Subnanosecond pulse duration measurements by noncollinear second harmonic generation

Volume 38, number 5,6

OPTICS COMMUNICATIONS

1 September 1981

SUBNANOSECOND PULSE DURATION MEASUREMENTS BY NONCOLLINEAR SECOND HARMONIC GENERATION S.M. SALTIEL, S.D. SAVOV, I.V. TOMOV Faculty of Physics, Sofia University, BG-1126 Sofia, Bulgaria and

L.S. TELEGIN Faculty of Physics, Moscow University, 11 7234 Moscow, USSR

Received 9 February 1981

A new scheme for measuring the pulse duration using noncollinear second harmonic generation is proposed. Correlation functions of single subnanosecond pulses may be recorded with short crystals by introducing a proper delay. Pulsewidth in the 100 ps-1 ns range was measured using this technique.

In the past decade the development of ultrashort pulse generation techniques has been accompanied by a corresponding development of the methods for pulse duration measurements. Two methods of short pulse duration measurements have been most frequently used - n o n l i n e a r autocorrelation techniques and the streak camera [ 1]. The streak cameras commercially available are expensive; for this reason the autocorrelation technique employing either two-photon fluorescence or second harmonic generation has been widely used. More recently, it was noticed that using noncollinear second harmonic generation, the autocorrelation function of a single ultrashort pulse may be recorded in a single shot [ 2 - 4 ] . Both two-photon fluorescence and second harmonic techniques have been extensively studied with respect to the shortest pulse duration measured. However pulses o f duration in the order of tens and hundreds o f picoseconds have been used in many applications. Such pulses are produced in the most actively mode-locked pulse lasers [5]. When measuring laser pulses o f 5 0 - 5 0 0 ps duration using autocorrelation technique, some difficulties arise because of the long tracks to be recorded. We present here the results of a study of the noncollinear second harmonic (NSH) generation for single subnanosecond pulse duration measurements. The

basic idea of the NSH method is outlined in fig. la. The expanded laser light beam is divided into two beams which are directed onto the nonlinear crystal so that the phase matching condition k 1 + k 1 = k 2 should hold. For sufficiently large diameters (D) of the incoming beams the intensity distribution of the second harmonic in the x-direction represents the

'C

\

m .--~?

a)

6121(~1

b)

Fig. 1. a) Schematic of the noncollinear second harmonic pulsewidth measurement technique. NLC: nonlinear crystal, ra(X): delay in a from of Michelson echelon, b) Modification of second harmonic order correlation function G(2)(z) resulting from Michelson echelon delay: solid line, and G(2)(r) without delay: dotted line. The ratio between the intensities l m and Iq measured by ruth and qth photodiodes in this two cases determine R 2 and R I, respectively.

0 0 3 0 - - 4 0 1 8 / 8 1 / 0 0 0 0 - 0 0 0 0 / $ 02.50 © North-Holland Publishing Company

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autocorrelation function of the pump laser pulse G(2)(r(x)) [3,6] . By measuring the spatial width (S) of the autocorrelation trace, the pulse duration rp (FWHM) can be derived from the relation S sin (Y 7P =Y-

(1)

>

where cyis half of the angle comprised between the interacting beams outside the crystal, c is light velocity and y is a form factor of the pulse. For a gaussian pulse y = & and for other pulse shapes, these factors are given in [7]. To measure a pulsewidth rp one needs a nonlinear crystal with L > S = rpc/y sin (Y length along the x-axis. Fig. 2 presents the maximum pulsewidth which can be measured with a 1 cm long crystal at different wavelengths and 90” phase matching in KDP and LiIO,. Thus for example, to measure a 300 ps pulse at h = 1.06 pm, 10 cm long LiI03 crystal is required. For the same pulsewidth in the visible range (X = 0.55 pm) a 50 cm long KDP is necessary. To measure longer pulses, we have to record long autocorrelation tracks with short crystals. This can be done by introducing a proper delay function ra(x) in one of the light beams. Depending on the type of ra(x), different modifications of the autocorrelation function Gc2)(r) may be achieved. A very useful function ra(x) may be produced by a trans-

1 September

mission Michelson echelon as shown in fig. ia, which will modify the corelation curve as shown in fig. 1b. In such a scheme only parts of the autocorrelation function are obviously recorded but by choosing properly ra(_x), the points recorded may be selected from desirable parts of GC2)(T) and thus the required information may be obtained. To elucidate the above, we shall consider a gaussian pump pulse shape: AI(r) =A0 exp(-t2/2T2)

(2)

where T = rp/2m. When ra(x) = 0, the second harmonic the x-axis is given by: Z(x) =Z(O)

exp[-

2(+&?r].

Zk =I,

1.0

2.0

20 , yn

Fig. 2. The maximum pulsewidth which can be measured with LiIO, and KDP versus fundamental wavelength.

444

on

(3)

,

exp[-2(*fk2]

(4)

where I, is the intensity at the first photodiode located on the point with a zero delay, and AX is the space between two neighbouring photodiodes. The pulse duration 7p may be derived from the measured ratio of the second harmonic intensity which is recorded at any two photodiodes. If we define/, /Iq =R1,(m
c2 1

FUNDAMENTAL WAVELENGTH

intensity

It should be noted that a point xi on the x-axis corresponds to a delay rj = 2(x,jc)sin cr. Let us assume that the second harmonic intensity along x is measured by n equally spaced photodiodes. We consider I(x) in fig. 1 only forx > 0. The intensity at the kth photodiode is

-q2)21n2 rp = 2 (m2 [ lnR,

I

1981

112axsina.

(5)

is desirable and this implies In practice R 1 - 1.5-2.5 that for longer pulses a bigger separation between the mth and qth photodiodes is necessary. Let one of the incident beams pass a Michelson echelon as shown in fig. la, and the photodiode separation Ax be such that every photodiode is getting a signal which experiences a different delay. We assume that the delay is 6, = (k - 1)8, for the kth photodiode. Then, the second harmonic intensity on the

kth photodiode

is: sin (Yt c00)2 k2

exp - k1(2Ax I

fk=Il

1 September 1981

OPTICS COMMUNICATIONS

Volume 38, number 5,6

1 (6) .

In this case, the ratio of the second harmonic intensity, recorded by the mth and qth photodiodes will differ frornRl and (Im/Iq)M =R, (fig. lb). The pulsewidth is derived from: l/2

“1,2::,2f”‘]

(2fJx

rp = [

sin 0~ t &I,).

(7)

2

Comparing (5) and (7), we find 2

lnR, -----Z In R 1

1 + _--m?_oL

(

2 Ax sin o 1

‘3)

By selecting a proper delay 8, of the Michelson echelon, we can attain R 2 > R 1 which implies that the delay introduced is equivalent to a “squeezing” of the correlation function (see fig. lb). It should be noted that every pair of photodiodes (m, q) must produce the same pulsewidth rp. This is a simple way to verify the gaussian pulse shape. For other pulse shapes, similar expressions for 7P may be derived. To demonstrate experimentally this multistep delay function technique we have used the set-up shown in fig. 4 and which is further desribed in details. A simple echelon, consisting of a stack of four parallel glass substrates each 15 mm thick (thus B0 = 16.6 ps), was constructed. The photograph and the corresponding microdensitogram of the second harmonic distribution along the x-axis are shown in fig. 3. The irregular modulation of the second harmonic results from the poorly polished crystal surfaces. Taking into account the reflection losses in the stack and echelon delays several points from autocorrelation function G(2)(r) have been reproduced as shown in fig. 3. In the same figure the dotted curve represents the theoretical autocorrelation function of a gaussian pulse with 166 ps (FWHM) pulsewidth. The experimental points fit very well on the calculated curve. The pulsewidth derived from eq. (7) is rp = 160 ps 5 6%. An interesting conclusion which may be derived from the results given above is that if the pulse shape has preserved from shot to shot, only two photodiodes should be required to measure the pulsewidth. In this

10

20

30

x. mm

b) Fig. 3. Experimental picture taken with a stack of 4 glass substrates. a) Photograph of second harmonic trace. b) Microdensitogram of the picture above. The dotted curve represents the theoretical COrrehtiOn function of a gaUSSian pulse with 7p = 166 ps. The points mark the reproduced correlation function from the recorded second harmonic intensity.

case a simple delay r, may be used instead of the Michelson echelon. Eq. (6) reduces to:

f2=Il

- k2

exp

(2 Ax sin cy+ u~)~]

[

The pulsewidth 11II, : rp =

(

(9)

is derived from the measured ratio

2 Ax sin cy C

.

+&gg2.

(10)

The proposed scheme was studied with an arrangement shown in fig. 4. One half of the expanded light beam is directed on the nonlinear crystal at the proper angle cr. The second half of the beam after reflection from mirror M is incident on the crystal at the same angle. Without additional delays 7, and 70 in the set445

Volume 38, number 5,6

OPTICS COMMUNICATIONS

1 September 1981

I

L NLC

Fig. 5. Schematic of the set-up from fig. 4 employing noncollinear second harmonic generation on reflection.

Fig. 4. Experimental TV:additional delay, nonlinear crystal, F: element photodiode,

set-up in pulse duration measurements; 7,~: zero point adjustment delay, NLC: filter, M: aluminium mirror, PD: two-

A/D: analog-to-digital convertor.

up, the zero delay in the autocorrelation

function Gc2)(0) corresponds to the point of conjunction of the mirror M and,the nonlinear crystal NLC. Only half of the autocorrelation function Gc2)(7) is recorded in this case. However, since the second order autocorrelation function is symmetrical with respect to the zero point, the total information is available from the recorded portion. By introducing a constant delay 70, a zero point can be translated along the x-axis and if a short pulse was measured, the whole autocorrelation function would be recorded. We have used this scheme to measure experimentally the pulsewidth of the output of an actively mode-locked and Q-switched Nd : YAG laser [8,9]. By changing the depth of modulation the pulsewidth was varied in the 100 ps-I ns range. A 2.3 cm long and 4 mm thick LiI03 crystal, cut for noncollinear phase matching, was used. The beam crossing angle inside the crystal was 36”30’. Plane parallel glass substrates were used as 7, and 70 delays. In the cases where a longer delay 7, was required, a Nd : glass rod was used. The second harmonic from the nonlinear crystal, after passing the filter F, 446

is blocked by a screen A with two holes. A lens L directs the transmitted light to a mcnolithic twoelement silicon photodiode (Centronic LD2-ST). The signals from the photodiode after analog-to-digital conversion are fed either to counters or to a minicomputer. Details of these measurements are presented in [9]. The scheme described for autocorrelation pulse measurement may be used to normalize directly the experimental results in every shot and used further for data processing. In conclusion, we shall note that the developed scheme is also convenient for measuring the shortest pulses. The delay 7, is not required in this case. The scheme has some advantages over systems reported in the literature since no dispersive elements such as prisms are used. The scheme reported can also be used to extend the spectral range of measurements. By replacing the nonlinear crystal with a nonlinear mirror, a noncollinear second harmonic can be generated upon reflection [lo], Fig. 5 represents a possible implementation of such a scheme. The second order nonlinear susceptibility of semiconductors such as GaAs, Te, Se are 103-lo4 times higher than that of KDP and this will provide a detectable second harmonic signal. The authors would like to thank Prof. K. Stamenov for supporting this work and L. Detchkov for his participation in the initial stage of the experiment.

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References [1] D.J. Bradley and G.A.C. New, Proc. IEEE 62 (1974) 313. [2] G.V. Krivoshtshekov, V.I. Stroganov, in: Nelineynie processi v optike (Nauka, Novosibirsk, 1970). [3] J. Janszky, G. Korradi and R.N. Gyuzalian, Optics Comm. 23 (1977) 293; R.N. Guyzalian, S.B. Sogomonian and Z.G. Horvath, Opncs Comm. 29 (1979) 239. [4] A.P. Sukhorykov, A.K. Sukhorukova, L.S. Telegin and I.B. Yankina, Xth Allunion Conf. on Coherent and nonlinear optics, Abstracts, p. 159, Oct. 1980, Kiev. [5 ] I.V. Tomov, R. Fedosejevs and M.C. Richardson, Kvant. Electr. 7 (1980) 1381.

1 September 1981

[6] C. Kolmeder, W. Zinth and W. Kaiser, Optics Comm. 30 (1979) 453. [7] K.L. Sala, G.A. Kenney-Wallace and G.E. Hall, IEEE J. Quantum Electron. QE-16 (1980) 990. [8] S.D. Savoy, S.M. Saltiel and I.V. Tomov, 1980 European Conf. on Optical systems and applications, Abstracts, Utrecht (to be published in SPIE 1980). In all equations in this reference sin a should be replaced with 2 sin c~. [91 S.D. Savoy, S.M. Saltiel and I.V. Tomov, Opt. Laser Technol. (to be published). [10] I.V. Tomov, Optics Comm. 10 (1974) 154.

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