Sum Frequency and Higher Harmonic Generation

Some examples shall demonstrate experimental realizations of the sum-frequency mixing technique. 

Because of the lower densities of gases compared with solid crystals the efficiency I(3w)/I(w) is much smaller than in crystals. However, there is no short wavelength limit as in crystals and the spectral range accessible by optical mixing can be extended far into the VUV range [5.238]. 

The lower-wavelength limit for nonlinear processes in crystals (SHG or sum-frequency mixing) is generally given by the absorption (transmission cut-ofi) of the crystals. 

Windows cannot be used for wavelengths below 120 nm because all materials absorb the radiation, therefore apertures and differential pumping is needed. An elegant solution is the VUV generation in pulsed laser jets (Fig. 5.125), where the density of wanted molecules within the focus of the incident lasers can be made large without having too much absorption for the 

An intense coherent tunable Fourier-transform-limited narrow-band all-solid-state vacuum-ultraviolet (VUV) laser system has been developed by Merkt and coworkers [5.261]. Its bandwidth is less than 100 MHz and the tuning range covers a wide spectral interval around 120,000 cm (15 eV). At a repetition rate of 20 Hz the output reaches 10 photons per pulse, which corresponds to an energy of 0.25 nJ per pulse, a peak power of 25 mW for a pulse length of 10 ns, and an average power of 5 nW. For these short VUV wavelengths of around A. = 80 nm this is remarkable and is sufficient for many experiments in the VUV. 

A novel device for efficiently generating intense radiation at wavelengths around 202 nm is shown in Fig. 5.110. A laser diode-pumped Nd YV04 laser is frequency doubled and delivers intense radiation at X = 532 nm, which is again frequency doubled to A. = 266 nm in a BBO crystal inside a ring resonator. The output from this resonator is superimposed in a third enhancement cavity with the output from a diode laser at A = 850 nm to generate radiation at A = 202 nm by sum-frequency mixing. This 202-nm radiation is polarized perpendicularly to that at the two other waves and can be therefore efficiently coupled out of the cavity by a Brewster plate [5.255]. 

More information on the generation of VUV radiation by nonlinear mixing techniques can be found in [5.254-5.269]. 

Possible combinations of wavelength pairs (Xi,X2) which allow.phase-matched sum-frequency generation in ADP, 

Experimental arrangement for optical mixing and harmonic generation to produce coherent tunable vuv radiation [7.86a] 

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Figure 10 shows a typical measured homodyne waveform and the corresponding numerical fit (solid lines). The measured THz waveform exhibits both the fundamental ECDL difference frequency (Fig. 10(a)) and higher harmonics - predominantly the third harmonic (Fig. 10(b)). Multiple harmonic generation in THz photo-mixers has been previously reported [103], By fitting the observed waveform to a sum of harmonic sinusoidal functions, the amplitude and phase of the THz electric field can be determined separately for the fundamental and third harmonic. The solid line shows a numerical fit to the data. The fundamental extracted frequency, 0.535 THz, compares well to the expected frequency based on the frequency difference of the two ECDL. The extracted E field amplitudes and phases are 3.37 x 10 4 and 2.17 radians for 0.535 THz (Fig. 10(a)) and 5.61 x 10-5 and 3.94 radians for the 1.605 THz third harmonic, respectively (Fig. 10(b)). 

We believe that our model can be extended even further to accurately describe other nonlinear optical interactions such as sum and difference frequency mixing, as well as higher-order harmonics generation. 

Periodic oscillations in this dipole can act as a source term in the generation of new optical frequencies. Here a is the linear polarizability discussed in Exps. 29 and 35 on dipole moments and Raman spectra, while fi and x are the second- and third-order dielectric susceptibilities, respectively. The quantity fi is also called the hyperpolarizability and is the material property responsible for second-harmonic generation. Note that, since E cos cot, the S term can be expressed as -j(l + cos 2 wt). The next higher nonlinear term x is especially important in generating sum and difference frequencies when more than one laser frequency is incident on the sample. In the case of coherent anti-Stokes Raman scattering (CARS), X gives useful information about vibrational and rotational transitions in molecules. 

This method [6.34] relies on the fact that of all physical quantities, it is the frequency which can be measured most accurately. With modern fast counters, frequencies up to 500 MHz can be counted directly and calibrated against frequency standards. At higher frequencies, a heterodyne technique may be used whereby the difference between the unknown frequency and a known, nearly equal frequency is generated by a nonlinear detector and can be counted directly. The known frequency is synthesized from two or more known lower frequencies by a nonlinear device which can generate harmonics or which can sum different frequencies [6.35]. 

Applications of second order nonlinear optical materials include the generation of higher (up to sixth) optical harmonics, the mixing of monochromatic waves to generate sum or difference frequencies (frequency conversion), the use of two monochromatic waves to amplify a third wave (parametric amplification) and the addition of feedback to such an amplifier to create an oscillation (parametric oscillation). 

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