Photothermal refraction spectrometry detects the refractive index change resulting from optical absorption in a high transmittance sample.¹ Optically excited states relax, producing a refractive index change, the imaginary component of the complex transmission coefficient, due to the resulting temperature increase in the sample. A continuous probe laser is often used to monitor index changes resulting from periodic laser excitation. Photothermal refraction apparatuses convert the imaginary transmission change to a real change in transmission, and subsequently probe laser power. Apparatuses based on spatial filtering develop real transmitted power signals. Common examples are photothermal lens and photothermal deflection apparatuses, which use, respectively, pinhole and knife-edge spatial filters to produce real transmittance changes. Alternatively, various interferometer designs can detect the imaginary transmission change through relative probe phase shifts.

Optical novelty filtering (ONF) can also be used to increase the image contrast of dynamic phase-altering signals.^2-5 The first demonstration of the ONF was based on a Michelson interferometer utilizing a self-pumped phase conjugate mirror.³ The resulting interferometer produces a dark fringe across the output branch due to a p phase shift between the two returning beams. After dark fringe formation, rapid phase shifts introduced into one arm of the interferometer produce in-phase fields at the beamsplitter. Light subsequently exits the output branch of the interferometer. Light exiting the output branch is the 'novel' component of the imaginary transmission.

Several variations of the ONF have been introduced. Two-wave mixing⁴ and beam fanning limiter⁵ designs are similar in that short-duration, phase-altering signals pass through normal ray paths. The beam fanning limiter apparatus is simple to set up and operate since it only requires a single beam. Beam fanning is based on asymmetric self defocusing of a laser beam passing through a photorefractive medium.⁶ Fanning redistributes power over a wide angle in the plane of the optic and incident beam axes. Acting this way, the material is an 'optical limiter' since it removes excess power from the normal beam path.^2,7

Use of the ONF in photothermal refraction spectrometry may overcome some problems in using interferometry methods for quantitative studies. Spatial filter and beam alignments are critical in phase contrast apparatuses. The ONF uses real-time photorefractive optics to overcome this problem. The optical element is continuously adapted to the irradiance profile of the probe laser. Alignment errors are reduced, images or signals are reproducible, and possess enhanced contrast. Contrast is proportional to signal-to-noise ratio in shot noise limited measurements.^8-10

Pulsed laser excited photothermal spectroscopy is well understood and documented in the literature.¹ A pulsed, TEM₀₀ mode laser produces a time- and space-dependent temperature change, d T(x,y,z;t) (K), in a homogeneous absorbing sample

(1)

a (m^-1) is the absorption coefficient, Q (J) the excitation laser pulse energy, r (kg m^-3) the density, and C_P (J kg^-1 K^-1) the specific heat of the sample. The time-dependent Gaussian radius parameter is w(t)²=w(z)²(1+2t/t_c) where w(z) (m) is the excitation laser beam waist radius and

t_c (s) is the characteristic thermal diffusion time constant given by t_c=w(z)²/4D_T where D_T (m² s^-1) is the thermal diffusion coefficient. The temperature change results in a change in the refractive index

(2)

Pulsed excitation and continuous probe lasers counter-propagate collinear through a sample cell. Laser light propagating through the sample will have an optical pathlength of n₀l, where n₀ is the refractive index and l (m) the physical length through the sample. Assuming that the excitation laser beam waist is constant through the sample, probe laser light propagating through the heated region will have an optical pathlength of (n₀+d n)l. The difference between these two pathlengths is simply d nl. The differential phase shift, d f (rad), between rays passing through heated and unheated sample regions is d f =2p d nl/l where l (m) is the probe laser wavelength.

Kalaskar and Bialkowski¹⁰ developed a model for the pulsed laser excited ONF photothermal refraction apparatus based on the 4F optical correlator.¹¹ The irradiance image formed one focal length beyond the first lens, the image plane, writes a spatial rejection filter into the photorefractive BaTiO₃ which is matched to spatial information at the front focal length, or object plane of the lens. A second lens, placed one focal length beyond the matched spatial filter, images the convolution of the ONF with the input beam at the second image plane.¹¹ The final image is related to the photothermal induced phase shift for an infinite plane-wave probe laser. The plane-wave approximation simplifies the model since its image is a spatial delta function. The time-dependent probe laser power in the image plane resulting from inducing an optical phase shift in the sample on time scales much shorter than those required to form the ONF is related to the phase shift by

(3)

F (x,y;t) (W) is the optical power in the image resulting from a probe laser with a total power of F ₀ (W), T_min is the minimum transmission and T_max is the maximum transmission through the holographic medium of the ONF. The time-dependent photothermal signal magnitude obtained using a spatially integrating, single channel detector obtained by substituting the photothermal phase shift into the ONF signal equation, then integrating over space, is

(4)

Images can be obtained just prior to and following pulsed laser sample excitation. The background component is subtracted and phase shift or temperature change information is obtained by taking the square root of the result

(5)

The thermal-optical coefficient has been used to relate temperature to path-integrated index change and the phase shift is accommodated in the 2p /l term.

The apparatus uses counter-propagating collinear excitation and probe lasers to detect the infrared absorption of gas samples. The probe laser is a linear polarized, continuous 514.5 nm Ar⁺ laser (American Laser 905), operating TEM₀₀, and delivering less than 1 mW. The probe beam passes through a laser line filter, to eliminate plasma emission, a l /2 plate, to adjust the polarization direction, and a spatial filter. Spatial filter output is collimated with a 5 cm fl. lens to a beam radius of ~1 cm and passes through the sample cell. The sample cell is a 7 cm long, stainless steel gas cell with NaCl windows. Gas samples are introduced and removed through a vacuum manifold with 1/4" fittings and pressure transducers. The manifold is evacuated through diffusion and rough pumps. The ultimate vacuum at the sample cell is about 0.001 Pa. The probe beam is focused through a 5 mm cubic BaTiO₃ crystal (Sanders) with a 17.5 cm fl. lens placed 17.5 cm after the sample cell center. The BaTiO₃ crystal was poled, cut, and polished 45^o relative to the c-axis. Maximum beam fanning occurs for acute incidence angles. The excitation source is a line-tunable TEA CO₂ laser (Tachisto). Maximum energy at the sample is about 20 mJ in a pulse of 120 ns duration. The laser produces multiple transverse modes. The excitation laser is focused through the Ge beamsplitter into the sample cell with a 18 cm fl. BaF₂ lens. About 20%, of the beam is reflected and detected with an energy monitor (Laser Precision RjP-735).

Time resolved signals are detected with a wide area Si photodiode or a photomultiplier tube. Transient signals are captured with a transient waveform recorder (Markenrich model WAAG) and averaged on the PC computer. Video camera (Sony XC-77) images are captured with an Imagenation CORTEX-I video frame grabber. 1,3 butadiene is the absorbing species because it linear irradiance-dependent absorption with excitation conditions used in these studies.¹² The 1,3 butadiene was obtained from Matheson, 99.86%. Argon (Liquid Air, 99.999%) is the matrix gas. Total pressures in the sample cell are 100 kPa. The partial pressure of 1,3, butadiene is adjusted to give an absorbance of A» 10^-3. The TEA CO₂ laser is tuned to the 9P28 line at 1039.36 cm^-1. Butadiene has an exponential absorptance of 1.88´ 10- ³m^-1Pa^-1 at this wavelength.

Figure 3 Time resolved transient obtained with ONF

The purpose of this study is to compare time-resolved transients and images and to those predicted in the model for the operation of the optical tracking novelty filter in the 4F optical correlator configuration.¹⁰ Main assumptions in the derivation are; 1) the photothermal-induced perturbations to the imaginary transmission are short-lived compared to the time scale required to write the optical beam fanning limiter into the BaTiO₃ crystal; 2) a matched spatial rejection filter is formed over an area equal to that of the Ar⁺ laser beam; 3) the relatively large beam waist of the Ar⁺ laser in the volume perturbed by the focused excitation laser will result in spatial frequencies high enough to be efficiently couple past the matched spatial rejection filter yet small enough to be detected along the normal beam path.

If the first assumption is valid, one should observe a time-dependent transient that decays monotonically, as predicted by Equation 4. The data shown in Figure 3 does show deviation in the signal decay. The time-dependent log data has a slope of -1.28 and is slightly curved, concave up. However, this deviation could also be to variation of excitation beam waist radius through the sample.

The data in Figure 3 is obtained from a 0.001 AU sample being excited with 1 mJ laser pulses. Small ripples observed on the thermal decay are due to the photoacoustic effect. The contrast, i.e., signal to background, is about 10. The signal enhancement factor is thus 10,000.

However, Eq. 4 predicts that the signal enhancement is not linear in absorptance or excitation energy, but rather increases as the square. The quadratic dependence of signal on excitation energy is shown in Fig. 4. The relative signal is quadratic up to about 0.5 mJ. The linear signal, observed above excitation energies greater than 0.5 mJ, may be due to the relatively high probe laser transmission. The relative signal must saturate near the point where transmission through the optical beam fanning limiter approaches unity. Changes in imaginary transmission greater than that producing 100% optical limiter transmission results in equivalent signals. Apparently, this signal saturation effect occurs at relatively low transmission; about 50%.

Finally, images have been obtained and analyzed in accord with Eq. 5. Neglecting distortion, probably due to imperfections in parallel faces of the BaTiO₃ crystal, the images appear to be Gaussian in form. However, image analysis is difficult owing to the limited, 8-bit precision of the frame grabber board. Although images of the flashing spot produced with each excitation laser pulse are obtained, these pictures do not reflect the dynamic character of the signals. For example, adjusting the excitation laser mirror moves the focus position within the sample cell. Doing this while observing the spot on a screen past the optical limiter shows that the spot tracks the photothermal perturbation in the sample cell. Also, placing a small venetian blind in front of the excitation laser lens produces several focus spots within the sample. These are clearly observed in the ONF image. The real time imaging aspects of the ONF are quite apparent.

In summary, ONF-based photothermal refraction apparatus signals appear to follow a model based on a 4F optical correlator, which operates in much the same fashion as a schlieren apparatus, but with an adaptable spatial filter. Apparent differences between the model and the experimental results may be attributed to signal saturation effects.

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