Available online at www.sciencedirect.com ScienceDirect Physics Procedia 84 (2016) 135 – 141 International Conference "Synchrotron and Free electron laser Radiation: generation and application", SFR-2016, 4-8 July 2016, Novosibirsk, Russia Observation of the Formation of 0-π Pulses in Rotation Spectra of HCN and HBr E.N Chesnokov*, V.V Kubarev2,3, P.V Koshlyakov1 Institute of Chemical Kinetics and Combustion, Novosibirsk, 630090, Russia, Budker Institute of Nuclear Physics, Novosibirsk, 630090, Russia Novosibirsk State University, Novosibirsk, 630090, Russia Abstract We present the first experimental study of the formation of 0-π pulses in the far infrared region Experiments were made in rotation spectra of HCN and HBr molecules using a Novosibirsk terahertz free electron laser (NovoFEL) as a source of optical pulses and ultra-fast Schottky diode as detector Transformation of the shape of 0-π pulses was explored within a wide range of optical density Throughout the range of experimental conditions, the observed pulse shape is well described by the analytical formula of Grisp (Phys Rev A (1970) 1604) The observed effect can be used for time-domain measurements of the oscillator strength of the absorption line © 2016 Published by Elsevier B.V This is an open access article under the CC BY-NC-ND license © 2016 The Authors Published by Elsevier B.V (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility the organizing committee of SFR-2016 Peer-review under responsibility of theoforganizing committee of SFR-2016 Keywords: Novosibirsk terahertz free electron laser , Terahertz, 0-π pulses, time-domain measurements, rotation spectra of HCN and HBr Introduction The propagation of short light pulses in resonant and optically dense medium is accompanied by various remarkable effects The most striking effect is self-induced transparency (S L McCall et.al 1969, C.K Patel et.al 1967) In this case, light pulse experiences lossless propagation with absorption during a half of the pulse and * Corresponding author E.N Chesnokov Tel.: +7 383 333 29 44; fax: +7 383 330 73 50 E-mail address: chesnok@kinetics.nsc.ru 1875-3892 © 2016 Published by Elsevier B.V This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the organizing committee of SFR-2016 doi:10.1016/j.phpro.2016.11.024 136 E.N Chesnokov et al / Physics Procedia 84 (2016) 135 – 141 forward emission with energy restitution during the second half Commonly known is the exact solution of 2-π pulses that propagate in a medium without energy absorption and reshaping (G.L Lamb, 1971) Such pulses must have a significant energy which is required for complete translation of the medium to the excited state Propagation of short light pulses without energy absorption or with low energy loss is possible for weak pulses also This is the case of so-called 0-π pulses or zero area pulses (J.C Delagnes, M.A Bouchene, 2008) Such pulses have several steps in which energy is transferred from light to the medium, and then back from the medium to light The direction of energy transfer is determined by the phase of electromagnetic wave In contrast to 2-π pulses, the shape of 0-π pulse is permanently changing during the propagation in the medium The formation of 0- π pulses in the case of a single Lorentzian absorption line has been first investigated theoretically by Crisp (1970) He derived an analytical formula describing the transformation of a weak short pulse while it propagates through optically dense medium The formula predicts the emergence of the oscillating tail of the input pulse that has a number of unusual features First, oscillating is aperiodic, and the apparent period increases with time The phase of the wave changes by 180 degrees for every oscillation The Grisp’s solution is self-similar with increasing the sample thickness all oscillations become shorter and higher in amplitude The first experimental study of the formation of 0-π pulses was made using a picosecond dye laser with sodium vapor (J.E Rothenberg et.al 1984) Later, a similar study was conducted with rubidium vapor (U Kallmann et Al 1999) In addition to the studies of atomic vapor media, investigation of pulse reshaping in molecular gases Na2 and I2 was published (J N Sweetser and I A Walmsley 1996) In these experiments, several lines of molecular spectra were excited, and the effect of 0-π pulse formation was masked by the beats of these lines Formation of the zero area pulse was studied in visible region for excitonic absorption lines The signal observed in Cu2O (D Fr.ohlich et.al 1991) continued 2.5 nsec and contained many oscillations in good accordance with Crisp’s (1970) analytical formula Similar signals were observed in femtosecond time scale for 1s-exciton resonance in InSe (S Năusse et.al 1997) and CdS (M Jăutte et.al 1996) In infrared region (H.J Hartmann et.al 1984) the speed up of the initial decay of optical induction was studied In addition to experiments in visible region, exactly the same effect was observed in -wavelengths in experiments with synchrotron radiation (U van Băurck, et.al 1998) Experiments were performed at 14.4 Kev (wavelength 0.86 Ả), which corresponds to the nuclear transition in 57Fe The samples of (NH4)2Mg57Fe(CN)6 powder were used; they have a single narrow absorption line in this region The time evolution of the transmitted radiation was recorded up to 200 nsec after the input pulse It clearly demonstrates the characteristic features of the zero area pulses, in particular an increase of the apparent beat period with time, and a decrease of the apparent beat period with increasing sample thickness All experiments that had been done in case of molecular, atomic, excitonic and nuclear resonances confirm an astonishing universality of this phenomena In this paper we describe the first observation of 0-π pulse formation in the case of rotation molecular spectra in the far infrared region Experimental Experiments were made using the high power terahertz free electron laser (NovoFEL N.G Gavrilov, et.al., 2007) as a source of short pulses of radiation The laser emits a continuous train of pulses, at a repetition rate of 5.6 MHz with the duration of 120 ps The frequency of laser radiation is tunable in 40 – 80 cm-1 region, spectral width is about 0.15 cm-1 The laser radiation passes through a glass cell with polypropylene windows containing gas at low pressure In order to observe the optical FID signal, we used ultrafast Schottky diode detector (V.V Kubarev et.al 2009) and a 30 GHz digital oscilloscope The rise time of the detection system was less than 25 ps FID signals were observed in real time without using any scanning technique More details of the experimental setup were described previously (E.N.Chesnokov et.al Appl Phys Lett (2012), E.N.Chesnokov et.al Las Phys Lett (2013)) Grisp’s formula M.D Grisp (1970) studied the propagation of small-area pulses of coherent radiation through resonant media, which is characterized by single Lorentzian line The analytic solutions for different input pulses were obtained The most important is the case of ultrashort pulse, because other solutions can be easily obtained from this case Here we 137 E.N Chesnokov et al / Physics Procedia 84 (2016) 135 – 141 present this result in another notation, in order to identify the contribution of various factors in the rate of decay of the free induction and make explicit the role of the integral intensity of the absorption line The absorption line is characterized by the frequency-integrated absorption coefficient E ³ D Z d Z , [cm-1sec-1], central frequency Z , and width of the line J The input pulse is assumed to be much shorter than the reciprocal value of the width of the absorption line Since the solution was obtained in the linear approximation, the amplitude of the output pulse is proportional to the amplitude of the input For simplicity, we denote electric field of the input pulse as: ܧሺݐሻ ൌ ߜሺݐሻǡ where δ(t) – is delta function In this notation, Grisp’s formula for the electric field of the output pulse is: E t G t F t § J J Ft exp ăă t â Ã exp iZ t (1) where F l E / S , l is sample length J1 is Bessel function Note that formula (1) corresponds to the area theorem Integration of (1) reveals that the area of the output pulse depends on absorption as Tout Tin exp D 0l , where α0 is absorption coefficient in the center of the line The second term in (1) describes time evolution of the free induction The intensity of the FID signal is given by: I t F (2) J12 F t exp J t t According to (2), the temporal behavior of FID intensity has two factors One is exponential decay with the rate equal to the width of line J Second factor J12 F t / t has oscillating nature and its rate F l E / S is determined by line intensity The role of these factors depends on values J and F For strong lines in pure rotational spectra, the condition F ! J is easily achieved, so the oscillating factor dominates in the decay of FID intensity Note that optical density in the center of line is: D (Z0 )l F / J (3) If optical density of the sample is high, the oscillating factor dominates Fig.1 shows the oscillation factor in the dimensionless form and exponential factor, calculated for the sample containing Torr HCN, 10 cm long The timescale for the oscillation factor is determined from the integrated intensity of the rotational line at 70.796 cm-1 E = 0.763 nm2MHz = 4.79·10-8 cm2 sec-1 (from database (H M e x p J t Pickett, et.al, 1998)) The value of J at Torr was obtained 0.1 J 12 Ft from collision self-broadening of rotation HCN spectra Ft 0.01 (V.M.Devi et.al 2003.and L.S.Rothman et.al 2004) J = 0.155109 sec-1 1E-3 Figure shows the oscillation factor in dimensionless form and exponential factor for these conditions 1E-4 The dimensionless oscillating factor is a universal function for different conditions only timescale is changing The 1E-5 remarkable fact is that the timescale of these oscillations 10 depends only on the oscillation strength of the absorption line t, ns The position of the first minimum of the oscillation factor t1 directly determines the value of χ parameter Fig.1 Oscillating and exponential decay factors for FID intensity Calculations for HCN absorption line at 70.796 cm-1 P = Torr, l =10 cm Values of the rates: γ = 0.155109 sec-1 and χ = 9.9109 sec-1 F 3.67 / t1 At higher pressure of the absorbing gas, the characteristic time of oscillations becomes shorter and can be made even shorter than the laser pulse The shape of the FID under these conditions can be calculated by the convolution procedure The 138 E.N Chesnokov et al / Physics Procedia 84 (2016) 135 – 141 electric field of the response to a short pulse is given by formula (1) The response to the pulse of any duration can be calculated by: Econv t F § O · J1 FW exp ă W exp iZ0W dW W 2ạ â ELas t ELas t W Iconv(t) Econv(t) E(t) 0.0 0.5 1.0 1.5 2.0 (4) where ELas t is the electric field of laser pulse Figure demonstrates convolution procedure for a Gaussianshape laser pulse In this example, the duration of the laser pulse was 120 ps, the carrier frequency of the laser field coincided with the center of the absorption line ω0 Parameter χ = 2.5·1011 s-1 is large making several early oscillations shorter than the laser pulse Parameter γ = 6.3·108 s-1 corresponded to 100 MHz collision broadening The top panel shows the amplitudes of the response function E(t) and the electric field of the laser pulse The bottom panel shows the result of convolution: the amplitude of electromagnetic wave Econv(t) and its intensity Iconv(t) The convolution procedure changes the shape of the FID signal significantly The early short oscillations become almost negligible Later oscillations, which have characteristic time approximately equal to the pulse duration, dominate in the signal Positions of the minima of the signal correspond to zeros of J1 F t function 20*E(t) 0.0 2.5 t Power, arb un Fig The results of the convolution of the response function with the amplitude of laser field Top panel shows the response function (black thick) and laser field (blue dash line) The tail of response function is magnified Bottom panel shows result of convolution: electric field of FID and intensity of the FID signal 0.04 Torr 0.01 1E-3 1E-4 1E-5 1E-6 10 20 30 40 Power, arb un t, ns 0.1 Torr 0.01 1E-3 1E-4 1E-5 10 20 30 40 50 60 Power, arb un t, ns 0.1 0.36 Torr 0.01 Experimental results Most experiments were made with absorption lines of HCN This gas was chosen because it has strong absorption and it was easy to reach conditions when a single absorption line is excited The rotation spectrum of HCN consists of individual lines separated by 1.47 cm-1 interval, which is much more than the width of the laser radiation (F Maiwald, et.all., 2000) Moreover, rotation lines of HCN not have any additional small scale structure - according to high resolution investigation (V.Ahrens et.all., 2002) hyperfine splitting in this spectral region is < 0.1 MHz Figure demonstrates the FID signals observed at 70.796 cm-1 In these experiments the intensity of FID was 10 – 1000 times smaller than the intensity of the laser pulse To obtain pure FID, we accumulate the signal of laser pulse passed through the empty cell and the cell filled with HCN The FID signal was calculated as the difference of the two measurements This procedure removed also various undesirable signals originated from the reflection of the high power laser pulse Following this procedure, the FID signal of up to 50 -70 ns time interval with the dynamic range of (1 – 5)·103 could be measured Red lines in Fig.3 show the plots of J12 F t F t These plots were adapted from Fig.1 by choosing an individual timescale for each experiment All experimental data clearly demonstrate the existence of the expected oscillations Moreover, the timescale 1E-3 1E-4 10 20 30 40 t, ns Fig.3 FID signals in HCN at 70.8 cm-1 (black) Red lines show the decay calculated using (2) 139 E.N Chesnokov et al / Physics Procedia 84 (2016) 135 – 141 of these oscillations became shorter for higher pressure as the theory predicts The positions of the first minimum of experimental signals are presented in Table together with the calculated positions Calculations were made using the literature data for the integrated intensity of HCN absorption line (H M Pickett,et.al., 1998) A good agreement with the calculated data confirms the nature of the experimentally observed oscillation Table Calculated and experimental positions of the first minimum of FID signals at different pressures Pressure 0.04 Torr 0.1 Torr 0.36 Torr And an entry 39 ns 17 ns 5.5 ns And another entry 37 ns 15 ns 4.1 ns In addition to expected slow oscillations, the observed FID signals also have fast oscillations with a period of about 250 ns These oscillations originate from HCN molecules in the lowest vibrational excited state v2 = 712 cm-1 The absorption line of excited molecules is shifted by 370 MHz with respect to the ground state absorption line (A.G.Maki et.al 2000 and H M Pickett, et.al., 1998) Although only 5.7% of HCN molecules are excited at ambient temperature, at high concentration the absorption of this line becomes comparable with the ground state absorption Fast oscillations appear as a beat of these two lines This beat strongly complicates the signal at higher pressures when the characteristic time of slow oscillations becomes comparable with the period of the beat Transformation of FID signals for high absorption, which is shown in Fig.2, were observed for gaseous HBr The pressure of HBr was varied within 4.4 – 16 Torr interval The cell 20 cm long was used in the experiment The laser was tuned to 66.7 cm-1, which corresponds to (J=3) Ỉ (J=4) transition in HBr molecule The absorption line has isotopic and quadrupole splitting, but due to the collision broadening at experimental pressures it acts as a single line Observed signals are shown in the lower panel of Fig.4 Experimental signals clearly demonstrate shortening of the oscillation timescale for higher absorption According to the theory, the minima of the experimental signals should correlate with the zeros of the J1 F t function This correlation is shown on the upper panel of Fig.4 for each experimental signal The slopes of the straight lines on this panel 500 16 Torr directly determine parameters F for each experiment The values of F 400 are approximately proportional to HBr pressure, average value is 8.5 Torr 300 Fexp 2.19 1010 s 1 for Torr Theoretical value of this parameter, calculated by summation over all components of the quadrupole 200 4.4 Torr structure (H M Pickett,et.al., 1998), is 2.01·1010 s-1 100 This method can be used for accurate time-domain measurement of integrated intensity of the absorption line If concentration of the 16 Torr molecules is known, integrated intensity directly determines the oscillator strength of corresponding transition The accuracy of 8.5 Torr oscillator strength determination in our experiments is limited by the uncertainty of the actual concentration of HBr molecules We observed significant adsorption of HBr on the cell walls and windows The 4.4 Torr concentration in the experiment might change due to desorption of the molecules under laser irradiation P=0 Experiments described above were deliberately performed under the 0.0 0.5 1.0 1.5 2.0 2.5 conditions when only one absorption line interacts with the laser t, ns radiation For a more complex molecule, a laser spectrum would Fig.4 Lower panel - optical FID observed unavoidably cover several absorption lines If the absorption spectrum in HBr at different pressures Path length is 20 is resolved, individual lines not overlap, and the electric field of the cm Dash line – laser pulse Upper panel shows a total FID can be calculated by superposition of partial FID, each term correlation of the positions of the minima for of the superposition is given by equation (1) If the absorption lines each signal with the theory overlap, there is no analytical equation for the shape of FID signal, which can only be assessed numerically Nevertheless, the qualitative Power Zeros of J1(2 x)) 140 E.N Chesnokov et al / Physics Procedia 84 (2016) 135 – 141 conclusion that for high optical density the shape of the signal is very sensitive to the intensities of the absorption lines holds also for the complex spectra It should be pointed out that narrow absorption lines and high optical density are very common conditions for optics of the atmosphere For example, the absorption spectrum of water vapor in the atmosphere in terahertz region (V.B Podobedov,et.al 2008) has narrow lines with D Z0 > 0.01 cm-1 Therefore even 10 m path is enough to form zero area optical pulse under such conditions Conclusion Our experiments have confirmed exceptionally great universality of the common scenario of 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40 50 60 Power,... are the same as in visible and in γ-ray regions We investigated the transformation of the shape of 0- π pulses within a wide range of experimental conditions, from the incipience of the oscillating... permanently changing during the propagation in the medium The formation of 0- π pulses in the case of a single Lorentzian absorption line has been first investigated theoretically by Crisp (19 70) He derived