixing, while maintaining the non-colinear phase-matching scheme of Figure 6 and the oval shape of the input beam 170. More generally, frequency mixing techniques based on non-colinear phase-matching Figure 600 in conjunction with the oval input beam 170 are applicable to sum- or difference-frequency mixing processes, where one or more walk-offs of the interacting laser beams result in the output beam's Poynting vector being non-colinear with one or both of the input beam's Poynting vectors in the colinear phase-matching scheme. Two examples are discussed below with reference to Figures 12 and 13.

[0062] Figure 12 is a phase matching diagram 1200 for non-colinear type II phase-matched difference frequency generation in a positive uniaxial nonlinear crystal, where input beam 160 is a longer wavelength extraordinary beam, input beam 170 is a shorter wavelength ordinary beam, and output beam 180 is an extraordinary beam. In this example, both input beam 160 and output beam 180 undergo walk-off, with a walk-off angle θ relative to input beam 160. WO、1 This is the walk-off angle θ with respect to the output beam 180. WO、3 It exceeds the angle θ between the wave vectors of input beams 160 and 170. 12 The Poynting vector S1 of the input beam 160 is selected to align more closely with the Poynting vector S3 of the output beam 180. The oval shape of the input beam 170 helps maintain good spatial overlap between the input beams 160 and 170, even if the Poynting vector S2 of the input beam 170 does not align very well with the Poynting vector S3 of the output beam 180.

[0063] Figure 13 is a phase matching diagram 1300 for non-colinear type I phase-matched difference frequency generation in a negative uniaxial nonlinear crystal, where both input beams 160 and 170 are extraordinary light beams, and output beam 180 is an ordinary light beam. Here, the Poynting vector S3 of output beam 180 is parallel to its wave vector k3. Again, the angle θ between the wave vectors of input beams 160 and 170. 12 The configuration is selected to more closely align the Poynting vector S1 of the input beam 160 with the Poynting vector S3 of the output beam 180. In this case, the oval shape of the input beam 170 also helps maintain good spatial overlap between the input beams 160 and 170, even if the Poynting vector S2 of the input beam 170 does not align very well with the Poynting vector S3 of the output beam 180.

[0064] The preceding discussion of the apparatus 100 and its embodiments, as well as modifications for implementing other types of sum-frequency or difference-frequency mixing besides Type I sum-frequency mixing, can be extended to the non-oval shape of the input beam 170. While the oval shape of the input beam 170 is optimal for frequency conversion efficiency, improved output beam quality does not require the input beam 170 to be oval. More generally, improved beam quality is achieved when the lateral size of the input beam 170 exceeds the corresponding lateral size of the input beam 160 in the walk-off plane. For example, both input beams 160 and 170 may be circular, but the lateral size of the input beam 170 exceeds the size of the input beam 160.

[0065] The present invention has been described above in terms of preferred and other embodiments. However, the present invention is not limited to the embodiments described and depicted herein. Rather, the present invention is limited only by the claims appended herein.

Claims

1. A laser device with non-colinearly phase-matched frequency mixing, wherein the laser device is A first laser source configured to generate a first input laser beam, A second laser source configured to generate a second input laser beam, A first nonlinear crystal is arranged to generate an output laser beam from a non-colinearly phase-matched frequency mixing of the first input laser beam and the second input laser beam. Equipped with, (a) The output laser beam undergoes a walk-off in the walk-off plane within the first nonlinear crystal, (b) The wave vectors of the first input laser beam and the second input laser beam are non-colinear and intersect within the first nonlinear crystal. (c) The second input laser beam has a lower output than the first input laser beam in the first nonlinear crystal, (d) In the first nonlinear crystal, the angle between the Poynting vector of the first input laser beam and the Poynting vector of the output laser beam is smaller than the angle between the Poynting vector of the second input laser beam and the Poynting vector of the output laser beam. (e) The second input laser beam has a larger lateral size than the first input laser beam in the walk-off plane within the first nonlinear crystal. Laser device.

2. The laser apparatus according to claim 1, wherein the second input laser beam has an oval transverse intensity distribution that is extended in the walk-off plane.

3. The laser apparatus according to claim 1 or claim 2, wherein the second input laser beam is ultraviolet light.

4. The laser apparatus according to any prior claim, wherein the first input laser beam is near-infrared, and the non-colinearly phase-matched frequency mixing is sum-frequency mixing.

5. The laser apparatus according to any prior claim, wherein the non-colinearly phase-matched frequency mixing is a type I sum-frequency mixing.

6. The laser apparatus according to any prior claim, wherein the second laser beam is an elliptical Gaussian beam, or the oval transverse intensity distribution has a flat top or supergaussian profile in the walk-off plane.

7. The laser apparatus according to any prior claim, wherein the output of the second input laser beam is up to 10 percent of the output of the first input laser beam when incident on the first nonlinear crystal.

8. The laser apparatus according to any prior claim, wherein the second laser source includes a second nonlinear crystal configured to generate the second input laser beam by frequency-converting a third laser beam using colinear phase matching, and the oval transverse intensity distribution is caused by a walk-off of the second input laser beam in the second nonlinear crystal.

9. The laser apparatus according to claim 8, wherein the first input laser beam and the second input laser beam are continuous wave laser beams, and the apparatus further comprises an imaging module configured to image the second input laser beam from the second nonlinear crystal to the first nonlinear crystal.

10. The laser apparatus according to claim 8 or 9, wherein the second nonlinear crystal is configured to form the second input laser beam as the second harmonic of the third laser beam.

11. The laser apparatus according to any prior claim, wherein the first laser source includes a laser resonator, and the first nonlinear crystal is located within the laser resonator.

12. The laser apparatus according to any prior claim, further comprising a resonant enhancement cavity arranged to receive a first input laser beam from a first laser source, wherein the first nonlinear crystal is located within the resonant enhancement cavity.

13. The laser apparatus according to any preceding claim, wherein the intersection point between the lateral centers of the first input laser beam and the second input laser beam is located in the central third of the propagation path of the second input laser beam through the first nonlinear crystal.

14. The laser apparatus according to any prior claim, wherein in the first nonlinear crystal, the output laser beam has a walk-off angle, and the Poynting vector of the first input laser beam is oriented within half the walk-off angle of the output laser beam.

15. The laser apparatus according to any prior claim, wherein the lateral size of the second input laser beam is at least 75 percent greater than the lateral size of the first input laser beam.

16. The laser apparatus according to any prior claim, wherein the second input laser beam is the fourth harmonic of the first input laser beam, and the output laser beam is the fifth harmonic of the first input laser beam.

17. A method for non-colinearly phase-matched frequency mixing of laser beams, wherein the method is To generate a first input laser beam and a second input laser beam, The first input laser beam and the second input laser beam are directed into the first nonlinear crystal, thereby, (i) The wave vectors of the first input laser beam and the second input laser beam are non-colinear and intersect within the first nonlinear crystal; (ii) The first wave vector and the second wave vector cooperate with the orientation of the first nonlinear crystal to promote non-colinear phase-matched frequency mixing of the first input laser beam and the second input laser beam, resulting in the generation of an output laser beam, the output laser beam undergoing a walk-off in the walk-off plane within the first nonlinear crystal; Includes, The first input laser beam has a higher output than the second input laser beam. The lateral size of the second input laser beam exceeds the corresponding lateral size of the first input laser beam in the walk-off plane. In the first nonlinear crystal, the angle between the Poynting vector of the first input laser beam and the Poynting vector of the output laser beam is smaller than the angle between the Poynting vector of the second input laser beam and the Poynting vector of the output laser beam. method.

18. The method according to claim 17, wherein the second input laser beam has an oval transverse intensity distribution that is extended in the walk-off plane.

19. The method according to claim 17 or 18, wherein at least 25 percent of the output of the second laser beam is converted into the output laser beam.

20. The method according to any one of claims 17-19, wherein the non-colinearly phase-matched frequency mixing is a type I sum-frequency mixing.

21. The method according to claim 18, wherein the generating step includes the step of frequency-converting a third laser beam in a second nonlinear crystal to generate the second input laser beam, and the oval transverse intensity distribution is caused by a walk-off of the second input laser beam in the second nonlinear crystal.

22. The method according to claim 21, wherein the frequency conversion step is to cause the oval transverse intensity distribution to have a flat top or supergauss profile in the walk-off plane.

23. The method according to any one of claims 17-22, wherein the step of generating includes the step of generating the second input laser beam as the fourth harmonic of the first input laser beam.

24. The method according to any one of claims 17-23, wherein the generating step includes generating the first input laser beam inside a laser resonator containing the first nonlinear crystal.

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