Baryscan: a sensitive and user-friendlyalternative to Z scan for

weak nonlinearities measurementsThomas Godin,* Michael Fromager, Emmanuel Cagniot, Richard Moncorgé, and Kamel Aït-AmeurCentre de recherche sur les Ions, les Matériaux et la Photonique (CIMAP), UMR 6252 Commissariat à l’Energie

Atomique et aux Energies Alternatives, CNRS, Ecole Nationale Supérieure d’Ingénieurs de Caen,Université de Caen, 6 Boulevard du Maréchal Juin, 14050 Caen cedex 4, France

*Corresponding author: thomas.godin@ensicaen.fr

Received February 22, 2011; revised March 21, 2011; accepted March 22, 2011;posted March 23, 2011 (Doc. ID 142877); published April 13, 2011

A new and efficient technique for measuringweak optical nonlinearities is reported. Like Z scan, its implementationis basic, both experimentally and theoretically, but leads to an improved sensitivity of λ=5:104, which represents, todate, one of the highest observed enhancements. With this technique, which is based upon the use of a positionsensitive detector, nonlinear properties are deduced by monitoring the barycentric position of a truncated pump–probe laser beam as the sample is moved along the optical axis. The technique is experimentally validated bymeasuring the pump-induced refractive index change and the underlying polarizability variation resulting fromthe excitation of the Cr3þ ions in ruby. © 2011 Optical Society of AmericaOCIS codes: 160.4330, 190.4420, 260.5950, 050.5080.

Measurement of refractive index changes induced bysmall optical nonlinearities or thermal effects is a chal-lenge that has been widely investigated. Many paperswere dedicated in the past to that question, and a list ofcommonly used experimental techniques can be found,for instance, in [1]. Several groups of methods emerge,however, from this plethora of possibilities: the wavemixing methods [2], the interferometric ones [3,4], andthe distortion techniques based on beam self-focusing[5]. Even if the pertinence and the reliability of thesetechniques may be unquestionable, the nearly 3000-times-cited paper by Sheik-Bahae et al. tends to provethat the most popular one is the Z-scan technique [6].The main reason of this success is the simplicity of itsexperimental implementation and of its theoretical anal-ysis of the results. A nonlinear sample is translated alongthe optical axis of a focused and perfectly Gaussian beam(i.e., M2 ¼ 1); during this translation, the material thusexperiences a variable radial intensity leading to a beamdistortion, which is the signature of the investigated non-linear effect, that is monitored through the transmissionof a circular aperture set in the far field. This trivial setup,studied in minute detail in [7], allows measurements ofnonlinearly induced phase distortions with a sensitivityof about λ=300. Based on this method, a myriad of var-iants were studied in order to bypass this limit, in parti-cular to investigate weak nonlinearities as those met, forinstance, in thin films or to simply reduce the power ofthe probe beam. Several ways were thus explored: eithera change in the incident beam shape [8,9], a more sophis-ticated theoretical treatment [10], a change in the detec-tion [11–13], or more drastic modifications of the originalexperimental setup geometry [14–17]. This overview candefinitely not be exhaustive, and the number of proposeduseful techniques is still growing [18]. All these tech-niques bring some improvements (with sensitivities ex-ceeding some λ=15000 [19]), but most of them imply animportant drawback in terms of simplicity, making themless attractive than the original technique. This is the rea-son there is still a very active search in this domain; a

search that is also motivated by the inaccuracy of themeasurements justifies the ongoing work since even forreference materials such as CS2 and fused silica a greatdispersion is found between the experimentally derivednonlinear parameters [20].

We propose another variant of Z scan, called “bary-scan,” filling two important requirements: (i) global sim-plicity of the original technique, by keeping unchangedthe basic Z-scan hypotheses and overall scheme, and(ii) increased sensitivity by changing the detection sys-tem. The usual photodiode is indeed replaced by a posi-tion sensitive detector (PSD) (see Fig. 1) known for itsnanometer scale resolution [21,22].

The trick lies in the way to transform the focusing (ordefocusing) effect induced by the nonlinearity into a dis-placement of the beam centroid, which does not occur fora pure symmetrical lensing effect. This function isachieved by a standard razor blade set close to the PSDand truncating half of the probe beam. It is then obviousthat an increase (or a decrease) of the beam size changesthe position of the beam barycenter on the PSD (Fig. 2).

Relation (1) gives the relation between the barycenterposition B and the knife edge position a relative to thecenter of the beam:

B ¼ 1ffiffiffiffiffi2π

pW exp

�−

2a2

W2

��1 − erf

�a

ffiffi2

pW

�� ; ð1Þ

Fig. 1. (Color online) Principle of the baryscan technique.

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0146-9592/11/081401-03$15.00/0 © 2011 Optical Society of America

whereW is the beamwaist radius on the PSD. For a givenvalue of parameter a, B depends only on W . More speci-fically, when the knife edge is positioned exactly in themiddle of the beam (a ¼ 0), relation (1) gives B ¼ð1= ffiffiffiffiffi

2πp ÞW , which means that the barycenter position

is directly proportional to the beam radius. As a PSDcan measure nanometric displacements, the PSD asso-ciated with the knife edge is able here to give the sizeof the beam with a high accuracy.In the standard Z scan experiment [6], such measure-

ment is performed via the transmission of a circular aper-ture, and this transmission, making some assumptions, isgiven by the equation

T ¼ 1þ 4xΔϕ0

ð1þ x2Þð9þ x2Þ ; ð2Þ

where T is the normalized transmission (the transmissionwith lensing effect divided by the one without lensing ef-fect), x ¼ z=z0, where z0 is the Rayleigh range of the fo-cused beam, x ¼ 0 denotes the position of the focal planeof the lens L and ΔΦ0 the value of the on-axis nonlinearphase shift.Since in our baryscan experiment we are making the

same kind of assumptions as for the Z scan, i.e., a samplethickness that is smaller than z0 and weak nonlinear ef-fects, the same equation can be used. From relations (1)and (2), the evolution of the barycenter position BðxÞthroughout the sample translation thus can be written as

BðxÞ ¼ B0

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

1þ 4xΔϕ0

ð9þx2Þð1þx2Þ

vuut ; ð3Þ

where B0 is the barycentric position without lensing ef-fect. The obtained shape is very similar to the one usuallyplotted in a Z-scan experiment: a curve presenting a peakand a valley. Namely, the baryscan technique keeps atleast one important advantage that characterizes theZ-scan one, i.e., its ability to give at a glance the signof the nonlinear effect. Indeed, a positive (respectivelynegative) lensing effect leads to a curve presenting apeak then a valley (respectively a valley and a peak)as z is increasing. The presence of a square root, how-ever, makes the curve no longer symmetric and the valleyis less deep than the peak (for a positive lensing effect).Important experimental parameters like Rayleigh

range z0 [Eq. (4)] and ΔΦ0 [Eq. (5)] can be derived in

a very simple analytical way. z0 is given, as in thestandard Z-scan theory, by

z0 ¼ 0:582Δz; ð4Þwhere Δz is the distance between peak and valley posi-tions. Note that it is exactly the same expression than inthe Z-scan theory. Moreover,

Δϕ0 ¼ð9þ x2Þð1þ x2Þ

�B2valley

B2peak

− 1

�

4

�xpeak −

B2valley

B2peak

xpeak

� ; ð5Þ

where xpeak (respectively xvalley) and Bpeak (respectivelyBvalley) are the positions of the sample and of the bary-center corresponding to the peak (respectively the val-ley). The fit of the experimental curve with Eq. (3) alsoleads directly to these values.

It is worth noting that a knife edge position exactly trun-cating half of the beam is not necessary, but it is the mostsensitive position considering ΔB measurements. In or-der to estimate the gain in terms of sensitivity, the mostimportant point is the PSD resolution. Considering thesmallest barycenter displacement observable by a stan-dard PSD, the baryscan sensitivity should reach at leastλ=5:104, which represents one of the highest improve-ments which can be performed so far.

The experimental validation of this new technique wasperformed by measuring the pump-induced electronic re-fractive index change (e-RIC) [3], which results from theexcitation of the Cr3þ ions in ruby (Cr3þ:Al2O3). This wasperformed with this particular material because Z-scanmeasurements have been already reported in the pastby several authors [23], and it appears now as a referencematerial. The pump-induced e-RIC, which is measuredwith this material, is due to a pseudononlinear effect,which is usually assigned to a variation of the polarizabil-ity Δαp between the excited and ground states of the ac-tive ions in the laser material [24].

The ruby crystal (the same as in [23]) is pumped with agreen and CW solid-state laser (λ ¼ 532 nm, diode-pumpedand intracavity frequency-doubledNd:YVO4 laserfromCoherent, Inc.) having aM2 very close to 1. Thebeamis focused with a converging lens, and the PSD (ThorlabsPSDM4) is set in the far field. The translation of the samplearound the focal plane could be performed in a range of250mm with a resolution of 5 μm. The knife edge ismounted as close as possible to the detector sensitive areain order to limit the near-field diffraction effects. The low-est pumppower leading to a goodbaryscan signalwas lessthan 3mW, while it was above 10mW by using the stan-dard Z-scan technique, as reported in [23]. This is a firstdemonstration of the sensitivity enhancement brought bythe baryscan technique, since the focusing conditionswere the same in both cases. An experimental curve isshown in Fig. 3.

This curve is nicely fitted with the above analytical ex-pressions, and a Δαp value of about 2:1 × 10−25 cm3 wasderived by using an expression given in [17,23]. This isvery close to the 2:2 × 10−25 cm3 value, which is derivedby using the standard Z-scan technique. It definitely con-firms the reliability of the baryscan method.

Fig. 2. (Color online) Evolution of the barycentric position Bof a truncated beam with its size. NL, nonlinear.

1402 OPTICS LETTERS / Vol. 36, No. 8 / April 15, 2011

Now, the technique needs to be investigated in minutedetail in order to go further than this feasibility study andthus to approach the expected theoretical sensitivity.Modulated pumping coupled with a synchronized detec-tion is recommended instead of a rough averaging. Notethat the sample quality can impose to monitor in a firstpass the position of the barycenter without razor blade inorder to remove parasitic effects.To summarize, the main advantage of the baryscan

technique compared to the standard Z scan and its nu-merous variants lies in its improved sensitivity and inthe fact that this sensitivity improvement is not subjectto artifacts linked to a normalization process [13,25]. Itremains a very practical technique. It keeps all the advan-tages of the standard Z-scan technique: a very simple set-up, fully analytical formulas without any numericalmodel to be implemented, and all the values of interestand the sign of the nonlinear effect being deduced fromthe peak and valley relative positions.In the end, in the particular case of e-RIC measure-

ments, baryscan also provides a signal that does not needto be normalized by the absorption of the medium.

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Fig. 3. (Color online) Baryscan curve for ruby.

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