CA2253271A1

CA2253271A1 - Electro-optical phase modulator with direction-independent pulse response

Info

Publication number: CA2253271A1
Application number: CA 2253271
Authority: CA
Inventors: Gunter Spahlinger; Manjeet S. Ner
Original assignee: Individual
Current assignee: Northrop Grumman Litef GmbH
Priority date: 1996-07-19
Filing date: 1997-07-18
Publication date: 1998-01-29
Also published as: EA199900133A1; EP0912912A1; JP2000515260A; WO1998003895A1; DE19629260C1

Abstract

An electro-optical phase modulator, in particular for use in a fibre-optical gyroscope (FOG), is characterised, as long as the time it takes for the light to make one revolution is made to match the working cycle, in that the same pulse response is ensured in both directions of rotation of the light. For that purpose, the modulation electrodes (13, 14...) are arranged in relation to a common counter-electrode (12) in such a way that the propagation in space and time of the potentials on the modulation electrodes and of the electric fields between the electrodes generates a pulse response which is always symmetrically distributed.

Description

CA 022~3271 1998-10-29 Electro-optical phase modulator with non-directional pulse response The invention relates to an electro-optical phase modulator having an integrated optical waveguide and modulation electrodes disposed on both sides at a constant mutual spacing from the optical axis along the waveguide.

Phase modulators of this category are principally used in fibre-optic Sagnac interferometers which form the actual instrument for measuring rate of rotation in fibre-optic gyroscopes (FOGs), or also as core element in other interferometric measuring devices, for example in Mach-Zehnder interferometers.
However, the complex of problems and set object underlying the invention are to be explained, in the text which follows, with reference to a fibre-optic gyroscope.

CA 022~3271 l99X-10-29 In fibre-optic gyroscopes of modern construction, use is frequently made of an _ntegrated optical chip (IO
chip) which has on the entrance side as a rule an integrated polarizer, and a Y branching and two electrodes of two phase modulators, which electrodes are disposed at equal spacing along the optical axes after the Y branching in a specified configuration, and which phase modulators modulate the two light beams injected into the ends of a fibre coil in opposite directions, in a manner which is explained in greater detail hereinbelow. Various variant embodiments of such phase modulators or digital phase shifters are described in the publications US 5 137 359, US 5 237 629 and US S 400 1~2. An FOG with this type of phase modulator has a sensitivity to disturbance signals scattered into the phase modulator.

The coupling-in of such disturbance signals into the MIOC path (MIOC = modulatins IO chip) including the phase modulator may be analysed as explained hereinbelow.

Disturbance signals which couple into the MIOC path may under specified circumstances generate bias errors. In the text which follows, an investigation is to be carried out as to how periodic disturbance signals act when there is mistuning of the gyroscope scanning cycle as compared with the transit time of the light through the fibre. Besides an increased sensitivity to such couplings-in, a mistuning also gives rise to further disturbing effects such as, for example, increased random walk. However, these effects are not to be investigated here. In order to make it possible for the reader to make himself familiar with the mode of operation of Sagnac interferometers with random CA 022~3271 1998-10-29 modulation and a closed resetting control loop, reference should be made to the European Patents EP 0 498 902 and EP 0 551 537.

In order to be able to record the effect of disturbance couplings-in in the event of mistuning, it is sufficient to consider the Sagnac interferometer with an open control loop (cf. Fig. 1). Let T be the scanning cycle of the system and at the same time the period of a coupling-in disturbance voltage. Let To be the transit time, deviating therefrom, of the light, ~(t) the phase modulation caused by the modulator and (t) the Sagnac phase. Disregarding direct voltage components and amplification factors in the detector path, the following applies to the output signal y(t) of the interferometer:

y(t) = cos(~(t) - ~(t - To) + ~s(t)) (1) If it is now assumed that, by means of a suitable modulation voltage which acts in the cycle T and which is superposed upon the signal ~(t) in a known manner modulation control to the turning points of the interferometer characteristic is undertaken and the respectively effective sign of the gradient of the characteristic is compensated by a demodulator signal which likewise acts in the cycle T, then the interfero-meter can as an approximation be described by the characteristic~0 y(t) = sin(~(t) - ~(t - To) + ~s(t)) (2) without modulation signals and demodulation signals.
Strictly speaking, the approximation applies only for ~ CA 022~3271 1998-10-29 .

T = To. For T ~ To, additional transients occur within narrow transition regions, which transients are not taken into consideration in the above equation. Since these transients contribute only to an increase in the random walk, and in order to simplify the computation, let the validity of (2) be assumed also for T ~ To, as long as the mistuning is not excessively great. A
further simplification arises by linearization of the sine function:
y(t) = ~(t) - ~(t - To) + ~s(t) (3) This signal is filtered by a filter disposed in the data path and then sampled; in this case, the n-th sampled value yn is computed by a weighted averaging in the interval [(n - l)T, nT]. The weighting function is the pulse response h(t) of the filter, which pulse response is reflected at the time axis. Outside the interval, there are no contributions, even when the pulse response does not vanish there, because, by reason of the statistical modulation, demodulated signal components are uncorrelated outside the mentioned interval. Thus:

Yn = ¦h(t)y(nT-t)dt (4) Without a finding to the contrary, let the function h(t) be normalized so that ¦h(t)dt =1 (5) is applicable. The averaged rate of rotation is obtained from y~ Y, I ~Y' Thus:

y ~ V~ n~ (n~ (nT- t~

l~
In the case of sufficiently steady signals, the average value formation over a sequence xn is independent of an index shift, i.e. the following is applicable:

V_ I ~ ~ Y_ -~tV r I ~v (8) Thus, the index n can be replaced by n + 1 in the second integral of (7). Let ~T = To - T be the cycle detuning. Then:

9 - l~m V~ XtP(nr~ p(nT'-~r--)3dt 1 ¦Jr(r3~,(nr-~)~r (~) With sufficiently small ~T, ~'(t)~T ~ ~(t) - ~(t-~T).
Using this approximation, the final result is the following:

j-yim hV~ , J~(r)~ nT-t)~ 7,-~ r ~101 Now, let ~(t) = ~(t + nT) be a signal which is periodic with T. Furthermore, let ~S(t) = ~5 = const. Then:

~-Jht~ Tdt~

CA 022~3271 1998-10-29 E x a m p 1 e By way of example, let it be assumed that h(t) = 2/T
for t < T/2 and h(t) = 0 for t > T/2. For ~(t) let within the range t ~ [0, T] ~(t) = ~0 for t ~ [0, T/4]
v t ~ [3T/4, T] and ~(t) = -~0 for t ~ [T/4, 3T/4].
Outside the range t ~ ~0, T], let ~(t) be continued in periodic fashion in accordance with ~(t) = ~(t+nT).

~ [g~ r~Jt~(t)~ n~o(o)~r~ h ~J tl2~

The measured phase y is therefore proportional to the relative detuning ~T/T and to the amplitude of the pickup ~0. If the relative detuning is assumed to be l00 ppm (~T/T = 10-4) and the amplitude of the pickup is assumed to be ~0 = 2~-l0-2, then in the case of a gyroscope having a 2~ rate of rotation of 2000~/s the bias error caused by the pickup is:
Q ~ 2C00- 4-3600 2~ ~/h ~131 h-10 The object of the invention is to provide an electro-optical phase modulator for fibre-optic interferometers, in particular for fibre-optic gyroscopes, in the case of which modulator the previously observed sensitivity to disturbance signals picked up is completely or at least to a large extent eliminated.

The starting point for the invention is the recognition that the sensitivity of electro-optical phase modulators of the mentioned type may in theory be reduced to zero if the time of the working cycle of the interferometer or gyroscope is brought into concordance ~, CA 022~3271 1998-10-29 with the circulation time of the light from the first phase modulator via the fibre coil to the opposite phase modulator. It was recognized that to this end it is necessary to take measures which ensure that the phase modulator possesses the same pulse response in both circulation directions of the light.

Accordingly, the technical teaching of the invention may be characterized, for an electro-optical phase modulator having an integrated optical waveguide and modulation electrodes disposed on both sides at a constant mutual spacing from the optical axis along the waveguide, in that the electrodes are disposed in such a way that the spatiotemporal propagation of the potentials of the electrodes and of the electric field between the electrodes generates a symmetrically distributed pulse response.

This fundamental concept of the invention is suitable both for analogue and for digital phase modulators when used in FOGs.

For a digital phase modulator, a preferred embodiment is considered to be one in which a plurality of pairs of electrodes, which can be driven in parallel and which are binarily stepped with respect to their longitudinal extent, with a counter electrode disposed between these binarily stepped electrodes, are provided, each binary stage consisting of two partial electrodes and the points of symmetry of all binary stages being concordant, in such a manner that the complete electrode arrangement generates a symmetrically distributed pulse response.

In the text which follows, the conditions are derived, and individual constructional forms for phase modulators are explained, which, according to the invention, deliver the same pulse response in both circulation directions of the light.

In the case of the nowadays used constructional forms of such phase modulators on integrated optical chips, in particular in the case of the digital variants (cf.
US 5 137 359), as a rule the symmetry condition derived hereinbelow is not satisfied. In the case of highly precise fibre-optic measuring devices, in particular in the case of FOGs, the re~uired balancing of the sampling cycle time to the light transit time is accordingly not possible.

In the first instance, the conditions for an ideal modulated Sagnac interferometer will be described:

In the case of the ideal modulated Sagnac interfero-meter, the readout function at the photodetector after demodulation with the omission of the modulation signals, independently of the modulation process, is the following, as has already been stated hereinabove:~5 y(t) = au(t) - au(t - To) + ~5(t) (14) In this expression, u(t) is the reset voltage (or disturbance voltage) acting at the phase modulator, a the electro-optical transmission factor, ~5(t) the Sagnac phase and To the light transit time from the centre to the centre of the phase modulators through the coil of the FOG. In the text which follows, let u(t) = u(t+T) (15) CA 022S327l l998-l0-29 be a disturbance voltage which is periodic with the working cycle T. Using this, and with ~s = ~, y(t) = a(u(t) - u(t - To + T)) (16) In the case of ideal tuning, T = To becomes as y(t) = 0.

The construction of a real fibre-optic interferometer is represented in Fig. 1 of the accompanying drawings.
The light originating from a light source D is split, at a Y branching Y into two parts which then pass through the modulators m1 and m2, then in the opposite direction the coil S and then once again the two modulators m1, m2. The light beams are recombined with a mutual phase shift ~ = ~m + ~s (17) where (Pm iS the phase generated by the modulators and (p5 is the Sagnac phase. Both modulators are driven by the same voltage u(t). Let the transit time of the light from the centre of the modulator m1 to the centre of the modulator m2 be To. There is then obtained for the phase (pm in the case of opposite polarity of the two modulators:

(Pm =a,+ (t) *u(t)+a2 (t)*u(t) -a~ (t)*u(t-To)-a2(t)*u(t-T0) (18) In this expression, an+(t) is the electro-optical pulse response of the modulator mn(n = 1, 2) in the transit direction from right to left, while an~(t) is the electro-optical pulse response of the modulators for ~..

CA 022~3271 1998-10-29 .

the transit direction from left to right. The star characterizes the folding:

a(t) * u(t) = J a(T)u(t - ~)d~ (19) If now the interferometer is operated with T = To and is acted upon by a voltage u(t) which is periodic in T, the result is y(t)=(a' (t) + a~(t) - a' (t) - a2(t)*u(t) In the text which follows, the invention and advantageous details are explained in greater detail with reference to drawings. In the drawings:
Fig. 1 shows the basic construction - already briefly explained hereinabove - of a real Sagnac interferometer;

Fig. 2 shows an electro-optical phase modulator, according to the invention as a system with distributed pulse response;

Fig. 3 shows, in diagrammatic representation, the electrode arrangement for a fundamental solution variant of an electro-optical digital phase modulator with optimized distributed pulse response according to the invention;
~0 Fig. 4 shows another fundamental embodiment of an electrode arrangement for a digital phase modulator which, with respect to the spatio-temporal propagation of applied potentials, CA 022~3271 1998-10-29 complies with the symmetry requirements according to the invention; and Figs 5A, B show, in diagrammatic representation, the electrode arrangement of analogue phase modulators according to the invention, ~ig. 5A
illustrating an electrode arrangement with mirror symmetry and Fig. 5B illustrating an electrode arrangement with point symmetry.
Phase modulators which are in accord with the invention are in principle constructed as represented in Fig. 2.
The optically active region, characterized by the rectangle R which is shown, extends along the x axis extending from right to left; in this case, its extent is limited by the interval [-xO, xO]. The control voltage u(~) now couples in, with a pulse response h(x, t) dependent upon x, to each point of the active region and there generates an incremental phase shift.
If now v is the speed of propagation of the light in the active region, the electro-optical pulse responses become:

~, ¢~ (rJ - ~ h"~.r, r ~
'~ (2 11 and C~ J k~(-x.~ (22J-CA 022~327l l998-l0-29 . - 12 -The aim is .o make y(t) in (20) equal to zero.
According to the invention, there are two possibilities for doing this. In the firs~ case, there is selected an= an (23) According to (21) and (22), this is satisfied for hn(x, t) = hn(-x, t) (24) The second possibility leads to ~I =a2 (25) From this there follows h1(x, t) = h2(-x, t) (26) whereby h2(x, t) = hl(-x, t) (27) and thus a, = a' (28) are automatically also satisfied. Finally, there follows from this y(t) = 0.

The symmetry requirements appertaining to an electrode layout which satisfies the conditions of the invention are explained hereinbelow:

The phase modulator of the type according to the invention, in particular for a fibre-optic gyroscope, CA 022~3271 1998-10-29 can be manufactured as an integrated optical component (chip); in this case, an optical waveguide is diffused into a suitable material, in particular LiNbO3 or LiTaO3. This waveguide has an optical refractive index which is dependent upon an applied electric field. The necessary electric field is generated by the electrodes which are disposed on the surface of the component parallel to the waveguide.

An electrode arrangement corresponding to the above-explained first case (Equation (23)) is shown in Fig. 3 for an active channel 1 of the symmetrically constructed pair of phase modulators m1 or m2. Electrode terminals for the binarily drivable electrodes of the digital modulator are designated by 2. Reference symbol 4 identifies a counter electrode which is allocated in common to both modulators m1, m2-Accordingly, the distributed pulse response h(x, t) is20 dependent upon the spatiotemporal distribution of the generated electric field. The symmetry requirements, derived in the preceding section, appertaining to the distributed pulse responses hn(x, t) can be satisfied by symmetric electrode arrangements on the phase modulatori in this case, the spatiotemporal propagation of the potentials of the electrodes must also comply with the symmetry requirements. This applies both to digital (Figs 3 and 4) and also to analogue modulators (Figs 5A, B).
In the case of digital modulators (cf. Fig. 3), for each bit significance there is provided its own electrode arrangement; in this case, the weightings are realized by corresponding surface ratios. The symmetry conditions must be satisfied for each individual bit;

CA 022~3271 1998-10-29 in thls case, the points of symmetry of all bits must be concordant, so that in the final analysis the symmetry condition for the complete electrode arrangement is satisfied.

For both of the mentioned solution cases, the following arrangements thus arise for digital modulators:

In the first case, the modulators must possess an electrode layout which is mirror-symmetric with respect to the axis x = 0, so that a propagation which is also spatiotemporally symmetric with respect to this axis is guaranteed. For a digital modulator, the result of this is, for example, the layout shown in Fig. 3. The optical waveguide is rep-esented by the arrow (active channel 1) extending at the centre between the electrodes. Only one of the two modulators is shown;
the other must be designed in corresponding fashion.

The second case leads to an electrode layout in which the electrode geometries of the two modulators proceed by rotation apart through 180~. Fig. 4 shows the basic representation of such an electrode layout. In the basic representation, the active channel of the modulator ml is designated by 10, the active channel of the modulator m2 is designated by 11, the common counter electrode by 12, the binary electrode array of the modulator ml by 13 and the binary electrode array -rotated through 180~ in its arrangement - of the modulator m2 by 14.

The corresponding conditions appertaining to the mirror-symmetric or the point-symmetric design of the electrode layout for analogue phase modulators of the type according to the invention are immediately CA 022~3271 1998-10-29 discernible from Fig. SA and 5B respectively, from the point of view of the person skilled in the art.

On the basis of the invention, at least two types of electrode layouts for Sagnac interferometers, and indeed both of analogue and also of digital phase modulators, may be realized in such a way that in the case of ideal working cycle tuning, the influence of periodic disturbance signals is reliably suppressed.

........ . ... .

Claims

1. Electro-optical phase modulator having an integrated optical waveguide and modulation electrodes disposed on both sides at a constant mutual spacing from the optical axis along the waveguide, characterized in that the modulation electrodes comprise a plurality of pairs of electrodes which are driveable in parallel and which are binarily stepped with respect to their surface conditions and a counter electrode (4) disposed between these binarily stepped electrodes, each binary stage consisting of two partial electrodes and the points of symmetry of all binary stages being concordant, in such a manner that the complete electrode arrangement generates a symmetrically distributed pulse response.

2. Integrated optical arrangement having two phase modulators and a Y branching which are integrated together on an integrated optical chip, at least one of the phase modulators being an electro-optical phase modulator according to Claim 1.

3. Integrated optical arrangement according to Claim 2, characterized in that the arrangement of the modulation electrodes of one of the phase modulators (m1) is rotated through 180° relative to the arrangement of the modulation electrodes of the other phase modulator (m2).

4. Integrated optical arrangement according to Claim 2 or 3, characterized in that a polarizer is additionally integrated in the IO chip.

5. Integrated optical arrangement according to Claim 4, characterized in that the polarizer has been generated by proton exchange technology together with the integrated waveguide in an LiNbO3 or LiTaO3 substrate.

6. Use of an electro-optical phase modulator according to Claim 1 as part of the optical structure of a fibre-optic Sagnac interferometer.