A compact modular high-speed high-sensitivity second-harmonic interferometer is used to characterize a pulsed gas jet. The temporal evolution of the line-integrated gas density is measured with a resolution of 1 μs revealing detailed information on its dynamics. The actual radial gas density distribution in the jet is obtained applying the Abel’s inversion method. The sensitivity of the interferometer is 1 mrad, and its robustness, compactness and modularity make the instrument suitable for practical application. Possible use of the instrument in monitoring cluster formation, and phase-dispersion microscopy is discussed.
© 2011 Optical Society of America
The accurate knowledge of the molecular density in pulsed gas jet is of great importance for laser generated plasma experiments [1, 2], and high-order harmonic generation studies . Temporal evolution of pulsed gas jet have been investigated by means of third-harmonic generation , fluorescence , Rayleigh scattering , and Mach-Zender interferometry . These techniques relay on pulsed laser source and repeated measurements varying the time delay between laser pulses and valve opening, and cannot be implemented for on-line monitoring of the gas density temporal evolution.
The optical dispersion, i.e, the wavelength dependent refractive index n(λ), is a basic property of matter whose accurate measure is used in many applications, e.g., to monitor free electron density in plasma , to image biological tissues with phase-contrast measurements [9, 10], or to accurately measure distance . By measuring optical dispersion, also the molecular density of gases can be determined provided that the dispersion is known for a defined density value, e.g., standard condition for temperature and pressure.
An attractive and accurate method to precisely measure the optical dispersion is based on the so-called second harmonic interferometer (SHI) [12, 13] that is a special common-path, two-color interferometer. The SHI principles of operation are the following: i) the second harmonic of a laser beam is generated in a single pass frequency converter; ii) the fundamental and second harmonic beams propagate collinearly through the sample; iii) the fundamental beam is frequency doubled again in a second frequency converter; iv) interference then takes place between the two collinear second harmonic beams. The measured phase shift between the second harmonic beams is , where Δn(λ) = n(λ) – n(λ/2), and L is the optical path between the two harmonic converters. Being a common-path interferometer the SHI is insensitive to vibration, and compared with typical two-color interferometers it has the advantage of using a single laser source. For non-homogeneous samples with cylindrical symmetry, the actual radial distribution of the refractive index dispersion can be obtained by measuring the phase shift along several chords and then applying the well known Abel’s inversion technique. Pulsed laser sources are used in SHI to enhance the efficiency of single-pass second-harmonic generation, however this limits the temporal resolution and measurable time window range, depending on the laser repetition rate and the pulse time duration. The fastest SHI developed up to date has a time resolution in the ns range , and it comprises the pulsed amplification of a CW laser source limiting the measurable interval to tens of μs. With a 100kHz Nd:YAG mode-locked laser a time resolution of 10 μs and sensitivity of about 1 mrad have been achieved . In  an accurate measurement of the optical dispersion of several gases between 1064 nm and 532 nm has been performed in a static cell using a pulsed laser source, resulting in the determination of optical dispersion at standard temperature and pressure. Using a Nd:YAG mode-locked ps laser third-harmonic interferometry has also been demonstrated , thus bringing dispersion interferometry in the UV wavelength range.
The use of a continuous-wave (CW) laser source has in principle no limit in terms of time resolution, the only constrain being given by the detection system. A SHI based on a CW CO2 laser was developed  resulting in a sensitivity of 10 mrad with time resolution of 1 ms. A CW SHI was used to demonstrate modulation-free sub-Doppler laser frequency stabilization on a molecular iodine transition . Recently, we have demonstrated a high-speed high-sensitivity SHI employing a CW Nd:YAG laser , and a remotely controlled version of such device has been used on a large plasma machine to measure free electron density .
Here we present a complete spatiotemporal characterization of the gas density in a pulsed jet using an improved compact and modular high-speed CW SHI with phase sensitivity of 1 mrad, and spatial resolution of 400 μm. The time resolution of 1 μs allows for real-time monitoring of the gas dynamics. To our knowledge, on-line high-resolution measurement of temporal evolution of a gas density in a pulsed jet have not been reported to date.
Possible implementation of the technique in monitoring cluster formation, and in phase-dispersion microscopy is also discussed.
2. The experimental setup and procedure
The schematic of the experimental setup is shown in Fig. 1(a). The SHI is composed by a fiber coupled CW Nd:YAG laser (λ = 1064 nm, output power 500 mW) and two compact optical units (OUs) with dimensions of about 10×10×20 cm3. The optical elements inside the OUs are aligned and define the optical axes of each OU. The OUs are supported by tilt stages used to align the optical axes. The beam from the laser is brought to the first OU by a single-mode polarization-maintaining optical fiber. The first OU comprises an adjustable collimator, a temperature stabilized second harmonic generatio (SHG) unit, and a dual-wavelength wave-plate, half-wave at 532 nm and full-wave at 1064 nm. The adjustable collimator at the fiber out-put is set such that: i) the polarization axis of the fundamental beam matches the optical axis of the SHG crystal; ii) the fundamental beam waist radius is 400 μm, while the beam diameter on the SHG crystals is about 1mm. The second OU comprises a tilted BK7 window AR coated at both 1064 nm and 532 nm (C), a second temperature stabilized SHG unit, a harmonics separator (HS) with high reflectivity at 1064 nm and high transmission at 532nm, a beam dump (BD) for the 1064 nm reflected beam, an interferential filter centered at 532 nm (F), a polarizing beam splitter (PBS), and two collimators. The nonlinear crystals are BIBO cut for Type I SHG at 1064 nm, with dimension 4x4x10 mm3, and anti-reflection coated for both fundamental and second harmonic radiation. The axes of the two BIBO crystals are set parallel and the DW is used to rotate by 90° the polarization of the first second harmonic beam (SHB) while leaving unaffected the polarization of the 1064 nm beam. In this way the second SHG process is independent on the first SHG process, in order to obtain the proper interferometric signal . The window C is held on a motorized mirror mount which allows remote control of the tilt angle in order to obtain very good compensation of the spurious phase signal due to the dispersion in BK7 glass. The tilted window also induces a transversal displacement between the fundamental beam and SHB, however its magnitude is small and does not affect the interference signal significantly. The HS and the filter F are used to completely suppress the fundamental radiation. The actual interference between the two SHBs takes place at the PBS which is set with transmission axis at 45° with respect to the polarization of both SHBs. The transmitted and reflected beams show interference signals with a π phase shift off-set one with respect to the other, and are sent to the detector by means of multi-mode fibers. The detector is a Si-PIN photodiode with a transimpedance gain of 107 Ohm and a response time of 0.9 μs. The signals are acquired with a digital card (NI PCI 6120, 1 MS/s, 16 bit) and saved in a personal computer for on-line analysis and data storage.
The sample to be tested is placed in between the two OUs. In the present experiments the sample is a pulsed xenon gas jet free expanding in a vacuum chamber. The light beams pass the chamber through two AR coated windows, and the residual pressure in the chamber is kept at about 10−2 mbar by means of a rotative pump. The pulsed gas jet is produced with a fast solenoid valve (Parker-Pulse Valve series 9) operated at 10 Hz, whose pulse width can be set from few hundred microsecond upwards using the valve driver (Parker-IOTA ONE). The valve has a 0.79 mm cone shaped orifice with 45° nominal half-angle. In Fig 1(b) a schematic of the valve is presented. A poppet, held by a magnetic armature, is pushed forward by the main spring and closes the orifice. A second spring is used as buffer for the armature. When a current pulse flows in the solenoid coil the generated magnetic field pushes backwords the armature and the poppet, opening the orifice. The armature has a mechanical stop that set the full opening. The valve is mounted on a translation stages that allows movement in all three spatial directions, and it is set on the beam waist position along the optical axis direction x.
It is worth mentioning that the apparatus, comprising the SHI and the vacuum chamber, is held on an optical table without vibration dumping systems, and no realignment was needed during the experimental campaign, which demonstrate the stability and insensitivity to vibration of the device.
The photodiode signals are
The recorded quantity isEq. (2) can be approximated by (V+ – V−)/(V+ + V−) = V×Δϕ + Δϕ0. The value of V is directly obtained by scanning the tilt angle of the compensator window over half fringe, as reported in [8, 23], and for the present experiments is V = 0.95.
3. Experiments, results and discussion
3.1. Gas jet temporal evolution
The phase shift induced by a xenon pulsed gas jet measured for a backing pressure of 5 bar at different values of the valve opening time setting τ is shown in Fig. 2, where the baseline of each curve is vertically shifted for clarity. The valve orifice is centered on the laser beam and set at 1 mm distance from the beam waist in the z direction. The phase shift reflects the line-integrated gas density temporal evolution which has distinctive profiles depending on the opening time setting. For τ < 500 μs the gas pulse has a quasi-symmetric bell-shaped temporal evolution. For 1 ms < τ < 2 ms the gas pulse has a fast rising edge of few hundreds μs followed by oscillations. At longer opening time settings, τ > 2 ms, a steady gas flow is achieved. Since the valve orifice is set close to the laser beam the measured temporal evolution of the gas jet follows the motion of the poppet. Specifically, the data are interpreted as follows: i) for τ in the range of the pulses valve response time the poppet is pressed back by the main spring in the closed position before reaching the mechanical stop, and so a smooth temporal profile of the gas jet is obtained; ii) for intermediate opening time settings the armature reaches the mechanical stop, then it bounces back several time inducing the sharp peaks in the gas density, before the solenoid get discharged and the poppet is press back to the closed position; iii) for τ >2 ms the armature reach stably the complete opening after the bouncing on the mechanical stop is damped, and the steady gas flow is archived.
Thanks to the high-speed of the interferometer it is possible to investigate in detail the transition between the different temporal profiles. In Fig. 3 a the phase shift temporal evolution between 400 μs and 1.4 ms from the valve opening is reported for three opening time settings, clearly showing the different temporal evolutions. It is noticeable that the first bounce of the armature on the mechanical stop has a duration shorter than the temporal resolution of the SHI, i.e. 1 μs, due to the high velocity, i.e., momentum, acquired by the armature during the fast opening. The subsequent bounce lasts about ten μs and is resolved by the SHI.
The effect of the gas backing pressure is also investigated. In Fig. 4 the measured temporal evolution of the phase shift as function of the backing pressure is shown for an opening time setting of 400 μs. In the inset of Fig. 4 the maximum value of the phase shift is plotted clearly revealing a linear increase on the gas density as function of the backing pressure in agreement with previous findings reported in the literature [4, 5, 7].
3.2. Gas jet spatial distribution
The actual spatial distribution of the gas density in the jet is investigated by measuring the phase shift for several chords, i.e., y values, along a x – y plane at z = 3 mm from the valve orifice. An opening time setting of 3.5 ms, and a backing pressure of 5 bar are used. The results are reported in Fig. 5(a), where the measured phase shift Δϕ(y) shows a symmetric profile falling to zero at 4.2 mm from the central axis. A cylindrical symmetry of the gas jet around the central axis of the valve is assumed, thus17], N0 = 2.69 × 1019 cm−3 is the Loschmidt’s number, i.e., the density of an ideal gas at 0 °C and 1 atm, and N(r) is the xenon atomic density in the gas jet. To retreive the radial gas density distribution an analytical method to performe the Abel’s inversion is used . The measured phase shift is fitted with a polynomial curve to the power sixth, Δϕ(y) = a + cy2 + ey4 + gy6, as shown by the dashed line in Fig. 4(a). Note that only even powers are used due to symmetry reasons. The polynomial curve very well follows the experimental data points. The radial gas density distribution, shown in Fig. 5(b), is obtained from the formula N(r) = −(λN0)/(4π2Δn0)[2cu + 4e(ur2 +u3/3)+6g(ur4 + 2u3r2/3 + u5/5)] , where , with r0 = 4.2 mm. The full-width half-maximum of the gas density radial distribution is D(3mm)=6.7 mm. Assuming a conical expansion of the gas jet, D(z) = D0 + 2tan(β)z where D0 = 0.79 mm is the orifice diameter, a cone half-angle β = 44.6° is obtained in very good agreement with the nominal value of the valve orifice cone angle.
4. Conclusions and outlook
A compact second-harmonic interferometer capable of fully characterize a pulsed gas jet is presented. Temporal evolution of the gas density is measured with a resolution of 1 μs. The observed gas density dynamics is explained in terms of the pulsed valve poppet motion. Precise reconstruction of the actual radial gas density distribution is obtained by applying Abel’s inversion. Detail knowledge of pulsed gas jet dynamics can aid research in high-intensity laser-matter intercation, like optimization of high-order harmonic generation, and laser generated plasma.
In the present experimental conditions (backing pressure ≤ 5 bar) cluster formation in the expanding pulsed gas jet is limited, and therefore neglected. In general, cluster formation in an expanding gas jet with high backing pressure is monitored by means of Rayleigh scattering measurements . However, Rayleigh scattering alone cannot be used to determine cluster average size and density since both quantities are unknown. In , an elegant all-optical method to measure both the cluster average size and density has been presented based on the combination of Rayleigh scattering and classical Mach-Zender interferometry. In principle also second-harmonic interferometry can be implemented, in combination with Rayleigh scattering, to characterize a gas jet containing a significant amount of clusters, provided that the dielectric function of the bulk material internal to the cluster is known at the fundamental and second harmonic wavelength, and that the contribution of residual monomers, i.e., isolated atoms, on the optical dispersion of the gas jet can be neglected .
Due to its high-sensitivity the presented SHI is an ideal instrument to monitor small variation of dispersion at high-speed. Also, the compactness and stability of the instrument enable its operation in any laboratory and field conditions, as well as its integration into existing apparatus. As outlook, the implementation of the SHI in microscopy is forseen. The spatial resolution can be reduced to the μm level by using diffraction limited microscope objectives, while the common-path geometry allows for an easy integration into standard transmission microscopic devices. As application example we consider the imaging of biological tissues. In  an harmonic phase-dispersion microscope at λ = 1064 nm comprising a Mach-Zender interferometer and two acusto-optic modulators has been presented. Biological samples have been imaged with a phase resolution of 7 × 10−2 rad. However, the acquisition time of 50 ms/pixel hampers practical application of such system. The present SHI has a simple optical setup, with a sensitivity of 10−3 rad for a time resolution as small as 1 μs, reducing the acquisition time by 4 orders of magnitude and thus enabling practical implementation of harmonic phase-dispersion microscopy. Moreover, the sensitivity can be increased to the 10−4 rad level , for an acquisition time of 10 μs, further improving the potential capability of the SHI for challenging microscopic measurements.
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