664 OPTICS LETTERS / Vol. 19, No. 9 / May 1, 1994

Time-to-space mapping of femtosecond pulses

Martin C. Nuss, Melissa Li,* and T. H. Chiu

AT&T Bell Laboratories, 101 Crawfords Corner Road, Holmdel, New Jersey 07733

A. M. Weiner

Department of Electrical Engineering, 1285 Electrical Engineering Building, Purdue University, West Lafayette, Indiana 47907

Afshin Partovi

AT&T Bell Laboratories, 600 Mountain Avenue, Murray Hill, New Jersey 07974

Received December 17, 1993

We report time-to-space mapping of femtosecond light pulses in a temporal holography setup. By reading out atemporal hologram of a short optical pulse with a continuous-wave diode laser, we accurately convert temporalpulse-shape information into a spatial pattern that can be viewed with a camera. We demonstrate real-timeacquisition of electric-field autocorrelation and cross correlation of femtosecond pulses with this technique.

During the past few years, various groups havereported shaping of short optical pulses by use oflinear filtering in the frequency domain.'"5 Thistechnique is highly attractive, as it performs oper-ations such as matched filtering and generation ofspecific pulse patterns in the Fourier (spectral) do-main in parallel, rather than serially, in the time do-main. Recently this technique has been extended totemporal holographic processing of femtosecond lightpulses in the frequency domain,6'7 and storage andrecall of femtosecond pulses as well as some elemen-tary signal-processing operations were demonstratedwith this technique.8 It is striking how closely sucha temporal holography setup resembles the Fourier-transform correlator,9 which is used in optical imagecorrelation and spatial pattern recognition.'0 Thisresemblance is no accident: while a spatial correla-tor records a hologram of the spatial frequencies kof the object shape, a temporal correlator records ahologram of the temporal frequencies co of the pulseshape.

The similarity between spatial and temporalFourier-transform holography opens up the possi-bility of mixing temporal and spatial informationand may lead to numerous applications ranging fromtemporal pattern recognition to multiplexing, de-multiplexing, and routing of optical signals. In thisLetter we demonstrate the fundamental equivalenceof time and space in Fourier-transform holography.We show that with this equivalence we can con-vert temporal information directly into spatial infor-mation. The use of a novel multiple-quantum-well(MQW) photorefractive device as a fast holographicmedium further allows us to record and read suchholograms in real time. As a first demonstration,we apply this technique to measure electric-fieldautocorrelation and cross correlation of femtosecondpulses in real time.

For formation of a temporal hologram, a signalpulse ES(t) carrying the temporal information and a

short, featureless reference pulse ER(t) are spectrallydispersed by a diffraction grating in the input plane,collimated by a lens, and interfere in a holographicmedium placed at the spectrum plane (Fig. 1). Theintensity of the interference fringes in the spectrumplane is described in the Fourier domain as8

IEs(w) + ER(w)I2

= IEs(w)1 2 + IER(w)12

+ Es*(c)ER(w) + Es(co)ER*(C) - (1)

This equation also describes the fringes recorded ina spatial Fourier-transform correlator when oi is re-placed by k. When the fringes are read out with apoint source (in time or space), either one of the lasttwo terms in Eq. (1) describing correlations of signaland reference is recovered. The equivalence betweenspatial and temporal holography becomes even moretransparent when we describe the action of the grat-ing in the space-time domain. It is known that theeffect of the grating on an optical pulse EO(t) is foundby multiplying its spectrum Eo(cw) with a complex fil-ter function":

E(x, co) = exp[i3(co) - wto)x/c]Eo(co), (2)

where the x axis points along the surface of the inputplane and lies in the plane defined by input anddiffracted beams, 0)o is the center frequency of thepulse, /3 = coo dO/dw = Ao/d cos 0 is the dispersionparameter of the grating, AO = 27r-c/swo, d is the pitchof the grating, 0 is the angle of diffraction, and c isthe speed of light. Transforming back into the timedomain, we find that immediately behind the gratingthe diffracted optical pulse has the form

E(x, t) = Eo(t - fX/c). (3)

This equation describes a spatial image of the inputpulse projected onto the grating, with a time-to-spacescaling factor of ,//c and surfing across the grating

0146-9592/94/090664-03$6.00/0 © 1994 Optical Society of America

May 1, 1994 / Vol. 19, No. 9 / OPTICS LETTERS 665

Signal Pulse

Lens< f >

Laser Diode

MaWDeviceI v It

BS V

Grating

Camera

Fig. 1. Schematic of our setup for time-to-space map-ping. Although a transmission grating is shown here forclarity, the experiment uses a regular reflection grating.

at a speed v = c/,8. A conversion of the temporalinformation into spatial information has taken placein the grating plane, and the signal pulse shape ispresent (in amplitude and phase) as a spatial imagein this plane. Hence the temporal holography setupis identical to a spatial correlator,'0 in which scaledversions of the pulse shapes are presented as imagesby a screen or a spatial light modulator in place of thegrating. The only difference between an image froma screen or light modulator and from a temporal pulseis that the image from the pulse is not static but surfsacross the grating at a speed c/l,. However, as longas the reference pulse does the same, the interferencefringes in the spectrum plane S will be stationary andcan be recorded as a hologram.

The idea behind the present experiment is that,once the hologram is written, one cannot fundamen-tally distinguish whether the hologram was recordedwith the use of temporal or spatial information.Consequently this offers the opportunity of convert-ing temporal data into spatial data and vice versa.For example, in the experiment described below weaccomplish time-to-space mapping by writing a tem-poral hologram with spectrally dispersed pulses butthen interpret the temporal hologram as a spatialhologram by reading it out with a monochromaticplane wave (Fig. 1). Conversely, one can achievespace-to-time mapping by using a spatial light mod-ulator to write a spatial hologram and then readingout the hologram with a spectrally dispersed shortoptical pulse.

In the experiment, we use a 600-line/mm diffrac-tion grating and a 200-mm focal-length Fourier-transform lens. The center wavelength Ao of thefemtosecond laser is approximately 830 nm, and eachof the two beams has approximately 5-mW averagepower. The angle of incidence is chosen so that thediffracted beam is parallel to the surface normal ofthe grating in all our experiments (i.e., 0 = 00, sothat /3 = A/d). A MQW photorefractive device, lo-cated at the spectrum plane, serves as a real-timeholographic medium.2 Since the MQW photorefrac-tive device is not the main subject of this Letter, werefer the reader to previously published reports fordetails.2" 2 The MQW device has a response time ofless than 1 1-s at an energy density of 1 _tJ/cm

2 anda diffraction efficiency of a few percent. It is readout with a few milliwatts of power from a collimatedsingle-mode diode laser at 850 nm. At this wave-length, just below the exciton peak of the MQW, the

diffraction efficiency of the device is the largest.'2The diffracted light travels back through the setup,is being picked off by a thin beam splitter, BS, and isfocused onto the detector plane by a second Fourier-transform lens of 190-mm focal length (for clarity,Fig. 1 shows only a single lens for both these pro-cesses). The correlation peaks in the detector planeare recorded either by a CCD video camera or by asilicon diode array. For the experiments given be-low, we used a 1024-element silicon diode array witha 25-Am pixel-to-pixel spacing.

Figure 2 shows the correlation peaks for differenttime delays between the signal and reference pulsesin the case for which both the signal and the refer-ence are identical 100-fs laser pulses. The time de-lay between successive traces is 333 fs. As the timedelay between the two input pulses is varied, thecorrelation peaks move on the detector array. Wecan obtain a calibration of the time-to-space map-ping process by plotting the position of the correlationpeaks versus the time delay between the two fem-tosecond input pulses (see the inset of Fig. 2). Thiscalibration constant is 1.684 ± 0.03 fs/,um. The cal-culated calibration constant, when we take into ac-count the different writing and reading wavelengthsAs and Ar as well as the different focal lengths fw =

200 mm and fr = 190 mm, is given by

At = / ALf.,Ax c Arfr

(4)

which gives At/Ax = 1.703 fs/Am, close to the ex-perimentally obtained value. Figure 2 also showsthat there is a limited range over which the inputdelay can be changed and one is still able to seea correlation peak. This window AT results fromthe finite beam size at the grating. All temporalinformation projected onto the grating plane has tofit within the beam size without truncation. An-other yet identical way of looking at this window isthat the input pulses are spread out by the grat-ing to a duration AT corresponding to the inverseof the spectral resolution At, of the setup. Only ifthe delay between the two pulses is less than ATwill the pulses be able to interfere in the MQW.In our particular setup with a beam diameter of3 mm, this window is approximately 7 ps. For a1200-line/mm grating, AT = 45 ps, and for largerbeam diameters, the window can be hundreds ofpicoseconds, assuming that the diffracted beam al-ways leaves the grating in the direction of the sur-face normal.

The FWHM of the first-order correlation peaks is85 ,tm, which translates into 145 fs. Assuming asech2-shaped pulse, this is very close to the theoret-ical electric-field autocorrelation width of a 100 fspulse. It may be noted in this context that generallythe field autocorrelation is the Fourier transform ofthe spectrum of the pulse. In the particular case oftransform-limited pulses, however, the square of thefield autocorrelation closely resembles the standardintensity autocorrelation.

When the signal pulse is longer than the inputpulse, we obtain the square of the electric-field cross

666 OPTICS LETTERS / Vol. 19, No. 9 / May 1, 1994

a, -2

12 13 14 15 1 5 fPosition (mm)

10 12 14

Position (mm)

Fig. 2. Autocorrelation peaks as recorded by an arraydetector in the detector plane with 100-fs pulses for boththe signal and the reference beams. The different tracesare for different time delays between both pulses, with a333-fs delay between successive traces. The FWHM ofeach peak is 85 Am, corresponding to approximately 145fs. The inset shows the position of the correlation peaksas a function of the time delay between the two inputpulses.

1.0

Cin

C

.6

(a

C.2)Cl)

0.5

0.0

-2 -1 0 1 2

Position (mm)

Fig. 3. Cross correlation between two 100-fs pulses,where one of the pulses has been stretched by propagationthrough a 50-cm-long single-mode fiber. Compared withthat in Fig. 2, the FWHM is broadened to 0.2 mm(-340 fs).

correlation between signal and reference pulse. Todemonstrate this, we let one of the 100-fs pulses prop-agate through approximately 50 cm of single-modefiber to stretch out the pulse duration. The powerin the fiber is less than 5 mW, so that mainly lin-ear dispersion occurs in the fiber without much self-phase modulation. Then the signal pulse emergesfrom the fiber stretched out and with a linear fre-quency chirp. The cross-correlation profile recordedin the detector is shown in Fig. 3. The FWHM isnow 200 Aum, corresponding to 340 fs. Within a fewpercent, the same pulse duration is also measured byconventional intensity cross correlation at the setup.The pulse is also slightly asymmetric, presumablybecause of some third-order dispersion. It is illumi-nating to compare the case of chirped and unchirped

pulses in the spectral domain by looking at. the in-terference fringes recorded in the MQW. For thetwo transform-limited pulses, the time delay resultsin a linear spectral phase shift, which in turn re-sults in equidistant fringes, with the pitch becom-ing smaller with increasing time delay. As the pitchvaries, the diffracted diode laser beam is steered intodifferent directions. For the pulse that has propa-gated through the fiber, the fiber dispersion leads toa quadratic phase shift, resulting in a chirped holo-gram with a fringe spacing linearly varying over thewidth of the hologram. The diffracted beam will bedefocused from such a hologram, leading to a largercorrelation spot on the detector array.

In conclusion, we have demonstrated conversionof temporal information into spatial informationin Fourier-transform holography. The key to theunderstanding of our experiment is that there isno significant difference between recording a tempo-ral hologram, in which temporal frequencies (wave-lengths) are recorded, and recording a spatial holo-gram, in which spatial frequencies are recorded.The temporal hologram can then equally be readout with a continuous-wave laser, thus permittingthe temporal information recorded in the hologramto be interpreted as spatial information. As a firstdemonstration of this principle, we measure auto-correlation and cross correlation of femtosecond laserpulses with a video camera in real time. We suggestthat this technique will open a new field of spatiotem-poral holographic processing, in which time and spacecan be interchanged and converted into each otherat will.

*Present address, E. L. Ginzton Laboratory, Stan-ford University, Stanford, California 94305.

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