1 + tan2(θ)
1 + (no/ne)2tan2(θ) (5.7) Note that if the polarization states of the three interactive waves are the same, the left-hand side of Eg.(2.6) is always larger than the right-hand side, resulting in no so-lution for phase-matching condition. In order to fulfill the phase-matching condition, differently polarized waves should be used. Therefore, there are two types of angle phase matching. Type I refers to the situation where the pump and signal waves have the same polarization. In type II phase matching, the two waves are orthogonal polarizations. In this studies, the type I phase-matching was used because of the smaller phase-matching angle, which result in less Fresnel’s losses.
5.2 Calculations of Tuning Curves Based on Quasi-phase Matching in PPLN Crystal
Over the last decade there has been a rapid development in quasi-phase matching (QPM) technique. QPM materials have proven to be very valuable for efficient fre-quency conversion. For example periodically poled LiNbO3 (PPLN), KTiOPO4 (PP-KTP), RbTiOAsO4 (PPRTA), LiTaO3 (PPLT), and QPM-GaAs are commercially available or experimentally investigated. In the QPM scheme, periodic structures are used to achieve phase-matching. In order to offset the accumulated phase mismatch
the signs of the optical nonlinearity of the crystals are modulated along the propaga-tion direcpropaga-tion so that the phase is periodically reset by π with half-period equal to the coherence length. Two techniques are involved: (1) electric-field poling ferroelectric materials (such as LiNbO3), and (2) stacking-bonding semiconductor plates (such as GaAs) by rotating alternative wafers. In contrast to birefringent phase-matching, since QPM does not rely on birefringence, it can thus be achieved at any wavelength within the transparency range of the crystal by selecting the modulation period of the nonlinearity grating Γ and it allows a free choice of polarization of the interacting waves, permitting to use the largest nonlinear susceptibility.
According to the original idea of QPM, the phase-matching condition, Eq. (2.6) can be modified to become:
here the parameter Γ presents the period of domain inversion or the χ(2) coefficient distribution of the nonlinear medium; the integer m stands for the order of QPM.
Because of thermal expansion, Γ is usually a function of temperature T. In general, one set of ωp, ωs, and ωi only has a unique period Γ to satisfy the phase-matching condition (Eq. (2.8)) at a temperature. Since the period Γ is well defined after the material process, we can only fine tune the frequency sets by changing temperature of the nonlinear optical crystal in the normal incident collinear configuration or changing the incident angle to slightly modify the effective period Γ.
Chapter 6
Difference Frequency Mixing in GaSe Crystal
6.1 Introduction
Nonlinear optical frequency down-conversion by means of a χ(2) parametric inter-action process, such as difference-frequency generation(DFG) and optical parametric oscillation(OPO), can be employed to generate coherent sources at mid-infrared wave-lengths in which there exist no convenient direct lasering sources. Coherent sources in the mid-infrared ray are of prime importance for molecular spectroscopy, eye-safe medical instrumentations, radar and remote sensing of atmospheric constituents, and numerous military applications. In order to generate high power IR coherent source, suitable nonlinear optical materials with large magnitude of second-order suscepti-bilities are considerable. Among different classes of second-order nonlinear optical materials, GaSe crystal has comparatively lower absorption coefficients and appropri-ate amount of birefringence for phase-matching(∆n≈ 0.35 at 1 µm). On the negative side, GaSe is a soft, layered material that can be cleaved only along the 001 plane (z-cut orientation); it also provides a large walk-off angle. Recently, Y.J. Ding et
al.[18] demonstrated a continuous-tunable and coherent radiation in the extremely-wide range of 2.7-38.4 µm and 58.2-3540 µm based on different-frequency mixing in GaSe crystal for the first time. Such amazingly tunable range in Ding’s results proved that GaSe possesses great potential for nonlinear frequency down-conversion.
Therefore, using GaSe crystal to generate infrared light source based on parametric interaction process is a interesting subject.
During the past two decades, extensive experimental studies had been carried out in this field of research in the continue-waves, nanosecond, picosecond and fem-tosecond regime applied with GaSe crystals. In application of applied spectroscopy such as biomedical diagnostics and chemical identification, high spectral purity, wide wavelength tunability and appropriate output power are considered. For these ex-perimental applications the nanosecond time domain is optimal, because it offers a high spectral resolution and output average power of the order of few watts. An-other attractive application is the studies of intersubband lifetimes and free carrier effects in semiconductor quantum wells. Electron intersubband lifetimes in the pi-cosecond regime can be measured by using a pump-probe far-infrared technique. In order to achieve a population inversion between the second excited subband, the es-timated threshold pump power is in the region of 100 kWcm−2. Consequently, IR picosecond pulse is suitable for the time resolved investigations of the dynamics of infrared states. Besides, high output energies in the microjoule range are also es-sential to achieve substantial excess populations. In this chapter, therefore, both the nanosecond and picosecond radiations in the mid-infrared based on DFG in GaSe were studied. Additionally, N.B. Singh et al.[50] reported that the silver gallium selenide doped GaSe crystals possessed a high nonlinear coefficient of 75 pm/V resulting in
significant increase of the d2/n3. This dopant in GaSe enhanced the intrinsic value of the nonlinear coefficient. In the case of the indium doped GaSe,[51] it showed the im-provements in second-harmonic generation efficiency and the mechanical properties.
Both improvements are ascribed to better crystal quality by means of doping indium.
Consequently, the variation in nonlinear coefficient is possibly the origin of crystal quality and doping impurity. The erbium doping in GaSe causing the substitution or interstitial were interesting. In addition to the investigation on the optical and electrical properties of erbium doped GaSe crystals, the nonlinear optical property will be examined in this chapter.
In this thesis, we successfully demonstrated that our GaSe crystals can be used to generate mid-infrared sources with both pulse durations of 5 ns and 5 ps, respectively, from different-frequency mixing systems. In the nanosecond regime, the signal and idler waves output from Nd:YAG-laser-pumped PPLN OPO were collinear mixing in GaSe crystal to generate tunable radiation from 4.35 to 14.25 µm. The conversion efficiency and tuning characteristics of different-frequency mixing were discussed in detail. In the picosecond regime, the picosecond infrared pulses were generated by using the 1.064 µm pump and signal pulses of a parametric device based on a 10 Hz Nd:YAG amplifier system. Besides the characteristics of output picosecond pulses, the effect of erbium doped GaSe crystals in this system of different-frequency mixing were also discussed.