Planar diffusion glass waveguides obtained by immersing in molten KNO₃

Planar diffusion glass waveguides obtained by immersing

in molten KNO,

Józef Fina k, Hubert Jerominbk

Institute o f Physics, Silesian Technical University, Gliwice, Poland.

Zbigniew Opilski, Krzysztof Wojtala

Institute o f Fundamental Technological Research, Polish Acadamy o f Sciences, Warsaw, Poland.

The paper presents the technology o f obtaining planar optical waveguides in soda-lime glass by immersing in molten K N 0 3 (T = 613-673 K, t = 1-25 hours). Based on the effective mode in­ dices and the IWKB method, the analytical forms o f refractive index profiles with TE and TM polarizations were determined in the waveguides. The waveguide mode attenuation measurements were made.

1 . Introduction

Except for LiN b03 monocrystals, glass belongs to the materials most frequently used in the production of strip and planar optical waveguides. Such waveguides may be ob­ tained either by ion-exchange Ag* *-* Na+ [1], Li+ <-+ Na+ [2] or by the diffusion of Pb

[3] or T1 [4] into glass. These technologies are very simple, moreover, the waveguides

obtained in these ways have low attenuations 1 dB/cm) and their surface refraction

indices range from 1.520 to 1.605.

Diffusion glass waveguides constitute a basic constructional element of many de­ vices in integrated optics, e.g., branching structures [5], fibre coupling structures [6], switches [7], polarizers [8], and many others.

Our paper presents the technology of producing planar optical waveguides in soda- lime glass by immersing in molten K N 0 3.

2 . Technology o f producing diffusion glass waveguides

Planar optical waveguides were formed in soda-lime glass (microscope slides of the com­ position: Si02 - 72.11°/0, A120 3 - 1.63%, Fe20 3 -0 .0 1 % , MgO - 3.90%, CaO - 7.31%, alkaline oxides - 14.91%, the index of refraction being nb = 1.512 for the He-Ne laser light, A = 0.6328 /mi) by immersion in molten K N 0 3. The technological processes were carried out in a porcelain crucible, placed in a chamber oven equipped with a tempera­ ture stabilization device ±0.5 K. The temperature was measured by the thermo-couple

12 J. Finak et al.

Ni-NiCr drawn in a quartz shield and immersed in a bath. The bath temperature ranged from 613 to 673 K. The immersion time ranged from 1 to 25 hours.

Under the above conditions such waveguides were produced in which 1-6 TE (TM) modes could propagate.

3. Optical parameters o f glass waveguides

3 .1 . Determination o f the refractive index profile in waveguides

The effective refractive indices nm of guided modes (TE and TM) were determined with the accuracy of ±0.0008 by measuring the synchronous coupling angles of the above modes [9].

The obtained values of nm were used to define the refractive index profile n{x) in wa­ veguides (x — direction is perpendicular to the surfaces of the planar waveguides) by applying the procedure followed by the IWKB method [10].

According to this method n(x) appears in the form of a piecewise linear function

n(x) = nk-\- ^—— (xk—x), for xk_ x < x ^ x k, (1)

X k Xk- 1

where xk represents the turning points of the modes with effective indices nk. Having substituted (1) to a characteristic equation:

rm / 3 \ / n2—\ \ 1/2

k0 J [n2(x )-n 2mY,2dx = n | m - — j ± arc tanq | (2)

where

m = 1, 2, 3 ,..., M (M — number of modes propagating in a waveguide), k0 — light wave number in vacuum,

«o — refractive index on the waveguide surface, for TE modes,

for TM modes,

xm — turning points of modes defined by the following equation, n(xm) = nm,

the following recurrent equation for xm was obtained: t - l / 2 Q j *

- I 11

K

[T +“

ef e ; ) J'

j

The value of n0 indispensible for finding the first turning point x{, was determined by making use of the fact that changes in the value of this parameter cause significant changes in the profile curvature n(x). To measure the curvature we made use of the field sum of triangles with the following vertices:

(*fc ’ n k ) ’ (·*·&+15 n k + l)j (.x k + 2 ’ n k + 2) ’

k = 0, 1, 2 , M —2. Attempts were made to find such a value of n0 for which the field sum would assume the least possible value.

Basing on equation (3), the turning points xm of the modes TE and TM were found. Data sets (xm, nm) served to find the analytical form of n(x).

For the approximation, carried out by the method of the least mean-square error, the following functions were chosen:

a linear function n(x) — n0—An0 j, for x < d, n(x) — nb, for x ^ d, an exponential function n(x) = nb+A nc a Gaussian function n(x) = nb-\-An0txp

a second-order polynomial function

H i l T · n{x) - n0—An0 n(x) = nb, for x ^ dt , for x < dL where dt is conditioned by I — -\-b (— 11 = \ , L d \ d )\ x=di an erfc function n{x) = nbf An0tvic a linear segments function

x n(x) = n0A-(nw—n0) ----, for 0 < x < Xw X — X n(x) = nw+ (n b—nw) ---—, for X < X < xb. Xb ~ X w

In the above formulae nb is the bulk substrate refractive index, An0 — n0—nb.

(

4

5

(

)

7

9

14 J. Finak et al.

The calculations were made for the waveguides produced under different technol­ ogical conditions (temperature and time).

The calculations proved that the best approximation n(x) in every case is obtained by means of a linear segment function (9), however, due to the way of defining the above function, it cannot be applied to describe optical properties of the whole waveguide range but only to particular cases.

In regard to the total waveguide range, the best possible approximations were ob­ tained by applying the second-order polynomial and erfc functions; however, for th e re­ maining approximating functions, the following relations are as a rule, fulfilled:

| (^m)measured theoretical] ^ 0.0008.

For the indices n0 and b of a parabola (7) the following mean values were assumed: n0 = 1.524, b = —0.270 for TE modes.

«o = 1.526, b — —0.245 for TM modes.

♦

Standard deviations of the indices b for TE and TM modes were: 0.011 and 0.014, re­ spectively. In the case of erfc function (8) the indices n0 took on the same values as for a quadratic polynomial function.

The examples of the results of approximation n(x) by the functions (4)—(9) for one

waveguide are given in the table.

It has been proved, morover, that the changes in temperature and duration of a waveguide formation process do not cause changes in the value of the indices n0 and b.

The relation n^E < n™ between the values for TE and TM modes is a consequence of the noted relation between the effective refractive indices of TE and TM modes of the same orders: n™ < n™. This situation is reverse to what would result from a char­ acteristic mode equation. It was not influenced by the force of prism couplers clamping to a waveguide. Thus, the temporary double refraction should be related to mechanical stresses which could appear in glasses during a waveguide formation process. Similar effects have already been observed in waveguides by the ion-exchange method Ag+ <-> Na+

[11].

3 .2 . Attenuation measurements

The attenuation y of waveguide modes was measured in a system presented in a diagram (Fig. 1). A photomultiplier F was used to record the intensity changes of light, decoupled from the polished edge of a waveguide, as a function of the prism coupler distance from that edge. It is known [12] that the coupling efficiency is highly influenced by the width of the air gap which separates the prism from the waveguide; the gap width being adjusted by the clamping of both elements. In turn, the clamping force may be controlled on the basis of the picture of interference fringes visible at the prism base. The above method was used to control the efficiency of light coupling to a waveguide. The measurement method allows to determine the attenuation of waveguide modes with the accuracy of ±0.2 dB.

The measurements were repeated many times for TE and TM modes of different orders, propagating in waveguides produced under different technological conditions.

T a b le . T h e a p p r o x im a tio n o f a re fra ct iv e in x e d p ro fi le n( x ) o f a li g h t w it h p o la r iz a ti o n T E in a p la n a r w a v e g u id e o b ta in e d b y im m e r si n g a so d a -li m e g la ss i n m o lt e n K N 0 3 (T = 67 3 K , / = 25 h o u r s) 3 S H a. § 6 m ( S VO v—1 c s c n < N t/) _{v o} » o T f 1—HO a i —1m <N o 0 0 VO 0 0 U a> II T i ­ 1 ON OO VO » o T f Ctj E || II II II <N <D c bO_(D o * * «© ll » 0 v o VO v o » o </D s : s: H £ 2 m 25. · <N . S'_{m t w} ^ r<i ri_ts 11 II II 5? “Q *** 0 0 < N < N o r n o On o o r - V O T f < N » o » 0 * o » o V O » o 1 H a VO VO _ o v d ov m r s | o VO <1—1 © On OO VO T f CJ II II II ( N i-H C VO VO VO VO < o VO a x :o" Q •UjN ** ** — I £ 2 c ·« {N o i~ l 1 -1 s 8 " II II lH K ^ © r ^ 0 0 0 0 0 0 OS VO * o T f

CN i-H i—1 i—1

VO VO v o v o VO v o i—1 11—1 * " 1 i · ^ 1 . 5 2 4 =5. <N » o O ( N T“H<N ON Ov0 0 vo II f N CS i—1 Ov VOv o T t II II < N v o v n VO i-H » o ^-1v o o K * « •*A/> ' — — — o 6 S ?3 ^ ^ o o *g a § .1 i l l 9 O 3 _ _ ff D .C ft -Q “Q -Mj, — —1 M as © —I <N ON On00 ON vo »o -vfr 1-H i—1 1—1 •OVO voVO vo v’"1 i—1 Tf O v o 00 OnOOVO *oT f 1“H *0VO VO vo <o i—l 1-1 i—1 i—1 r- [<N 00 »o r-· o CN Tt- 00 i-Hi—1 1—< 1"H cs COT f VO VO

7

16 J. Finak et al.

Figure 2 illustrates the dependence of the TE mode attenuation on nm, and, in conse­ quence, on the mode order.

Figures 3a and b present the results of investigations of the TEX mode attenuation

being treated as a function of the K N 0 3 bath temperature and substrate immersion time.

i

Fig. 1. Block diagram o f the system for measuring the attenuation o f the dif­

fusion glass waveguide modes: P — po­

larizer, Ch — chopper, L — lens, PC —

prism coupler, PH — photomultiplier,

SNV — selective nanovoltmeter, LG — lg

amplifier, R — recorder, O — oscillosco­

pe, W — waveguide, S — shield

2.0 1.8 16 10 1512 1.514 ' 1516 1.518 1520 1.522 1.524 nm ·

-Fig. 2. Light attenuation for A = 0.6328

fim with polarization of TE in a diffu­

sion glass waveguide (T = 613-673 K,

t = 25 hours) as nm function

A considerable dispersion of the values may be noticed particularly well in Figs. 3 a, b. It seems that this dispersion results from the imperfections in the technological and meas­ urement methods, as well as from the scatter of properties of soda-lime glass substrates.

In view of the above situation the following equations:

7te 7t e1 yTEl — f i t ) f 2 D I 2 .0 I 1 .8 E 1 8 e o o - H . 1 .6 CD_{T J O o} c o “ ° U ° ° 1 . 4 ^ 1 .2 1 .2 II 1 .0 1 .0 613 63 3 653 673 6 93 1 3 5 7 9 11 13 15 17 19 21 2 3 25 Tt(<1— ^ t[ hours]----—

Fig. 3. Attenuation of TE0 modes as the function o f parameters of the waveguide formation process: a —

had to be tested statistically. The tests, based on f-Student’s distribution have showed

that at the significance level a — 10°/0 yTE is almost independent of nm, while is

almost independent of T and t. 4. Conclusions

In planar waveguides produced by dipping soda-lime glass substrates in molten K N 0 3, the refractive index profile may be approximated by either a quadratic polynomial function or by an erfc function. Such waveguides are optically anisotropic which is manifested by different n0 values of TE and TM modes: ir^ = 1.524, n™ = 1-526. The changes in the parameters of technological processes, like temperature and time, for the wave­ guide production have no influence on the values of n0. Moreover, they do not influence the waveguide mode attenuation which, irrespective of the mode order, takes on the value of about 1.6 dB/cm.

References

[1] Stewart G., Millar C , Laybourn P., Wilkinson C , De La RueR., IEEE J. Quant. Electron. QE-13 (1977), 192-200.

[2] Charties G., Jaussaud P., Oliveira A ., Parriaux O ., Electron. Lett. 13 (1977), 763-764. [3] Anikin V., Gorobec A ., Kvant. Elektronika 2 (1975), 1465-1470.

[4] Kawanishi H ., Suematsu Y ., Trans. IECE o f Japan E60 (1977), 231-236. [5] Lyndin N ., Sarkisov J., Sychugov W., Kvant. Elektronika 7 (1980), 134-141.

[6] Tangonan G ., Ramer O ., Friedrich H ., Asawa C ., Proc. o f Fifth Europ. Conf. Opt. Commun. and Second Int. Conf. o f Integrated Optics and Fibre Commun., Amsterdam 1979, p. 25.5-1-25.5-7.

[7] Chanturya G. F., KebuladzeN ., MshvelidzeG., TatulovR., Kvant. Elektronika 6 (1979), 1092- 1094.

[8] UeharaS., UesugiN ., Review o f Electrical Commun. Lab. 26 (1978), 557-564.

[9] Finak J., Jerominek H ., Żelechower M ., Optica Applicata 11 (1981), 61.

[10] White J., Heidrich P., Appl. Opt. 15 (1976), 151-155.

[11] ZelenkoA ., Lyndin N ., Sychugov V., TunchenkoA ., Chipulo G., Kvant. Elektronika 6 (1979), 1043-1047.

[12] Zolotov E., PelekhatyiV., Prokhorov A ., Kvant. Elektronika 4 (1977), 2196-2202.

Received January 16, 1981 Планарные диффузные стеклянные волноводы, полученные методом погружения В расплавленном К1Ч03 В работе представлена технология изготовления планарных световодов в натроизвестковом стекле методом выдержки в расплавленном КЬЮ3 (Т = 613-673 К , Г = 1-25 часов). На основе измерений эффективных коэффициентов преломления модов и метода ^ К В были определены аналитичес­ кие формы профилей коэффициентов преломления света с поляризацией ТЕ и ТМ в световодах. Произведены измерения затухания светловодовых модов (1,6 дБ/см). 2 — O p tic a A p p lic a t a X I I /l