OPTICAL TRANSISTORS WITH NEGATIVE FEEDBACK

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OPTICAL TRANSISTORS WITH NEGATIVE FEEDBACK

P. Mandel, S. Smith

To cite this version:

P. Mandel, S. Smith. OPTICAL TRANSISTORS WITH NEGATIVE FEEDBACK. Journal de

Physique Colloques, 1988, 49 (C2), pp.C2-19-C2-22. �10.1051/jphyscol:1988205�. �jpa-00227604�

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JOURNAL DE PHYSIQUE

Colloque C2, Supplgment au n06, Tome

49,

juin

1988

OPTICAL TRANSISTORS WITH NEGATIVE FEEDBACK

P. MANDEL and S.D.

SMITH*

Universite Libre de Bruxelles, Campus Plaine, CP 231, B-1050 Bruxelles, Belgium

* ~ e p a r t m e n t of Physics, Heriot-Watt University, Riccarton, GB-Edinburgh EX14 4AS, Scotland, Great-Britain

Resum6 - Nous proposons de renvoyer le faisceau reflechi par un transistor optique pour induire une stabilisation par la creation d'une boucle de retroaction negative.

Nous montrons theoriquement que le systeme resultant est moin; sensible aux fluctuations du bruit.

Abstract

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We propose to feed back the beam reflected by an optical transistor to provide a stabilising negative feedback loop. We demonstrate theoretically that the resulting device is less sensitive to noise fluctuations.

I -

INTRODUCTION

The optical transistor is likely to be one of the tools for optical signal processing for the same reasons that make the electronic transistor so useful in electronic signal processing.

This leads directly to a difficulty since the transistor will undiscriminatingly amplify the input signal as well as any noise, in particular the unavoidable fluctuations of the input beam. In this paper we propose a solution to reduce the sensitivity of the optical transistor by exploiting the optical nature of the device. More precisely we propose to feed back the reflected beam into the transistor. This should create a negative feedback loop for the following reason. In the transistor mode of operation, a small increase in the incident field will lead to an increase of the cavity intensity and therefore an increase in the transmitted intensity. Consequently the reflected intensity will decrease. Thus if we add to the input intensity the reflected intensity and consider the sum of these two beams as the holding intensity, a fluctuation of the input intensity will lead to a smaller variation of the holding intensity and therefore to an increased stability of the transistor. There is of course a trade-off since obviously the gain of the transistor will also have been reduced in this process. In this paper we analyse a simple model of an optical transistor to determine quantitatively the influence of the feed-back.

2 - THE OPTICAL TRANSISTOR WITHOUT FEEDBACK

We consider a nonlinear material in a Fabry-Perot resonator. This system is described by the Airy formulae :

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1988205

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C2-20 JOURNAL

DE

PHYSIQUE

The intensity which reaches the front face of the transistor is Ih, whereas I and It are the reflected and transmitted intensities, respectively. The incident light beam is monochromatic with wavelength A . The cavity has a width L and a finesse F-~R/(~-R)~ in terms of the reflec- tivity R of the Fabry-Perot mirrors. The nonlinear medium is characterised by a refraction index n-n +n I in terms of the cavity intensity I -I (l+R)/(l-R). Finally we assume that the

0 2 c c t

holding beam is nearly normal to the Fabry-Perot so that the influence of the incidence angle can be neglected. When the system is operating near a resonance, we may approximate the sine function in the Airy formula by its argument. Defining a normalised intensity J and a normalised cavity-field detuning 6 through

the approximate relation between the transmitted and the holding intensity becomes

2 2

The system displays optical bistability for 6 2 3 and a transistor characteristics for 6 5 3.

In the transistor domain, the point of maximum slope has coordinates

and the maximum =lope is given by

3

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OPTICAL TRANSISTOR WITH COLINEAR FEEDBACK

Let us modify the set-up characterised in the previous paragraph by using mirrors to redirect the reflected beam back into the Fabry-Perot cavity. Two restrictions will be made: (i)before the reflected beam is fed back to the device, it goes through an hrrdnuator which reduces its intensity by a factor a with 0 5 a 5 1; (ii)the true incident beam (i.e. the external source) and the back-reflected beam are combined into a single beam which becomes the new holding beam: I =I +a1 Using Eq.(l) this leads directly to the relations:

h i r'

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Thus the device will behave as a usual Fabry-Perotbut with an effective finesse F1=(l-a)FsF.

Thus this set-up realises an external control of the finesse.

4

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OPTICAL TRANSISTOR WITH OBLIOUE FEEDBACK

Again we consider the previous set-up but this time the reflected beam is fed back onto the device through an incidence angle which differs from the incidence angle. Thus in this situa- tion two beams interact with the nonlinear material. There are now two transmitted fields, one in the direction of the incident beam (I ) and one in the direction of the back-

it reflected beam (I ) . These intensities are given by

rt

The main difference is that there are two beams in the cavity and therefore in first ap- proximation the refraction index becomes

=~I~+;~I~,(I+R)/(~-R)

where we have introduced an effective field-induced refraction index

z2

^through

Obviously the dependence of the transmitted intensity Iit on the true input intensity Ii is much more complex than in the case without feedback. When the device is operated near a resonance, Eq.(6) can be simplified to give the analog of Eq.(4) for the transistor with feedback:

This last equation leads directly to the algebraic equation:

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JOURNAL DE PHYSIQUE

W a

0 m

I

0. B

B. 0 INPUT INTENSITY 3.8

7'B

W . .

a

0 -1 m

The four figures show how the slope of the transistor varies with increasing feedback for +1.6. This slope is a measure of the transistor gain at least at low gain values. The effect of the negative feedback loop is very clearly displayed by the progressive emergence of a small domain at the right of the peak where the slope of the transistor is nearly a constant.

In this domain the gain is reduced but the variations of the output beam due to the fluctuations of the input beam are aLsc reduced.

ACKNOWLEDGMENTS

This research was supported by a grant of the European commision.

B.B INPUT INTENSITY 3 . 0 B.O INPUT INTENSITY 3.E

alpha=B.BB 3.8

-

alpha=B.SB

I

w - a

0 -1 m -

B. B

B . B . I ~ ~ G ~ S C ~ I '