Laser Physics Research Relevant to Laser-Electron X-Ray Generator M.V. Gorbunkov, Yu.Ya. Maslova, Yu.V. Shabalin, A.V. Vinogradov P.N. Lebedev Physical Institute, Moscow, Russia Summary. A prototype of laser unit for Laser Electron X-Ray Generator is con- structed on the basis of the optoelectronic control. The laser system in which an optoelectronic negative feedback is realized by means of a signal reflected from an intracavity Pockels cell polarizer is proposed and tested. The design provides flexible control over pulse train time structure. 1 Introduction Laser produced plasma proved to be a convenient and flexible source of incoherent and coherent soft X-rays probably including water window in the near future. T3 and multiterawatt laser systems are being developed for efficient generation of hard X-rays [1]. However laser plasma X-ray sources are still uncompetitive with conventional X-ray tubes, synchro- trons and free electron lasers. Meanwhile a dramatic (several orders of magnitude) gap exists between X-ray tubes and accelerator based X-ray sources in respect of average power, brightness, sizes, cost, monochro- maticity, tunability etc. The filling in of this gap would be beneficial for various scientific and commercial applications. In other words a new X-ray source that could bring together the compactness of X-ray tubes and X-ray beam manipulation ability of synchrotron radiation (SR) beamlines with- out the substantial rise of cost and loss of average power is highly desir- able. The applications are biological and medical imaging, material struc- ture and chemical analysis, protein crystallography, microscopy and microtomography for life sciences, medical diagnostics, industrial online X-ray inspection, security and custom control in ports and border termi- nals. A promising candidate to fill in the gap between conventional and SR sources is laser-electron X-ray generator (LEXG) based on Thomson scat- tering [2]. The idea to use Compton and Thomson scattering of laser radia- 2 M.V. Gorbunkov, Yu.Ya. Maslova, Yu.V. Shabalin, A.V. Vinogradov tion by relativistic electrons to extend the output energy spectrum down to several tens keV [3] attracted last decade several research groups [4-12]. A project of LEXG developed jointly by Moscow State University and Institute of Quantum Radiophysics of P. N. Lebedev Physical Institute is aimed at the system containing pulsed synchrotron and a repetitive pico- second laser [11, 12]. Electron bunch is circulating in a storage ring and appears in the interaction chamber (IC) with the period 10-20 ns. Original laser beam time structure is a millisecond train of pulses separated by mi- crosecond-scale intervals. Thanks to multiplication in optical circulator the period of laser signal is transformed from microsecond-scale interval into 10-20 ns inside the IC that provides the most efficient coupling of the laser and electron beams. Since the microsecond interval is far above a master oscillator's resonator round-trip time Tr (generally about 10 ns), one has to use pulse picking by means of an electrooptical modulator as it was made in [13] (see Fig. 1). A well-known method to obtain highly stable trains of picosecond pulses is to apply a system of feedback loops, which proved to be efficient in hundred microsecond range [14, 15]. Furthermore, feed- backs allow not only to stabilize the pulse amplitude, but also to obtain regular pulsations with controlled period far exceeding Tr [16]. In this case a laser radiation looks like microtrains of picosecond pulses separated by microsecond intervals. It is important to note that such mode has an attrac- Fig. 1. The near analogue of the LEXG laser system [13]. Pulse picker Laser Physics Research Relevant to Laser-Electron X-Ray Generator 3 tive advantage. In fact, after single pulses at 0.5 MHz are picked from a train of pulses at 100 MHz, only 0.5% of average power is utilized. The mode of regular pulsations with 2-microsecond (0.5 MHz) period is more favorable, since it provides increase in intensity for the pulses picked in pulsation peaks. 2 Two Feedback Loops-Controlled Laser To investigate the dynamics of a picosecond laser controlled by feedbacks we use the approach describing a mode-locked laser as an object with dis- continuous control [16, 17]. In the simplest case of system with one nega- tive feedback (NFB) loop delayed by a resonator round trip the control can be described by means of the so-called logistic mapping ( ) 1 1 n n n x rx x + = - (1) where n x stands for a normalized energy at the n-th pass (a pass corre- sponds to a laser cavity round trip), r is an overall gain including active medium gain and passive losses, and the term in brackets represents the one-pass delayed feedback loop action. The maximum acceptable gain for steady operation is rmax = 3 [16]. When r exceeds the threshold value rmax, the logistic mapping demonstrates a well-known nonlinear dynamics [18]. Quite a different dynamics can be observed in a system controlled by two feedback loops (delayed by one and two round trips) described by the equation ( ) 1 1 1 n n n n x rx x x a + - = - - (2) where a is relative feedback sensitivity. Its negative value denotes that feedback loop delayed by a resonator round trip is positive (PFB). The analysis shows that if 1 1 a - < < a nonlinear dynamics displayed by (2) a Fig. 2. Calculated log of pulsation period T(rmax) against relative feedback sensitiv- ity: curves are in close agreement in the region of negative argument. The upper curve is an approximation. 4 M.V. Gorbunkov, Yu.Ya. Maslova, Yu.V. Shabalin, A.V. Vinogradov differs fundamentally from that of the logistic mapping (1): regular pulsa- tion with period above three round-trips appears. The values of pulsation period T (rmax) at r = rmax (a) calculated by means of the mapping station- ary point stability analysis and the approach based on differential equa- tions (approximation) are presented in Fig. 2. For negative a (i.e. positive and negative feedback combination control) at r = rmax (a) the pulsation is harmonic and the period can be expressed as ( ) ( ) max 2 1 T r p a a = + (3) Formula (3) implies that regular dynamics with large periods (tens and hundreds of round-trips) can be observed at a close to - 1 (see Fig. 2). 3 Optoelectronic Feedback Designed for Pulsation Mode The discussion above showed that pulsations with the period far exceeding a resonator round trip time are expected in a laser controlled by a combina- tion of feedbacks where a negative feedback loop is delayed by one reso- nator round trip with regard to the positive one. With this aim in mind we designed a laser system in which an optoelectronic negative feedback is realized by means of a signal reflected from an intracavity Pockels cell po- larizer. Self-mode-locking in the negative feedback-controlled laser is a known technique for stable ultrashort pulses generation [19]. The laser mode- locked by a fast time-shifted negative optoelectronic feedback loop [20] is a very simple and reliable source of light pulses with about hundred pico- second duration. In such a laser the losses caused by an intracavity Pockels cell look like a periodic asymmetric "saw" with a long rise time and short tail. The tail is formed due to fast charge of the Pockels cell capacity by photocurrent generated in optoelectronic element under ultrashort light pulse. The long front is formed by slow discharge of intracavity cell capac- ity through the control system resistor. Stable self-mode-locking occurs due to time delay in feedback control system corresponding to light pulse passage through the Pockels cell at the moment of low intracavity losses. The discharge time should be [20, 21] about several cavity round trip time Tr. Optimal delay for short pulse generation is approximately one Tr. Usu- ally the optical control signal is taken at the moment after passage of intra- cavity Pockels cell polarizer. The control proved to be efficient in laser output stabilization [16, 17]. The laser dynamics changes dramatically if the optoelectronic feedback is realized by means of a signal reflected from an intracavity Pockels cell Laser Physics Research Relevant to Laser-Electron X-Ray Generator 5 polarizer. The scheme of discontinuous control in the laser is shown in Fig. 3. When the laser pulse length varies slightly from pass to pass, the (n+1)-th pulse energy in the cavity En+1 is related to En as 2 1 n n n E E G RP + = , where G is a gain in a round-trip and R is an output mirror reflectivity (see Fig. 3). Similarly to [16,17], we use the Pockels cell transmission ( ) 0 1 n n P P B = - where n B is control signal, and P0 is the initial Pockels cell transmission when feedback is off. In the proposed laser design n B is the difference between incident light flux on the polarizer and transmitted flux. As a result for the recurrence relation we have ( ) ( ) 2 2 1 0 1 1 n n n n E E G RP E G R E + - = - - (4) Using 2 0 r G RP = and 0 n n P E x r = one obtains 0 1 1 1 n n n n P x x r x x r + - ? ? = - + ? ÷ è ? (5) Applying (3) and taking into account the Pockels cell transmission ( ) 2 2 cos 2 U P U Ul p ? ? = ? ÷ ? ÷ è ? (6) where U is a static bias voltage and 2 Ul is a cell half-wave voltage, we estimate the nonlinear dynamics development threshold gain rmax(U) and oscillation period T(U) in two limits. When U is far less than 2 Ul ( ) 2 2 2 U T U U l p = , ( ) 2 2 max 2 1 4 U r U Ul p ? ? = + ? ÷ ? ÷ è ? If 2 U Ul ? , then ( ) max 2 , ( ) 2 T U r U p ? ? . Polarizer, P Fig. 3. The scheme of discontinuous control in a laser with NFB: the control sig- nal is taken from Pockels cell polarizer. ?En Gain medium, G G2 REn-1 - En NFB Output mirror, R ?G2 REn-1 6 M.V. Gorbunkov, Yu.Ya. Maslova, Yu.V. Shabalin, A.V. Vinogradov So the laser controlled by the optoelectronic NFB with the control signal taken from the Pockels cell a large period regular pulsation can be ob- tained. The period increases and the nonlinear dynamics development threshold decreases when the Pockels cell bias voltage U decreases. 4 Laser Dynamics Simulation Results To complete our demonstration of the laser, where the optoelectronic con- trol signal is taken from the intracavity Pockels cell polarizer, however, we still have to show that the regime of pulsations can be reproduced qualita- tively by extending the mapping (5) to take into account the laser output radiation fine time structure evolution as well as Pockels cell voltage varia- tion at the time scale of Tr depending on the feedback delay time, Pockels cell capacity discharge time, active medium gain, and the cell bias voltage Ust We followed the same approach as in our previous works [16]. The goal is to investigate self mode- locking in pulsation regime with corresponding significant variation of control voltage and time-dependent Pockels cell transmission. In the numerical simulation spontaneous emission noise was placed in the laser cavity and subsequently transformed by time-dependent transmission P(t) of the Pockels cell. On the other hand P(t) is calculated from the feedback signal pro- portional to the laser intensity I(t) reflected from the intracav- ity polarizer. The simulation proved that the discussed laser scheme al- lows not only to obtain stable mode-locking in quasi CW mode, but also to generate regu- lar short pulses microtrains in pulsation regime with con- trolled period far exceeding Tr. When the laser parameters are optimal the Fig. 4. Simulated trains: r = 1.03 (a) and 1.09 (b). a b Laser Physics Research Relevant to Laser-Electron X-Ray Generator 7 microtrain consists of tens single (at the cavity round trip time) short pulses. To show gain sensitivity of the microtrains envelope the trains at gain r = 1.03 and 1.09 are displayed in Fig. 4 (in both cases Ust = 0.05 2 Ul ). 5 Experiment The experiments were performed using a flash-lamp pumped Nd:YAG la- ser (?6.3?60 mm rod was used). A PC-controlled laser pumping based on the incomplete discharge of large capacity allowed us to vary pump dura- tion up to 3.9 milliseconds. Laser cavity was made by flat wedge-shaped mirrors of 0.98 and 0.35 reflection coefficient. We introduced an intracav- ity mirror telescope 3:1 to enlarge a laser mode volume in the active media and thus to raise the laser output. Total cavity length was 150 cm. An iris aperture was used for mode selection. The Pockels cell was based on a Fig. 5. Millisecond lamp pumped YAG-Nd laser designed for microsecond scale pulsations. AM active laser medium; M1, M2 cavity mirrors; P polarizer; IA iris aperture; MT – mirror telescope; DKDP Pockels cell electrooptical crystal; CC feedback control circuits. Fig. 6. Traces of the lasing power (a) and pump lamp running (b) correspond- ing to discharge time 3.9 ms; time scale 0.5 ms/div. a b 8 M.V. Gorbunkov, Yu.Ya. Maslova, Yu.V. Shabalin, A.V. Vinogradov multilayer polarizer (Brewster angle) and 8?8?11 mm3 DKDP ( 2 Ul = 7.8 kV) crystal with antireflection faces placed close to the laser mirror. Static bias voltage Ust applied to the Pockels cell was varied in a range 0?2 kV. A high voltage silicon mesa-structure was used as a control element of the optoelectronic system. Discharge time of intracavity Pock- els cell capacity was set to 20 ns (2Tr). The control signal was taken from an intracavity Pockels cell polarizer (Fig. 5). A pin-diode and C8-14 stor- age (50 MHz) and digital TDS-3052 (5 GS/s, 500 MHz) oscilloscopes were used for the laser emission registration. Fine time structure of the la- ser light was investigated using streak-camera AGAT SF-3M (time resolu- tion < 2 ps) synchronized with laser pulses with specially-made electronic delay system. When kV range static bias voltage Ust was applied to the Pockels cell sta- ble mode-locking in quasi CW regime was observed. Setting the optimal diameter of intracavity iris aperture we obtained a picosecond pulse train of stable amplitude with total number of pulses up to 350000. The typical train shape and corresponding pumping pulse shape is shown in Fig. 6 a, b. By decreasing Ust and fine DKPD crystal tuning we obtained regimes of regular pulsations with periods 0.5, 1, 1.3, and 2 microseconds. The ex- Pulsations, 2 ms/div. Fig.7. The development of regular microsecond pulsations and a microtrain fine time structure in the mode-locked laser. Pulsation period is 200 round trips (2 mi- croseconds). The dynamics is shown in three time scales: millisecond, microsec- ond and nanosecond. Overview trace, 0.5 ms/div. Fine time structure, 50 ns/div. gain incre- ase Laser Physics Research Relevant to Laser-Electron X-Ray Generator 9 periments showed that despite of significant control voltage and time- dependent Pockels cell transmission variation in pulsation mode a single pulse was circulating in the laser cavity for the all regimes. An example of 2 microsecond period pulsation development is shown in Fig. 7. Millisecond time-scale oscilloscope traces (see Fig. 8) show that the peak pulsation power (feedback is on) is several times higher than a steady-state power level in free-running lasing (feedback is off, all other conditions be- ing equal). In conclusion the laser regime based on the combination of positive and negative feedbacks is obtained that provides efficient extraction of a single picosecond pulse with a microsecond period from mode-locked laser oscil- lator. We are grateful to N. A. Borisevich, V. G. Tunkin, V. A. Petukhov, Yu. S. Kasjanov, R. M. Feshchenko and A. M. Chekmarev for fruitful dis- cussions. The work was partially supported by the Subprogram "Laser sys- tems" of RAS and RFBR grant 05-02-17448a. References 1. R. Toth, J.C. Kieffer, A. Krol, et al.: 'Phase contrast micro-CT with an ul- trafast laser-based hard x-ray source', Proc. SPIE, p. 591813-1 – 591813-8, 2005. 2. P. Sprangle, A. Ting, E. Esarey, and A. Fisher: 'Tunable, short pulse hard x- rays from a compact laser synchrotron source', J. Appl. Phys. 72, p. 5032, 1992. 3. A. Luccio and A.B. Brik: 'Methods and Apparatus for Producing X-rays', US Patent 4,598,415 July 1 1986, European Patent 0,05032 24.08.1988. 4. Z. Huang and R.D. Ruth: 'Laser-Electron Storage Ring', Rhys. Rev. Letters, Vol. 80, No. 5, p. 976, 1998. Fig. 8. Millisecond oscilloscope traces: a – feedback is switched off, b – feed- back is switched on (time scale 0.5 ms/div). Vertical scales are equal. a b 10 M.V. Gorbunkov, Yu.Ya. Maslova, Yu.V. Shabalin, A.V. Vinogradov 5. R.J. Loewen: SLAC-R-632, June 2003, Ph.D. thesis, Stanford University, Stanford CA. 6. A. Agafonov, V. Androsov, J.I.M. Botman et al.: 'Status of Kharkov x-ray generator NESTOR', Proc. SPIE, 5917, p. 97, 2005. 7. F.E. Carroll: 'Tunable Monochromatic X Rays: A New Paradigm in Medi- cine', AJR 179, p. 583, 2002. 8. W.J. Brown, S.G. Anderson, S.P.J. Barty et al.: 'Experimental characterization of an ultrafast Thomson scattering x-ray source with three-dimensional time and frequency-domain analysis', Physical Review Special Topics – Accelera- tors and Beams, 7, 060702, p. 1, 2004. 9. K. Dobashi, A. Fukasawa, M. Uesaka et al.: 'Design of Compact Monochro- matic Tunable Hard X-Ray Source Based on X-band Linac', Japanese Journal of Applied Physics, Vol. 44, No.4A, p. 1999, 2005. 10. T. Yanagida, T. Nakajyo, S. Ito et al.: 'Development of high-brightness hard x-ray source by Laser-Compton scattering', Proc. SPIE, Vol. 5918, p. 231, 2005. 11. M.V. Gorbunkov, V.G. Tunkin, E.G. Bessonov et al.: 'Proposal of a Compact Repetitive Dichromatic X-ray Generator with Millisecond Duty Cycle for Medical Applications', Proc. SPIE, 5919, OU1-OU6, 2005. 12. I.A. Artyukov, E.G. Bessonov, A.V. Vinogradov et al.: 'Laser-electron X-ray Generator', Preprint INP MSU 2006-7/806. 13. S. Schreiber, I. Will, D. Sertore et al.: 'Running experience with the laser sys- tem for the RF gun based injector at the TESLA Test Facility linac', Nuclear Instruments and Methods in Physics Research A 445, 427-431, 2000. 14. M.V. Gorbunkov, Yu.Ya. Maslova, A.M. Chekmarev et al.: 'Pulse generation of a large number of picosecond pulses microtrains in Nd:YAG laser con- trolled by negative feedback loop', Proc. of MIPT, Moscow, p. 50, 2005. 15. M.V. Gorbunkov, A.V. Konyashkin, P.V. Kostryukov et al. 'Pulsed-diode- pumped, all-solid-state, electro-optically controlled picosecond Nd:YAG la- sers', RUS Quantum Electronics 35 (1), p.2, 2005. 16. I.M. Bayanov, V.M. Gordienko, M.G. Zvereva, S.A. Magnitski, A.P. Ta- rasevich. A High-Stable Negative-Feedback Picosecond YAG:Nd3+ Laser. RUS Quantum Electronics, 16 (8), p. 1545, 1989. 17. M.V. Gorbunkov, Yu.V. Shabalin: 'Two-Loop Feedback Controlled Laser: New Possibilities For Ultrashort Pulses Generation And High-Level Stabiliza- tion', Proc. SPIE, Vol. 4751, p. 463, 2002. 18. H.G. Schuster: Deterministic Chaos. An Introduction, Physik-Verlag, Wein- heim, 1984. 19. V.K. Makukha, V.M. Semibalamut, V.S. Smirnov: 'Simulated Emission of Ultrashort Pulses from a Negative Feedback Laser', Sov. Quantum Electronics 4, No.5, p.1023-1027, 1977. 20. D.B. Vorchik, M.V. Gorbunkov: 'Self Mode-Locked Nd-YAG Laser Under Fast Delayed Negative Feedback by Means of High-Voltage Assemblies of Inversely-Shifted Silicon p-n Junctions', Physical Foundations of Electronic Laser Engineering, Proceedings of MIPT, Moscow, p. 4 - 11, 1995.
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Laser Physics Research Relevant to Laser-Electron X-Ray Generator M.V. Gorbunkov, Yu.Ya. Maslova, Yu.V. Shabalin, A.V. Vinogradov P.N. Lebedev Physical Institute, Moscow, Russia Summary. A prototype of laser unit for Laser Electron X-Ray Generator is con- structed on the basis of the optoelectronic control. The laser system in which an optoelectronic negative feedback is realized by means of a signal reflected from an intracavity Pockels cell polarizer is proposed and tested. The design provides flexible control over pulse train time structure. 1 Introduction Laser produced plasma proved to be a convenient and flexible source of incoherent and coherent soft X-rays probably including water window in the near future. T3 and multiterawatt laser systems are being developed for efficient generation of hard X-rays [1]. However laser plasma X-ray sources are still uncompetitive with conventional X-ray tubes, synchro- trons and free electron lasers. Meanwhile a dramatic (several orders of magnitude) gap exists between X-ray tubes and accelerator based X-ray sources in respect of average power, brightness, sizes, cost, monochro- maticity, tunability etc. The filling in of this gap would be beneficial for various scientific and commercial applications. In other words a new X-ray source that could bring together the compactness of X-ray tubes and X-ray beam manipulation ability of synchrotron radiation (SR) beamlines with- out the substantial rise of cost and loss of average power is highly desir- able. The applications are biological and medical imaging, material struc- ture and chemical analysis, protein crystallography, microscopy and microtomography for life sciences, medical diagnostics, industrial online X-ray inspection, security and custom control in ports and border termi- nals. A promising candidate to fill in the gap between conventional and SR sources is laser-electron X-ray generator (LEXG) based on Thomson scat- tering [2]. The idea to use Compton and Thomson scattering of laser radia- 2 M.V. Gorbunkov, Yu.Ya. Maslova, Yu.V. Shabalin, A.V. Vinogradov tion by relativistic electrons to extend the output energy spectrum down to several tens keV [3] attracted last decade several research groups [4-12]. A project of LEXG developed jointly by Moscow State University and Institute of Quantum Radiophysics of P. N. Lebedev Physical Institute is aimed at the system containing pulsed synchrotron and a repetitive pico- second laser [11, 12]. Electron bunch is circulating in a storage ring and appears in the interaction chamber (IC) with the period 10-20 ns. Original laser beam time structure is a millisecond train of pulses separated by mi- crosecond-scale intervals. Thanks to multiplication in optical circulator the period of laser signal is transformed from microsecond-scale interval into 10-20 ns inside the IC that provides the most efficient coupling of the laser and electron beams. Since the microsecond interval is far above a master oscillator's resonator round-trip time Tr (generally about 10 ns), one has to use pulse picking by means of an electrooptical modulator as it was made in [13] (see Fig. 1). A well-known method to obtain highly stable trains of picosecond pulses is to apply a system of feedback loops, which proved to be efficient in hundred microsecond range [14, 15]. Furthermore, feed- backs allow not only to stabilize the pulse amplitude, but also to obtain regular pulsations with controlled period far exceeding Tr [16]. In this case a laser radiation looks like microtrains of picosecond pulses separated by microsecond intervals. It is important to note that such mode has an attrac- Fig. 1. The near analogue of the LEXG laser system [13]. Pulse picker Laser Physics Research Relevant to Laser-Electron X-Ray Generator 3 tive advantage. In fact, after single pulses at 0.5 MHz are picked from a train of pulses at 100 MHz, only 0.5% of average power is utilized. The mode of regular pulsations with 2-microsecond (0.5 MHz) period is more favorable, since it provides increase in intensity for the pulses picked in pulsation peaks. 2 Two Feedback Loops-Controlled Laser To investigate the dynamics of a picosecond laser controlled by feedbacks we use the approach describing a mode-locked laser as an object with dis- continuous control [16, 17]. In the simplest case of system with one nega- tive feedback (NFB) loop delayed by a resonator round trip the control can be described by means of the so-called logistic mapping ( ) 1 1 n n n x rx x + = - (1) where n x stands for a normalized energy at the n-th pass (a pass corre- sponds to a laser cavity round trip), r is an overall gain including active medium gain and passive losses, and the term in brackets represents the one-pass delayed feedback loop action. The maximum acceptable gain for steady operation is rmax = 3 [16]. When r exceeds the threshold value rmax, the logistic mapping demonstrates a well-known nonlinear dynamics [18]. Quite a different dynamics can be observed in a system controlled by two feedback loops (delayed by one and two round trips) described by the equation ( ) 1 1 1 n n n n x rx x x a + - = - - (2) where a is relative feedback sensitivity. Its negative value denotes that feedback loop delayed by a resonator round trip is positive (PFB). The analysis shows that if 1 1 a - < < a nonlinear dynamics displayed by (2) a Fig. 2. Calculated log of pulsation period T(rmax) against relative feedback sensitiv- ity: curves are in close agreement in the region of negative argument. The upper curve is an approximation. 4 M.V. Gorbunkov, Yu.Ya. Maslova, Yu.V. Shabalin, A.V. Vinogradov differs fundamentally from that of the logistic mapping (1): regular pulsa- tion with period above three round-trips appears. The values of pulsation period T (rmax) at r = rmax (a) calculated by means of the mapping station- ary point stability analysis and the approach based on differential equa- tions (approximation) are presented in Fig. 2. For negative a (i.e. positive and negative feedback combination control) at r = rmax (a) the pulsation is harmonic and the period can be expressed as ( ) ( ) max 2 1 T r p a a = + (3) Formula (3) implies that regular dynamics with large periods (tens and hundreds of round-trips) can be observed at a close to - 1 (see Fig. 2). 3 Optoelectronic Feedback Designed for Pulsation Mode The discussion above showed that pulsations with the period far exceeding a resonator round trip time are expected in a laser controlled by a combina- tion of feedbacks where a negative feedback loop is delayed by one reso- nator round trip with regard to the positive one. With this aim in mind we designed a laser system in which an optoelectronic negative feedback is realized by means of a signal reflected from an intracavity Pockels cell po- larizer. Self-mode-locking in the negative feedback-controlled laser is a known technique for stable ultrashort pulses generation [19]. The laser mode- locked by a fast time-shifted negative optoelectronic feedback loop [20] is a very simple and reliable source of light pulses with about hundred pico- second duration. In such a laser the losses caused by an intracavity Pockels cell look like a periodic asymmetric "saw" with a long rise time and short tail. The tail is formed due to fast charge of the Pockels cell capacity by photocurrent generated in optoelectronic element under ultrashort light pulse. The long front is formed by slow discharge of intracavity cell capac- ity through the control system resistor. Stable self-mode-locking occurs due to time delay in feedback control system corresponding to light pulse passage through the Pockels cell at the moment of low intracavity losses. The discharge time should be [20, 21] about several cavity round trip time Tr. Optimal delay for short pulse generation is approximately one Tr. Usu- ally the optical control signal is taken at the moment after passage of intra- cavity Pockels cell polarizer. The control proved to be efficient in laser output stabilization [16, 17]. The laser dynamics changes dramatically if the optoelectronic feedback is realized by means of a signal reflected from an intracavity Pockels cell Laser Physics Research Relevant to Laser-Electron X-Ray Generator 5 polarizer. The scheme of discontinuous control in the laser is shown in Fig. 3. When the laser pulse length varies slightly from pass to pass, the (n+1)-th pulse energy in the cavity En+1 is related to En as 2 1 n n n E E G RP + = , where G is a gain in a round-trip and R is an output mirror reflectivity (see Fig. 3). Similarly to [16,17], we use the Pockels cell transmission ( ) 0 1 n n P P B = - where n B is control signal, and P0 is the initial Pockels cell transmission when feedback is off. In the proposed laser design n B is the difference between incident light flux on the polarizer and transmitted flux. As a result for the recurrence relation we have ( ) ( ) 2 2 1 0 1 1 n n n n E E G RP E G R E + - = - - (4) Using 2 0 r G RP = and 0 n n P E x r = one obtains 0 1 1 1 n n n n P x x r x x r + - ? ? = - + ? ÷ è ? (5) Applying (3) and taking into account the Pockels cell transmission ( ) 2 2 cos 2 U P U Ul p ? ? = ? ÷ ? ÷ è ? (6) where U is a static bias voltage and 2 Ul is a cell half-wave voltage, we estimate the nonlinear dynamics development threshold gain rmax(U) and oscillation period T(U) in two limits. When U is far less than 2 Ul ( ) 2 2 2 U T U U l p = , ( ) 2 2 max 2 1 4 U r U Ul p ? ? = + ? ÷ ? ÷ è ? If 2 U Ul ? , then ( ) max 2 , ( ) 2 T U r U p ? ? . Polarizer, P Fig. 3. The scheme of discontinuous control in a laser with NFB: the control sig- nal is taken from Pockels cell polarizer. ?En Gain medium, G G2 REn-1 - En NFB Output mirror, R ?G2 REn-1 6 M.V. Gorbunkov, Yu.Ya. Maslova, Yu.V. Shabalin, A.V. Vinogradov So the laser controlled by the optoelectronic NFB with the control signal taken from the Pockels cell a large period regular pulsation can be ob- tained. The period increases and the nonlinear dynamics development threshold decreases when the Pockels cell bias voltage U decreases. 4 Laser Dynamics Simulation Results To complete our demonstration of the laser, where the optoelectronic con- trol signal is taken from the intracavity Pockels cell polarizer, however, we still have to show that the regime of pulsations can be reproduced qualita- tively by extending the mapping (5) to take into account the laser output radiation fine time structure evolution as well as Pockels cell voltage varia- tion at the time scale of Tr depending on the feedback delay time, Pockels cell capacity discharge time, active medium gain, and the cell bias voltage Ust We followed the same approach as in our previous works [16]. The goal is to investigate self mode- locking in pulsation regime with corresponding significant variation of control voltage and time-dependent Pockels cell transmission. In the numerical simulation spontaneous emission noise was placed in the laser cavity and subsequently transformed by time-dependent transmission P(t) of the Pockels cell. On the other hand P(t) is calculated from the feedback signal pro- portional to the laser intensity I(t) reflected from the intracav- ity polarizer. The simulation proved that the discussed laser scheme al- lows not only to obtain stable mode-locking in quasi CW mode, but also to generate regu- lar short pulses microtrains in pulsation regime with con- trolled period far exceeding Tr. When the laser parameters are optimal the Fig. 4. Simulated trains: r = 1.03 (a) and 1.09 (b). a b Laser Physics Research Relevant to Laser-Electron X-Ray Generator 7 microtrain consists of tens single (at the cavity round trip time) short pulses. To show gain sensitivity of the microtrains envelope the trains at gain r = 1.03 and 1.09 are displayed in Fig. 4 (in both cases Ust = 0.05 2 Ul ). 5 Experiment The experiments were performed using a flash-lamp pumped Nd:YAG la- ser (?6.3?60 mm rod was used). A PC-controlled laser pumping based on the incomplete discharge of large capacity allowed us to vary pump dura- tion up to 3.9 milliseconds. Laser cavity was made by flat wedge-shaped mirrors of 0.98 and 0.35 reflection coefficient. We introduced an intracav- ity mirror telescope 3:1 to enlarge a laser mode volume in the active media and thus to raise the laser output. Total cavity length was 150 cm. An iris aperture was used for mode selection. The Pockels cell was based on a Fig. 5. Millisecond lamp pumped YAG-Nd laser designed for microsecond scale pulsations. AM active laser medium; M1, M2 cavity mirrors; P polarizer; IA iris aperture; MT – mirror telescope; DKDP Pockels cell electrooptical crystal; CC feedback control circuits. Fig. 6. Traces of the lasing power (a) and pump lamp running (b) correspond- ing to discharge time 3.9 ms; time scale 0.5 ms/div. a b 8 M.V. Gorbunkov, Yu.Ya. Maslova, Yu.V. Shabalin, A.V. Vinogradov multilayer polarizer (Brewster angle) and 8?8?11 mm3 DKDP ( 2 Ul = 7.8 kV) crystal with antireflection faces placed close to the laser mirror. Static bias voltage Ust applied to the Pockels cell was varied in a range 0?2 kV. A high voltage silicon mesa-structure was used as a control element of the optoelectronic system. Discharge time of intracavity Pock- els cell capacity was set to 20 ns (2Tr). The control signal was taken from an intracavity Pockels cell polarizer (Fig. 5). A pin-diode and C8-14 stor- age (50 MHz) and digital TDS-3052 (5 GS/s, 500 MHz) oscilloscopes were used for the laser emission registration. Fine time structure of the la- ser light was investigated using streak-camera AGAT SF-3M (time resolu- tion < 2 ps) synchronized with laser pulses with specially-made electronic delay system. When kV range static bias voltage Ust was applied to the Pockels cell sta- ble mode-locking in quasi CW regime was observed. Setting the optimal diameter of intracavity iris aperture we obtained a picosecond pulse train of stable amplitude with total number of pulses up to 350000. The typical train shape and corresponding pumping pulse shape is shown in Fig. 6 a, b. By decreasing Ust and fine DKPD crystal tuning we obtained regimes of regular pulsations with periods 0.5, 1, 1.3, and 2 microseconds. The ex- Pulsations, 2 ms/div. Fig.7. The development of regular microsecond pulsations and a microtrain fine time structure in the mode-locked laser. Pulsation period is 200 round trips (2 mi- croseconds). The dynamics is shown in three time scales: millisecond, microsec- ond and nanosecond. Overview trace, 0.5 ms/div. Fine time structure, 50 ns/div. gain incre- ase Laser Physics Research Relevant to Laser-Electron X-Ray Generator 9 periments showed that despite of significant control voltage and time- dependent Pockels cell transmission variation in pulsation mode a single pulse was circulating in the laser cavity for the all regimes. An example of 2 microsecond period pulsation development is shown in Fig. 7. Millisecond time-scale oscilloscope traces (see Fig. 8) show that the peak pulsation power (feedback is on) is several times higher than a steady-state power level in free-running lasing (feedback is off, all other conditions be- ing equal). In conclusion the laser regime based on the combination of positive and negative feedbacks is obtained that provides efficient extraction of a single picosecond pulse with a microsecond period from mode-locked laser oscil- lator. We are grateful to N. A. Borisevich, V. G. Tunkin, V. A. Petukhov, Yu. S. Kasjanov, R. M. Feshchenko and A. M. Chekmarev for fruitful dis- cussions. The work was partially supported by the Subprogram "Laser sys- tems" of RAS and RFBR grant 05-02-17448a. References 1. R. Toth, J.C. Kieffer, A. Krol, et al.: 'Phase contrast micro-CT with an ul- trafast laser-based hard x-ray source', Proc. SPIE, p. 591813-1 – 591813-8, 2005. 2. P. Sprangle, A. Ting, E. Esarey, and A. Fisher: 'Tunable, short pulse hard x- rays from a compact laser synchrotron source', J. Appl. Phys. 72, p. 5032, 1992. 3. A. Luccio and A.B. Brik: 'Methods and Apparatus for Producing X-rays', US Patent 4,598,415 July 1 1986, European Patent 0,05032 24.08.1988. 4. Z. Huang and R.D. Ruth: 'Laser-Electron Storage Ring', Rhys. Rev. Letters, Vol. 80, No. 5, p. 976, 1998. Fig. 8. Millisecond oscilloscope traces: a – feedback is switched off, b – feed- back is switched on (time scale 0.5 ms/div). Vertical scales are equal. a b 10 M.V. Gorbunkov, Yu.Ya. Maslova, Yu.V. Shabalin, A.V. Vinogradov 5. R.J. Loewen: SLAC-R-632, June 2003, Ph.D. thesis, Stanford University, Stanford CA. 6. A. Agafonov, V. Androsov, J.I.M. Botman et al.: 'Status of Kharkov x-ray generator NESTOR', Proc. SPIE, 5917, p. 97, 2005. 7. F.E. Carroll: 'Tunable Monochromatic X Rays: A New Paradigm in Medi- cine', AJR 179, p. 583, 2002. 8. W.J. Brown, S.G. Anderson, S.P.J. Barty et al.: 'Experimental characterization of an ultrafast Thomson scattering x-ray source with three-dimensional time and frequency-domain analysis', Physical Review Special Topics – Accelera- tors and Beams, 7, 060702, p. 1, 2004. 9. K. Dobashi, A. Fukasawa, M. Uesaka et al.: 'Design of Compact Monochro- matic Tunable Hard X-Ray Source Based on X-band Linac', Japanese Journal of Applied Physics, Vol. 44, No.4A, p. 1999, 2005. 10. T. Yanagida, T. Nakajyo, S. Ito et al.: 'Development of high-brightness hard x-ray source by Laser-Compton scattering', Proc. SPIE, Vol. 5918, p. 231, 2005. 11. M.V. Gorbunkov, V.G. Tunkin, E.G. Bessonov et al.: 'Proposal of a Compact Repetitive Dichromatic X-ray Generator with Millisecond Duty Cycle for Medical Applications', Proc. SPIE, 5919, OU1-OU6, 2005. 12. I.A. Artyukov, E.G. Bessonov, A.V. Vinogradov et al.: 'Laser-electron X-ray Generator', Preprint INP MSU 2006-7/806. 13. S. Schreiber, I. Will, D. Sertore et al.: 'Running experience with the laser sys- tem for the RF gun based injector at the TESLA Test Facility linac', Nuclear Instruments and Methods in Physics Research A 445, 427-431, 2000. 14. M.V. Gorbunkov, Yu.Ya. Maslova, A.M. Chekmarev et al.: 'Pulse generation of a large number of picosecond pulses microtrains in Nd:YAG laser con- trolled by negative feedback loop', Proc. of MIPT, Moscow, p. 50, 2005. 15. M.V. Gorbunkov, A.V. Konyashkin, P.V. Kostryukov et al. 'Pulsed-diode- pumped, all-solid-state, electro-optically controlled picosecond Nd:YAG la- sers', RUS Quantum Electronics 35 (1), p.2, 2005. 16. I.M. Bayanov, V.M. Gordienko, M.G. Zvereva, S.A. Magnitski, A.P. Ta- rasevich. A High-Stable Negative-Feedback Picosecond YAG:Nd3+ Laser. RUS Quantum Electronics, 16 (8), p. 1545, 1989. 17. M.V. Gorbunkov, Yu.V. Shabalin: 'Two-Loop Feedback Controlled Laser: New Possibilities For Ultrashort Pulses Generation And High-Level Stabiliza- tion', Proc. SPIE, Vol. 4751, p. 463, 2002. 18. H.G. Schuster: Deterministic Chaos. An Introduction, Physik-Verlag, Wein- heim, 1984. 19. V.K. Makukha, V.M. Semibalamut, V.S. Smirnov: 'Simulated Emission of Ultrashort Pulses from a Negative Feedback Laser', Sov. Quantum Electronics 4, No.5, p.1023-1027, 1977. 20. D.B. Vorchik, M.V. Gorbunkov: 'Self Mode-Locked Nd-YAG Laser Under Fast Delayed Negative Feedback by Means of High-Voltage Assemblies of Inversely-Shifted Silicon p-n Junctions', Physical Foundations of Electronic Laser Engineering, Proceedings of MIPT, Moscow, p. 4 - 11, 1995.