May 15, 2008 / Vol. 33, No. 10 / OPTICS LETTERS 1123

Optical coherence pulsed interferometry: shapingprobe pulses in time-domain interferometry

Francesco Morichetti,1,2,* Andrea Melloni,2 and Mario Martinelli1,2

1CoreCom, Via G. Colombo 81, 20133 Milano, Italy2Dipartimento di Elettronica e Informazione, Politecnico di Milano, Via Ponzio 34/5, 20133, Milano, Italy

*Corresponding author: morichetti@corecom.it

Received January 28, 2008; revised April 7, 2008; accepted April 13, 2008;posted April 17, 2008 (Doc. ID 91951); published May 14, 2008

The autocorrelation of a modulated coherent light source is used as a probe pulse in a time-domain inter-ferometry scheme. With respect to conventional techniques, higher flexibility in selecting the shape of theprobe pulse can be achieved by simply acting on the modulation parameters. The complex amplitude of shortpulses propagating through a generic optical device can be directly measured, with no need for fast samplingand time synchronization. The potentialities of the technique are shown by reporting measurements of am-plitude distortion, group delay, and frequency chirp of optical pulses transmitted through integrated ringresonators. © 2008 Optical Society of America

OCIS codes: 120.0120, 120.3180, 120.5050.

Time-domain interferometry (TDI) has been exten-sively used in optics for either pulse or device char-acterization. Basically, it is based on the measure-ment of the cross correlation between two replicas ofan optical field, propagating separately in the twoarms of a variable-delay interferometer. The possibil-ity of achieving high time resolution, with neitherfast detection nor time synchronization, makes TDIattractive for ultrashort pulse characterization [1],and subpicosecond resolution has been demonstratedby means of either coherent [2] or low-coherent [3]broadband sources. Furthermore, TDI has the advan-tage of accessing both the amplitude and the phaseresponse of optical systems [4].

In this Letter, a scheme for TDI that we havenamed optical coherence pulsed interferometry(OCPI), is presented. The main idea consists of tailor-ing the autocorrelation of an externally modulatedcoherent source to control the shape and the width ofprobe pulses. The powerfulness of the technique,combining all the benefits of conventional TDI withthe flexibility of an adaptive source, is demonstratedby the measurement of pulse delay, amplitude distor-tion, and frequency chirp in integrated optical ringresonators.

Similar to conventional TDI, OCPI exploits theself-interference of an optical field s1�t� supplied to adevice under test (DUT), with a reference-delayedreplica s2�t ,��=s1�t−��, according to the scheme ofFig. 1(a). The time-averaged interference pattern(disregarding the mean intensity �s1�t��2+ �s2�t ,���2)gives the convolution product [5]

U��� = Re������� * h�t��cos�2�f0�� �1�

between the DUT complex impulse response h���and the source autocorrelation function ����=E�s1�t�s1

*�t−���, where f0 is the optical carrier fre-quency. The interference signal U��� provides a directmeasurement of the DUT output when a probe pulse

with envelope ������ is supplied at the input.

0146-9592/08/101123-3/$15.00 ©

The advantage of OCPI over conventional TDI con-cerns the possibility of arbitrarily shaping probepulses by modulating the amplitude and/or the phaseof a coherent source. Generally, any modulated signals�t� can be expressed as the sum of delayed wave-forms p�t� as s�t�=�n=−�

� anp�t−nT�, where an is thecomplex amplitude of the nth symbol and T is the in-verse of the symbol rate. The signal autocorrelation[6]

���� =1

T �m=−�

�

RA�m�Rp�� − mT� �2�

contains delayed replicas of the waveform autocorre-lation Rp���=E�p�t�p*�t−���, weighted by the se-quence autocorrelation RA�m�=E�anan−m

* �. The shapeof the even-symmetry envelope ������ depends on thechoice of either the modulation sequence an or thewaveform p�t�, while the maximum and the mini-

Fig. 1. (a) Schematic of the OCPI experimental setup. (b)Measured envelope of the probe pulse �Rp���� when theOCPI source is intensity modulated with 3.3 Gbits/s (solid

curve) and 10 Gbits/s (dashed curve) OOK NRZ format.

2008 Optical Society of America

1124 OPTICS LETTERS / Vol. 33, No. 10 / May 15, 2008

mum time width is fixed by the source linewidth andthe maximum modulation speed, respectively.

Common modulation formats can be employed togenerate suitable probe pulses in OCPI. For example,assuming a binary phase-shift keying (BPSK) con-stellation, an= �+A ,−A�, and in Eq. (2) all the termsRA�m� with m�0 vanish. As a result, the identityRA�m�= �A2 ��m,0 holds, where �m,0 is the Kroneckerdelta function, and the shape of ���� coincides withthat of Rp���. For on–off keying (OOK) modulation,an= �0,A� and ���� assumes the general form ����= �A�2�Rp���+�m=−�

� Rp��−mT�� /4T, containing infinitedelayed replicas of Rp���. If (super)Gaussian wave-forms p�t� are employed, all the contributions Rp��−mT� sum up to a constant value, and a probe pulseproportional to Rp��� can be extracted.

The OCPI technique has been implemented by us-ing the experimental setup shown in Fig. 1(a). Thefields from two light sources are split into the twoarms of a fiber Mach–Zehnder interferometer (MZI).The OCPI source consists of a coherent laser source,with �0=c / f0=1554.53 nm and linewidth �1 MHz,followed by an intensity modulator. The modulatorgenerates an OOK nonreturn to zero (NRZ) signal atup to 10 Gbits/s speed, providing an almost Gaussianprobe pulse Rp���, as shown in Fig. 1(b) for two dif-ferent modulation rates (3.3 and 10 Gbits/s). A2 MHz linewidth distributed feedback, centered at1310.25 nm, is added to control the reference arm un-balance with subwavelength resolution. The twosources are acquired simultaneously by the samephotodectector, which guarantees an intrinsic syn-chronicity at any acquisition speed, and then sepa-rated in frequency domain by a numerical filtering.The frequency distance between the two sources en-ables one to keep the cross-talk level below 30 dB af-ter the filtering. Currently, this residual noise is themain limiting factor to the phase sensitivity of thesystem, exhibiting a phase-error standard deviationof 0.01 rad. Two polarization controllers (PCs) areemployed to select the polarization state in the DUT(PC1) and to maximize the interference with the ref-erence field (PC2). The differential configuration ofthe two photodetectors (PDs) doubles the amplitudeof the interference pattern and removes the commonmode noise. The limited bandwidth of the detectors�125 KHz� operates the time averaging required bythe OCPI technique.

The OCPI technique can be applied to generic op-tical media and devices, such as bulk materials, mul-tilayers, fiber devices, or integrated components. Inthis Letter some experimental results concerningpulse propagation through an integrated ring-resonator phase shifter (PS) are reported. The device,shown in the inset of Fig. 2(a), has a 590 �m bendingradius and 50 GHz free spectral range and was real-ized in 4.5% index-contrast silicon oxynitride technol-ogy [7]. Figure 2(a) shows the PS power transmission(black curve) and group delay (green curve) mea-sured by phase-sensitive optical law-coherence inter-ferometry [8]. The bell-shaped group delay exhibits a

maximum value at the resonant frequency fR, where

a narrow notch (�3 GHz wide at 3 dB attenuation)opens in the spectral transmission because of thering’s loss. To investigate different propagation re-gimes, marked in Fig. 2(a), the PS resonance wasshifted with respect to f0 by heating the ring’s wave-guide. Figure 2(b) shows the simulated (dashedcurves) and measured (solid curves) output envelopeswhen the 86 ps pulse of Fig. 1(b) is used. As fR ap-proaches f0, the pulse experiences increasing delay,attenuation, and distortion, the latter due to the nar-row PS notch width. The black curves (circle) showthat propagation off-resonance �fR− f0=25 GHz�keeps the envelope unaffected. Yellow (square) andred (triangles) curves show that an almost symmetri-cal broadening occurs at the side of the PS notch be-cause of second-order dispersion effects [9]. Closer tofR, the third-order dispersion causes an asymmetricalenvelope distortion, with deep oscillations in theleading edge. When f0= fR (diamond) a maximum de-lay of 80 ps occurs, corresponding to the PS spectraldelay of Fig. 2(a) averaged over the 10 GHz signalbandwidth.

The time evolution of the phase and the frequencychirp across the output pulse can be accessed byOCPI measurements. Figure 3 shows the simulated(dashed curve) and the measured (solid curve) inten-sity and phase when f0= fR. The phase keeps an al-most constant value along the main lobe of the pulseyet exhibits an almost instantaneous � jump when

Fig. 2. (Color online) (a) Measured power transmissionand group delay of the ring resonator PS shown in the in-set. Chromium heaters deposited onto the waveguide en-able the thermal control of the ring’s resonance; (b) simu-lated and measured pulse envelopes at the output of the PSwhen the carrier frequency f0 is detuned with respect to thePS spectrum at the frequencies marked in (a). Time scale isnormalized by attributing zero delay to the pulse propagat-ing off-resonance.

power drops to zero. This feature, in agreement with

May 15, 2008 / Vol. 33, No. 10 / OPTICS LETTERS 1125

theoretical predictions, is a good test bed to demon-strate the very high temporal resolution of the tech-nique. Figure 4 refers to propagation at the two sidesof the PS notch, when f0= fR+1.5 GHz (dashedcurves) and f0= fR−1.5 GHz (solid curves), as markedby the triangles of Fig. 2(a). While no significant dif-ferences can be observed in the envelope (blackcurves), Fig. 4(a) shows that the phase evolves para-bolically with an opposite curvature at the two propa-

Fig. 3. (Color online) Simulated (dashed curves) and mea-sured (solid curves) power and phase of the pulse outgoingthe PS at the ring’s resonance �f0= fR�.

Fig. 4. (Color online) (a) Measured time evolution of thepulse phase at the PS output in anomalous dispersion (f0= fR+1.5 GHz; dashed curve, blue online) and normal dis-persion (f0= fR−1.5 GHz; solid curve, red online) regime; (b)shift of the instantaneous frequency across the pulse out-going the PS. The black curves show the output pulse en-velope at the two regimes.

gation regimes. This implies the opposite frequencychirp shown in Fig. 4(b), where the deviation of theoutput instantaneous frequency from the input car-rier f0 is reported. Below fR (solid curve, red online),normal dispersion causes a linear redshift, while atfrequencies higher than fR anomalous dispersion pro-duces a blueshift (dashed curve, blue online). In bothcases, the instantaneous frequency deviation aroundthe envelope peak has a slope of 27 MHz/ps.

Thanks to the high speed of the measurement (lessthan 4 s for the 250 ps delay range scanned in Fig. 4),time stability is not a critical issue in our OCPI sys-tem. The frequency drift of both sources is less than±0.1 GHz (over a more than 10 min measurement),far below the ±1.5 GHz frequency chirp measured inFig. 4. This source stability is expected to enablemeasurements of frequency chirps as low as1 MHz/ps.

To summarize, we have presented a novel TDItechnique extending and giving higher flexibility totime-domain measurements. The possibility of di-rectly measuring the amplitude and the phase ofpulses with different shapes and widths transmittedthrough generic optical devices is of great interest inoptical communications, which are evolving towardsdispersion-managed systems and phase modulationformats. Approaches based on the spectral slicing of abroadband source have not been demonstrated so farto offer comparable flexibility [4,10]. All the benefitsof conventional TDI, including the need for neitherfast sampling nor pulse synchronization, are pre-served. Recently, we have successfully employed theOCPI technique for the observation of slow and fastlight in coupled-resonator architectures; for brevity,these results are left to future contributions.

This work was partially supported by the Euro-pean Union (EU) FP6-FET SPLASH project.

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