Change in the shape of frequency-modulated light

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Change in the shape of frequency-modulated light pulses during amplification

This content has been downloaded from IOPscience. Please scroll down to see the full text. 1976 Sov. J. Quantum Electron. 6 699 (http://iopscience.iop.org/0049-1748/6/6/A13) View the table of contents for this issue, or go to the journal homepage for more

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2081 (1974). N. B. Baranova, N. E. Bykovskii, B. Ya. Zel'dovich, and Yu. V. Senatskii, Kvantovaya Elektron. (Moscow) 1, 2435, 2450 (1974) [Sov. J. Quantum Electron. 4, 1354, 1362 (1975)]. 9 D. C. Brown, Appl. Opt. 12, 2215 (1973). 10 G. Dube and N. L. Boling, Appl. Opt. 13, 699 (1974). u Yu. A. Anan'ev, A. A. Mak, and V. M. Sedov, Zh. Eksp. Teor. Fiz. 48, 7 (1965) [Sov. Phys.-JETP 21, 4 (1965)]. 12 Yu. A. Anan'ev, I. F. Balashov, and A. A. Mak, Dokl. Akad. Nauk SSSR 166, 825 (1966). 8

13

B. I. Stepanov (ed.), Laser Design Methods [in Russian], Nauka i Tekhnika, Minsk (1968). 14 J. A. Fleck Jr, J. Appl. Phys. 36, 1301 (1965). 1S B. A. Ermakov, A. V. Lykin, and A. A. Mak, Opt. Spektrosk. 18, 353 (1965) [Opt. Spectrosc. (USSR) 18, 201 (1965)]. 16 N. N. Rozanov, Opt. Spektrosk. 39, 724 (1975) [Opt. Spectrosc. (USSR) 39, 409 (1975)]. 17 J. A. Glaze, S. Guch, andj. B. Trenholme, Appl. Opt. 13, 2808 (1974). Translated by A. Tybulewicz

Change in the shape of frequency-modulated light pulses during amplification E. G. Lariontsev and V. N. Serkin Scientific-Research Institute of Nuclear Physics at the M. V. Lomonosov State University, Moscow (Submitted October 1, 1975; resubmitted December 30, 1975) Kvantovaya Elektron. (Moscow) 3, 1290-1294 (June 1976) An analysis is made of the propagation of a frequency-modulated light pulse in a linearly amplifying medium with an inhomogeneously broadened gain profile. It is shown that a pulse can be compressed considerably during amplification. Conditions are established under which strong distortions of the pulse shape may result in its splitting. An analysis is made of the influence of the phase self-modulation of radiation on the shape of ultrashort light pulses in oscillators and amplifiers. PACS numbers: 42.10.—s

Studies of the distortion of the shape and spectrum of frequency-modulated light pulses propagating in a resonantly amplifying medium have been reported in a fairly large number of papers.1"8 Such distortions appear in the course of amplification and generation of ultrashort light pulses.7'8 Studies described in Refs. 1 and 2 are concerned with the propagation of coherent frequencymodulated pulses in a linearly amplifying medium. Moreover, consideration is given to noncoherent interaction of pulses with an amplifying medium in the case of phase self-modulation resulting from the nonlinearity of the refractive index of the medium.3"8 As a rule, studies of this kind are based on results obtained by numerical solutions. We shall derive analytic solutions describing the propagation of a frequency-modulated pulse in a linearly amplifying medium with an inhomogeneously broadened gain profile. We shall consider the possibility of compression of light pulses. We shall determine the conditions under which a strong distortion of the pulse shape, resulting in splitting, may occur. Propagation of a frequency-modulated light pulse in an amplifying medium modulates the gain because of the frequency scanning relative to the center of the gain profile. This changes the pulse shape. Moreover, dispersion of the real part of the permittivity, associated with the resonant transition, alters the phase modulation itself and this is also accompanied by a change in the pulse shape. Propagation of a plane light wave in an amplifying medium (0 «# « I ) can be described by the following equation: 699

Sov. J. Quantum Electron., Vol. 6, No. 6, June 1976

d£

(1)

dE

Here, E = E(x, t) e «»t—kx]} + complex conjugate

(2)

Iri the case of an inhomogeneously broadened line with a Gaussian distribution function gfaq— fi)=g-(0)exp[- (co0 - fi)2/Ag] the polarization is related to the field by P= j P (x, t, O)o)g((o 0 -Q)do) 0 ;

where A = o> - o> 0 ; o>0 is the frequency of a transition in an individual atom; nz is the square of the matrix element of the dipole moments; Tz is the relaxation time of the polarization. Applying the Fourier transformation, we can write the solution of Eq. (1) in the form ^ ( A : ' / ) = Wi E ( A '° ) e X P

V (I) z'^dl- ikr] at,

J

(4)

where (0)!H; r=t—xlc; V (1) = exp [— S/r 2 — A->|V4 —1(01— Q)|].

We shall consider a pulse with linear frequency modulation u>(t) = u + (du/Bt)t = v + 2fit. We shall assume that the following conditions are satisfied during the propagatipn of this pulse: 1) the medium is linearly amplifying (the saturation gain is low); 2) the gain profile is inCopyright © 1976 American Institute of Physics

699

~E (X, 0 - V £«*» V Y-

exp f - VT°A§ (£ L

\

nb

(8)

0

where

P

FIG. 1. Changes in the shape of a frequency-modulated pulse during its propagation in a linearly amplifying medium with ~ 3xl012 sec"1 and al = l: a) incident pulse T0 = 10~ sec;b) evolution of a pulse for [(da)Att)/(T0/Ao)] = 6 = 10;, c), d) change in pulse shape for 6 = 100, calculated using Eqs. (6) and (8) (c and d, respectively); 4) evolution of a pulse for 6 = 300.

homogeneously broadened (^0»T~zl); 3) the pulses are sufficiently long (T O »AJ I ); 4) the phase modulation does not change significantly during the propagation of the pulse, which is valid if 4al (dia/dt)2 « AJ,

(5)

where at = 4i72fe{i2lV(0)Jg-(0)/7z is the gain factor for a monochromatic wave at the line center. In this case, Eq. (1) yields the following expression for the field amplitude at the exit from the medium; £ (1,1) = £ (0, t — //c)exp (a/ exp {— [a, (t— lie) — QP/AJ}}.

(6)

It follows from Eq. (6) that the gain of the medium depends on time and has its maximum at the moment when the frequency passes through the center of the gain profile [o>(£) = ft]. This may compress a pulse and produce a narrow intense peak against its background (Fig. 1). Such a peak forms if during the passage of the pulse the frequency o>(£) changes by an amount greater than or comparable with the width of the gain profile. In the case of a Gaussian pulse £(0, t) = E0exp(- tz/2r^> of frequency u(t) passing through the center of the line profile at the moment when the field has its maximum value [u>(0) = JJ], we obtain the following expression for the compression p of a pulse: p =

(7)

Here, 6 = (dw/rf^)(To/A0) is the ratio of the frequency shift during the passage of a pulse to the width of the gain line. Thus, a large value of 6 is required for significant compression of a pulse. However, when du/dt is increased, the condition (5) is no longer obeyed and we have to allow for the change in the phase modulation during pulse propagation. We shall obtain an exact solution by considering in the case when the field frequency coincides with the center of the gain profile [oj(0) = n]. In this case we can obtain the following expression from Eq. (4) for the complex field amplitude E(x, t): 700

Sov. J. Quantum Electron., Vol. 6, No. 6, June 1976

= ( 0 , *) -const;

fl)--^

arctg

The expression (8) describes the change in the shape of a pulse l(x, t) = I E(x, t) 12 and phase modulation /rf£)2 « Aj the distortion of the pulse shape is described well by Eq. (6). In the range 6> 1, the pulse is compressed and a narrow intense peak forms against the wide pedestal (Fig. 1) and the duration of this peak is given by Eq. (7), Beginning from values 4al(d = 200 nm. If the half-width of the gain profile is A 0 =13 nm, we find that 6 = Au/A 0 »l. Under these conditions it follows from the above discussion that the shape of ultrashort light pulses is strongly distorted in an amplifying medium.

in their pure form, i. e., not masked by self-focusing, because the frequency shift during a pulse can then be controlled within a wide range by altering the optical waveguide (fiber) length.

Our investigation of the shape of a frequency-modulated pulse traveling in an amplifying medium ignores self-focusing. This can be done if the length of the amplifying medium is much less than the self-focusing length. However, a considerable change in the pulse shape due to frequency modulation occurs if 6 = Aw/A 0 S1 (the frequency shift during the passage of a pulse should be greater than the width of the gain profile). If the frequency modulation of a pulse occurs in the amplifying medium itself due to self-modulation, then in the case of a medium with a sufficiently wide gain profile (for example, in the case of neodymium-glass amplifiers) the second condition is in conflict with the first and the pulse distortion occurs primarily as a result of self-focusing. All conditions can be satisfied simultaneously if the frequency modulation occurs before entry into the amplifying medium (for example, if it is due to external phase modulators). It may be convenient to use a system for preliminary scanning of frequency in optical waveguides9 followed by pulse amplification. In this case, the above effects may be observed

*M. D. Crisp, Appl. Opt. 11, 1124 (1972). \. A. Poluektov, Yu. M. Popov, and V. S. Roitberg, Kvantovaya Elektron. (Moscow) 1, 757 (1974) [Sov. J. Quantum Electron. 4, 423 (1974)1. 3 J. A. Fleck Jr and R. L. Carman, Appl. Phys. Lett. 22, 546 (1973). 4 R. 0. Eckardt, C. H. Lee, and J. N. Bradford, Opto-electroniCs 6, 67 (1974). 5 A. N. Zherikhin, P. G. Kryukov, Yu. A. Matveets, and S. V. fhekalin, Kvantovaya Elektron. (Moscow) 1, 956 (1974) [Sov,. J. Quantum Electron. 4, 525 (1974)]. 6 R. Aj. Fisher and W. K. Bischel, IEEE J. Quantum Electron. QE-flO, 747 (1974). 7 V. V. Korobkin, A. A. Malyutin, and A . M . Prokhorov, Pis'ma Zh. Eksp. Teor. Fiz. 12, 216 (1970) [JETP Lett. 12, 150 (1970)]. 8 P. G. Kryukov, Yu. A. Matveets, Yu. V. Senatskii, A. I. Fedt>simov, S. V. Chekalin, and O. B. Shatberashvili, Kvantovaya Elektron. (Moscow) No. 2(14), 102 (1973) [Sov. J. Quantum Electron. 3, 161 (1973)]. 9 V. N. Lugovol, Pis'ma Zh. Eksp. Teor. Fiz. 22, 416 (1975) [JETP Lett. 22, 200 (1975)]. Translated by A. Bryl

Visualization of an ultraviolet image with the aid of a spatial-temporal electro-optic light modulator I. S. Zakharov, P. A. Petukhov, V. M. Skorikov, I. M. JEfimenko, V. M. Andrianov, and P. A. Akinfiev N. S. Kurnakov Institute of General and Inorganic Chemistry, Moscow (Submitted January 6, 1975) Kvantovaya Elektron. (Moscow) 3, 1295-1298 (June 1976) The results are reported of experimental investigations of the use of bismuth germanate single crystals in spatial and temporal modulation of light. Such modulation was employed in the visualization of an ultraviolet image. PACS numbers: 42.30.Lr

Spatial-temporal light modulators are attracting a considerable interest. Such modulators may find extensive applications in optical instrument construction as major elements of analog optical systems, holographic memories, optical information processing systems, etc. Morevover, some of these modulators can transform an image from one part of a spectrum to another and at the same time amplify the image brightness considerably. This type of modulator includes those utilizing the linear electrooptic (Pockels) effect. The effect can be observed in a number of crystals. Our modulators were made of bismuth germanate (Bi12 GeO20) because this material is photosensitive and is characterized by a linear dependence of the change in the refractive index on the applied voltage. This makes it possible to modulate a polarized light flux. 701

Sov. J. Quantum Electron., Vol. 6, No. 6, June 1976

An ahalyzer can be used to convert such modulated polarization into an amplitude-modulated signal.1-7 The investigated modulators were layer structures with a basic element made of bismuth germanate, which was 450-500 jj, thick and about 20 mm in diameter. A plate of this kind was placed between insulating (dielectric) layers which carried semitransparent conducting electrodes. The bismuth germanate plates were oriented in the (100) plane and the resistivity of the plates was up to 1012 • fi cm. The plates were subjected to mechanical grinding and polishing. The insulator layers were films of organic dielectrics 5-25 /i thick. Semitransparent conducting electrodes Copyright © 1976 American Institute of Physics

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