September 15, 2009 / Vol. 34, No. 18 / OPTICS LETTERS
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Tilted-pulse time-resolved off-axis digital holography Tadas Bal~u¯nas,* Andrius Melninkaitis, Andrius Vanagas, and Valdas Sirutkaitis Laser Research Centre, Vilnius University, Vilnius LT-10223, Lithuania *Corresponding author:
[email protected] Received March 24, 2009; revised August 9, 2009; accepted August 10, 2009; posted August 12, 2009 (Doc. ID 109095); published September 4, 2009 In this Letter we present an improvement of time-resolved off-axis digital holography by the use of tilted femtosecond laser pulses. The pulse front tilting of the reference beam with respect to the phase front allows larger crossing angles to be used for recording of digital holograms without significant reduction of pulse interference area (typically limited by low temporal coherence of ultrashort pulses). Such approach increases the area of interference fringes, thus enabling the higher resolution of the reconstructed image as well as better separation of dc term. Temporal resolution is not deteriorated by this method, as only the reference pulse is tilted. The proposed technique was applied for direct intensity clamping observations of light filaments in water using the laser pulses of 30 fs duration. © 2009 Optical Society of America OCIS codes: 090.1995, 320.7100, 100.5070.
The digital holography technique (DH) was introduced as a method well suited for quantitative phasecontrast imaging [1]. Typically, a digital image sensor is used to record the interferogram of an overlapped object and reference waves, and subsequently, the numerical reconstruction of the original wavefront is performed using the algorithms described in [1]. Besides a large variety of applications in characterization of static objects, it was recently shown that timeresolved off-axis digital holography (TRDH) is a valuable tool for the investigations of ultrafast optical processes such as nonlinear propagation and filamentation of femtosecond (fs) light pulses [2,3]. The idea of TRDH is a combination of DH and conventional pump–probe technique: refractive index changes induced in Kerr media as well as plasma absorption during filamentation of fs pulse are imaged holographically (perpendicularly to the direction of filament propagation). To achieve high temporal resolution in TRDH, ultrashort light pulses have to be used for probing. The off-axis hologram recording geometry is superior to the in-line recording setup, because it allows clear separation of a twin-image and a so-called dc term of diffraction by means of simple digital spatial filtering [4]. However, several problems arise in off-axis digital holography when ultrashort pulses are used, namely, the interference zone where the pulses overlap in space and time is reduced due to limited pulse length as shown in Fig. 1. In the CCD plane, only part of the incident light overlaps in both time and space; the area where light impinges on the detector at different times results in an uniform illumination. The larger the angle of incidence, the smaller is the coherent zone. However, sufficiently large angle between object and reference wave is required in offaxis DH in order to separate the virtual image and the dc term. The resolution of the reconstructed hologram in case of monochromatic light is given by ⌬ = 0z / L, where z is the reconstruction distance and L is the width of the hologram covered with fringes [1]. However, in case of ultrashort pulses the maxi0146-9592/09/182715-3/$15.00
mum number of interference fringes is limited to 2c0 / 0 [5], where c is the velocity of light in vacuum, 0 is the central wavelength, and 0 is the duration of the pulse. Increasing the angle reduces the area where pulses overlap, as the fringes become more dense. For a given angle between two beams the spatial resolution is then limited to ⌬ = 0z sin共兲/共2c0兲.
共1兲
In other words, high temporal and spatial resolution cannot be achieved at the same time. In this Letter we demonstrate the improvement of time-resolved off-axis DH achieved by the use of tilted front pulses that allow us to overcome the above-mentioned limitation. Tilted pulses can be completely overlapped when interfered at an angle [5]. The pulse front tilt is acquired due to angular chirp [6]. The angular chirp was used in lowcoherence off-axis conventional holography to increase the field of view [7]. The pulse tilting, however, has not been analyzed from the point of view of application to ultrafast digital holography. A pulse can be tilted by introducing an angular dispersion, for example, using a diffraction grating [5] or a prism [7]. The tilt of the pulse front with respect to the phase front of central spectral component is defined by the angle ␣t ⬇ 0Ca [8], where Ca is an angular chirp of the pulse and can be generally expressed
Fig. 1. (Color online) Interference of ultrashort pulses. (a) Pulses without tilt resulting in limited coherent zone. (b) Tilted pulses that can interfere throughout whole surface. © 2009 Optical Society of America
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as: Ca = 兩共d / d兲0兩. The angular chirp of the pulse diffracted by a grating can be calculated using diffraction grating equation: d sin共兲 = m, where d is the period of the grating, m is the diffraction order, and is the angle of diffraction. Assuming that first diffraction order is used 共m = 1兲 and approximation sin共兲 ⬇ is valid, the following angular chirp expression is acquired: Ca ⬇ d−1. The resulting tilt angle of the diffracted pulse is ␣t = 0 / d. Note that the periods of the interference fringes of different spectral components are equal when pulse front tilt angle is matched. The fringe period ⌬x depends on wavelength and the wavelength-dependent angle of incidence (due to angular dispersion) between interfering pulses: ⌬x = / sin关共兲兴. In case of diffraction grating, it turns out that the fringe period is matched for all spectral components if the angle between the reference and the object pulses is equal to the diffraction angle. Therefore period of diffraction grating should be chosen according to the CCD pixel size in order to match interference fringe period with Nyquist frequency. If the relative phase of the spectral components of the reference and the object beam on the detector is the same, the position of the fringes is the same. As different spectral components of the tilted pulse travel at different angles, they will arrive at the detector at slightly different lateral positions. The socalled spatial chirp is undesirable, and the beam size should be sufficiently large in order to avoid this effect. In our case the relative carrier frequency change at the edge of detector was negligible 共 ⬍ 0.1% 兲. The optical scheme used for time-resolved holographic transmission measurements is a slightly modified Mach–Zehnder interferometer. A transmission diffraction grating is introduced to the reference arm of the interferometer. Note that only the reference pulse is tilted; therefore temporal resolution is not reduced. A large period diffraction grating (42 lines per mm) was used to achieve the desired 24 m interference fringe period in the hologram plane. The first-order diffraction maximum is selected by an aperture and is further used as the reference wave to interfere with an object wave at the hologram plane. The general layout of the experimental setup is shown in Fig. 2. A Ti:sapphire laser (P = 800 nm, P = 130 fs) was used to pump a noncollinear parametric amplifier (NOPA) and induce a plasma filament in a
water cell. Filament was induced by focusing 共NA = 0.06兲 a fraction of the pump pulse into the water cell. The probe pulse in the object arm of the interferometer was transmitted through the induced filament. The area around the waist (in linear regime) of the Gaussian pump beam in the water cell was selected for imaging. The NOPA (Topas White, Light Conversion) was used to generate the probe pulses down to 30 fs duration (wavelength probe = 550 nm). Compressing probe pulse to a duration shorter than that of the pump pulse 共probe Ⰶ pump兲 allows one to explore the early plasma formation dynamics within the pump pulse and its consequent decay. The spectrum and second-harmonic-generation autocorrelation trace of the probe pulse are shown in Fig. 3. To achieve overlap throughout a whole spectrum of a broadband pulse it is necessary to match the groupdelay dispersions (GDDs) of the object and reference pulses; otherwise the relative position of the fringes of each spectral component will be different, which will result in reduction of the contrast of the hologram and deterioration of the temporal resolution. The object wave propagates through the water cell and an imaging objective 共10⫻ 兲, while the reference wave travels through a dispersion compensation fused silica slab and a beam splitter. To calculate the thickness of the fused silica slab in the reference arm the GDD in the water cell, beam splitter, objective, and due to pulse tilting [6] were taken into account. Tilted pulses possess the negative group-velocity dispersion (GVD) that is not related to a material dispersion. Effective GVD coefficient due to pulse tilting can be expressed as g0 = −03 / 2d2c2 [6]. To verify the proposed measurement scheme, timeresolved phase-contrast images of the light-induced filament dynamics in water were measured. The lineouts of the hologram in case of nontilted and tilted reference pulse are shown in Figs. 3(c) and 3(d). In case of tilted reference pulse the detector is fully covered with interference fringes, while in the nontilted reference pulse case the spatial resolution is two times worse, because the detector is only partially covered with interference fringes.
Fig. 2. (Color online) Experimental setup of tilted pulse TRDH. P, polarizer; / 2, half-wave plate; M, mirror; BS, beam splitter; S, specimen; G, diffraction grating; A, aperture; CCD, digital camera; FS, fused silica slab.
Fig. 3. (a) Spectrum and (b) autocorrelation trace of the probe pulse. (c) and (d) are lineouts of ultrashort pulse interference pattern in the case of a nontilted and a tilted pulse reference pulse, respectively.
September 15, 2009 / Vol. 34, No. 18 / OPTICS LETTERS
Self-focusing of ultrashort light pulses is a complex phenomenon where spatial and temporal effects are interrelated. The experimental characterization of such wave-packet dynamics requires spatiotemporal (ST) methods. Pure spatial (time-integrated image) or pure temporal characterization does not provide enough information about the filamentation dynamics. A multispectral DH is capable of measuring the full ST field of an ultrashort pulse [9], but it does not allow directly observing the changes induced in the medium. Shadowgraphic [10] or interferometric techniques are common for evaluation of refractive index changes; however, they require careful calibration and are limited to the relatively simple and smooth objects. Our technique is capable of tracking the filament propagation dynamics and quantitatively measuring the free carrier density and light intensity without additional calibration [3]. By and large, filamentation results from the dynamical competition mainly between Kerr selffocusing and defocusing in electron plasma generated via multiphoton ionization [10,11]. A sequence of measured phase-contrast single-shot images at different pump pulse energies is shown in Figs. 4(a)–4(d). At the beginning of the filament the Kerr effect is clearly visible that induces positive refractive index change: ⌬nK = n2I, where I is intensity and n2 denotes Kerr coefficient. Promptly after that a plasma channel is visible that leads to the negative refractive index change: ⌬np ⬍ 0. The mean refractive index can be calculated from the measured data: ⌬n = ⌬ / 共k0L兲, where k0 = 2 / 0 is the wavenumber of
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the probe pulse. The diameter L and maximum phase shift ⌬ of the filament were taken from the lineouts that correspond to the peak of negative phase shift (proportional to the peak intensity) as shown in Figs. 4(e)–4(h). The ⌬n stays almost constant 关0.8− 共1.2 ⫻ 10−3兲兴, while the pump pulse energy is changed by 2 orders of magnitude 共0.3– 27 J兲. In other words, intensity is clamped to the I = ⌬n / n2 ⬇ 2TW/ cm2 intensity level. Intensity clamping was previously indirectly observed from analysis of supercontinuum spectra [11]. TRDH, on the other hand, allows direct quantitative measurement of intensity within the filament. To our knowledge, we present the first direct observation of intensity clamping in condensed media. In conclusion, we have demonstrated the usage of tilted pulses in TRDH that helps to overcome recording angle limitation when broadband ultrashort pulse light sources are used. Time-resolved phasecontrast images with superior spatial resolution using 30 fs duration pulses were recorded to test the proposed experimental setup scheme. The measured phase-contrast images reveal the direct observation of intensity clamping at different pump pulse energies. We anticipate that the proposed improvement opens the possibility to improve the temporal resolution of TRDH technique down to few-cycle pulse durations. The authors are thankful to M. Vengris for valuable discussions, project Laserlab-Europe, and the Lithuanian State Science and Studies Foundation for support. References
Fig. 4. (Color online) (a)–(d) Phase contrast images of the filament and (e)–(h) lineouts at different pulse energies. Units are radians.
1. E. Cuche, P. Marquet, and C. Depeursinge, Appl. Opt. 38, 6994 (1999). 2. M. Centurion, Y. Pu, Z. Liu, D. Psaltis, and T. Hänsch, Opt. Lett. 29, 772 (2004). 3. T. Balciunas, A. Melninkaitis, G. Tamosauskas, and V. Sirutkaitis, Opt. Lett. 33, 58 (2008). 4. E. Cuche, P. Marquet, and C. Depeursinge, Appl. Opt. 39, 4070 (2000). 5. A. A. Maznev, T. F. Crimmins, and K. A. Nelson, Opt. Lett. 23, 1378 (1998). 6. O. E. Martinez, Opt. Commun. 59, 229 (1986). 7. Z. Ansari, Y. Gu, M. Tziraki, R. Jones, P. M. W. French, D. D. Nolte, and M. R. Melloch, Opt. Lett. 26, 334 (2001). 8. G. Pretzler, A. Kasper, and K. J. Witte, Appl. Phys. B 70, 1 (2000). 9. P. Gabolde and R. Trebino, Opt. Express 14, 11460 (2006). 10. S. Minardi, A. Gopal, M. Tatarakis, A. Couairon, G. Tamošauskas, R. Piskarskas, A. Dubietis, and P. Di Trapani, Opt. Lett. 33, 86 (2008). 11. W. Liu, S. Petit, A. Becker, N. Aközbek, C. M. Bowden, and S. L. Chin, Opt. Commun. 202, 189 (2002).
