Deterministic passive mode locking of solidstate lasersOscar Eduardo Martínez and Luis Alfonso Spinelli Citation: Applied Physics Letters 39, 875 (1981); doi: 10.1063/1.92590 View online: http://dx.doi.org/10.1063/1.92590 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/39/11?ver=pdfcov Published by the AIP Publishing Articles you may be interested in 2μm solid-state laser mode-locked by single-layer graphene Appl. Phys. Lett. 102, 013113 (2013); 10.1063/1.4773990 Femtosecond passive mode locking of a solidstate laser by a dispersively balanced nonlinear interferometer Appl. Phys. Lett. 58, 2470 (1991); 10.1063/1.104847 All solidstate cw passively modelocked Ti:sapphire laser using a colored glass filter Appl. Phys. Lett. 57, 229 (1990); 10.1063/1.103724 Perfect mode locking of solidstate lasers by a double passive modulation J. Appl. Phys. 53, 6673 (1982); 10.1063/1.330049 Locking in Multimode SolidState Lasers J. Appl. Phys. 40, 377 (1969); 10.1063/1.1657065

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Deterministic passive mode locking of solid-state lasers Oscar Eduardo Martinez and Luis Alfonso Spinelli CEILAp, CiteJa-Conicet. ZuJriategui y Varela. Villa Martelli 1603. Pda. de Buenos Aires. Argentina

(Received 31 July 1981; accepted for publication 22 September 1981)

An additional passive modulation is inserted in the cavity of a passive mode-locked Nd:glass laser in order to provide the conditions for a complete selectivity of the system. A rate equation approach shows that a stationary condition is reached in which only one pulse of the original fluctuation pattern is left. Computed simulations and experimental results are also shown confirming the theoretical predictions.

PACS numbers: 42.60.By, 42.55.Rz

Passive mode locking of solid-state lasers has provided a simple tool for the generation of powerful picosecond light pulses. Nevertheless, this method has the important draw­back that the quality of the laser output, i.e., the contrast between the most intense pulse and the background radi­ation, has a statistical nature and great effort must be done if one expects to obtain reliable mode-locked pulse trains. 1-3

A theoretical analysis4-6 shows that the saturable ab­

sorber selects the most intense fluctuation peak from the initial noise pattern of the radiation inside the cavity. Other pulses may also be amplified if their initial intensity is close to that of the highest one, and hence the selectivity of the system may not be complete. As it has been shown by New,? saturation of the amplification plays an important role in minimizing the probabilistic behavior of the laser but cannot eliminate it.

In the present letter we describe a new configuration in which a double passive modulation with a saturable absorber (SA) and an electrooptic modulator (EOM) gives rise to a complete selectivity of the most intense pulse providing the ideal conditions for a deterministic mode locking.

The method can be described qualitatively as follows: once the system reaches threshold laser action begins and the EOM inserts an additional loss proportional to the mean power in one round trip in the cavity (Tcav). As the laser power grows, the gain decreases and the smaller pulses, that see more absorption from the SA, come below the threshold first and disappear. Gain will continue to decrease until only one pulse is left in a round trip and hence perfect mode lock­ing has been reached.

Following New 7 a rate equation approach may be done to show the selection process. We will work well above the second threshold, and far from saturating the SA, so that we may write

(1 )

where Un is normalized intensity of the nth fluctuation peak, k = t /Tcav counts the transits inside the cavity, G is the net gain for zero intensity, B is the small-signal absorption of the SA, Au is the additional loss due to the EOM, and u is the mean normalized intensity of the laser radiation in one round trip inside the cavity.

The parameter A is chosen so that in the first stage,

before selectivity begins,

Au>Bu n (2)

and u grows until the net gain approaches zero, that is, the solution tends to

Au = G. (3)

The value of u when this solution is approached de­pends on the pumping rate. When BUn becomes of the order of(G - AU) the second stage proceeds in which the most intense pulse is amplified while the others are attenuated.

Let U 1 be the highest peak of the initial fluctuation and TI its pulse width defined as the width of a rectangular pulse of the same energy and peak power. If the condition

Ln(ll} 3

2

1

A~/~">B ~

o 0 2000 4000

-1

-2

-3

Ln(uJ 4

3

2

0 0

100

-1 ~

-2

-3

-.(

(b) -5

FIG. 1. Numerical simulation of the evolution of the initial noise patterns: The three most intense pulses are shown: (a) with the additional modulation of the EOM and (b) in the conventional mode with the same initial noise pattern and laser parameters.

875 Appl. Phys. Lett. 39(11), 1 December 1981 0003·6951/81/230875-03$00.50 @ 1981 American Institute of Physics 875

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M1 OUTPUT

FIG. 2. Experimental setup: M I is the 100% reflecting mirror contacted with the flowing dye cell DC. M 2 is the 100% reflecting mirror r = I m. LR is the laser rod. PI, and PI, are polarizers. D is the modesecting diaphragm. F is a filter. M 3 is a 95% reflecting mirror. PD is the photodiode of the feedback circuit shown in Fig. 3.

is fulfilled, Eq. (I) will have a stable stationary solution:

G U I = ,

ATJTcav - B (5a)

un =0 forn#l, (5b)

and the additional losses inserted by the EOM would be

rma,=AU=G(I+ I ). ATIITeav - B

(6)

If the maximum losses the EOM can add (Tsat) are smaller than r max but bigger than G [condition imposed by Eq. (3)], the system may also be Qswitched without losing its selectivity. This would provide a third threshold condition. Figure I(a) shows a numerical simulation of the system, where the different stages of the pulse evolution may be easi­ly visualized, only the evolution of the three most intense pulses were drawn. The parameters used were T, = 5 ps, Teav = 5 ns, B = 0.7, A = 2000, G = Ok with e = 5x 10~5, r sat = 0.6, and the number of pulses per round trip N = 1000. The stationary solution is reached at about k = 7000, which corresponds to u, = 0.27 and r rna, = 0.56, so that the system is very close to the third threshold condi­tion. As the laser is pumped far above the second threshold, before the gain saturates the third threshold is reached and giant pulse emission is obtained at about k = 8900.

r--------, I

: EOM I I I I I I I I

iCMI I ~ 1- ____ ~~_.J

FIG. 3. Circuit used for the EOM feedback. R, = 560 n, V, = 1500 V, V, = 200 V. Rc are the power supply internal resistance. C, and C, are low inductance ceramic capacitors acting as voltage sources. Cm is the capacity of the EOM and charging cable.

876 Appl. Phys. Lett., Vol. 39, No. 11, 1 December 1981

FIG. 4. Oscilloscope trace of the laser output: (a) without the EOM feed­back, i.e., in the conventional mode and Ib) with the EOM feedback. The long pulse train of low peak power shows that the system is below the third threshold.

before the gain saturates third threshold is reached and giant pulse emission is obtained at about k = 8900.

In Fig. I(b) the same initial noise pattern was amplified without the EOM, showing a very poor selectivity. Satura­tion of the SA and the amplifying medium, neglected in Eq. (1), were taken into account in the simulation. Further nu­merical computations are being carried out in order to deter­mine the optimal parameters for deterministic mode locking above the third threshold.

The experimental setup used to provide the additional losses is shown in Fig. 2. The laser cavity is the same de­scribed in Ref. 3. A 5% loss in PI, is attenuated by another polarizer Plz, a partially reflecting mirror M 3 and a 1.06-,u filter F, before its incidence on the photodiode. This variable attenuation scheme is used to adjust the parameter A. The photocurrent circulates through the resistor R I' shown in Fig. 3, and produces an additional voltage drop in the EOM (represented as a capacitor Cm). C, and C2 are big capacitors acting as voltage sources. VI is the initial voltage and deter­mines the output coupling of the laser. V2 is the maximum voltage increase that may be delivered by the photodiode as long as

(7)

where i max is the maximum photocurrent. A photodiode SGD-444 from EG&G was used; its rise

O. E. Martinez and L. A. Spinelli 876

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time is less than 10 ns, i max is about 1 A, and the typical breakdown voltage is 500 V. The time constant R ICm should be of the order of Tcav so that no integration of ii over several transits is made. As Cm ~ 20 pF, a value R I = 560 fl gives a low enough time constant and also satisfies condition (7).

In Fig. 4(a) an oscilloscope trace is shown of the laser output in the conventional mode-locking scheme, i.e., with­out the photodiode feedback; giant pulse emission is ob­tained because the laser is far above the second threshold but this gives rise to a very poor selectivity, as it may be seen in the photograph. The detection system was a TRG 105B vacuum photodiode and a Tektronix 7834 storage oscillo­scope with an overall rise time of 1. 7 ns.

Figure 4(b) shows a typical emission when the feedback is used and when the third threshold condition is not satis­fied. The pulse train is much longer and the peak power is about 104 times smaller than in the former case [a 90% at-

877 Appl. Phys. Lett., Vol. 39, No. 11, 1 December 1981

tenuation used in 4(a) was removed for 4(b)]. No pulse width measurement by two photon absorption fluorescence were carried out because of the low output power obtained. When the polarizer PI2 was rotated to change the parameter A the peak output power changed as predicted by Eq. (5). Further experiments are being carried out with different values of A, r sat , and () to determine the third threshold operation range.

The authors would like to thank Dr. F. P. Diodati and M. C. Marconi for their valuable assistance.

tH. Weichel, J. App!. Phys. 44,363511973). 'w. Koechner, Solid State Laser Engineering ISpringer, New York, 1976). 'M. C. Marconi, O. E. Martinez, and F. P. Diodati, Appl. Phys. Lett. 37, 684 (\980).

·P. G. Kryukoy and V. S. LetokhoY, J. Quantum Electron. QE-8, 766 11972).

'8. Ya. ZeI'doyich and T. I. Kuznetsoya, SOY. Phys. Usp. 15,2511972). oW. H. Glenn, J. Quantum Electron. QE-ll, 8 (1975). 7G. H. C. New, Proc. IEEE 67,380 (1979).

O. E. Martinez and L. A. Spinelli 877

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