Patent Application
20180203326
The present invention relates in general to frequency-conversion in optically nonlinear crystals. The invention relates in particular to conversion of laser-radiation at one wavelength to radiation at another wavelength using a series of optically nonlinear crystals.
Optical frequency conversion in optically nonlinear crystals is a process typically used to indirectly generate laser-radiation having a wavelength that cannot practically be generated directly from any laser gain-medium. This process is extensively used to generate laser-radiation having a wavelength in the ultraviolet (UV) region of the electromagnetic spectrum.
By way of example, laser-radiation having a wavelength of 1064 nanometers (nm) can be converted to radiation having a wavelength of 532 nm by frequency doubling in one optically nonlinear crystal. The 532 nm radiation can be converted to radiation having a wavelength of 266 nm or 355 nm in another optically nonlinear crystal by respectively frequency-doubling or sum-frequency mixing.
The frequency-conversion process in an optically nonlinear crystal has a conversion-efficiency (converted-power out versus input-power) determined by a number of factors other than basic properties of the optically nonlinear material of the crystal. One important factor is electric-field intensity of the radiation to be converted, on which the conversion efficiency is directly dependent. Another important factor is the type and accuracy of so called “phase matching” which can be described simply as arranging the optically nonlinear to crystal to maximize interaction of the converted frequency with the input frequency.
Phase-matching is dependent, inter alia, on the orientation of the axes of the crystal relative to the propagation direction, and on temperature of the crystal to a degree dependent on the type of phase-matching employed. Assuming temperature and phase-matching are optimized, one way of increasing frequency-converted output power as a fraction of input power would be to extend the length of the optically-nonlinear crystal. As nominally transparent optically nonlinear crystals still have a finite absorption coefficient, particularly for shorter-wavelengths, crystal temperature can increase dynamically during passage of radiation being converted. In a long crystal, this can result in the crystal temperature increasing to a point where the input and converted frequencies become progressively out of phase, thereby reducing interaction of the input and converted frequencies. This is often termed the “thermal de-phasing problem” by practitioners of the art.
One prior-art solution to this problem of extending crystal length while limiting thermal dephasing, is to replace a long crystal with two or more equal-length crystals having a total length about that of the long crystal. This is described in certain patent and open-literature references, which are a part of an information disclosure statement appended to this application.
Applicants have experimented with this solution and found that results were inconsistent and fell short of expectations. Applicants determined that a more detailed analysis of the thermal-dephasing problem was required to determine a solution that could provide consistent anticipated results.
In one aspect, optical apparatus in accordance with the present invention for performing a frequency-conversion operation comprises first and second optically nonlinear crystals located on a propagation-axis of the laser-radiation and numbered in consecutive numerical order in the propagation-axis direction. Each of the optically nonlinear crystals arranged to perform the frequency-conversion operation. The second optically nonlinear crystal has a length less than that of the first optically nonlinear crystal.
The accompanying drawings, which are incorporated in and constitute a part of the specification, schematically illustrate a preferred embodiment of the present invention, and together with the general description given above and the detailed description of the preferred embodiment given below, serve to explain principles of the present invention.
Beginning with an analysis of a prior-art solution to the thermal dephasing problem,
It should be noted here that in
In this prior-art description and in examples of inventive solutions to the thermal dephasing problem described further hereinbelow, it is assumed that radiation having a “fundamental” wavelength is being converted by frequency-doubling to UV wavelength radiation in each crystal. The fundamental wavelength, in this instance, may itself have been generated by frequency conversion from a different fundamental wavelength as discussed above.
The power-absorption rate along the z-axis is a function of fundamental wavelength power (PF) and UV wavelength power (PUV) that can be approximated by a quadratic equation:
dP
abs
/dz=ρ=α
F
P
F+αUVPUV+β1PFPUV+β2PUV2 (1)
where αF and αUV are linear absorption coefficients at the fundamental wavelength and UV wavelength, respectively, and β1 and β2 are two-photon absorption coefficients. The absorption coefficients are characteristic of the nonlinear crystal material.
Thermal analysis for this and inventive examples herein is based on assumption that crystals are in the form of cylinders having a circular cross-section with a radius of about 2.5 millimeters (mm) and that fundamental wavelength power in the crystal is in the form of a collimated beam having a diameter of 200 micrometers (μm). This is a less than rigorous assumption, as focused beam-waists for coherent radiation have a hyperbolic form in the z-axis direction. The assumption is, however, sufficiently adequate to identify the problem and formulate inventive solutions. Thermal analysis indicates that radial thermal gradients do not contribute significantly to the thermal dephasing problem.
Comparing the three equal-length crystals of
Turning now to a description the present invention,
It is expected that embodiment 30 may be only marginally less effective at providing a solution to thermal dephasing than embodiment 20. Embodiment 30 offers a practical advantage in that crystals of only two different lengths are required, thereby offering potential economies of scale in the production of the two shorter crystals.
In the example of
In above-described embodiments of the present invention, the lengths of the multiple crystals are selected, by various arbitrary or empirical criteria, as fractions of the length of a hypothetical, long single crystal. Set forth below is a description of a more analytical method of selecting crystal lengths, albeit with a somewhat arbitrary goal that each of the multiple crystals crystal contributes equally the thermal dephasing.
The goal of having each crystal in a sequence thereof contribute equally to the thermal dephasing can be expressed mathematically by defining a constant tolerable phase-mismatch contribution:
where Δk is the maximum mismatch between the wavevectors of the fundamental wavelength radiation and the converted radiation over the crystal length and L is the crystal length.
The phase-mismatch contribution φmax can also be expressed as:
φmax=a TR=a(Tout−Tin)L=b(ρout−ρin)L (3)
where TR is the “temperature range” for the crystal material, and both a and b are constants that correspond to the tolerable phase-mismatch. TR is typically expressed in units of Kelvin·centimeters (K·cm). The value of TR for a particular crystal material is available in software SNLO available online from www.as-photonics.com. This software is extensively used by those concerned with frequency-conversion in optically nonlinear crystals. The values of constants a and b are user-selected.
From equation (3), an expression for a suitable crystal-length can be formulated as follows:
The crystal-length selection for a series of crystals can be graphically determined by first rewriting equation (4) to represent (ρout−ρin) as a function of crystal length L. This provides an equation:
Next, the origin of curve B is moved to locus 1 and curves A and B again intersect, here, at a second locus (locus 2). The z-axis difference between locus 2 and locus 1 determines length L2 of crystal 62. Finally, the origin of curve B is moved to locus 2 and curves A and B again intersect at a third locus (locus 3). The z-axis difference between locus 3 and locus 2 determines length L3 of crystal 63. In this example, the sum of the lengths of crystals 62 and 63 is greater than the length of crystal 61. This again should not be construed as a limiting condition.
Recapitulating, the present invention is described above in terms of embodiments wherein a particular frequency-conversion operation for laser-radiation is performed in two or more elongated optically nonlinear crystals arranged is series along a propagation-axis of the radiation. It is emphasized here that the same frequency-conversion operation is performed in each of the crystals. Here, the terminology “same frequency conversion operation” means that each converts the same first frequency to the same second frequency.
The at least two crystals can be identified as first and second crystals, numbered in consecutive numerical order in the propagation-axis direction. In all embodiments of the present invention, the second crystal has a length less than that of the first crystal, with the lengths selected according to any of the above-described criteria. Preferably, but not necessarily, in a series of more than two crystals, each crystal should have a length less than that of a previous adjacent crystal. In such an arrangement, each crystal will have a length at least about 10% less than the length of a previous adjacent crystal in the series.
Those skilled in the art will recognize from the description of the present invention presented above, that embodiments and principles of the invention are applicable to frequency-doubling operations and sum-frequency mixing operations. Principles are also applicable for type-1 or type-2 frequency-conversion operations, critical or non-critical, and adjacent crystals in a series may have different axis-orientations for compensating spatial walk-off between interacting frequencies.
In summary, the present invention is described above with reference to preferred embodiments. The invention, however, is not limited by the embodiments described herein, but is limited only by the claims appended hereto.
