Temperature-dependent Sellmeier Equation Research Articles

Simultaneous Measurement of Group Refractive Index Dispersion and Thickness of Fused Silica Using a Scanning White Light Interferometer.

In this study, we simultaneously measured the group refractive index dispersion and thickness of fused silica using a scanning white light interferometer on a spectral range from 800 to 1050 nm. A delay error correction was performed using a He-Ne laser. The accuracy of the measured group refractive index dispersion of fused silica, when compared to the temperature-dependent Sellmeier equation, is within 4 × 10-5.

Temperature Dependence of the Thermo-Optic Coefficient of SiO2 Glass.

This paper presents a thorough analysis on the temperature dependence of the thermo-optic coefficient, dn/dT, of four bulk annealed pure-silica glass samples (type I-natural quartz: Infrasil 301; type II-quartz crystal powder: Heraeus Homosil; type III-synthetic vitreous silica: Corning 7980 and Suprasil 3001) from room temperature down to 0 K. The three/four term temperature dependent Sellmeier equations and respective coefficients were considered, which results from fitting to the raw data obtained by Leviton et al. The thermo-optic coefficient was extrapolated down to zero Kelvin. We have obtained dn/dT values ranging from 8.16 × 10-6 up to 8.53 × 10-6 for the four samples at 293 K and for a wavelength of 1.55 μm. For the Corning 7980 SiO2 glass, the thermo-optic coefficient decreases monotonically, from 8.74 × 10-6 down to 8.16 × 10-6, from the visible range up to the third telecommunication window, being almost constant above 1.3 μm. The Ghosh's model was revisited, and it was concluded that the thermal expansion coefficient only accounts for about 2% of the thermo-optic coefficient, and we have obtained an expression for the temperature behavior of the silica excitonic bandgap. Wemple's model was also analyzed where we have also considered the material dispersion in order to determine the coefficients and respective temperature dependences. The limitations of this model were also discussed.

Formula omitted] optical parametric oscillator with wide temperature tuning

This paper investigated the output characteristics of ZGP optical parametric oscillator (OPO) with tuning over a wide temperature range. The temperature-dependent Sellmeier equation of the ZGP crystal was obtained, and the temperature-tuned curves of ZGP OPO at different phase matching angles were calculated. For temperatures ranging from 25 °C to 200 °C, a tunable long-wave laser at 7.08–7.50 μm, 7.40–7.95 μm, and 7.79–8.47 μm was obtained when the phase matching angles were 51.3°, 50.95°, and 50.6°, respectively. The total tuning range was 1.39 μm. When the idler wavelength was 8.348 μm, the output energy was 0.520 mJ with a pulse width of 15.5 ns, the corresponding slope efficiency and optical conversion efficiency were 10.22% and 8.15%, respectively. The laser has advantages of a wide tunable range and compact mechanical configuration, extending the tuning method of ZGP OPO, which is important in promoting the development of long-wave lasers with a wide tuning range.

Temperature-dependent optical properties of AgGaS2 in the terahertz range

The temperature-dependent optical properties of the AgGaS2 crystal were characterized in the 0.2–2 THz range by terahertz time-domain spectroscopy (TDS). The refractive indices and the absorption coefficients along and orthogonal to the optical axis (c axis) were measured, and the temperature-dependent Sellmeier equations were fitted for various applications of linear and nonlinear optical devices. An E mode vibrating orthogonal to the c axis centering at 1.03 THz (34 cm−1) and a B2 mode along the c axis centering at 1.86 THz (62 cm−1), were observed for the first time. The phonon softening during the temperature rise was discussed and analyzed with the help of Raman spectroscopy. According to the measured absorption spectrum of AgGaS2, we also fitted the parameters of the low-frequency phonon modes at room temperature with the Lorentz dispersion model, which is helpful in predicting the lattice dynamics and optical behaviors of the crystal.

Experimental measurement of temperature-dependent sellmeier coefficients and thermo-optic coefficients of polymers in terahertz spectral range

Terahertz time-domain spectroscopy has been used to measure the temperature-dependent absorption coefficients and refractive indices of different polymers in 0.2–1.8 THz spectral frequency. The coefficients of temperature-dependent Sellmeier equation for all these polymers have also been evaluated by statistical fitting the measured data, which will be helpful for the evaluation of dispersion properties of the material. Additionally, the thermo-optic coefficients have been evaluated to be the range of −1.230×10−4 to −2.50×10−4 K−1 for 298–373 K. This data would be helpful for the applications of polymers as THz-waveguide and other temperature sensitive devices. These results provide a temperature-dependent database of optical properties of different polymers for their efficient utilization in THz technology.

Temperature dependent Sellmeier equation for the refractive index of GaP

A temperature-dependent Sellmeier equation for GaP, valid for wavelengths between 0.7 and 12.5 μm over a temperature range of 78 to 450 K, is presented. The temperature dependence values of the generated wavelengths in nonlinear frequency conversion calculated using this equation match well the experimentally measured values.

Refractive index of infrared-transparent polycrystalline alumina

The refractive index of fully dense, infrared-transparent polycrystalline alumina (PCA) with a mean grain size of ∼0.6 μm is reported for the wavelength range 0.85 to 5.0 μm over the temperature range T=296 to 498 K. The temperature-dependent Sellmeier equation is n2−1=(A+B[T2−To2])λ2/[λ2−(λ1+C[T2−To2])2]+Dλ2/(λ2−λ22), where λ is expressed in μm, To=295.15 K, A=2.07156, B=6.273×10−8, λ1=0.091293, C=−1.9516×10−8, D=5.62675, λ2=18.5533, and the root-mean square deviation from measurements is 0.0002. This paper describes how to predict the refractive index of fully dense isotropic PCA with randomly oriented grains using the ordinary and extraordinary refractive indices (no and ne) of sapphire spatially averaged over the surface of a hemisphere. The refractive index of alumina at 296 and 470 K agrees within ±0.0002 with the predicted values. Similarly, the ordinary and extraordinary optical constants ko and ke are used to predict the absorption coefficient of alumina. The refractive indices no and ne of sapphire grown at Rubicon Technologies by the Kyropoulos method were measured at 295 K and agree with published Sellmeier equations for sapphire grown by other methods within ±0.0002.

Temperature-dependent Sellmeier equation at terahertz frequency range for 1 mol % MgO-doped stoichiometric lithium tantalate

We first examined a temperature-dependent Sellmeier equation for the extraordinary refractive index of MgO-doped stoichiometric LiTaO3 (MgO:SLT) crystal via frequency-tunable narrowband terahertz (THz) generation at 0.4–1.8 THz and at a low temperature range of 80–300 K. The mean deviation of Sellmeier equation fit was less than 0.3%, being equivalent with the predicted measurement uncertainty of 0.3%. The temperature effect (dnTHz/dT) was 2.02 × 10−3/K at 1 THz. Moreover, we showed the smaller birefringence for MgO:SLT than MgO-doped stoichiometric LiNbO3 at 300 K from THz time-domain spectroscopy. This study is crucial for material study itself and THz device engineering.

Temperature-Dependent Sellmeier Equations of IR Nonlinear Optical Crystal BaGa4Se7

The thermal dependent principal refractive indices of a new promising IR nonlinear optical crystal BaGa4Se7 at wavelengths of 0.546, 0.5806, 0.644, 0.7065, 1.530, 1.970, and 2.325μm were measured by using the vertical incidence method within the temperature range from 25 to 150 °C. We derived equations of thermal refractive index coefficients as a function of wavelength that could be used to calculate the principal thermal refractive indices at different wavelengths. The temperature-dependent Sellmeier equations were also obtained and used to calculate the phase matching angles for the optical parametric process of BaGa4Se7 crystal at different temperatures.

Mid-infrared tunable, narrow-linewidth difference-frequency laser based on orientation-patterned gallium phosphide

We report on the first characterization of orientation-patterned gallium phosphide (OP-GaP) crystals used to generate narrow-linewidth, coherent mid-infrared (MIR) radiation at 5.85 μm by difference frequency generation (DFG) of continuous-wave (cw) Nd:YAG laser at 1064nm and diode-laser at 1301nm. By comparison of the experimental absolute MIR efficiency versus focusing to Gaussian beam DFG theory, we derive an effective nonlinear coefficient for first-order quasi-phase-matched OP-GaP at the generated DFG wavelength. Using d = (2/π)d14 and taking into account Miller’s delta rule, we retrieve an absolute value of the d14 quadratic nonlinear susceptibility coefficient of GaP of d14 = 27.2(3) pm/V at 5.85 μm, in good agreement with the latest absolute measurement of this nonlinear coefficient from non-phase-matched second-harmonic generation (1.32 μm → 0.66 μm) taking into account multiple reflection effects [Shoji et al 1997 J. Opt. Soc. Am. B 14 2268]. The temperature and signal-wave tuning curves are also in qualitative agreement with a recently proposed temperature-dependent Sellmeier equation for OP-GaP when focusing effects are taken into account.

Temperature-dependent Sellmeier equations of nonlinear optical crystal Na3La9O3(BO3)8

The principal refractive indices of Na3La9O3(BO3)8 (NLBO) crystal in the wavelength range of 0.363–2.325μm were accurately measured by using the minimum deviation method within the temperature range from 23.5°C to 160°C. We derived the expressions of thermal refractive index coefficient as a function of wavelength that could be used to calculate the principal refractive indices at different wavelengths. The temperature-dependent Sellmeier equations were also derived and used to calculate the phase-matching (PM) angles for a frequency conversion device based on NLBO crystal at different temperatures. We found that the thermal refractive index coefficients of NLBO crystal changed from positive to negative values with the increase of wavelength. In addition, the phase matching conditions for third harmonic generation (THG) at different temperatures were also investigated.

Temperature dependence of refractive indices for 4H- and 6H-SiC

The refractive indices of 4H- and 6H-SiC single crystals at wavelengths of 404.7, 435.8, 480.0, 546.1, 587.5, 643.8, 706.5, 852.1, 1014.0, 1529.6, and 2325.4 nm are carefully measured from 293 to 493 K by the method of minimum deviation. We find that ordinary (no) and extraordinary (ne) refractive indices for both crystals increase with the elevated temperature. The temperature-dependent Sellmeier equations of refractive indices for 4H- and 6H-SiC are obtained and then thermo-optic coefficients (TOCs) are derived. The TOCs diminish very quickly at visible light region and become less dependent in the infrared light region. Such changing trends of TOCs can be explained by single-oscillator approximation. The results may provide the important reference value for designing the optoelectronic and nonlinear optical devices based on SiC.

Temperature-dependent Sellmeier equations of nonlinear optical crystal La_2CaB_10O_19

The thermal dependence principal refractive indices ofLa(2)CaB(10)O(19) (LCB) crystal at wavelengths of 0.254, 0.365, 0.405, 0.480, 0.546, 0.644, 0.852, 1.014, and 2.325 μm were accurately measured by using the vertical incidence method within the temperature range from 25 to 170 °C. We derived equations of thermal refractive index coefficients as a function of wavelength that could be used to calculate the principal thermal refractive indices at different wavelengths. The temperature-dependent Sellmeier equations were also derived and used to calculate the phase-matching angles for the third-harmonic generation of LCB crystal at different temperatures. Theoretical and experimental phase-matching angles for the type I third-harmonic generation of LCB crystal at different temperatures were in good agreement.

Temperature-dependent Sellmeier equation for the extraordinary refractive index of 5 mol % MgO-doped LiNbO_3 in the terahertz range

We present a Sellmeier equation for the temperature- and wavelength-dependent extraordinary refractive index of 5 mol. % MgO-doped congruent lithium niobate, which is valid for frequencies from 1 to 3 THz in a temperature range from 30°C to 200°C. The determination of the Sellmeier coefficients is based on the tuning behavior of a quasi-phase-matched, continuous-wave optical parametric oscillator with its idler wave in the terahertz regime.

Temperature-Dependent Sellmeier Equation for Refractive Index of 1.0 mol % Mg-Doped Stoichiometric Lithium Tantalate

Mg-doped stoichiometric lithium tantalate (SLT) is a promising material in high power generation, due to its high thermal conductivity. The accuracy of the temperature-dependent Sellmeier equation for Mg-doped SLT is important for designing high-power-frequency converters. We propose a temperature-dependent Sellmeier equation for the extraordinary refractive index of 1.0 mol % Mg-doped SLT. The equation is fitted with measured data in the first-order quasi-phase-matched (QPM) second harmonic generation (SHG) and optical parametric oscillation (OPO) with the fundamental and pump wavelengths being both 1.064 µm and previously published data [Jpn. J. Appl. Phys. 41 (2002) 465] of SLT. The equation allows us to predict accurate QPM periods in the range of 0.5–4 µm wavelength and in temperature range of 30–170 °C.

Linear and nonlinear optical properties of MgO:LiTaO3

We derive new temperature dependent Sellmeier equations for the extra-ordinary and ordinary refractive indices of 0.5% MgO-doped stoichiometric LiTaO3 crystal. The equations are based on quasi phase-matched frequency conversion measurements, as well as on interferometric measurements of the thermal expansion and thermal dispersion. These equations fit experimental data over wide spectral ranges: 0.35–6 μm for the extra-ordinary wave and 0.375–3.75 μm for the ordinary wave, from room temperature up to 200°C. The nonlinear optical measurements set lower-limit values for the d 33, d 22, and d 24 elements of the second-order susceptibility tensor χ (2) of 12.9, 1.54, and 0.46 pm/V, respectively. The interferometric measurements enable one to determine the linear and quadratic expansion coefficients of 1.45762e−5 1/°C, and 2.68608e−8 (1/°C)2, respectively. The Sellmeier equations are in good agreement with previously published data.

Determination of the refractive index dispersion using multi-wavelength second-harmonic generation in an aperiodic LiTaO3 superlattice

Multi-wavelength second-harmonic generation in an aperiodic poled LiTaO3 superlattice was studied. By fitting the measured data of phase-matching wavelengths and temperatures, the temperature-dependent Sellmeier equation of the LiTaO3 crystal has been determined. This work provides a new method to measure the refractive index of the nonlinear crystal and its dispersion and therefore, is of benefit to the study of the quasi-phase-matching technique.

Temperature-dependent Sellmeier equation for the refractive index of Al_xGa_1−xAs

We derived a temperature-dependent Sellmeier equation for Al(x)Ga(1-x)As material by measuring the refractive index of GaAs and AlAs with temperature dependence in a resonant cavity enhanced structure. The equation is applicable in the range of 1460-1580 nm and 26-86 degrees C and can be extrapolated to the other wavelengths and temperature ranges as well.

Temperature-dependent Sellmeier equation in the MIR for the extraordinary refractive index of 5% MgO doped congruent LiNbO3

We present a temperature-dependent Sellmeier equation for the extraordinary refractive index of 5 mol % MgO doped congruent lithium niobate. This equation is adapted for wavelengths in the range of 1.3–5 μm and temperatures between 40 °C and 200 °C. The calculation of the appropriate Sellmeier coefficients is based on the wavelengths of the signal and idler radiation measured for quasi-phase-matched optical parametric generators excited by 10-ns-long, 1064-nm pulses of a Q-switched Nd:YVO4 laser.

Thermooptical sensitivity analysis of highly birefringent polarimetric sensing photonic crystal fibers with elliptically elongated veins

The spectral and thermooptical sensitivity responses of highly birefringent photonic crystal fibers (PCFs) with elliptically elongated veins integrated in their profile are being investigated using a novel sensitivity analysis based on an accurate semivectorial modal solver combined with temperature-dependent Sellmeier equations for pure silica and dry air. We demonstrate that by an appropriate selection of the design parameters it is possible to optimize the sensitivity of the modal birefringence or even to obtain null response at specific wavelengths. Thus, our investigation adds evidence to the potential use of highly birefringent PCFs as polarimetric sensors. Optimized overall temperature sensitivity could be obtained up to 7.5middot10-7 K-1 at operational wavelength of 1.55 mu m