The high optical intensities available from lasers have made practical the use of nonlinear methods to convert the laser wavelength to its harmonics. Nonlinear optical methods have also been used to mix laser radiation at two or more frequencies to produce radiation at the sum and difference frequencies. In addition, nonlinear devices have been placed within resonant cavities to form parametric oscillators that generate tunable radiation.
Practical applications of nonlinear methods require the efficient generation of optical harmonics or of sum or difference frequencies. Efficient nonlinear frequency conversion requires a material with a large nonlinear optical susceptibility and phase matching of the conversion process. Applications of nonlinear frequency conversion have relied almost exclusively on crystalline nonlinear optical materials because of their large nonlinear optical susceptibilities and their ability to phase match the nonlinear process. Efficient nonlinear conversion is typically achieved by selecting anisotropic crystals having large second-order nonlinear susceptibilities and that allow birefringence-based phase-matching schemes.
Prior art methods using anisotropic crystals and birefringent phase matching have significant limitations. First, most crystals are not transparent to radiation of wavelengths of less than about 200 nm, limiting the range of wavelengths that can be generated or used in nonlinear conversion processes. Second, dispersion in a crystal produces a large group velocity walk-off so that pulses of different wavelengths propagate at different speeds. In some cases, the pulses temporally overlap within the crystal only for very short distances, severely limiting the conversion efficiency, especially for very short (&lt;100 fs) pulses. Third, because of the broad spectral width of short pulses, phase matching is achieved only for very thin crystals, also limiting conversion efficiency. Finally, phase matching in crystals depends on the propagation direction of the laser beam with respect to the crystalline axes. Unfortunately, a tightly focused beam (for increased beam intensity and increased conversion efficiency) has a large divergence so that portions of such a beam propagate at angles for which the angle-dependent phase-matching condition is not satisfied.
In contrast to crystals, many gases are transparent to wavelengths as short as 100 nm; helium is transparent to wavelengths as short as about 50 nm. Gases are accordingly appropriate nonlinear materials for frequency-conversion into the deep and vacuum ultraviolet ("UV"), and x-ray regions of the spectrum. Unfortunately, the nonlinear susceptibilities of gases are relatively small and, more importantly, established phase-matching techniques based on crystalline birefringence are inapplicable because gases are isotropic. Nevertheless, the use of non-phase-matched harmonic conversion in gases has been used to generate light in the UV to soft x-ray regions of the spectrum but with the low conversion efficiencies expected without phase matching.
The nonlinear generation of short pulses at sum, difference, or harmonic frequencies presents an additional difficulty. Short pulses are necessarily spectrally broad and propagation in a dispersive material extends the pulse duration. To maintain a short pulse duration, thin crystals must be used, limiting the nonlinear conversion efficiency.
Optical parametric generators using crystals have been used to generate short pulses that are wavelength tunable, but these generators exhibit the problems associated with crystals. Because of absorption in the crystals, these generators are not generally efficient for wavelengths shorter than about 200 nm.
Other prior art short pulse sources for short wavelengths are expensive, inefficient, and produce much longer duration pulses. For example, short pulses from a synchrotron source have pulse durations of about 70 ps.
There are many applications for improved short-wavelength radiation sources. Some lithographic systems use ultraviolet radiation at wavelengths of about 250 nm to transfer patterns from a mask to a semiconductor wafer. Because the minimum feature size produced on a wafer is proportional to the wavelength used for the pattern transfer, higher resolution lithography requires even shorter wavelengths. In addition, short-wavelength radiation is required for optical testing at wavelengths between 2 nm and 200 nm.
It is apparent from the foregoing that improved methods and apparatus are needed for efficient nonlinear generation of short pulses and short wavelengths.