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High-power monolithic phase-locked arrays of antiguided semiconductor diode lasers. D. Botez. Indexing terms: Semiconductor lasers, Diodes. Abstract: ...
High-power monolithic phase-locked arrays of antiguided semiconductor diode lasers D. Botez

Indexing terms: Semiconductor lasers, Diodes

Abstract: All-monolithic phase-locked arrays of antiguided diode lasers have recently demonstrated exceptionally high diffraction-limited powers: 0.5 W continuous wave (CW) and 2.1 W peak pulsed. An overview of theoretical and experimental work to date is presented. The performance of antiguided arrays is compared to the best results from conventional array types (evanescent-wave, Y-junction, diffraction). The two basic types of array modes: evanescent-wave and leaky-wave are discussed. Resonant leakywave coupling in antiguided arrays is explained and interpreted. One key new insight is revealed: when gain is placed in the low-index regions of large arrays ( 210 elements) the array mode favoured to lase is the leaky mode (in-phase or out-of-phase) closest to its respective resonance. Thus the ‘classic’ prediction of coupled-mode theory that high gain in low-index regions automatically favours in-phase mode operation is incorrect. The intrinsic array modal discrimination mechanisms (mode overlap with the gain regions [i.e. the r effect]; edge radiation loss, and interelement loss) as well as Talbot-type spatial filtering are briefly explained, and their respective effects on resonant and nonresonant devices are discussed. Results of rigorous modelling of antiguided arrays using two-dimensional analysis are discussed and compared, for the first time, to results obtained via the effective-index method. Finally, key electro-optical characteristics of 20and 40-element arrays are described.

1

-

1 ,

Introduction

Phase-locked arrays of GaAs/AlGaAs diode lasers are sought as reliable sources of high coherent powers ( > 100 mW diffraction limited) for applications such as space communications, blue-light generation via frequency doubling, optical interconnects, parallel opticalsignal processing, and end pumping solid-state lasers. Conventional narrow-striple (3-4 pm wide) single-mode lasers provide at most 100 mW reliably, as limited by the optical power density at the laser facet. For reliable operation at Watt-range power levels, large-aperture (> 100 pm) sources are necessary. Thus, the challenge has been to maintain a single spatial mode, from largePaper 85605 (E3. E13). first received 29th July and in revised form 18th November 1991 The author is with the TRW Research Center, One Space Park, Dl,’ 2519, Redondo Beach, CA90278, USA 14

aperture devices, to high power levels (0.5-1 W). For this reason, phase-locked arrays have been the object of intensive research since 1978 [l]. The four basic types of phase-locked arrays are schematically shown in Fig. 1: evanescent-wave coupled, Yjunction coupled, diffraction coupled, and leaky-wave coupled. For the first decade (1978-1988) the first three types have been studied with less than encouraging results: maximum diffraction-limited powers of 50 mW or coherent powers (i.e. fraction of the emitted power contained within the theoretically defined diffractionlimited-beam pattern) never exceeding 100 mW. Thus, the very purpose of making arrays, surpassing the reliable power level of single-element devices, was not achieved. The real problem is that researchers have taken for granted that strong nearest-neighbour coupling implies strong overall coupling. In reality as, shown in Fig. 2, nearest-neighbour coupling is ‘series coupling’, a scheme plagued by weak overall coherence and poor intermodal discrimination [Z]. Strong overall interelement coupling happens only when each element equally couples to all others, so called ‘parallel coupling’ 121. In turn, intermodal discrimination is maximised and full coherence becomes a system characteristic. Furthermore, parallelcoupled systems have uniform near-field intensity profiles, thus being immune to the onset of high-order mode oscillation at high drive levels above threshold.

evanescent-wave

diffractlon coupled

Y-junction coupled

leaky-wave coupled (ROW array)

Fig. 1 Schematic representation of basic ~ y p e sof phase-locked linear arrays ofdiode lasers

IEE PROCEEDINGS-J, Vol. 139, No. I , FEBRUARY 1992

Table 1 summarises the characteristics of the phaselocked array types of Fig. 1. Evanescent-wave coupled diodes can be either series or parallel coupled depending on the degree of optical-mode confinement. For strong

Fig. 2

fundamental mode in a positive-index guide is a bound state in a potential well. Whereas in a positive-index guide, radiation is trapped via total internal reflection, in an antiguide, radiation is only partially reflected at the antiguide-core boundaries (Fig. 3b). Light refracted into the cladding layers is radiation leaking outwardly with a lateral wavelength 1,(Fig. 3c) [14]. I

b a Types oJoverall interelement coupling in phase-locked arrays

Weak: series coupling (nearest-naghbourcoupling; coupled-mode theory) poor coherence poor intermodal discrimination nonuniform intensity profile b Strong: parallel coupling full coherence large intermodal discrimination uniform intensity profile

(I

L

a

-

confinement (An the device is not affected by thermal and/or carrier-induced refractive-index variations, but overall coupling is weak. Best results are 40 mW diffraction-limited (DL) [3] and 200 mW in a beam 3 x DL [4]. To achieve parallel coupling the optical-mode confinement can be made weak (An the device beginning to look like a gainguided device. However, just as for gain-guided and broad-area type devices, the optical mode is not stable with increasing drive level above threshold or with varying drive conditions. Y-coupled devices, although very effective in suppressing out-of-phase mode oscillations [ 5 ] , are basically series coupled. Most results have been in the 200-400mW range with beams 45 x diffraction limit [SI, the sole exception [7] being 50 mW DL from a device which apparently had both Ycoupling and evanescent-wave coupling. Diffractioncoupled devices [S-101 have also relied on nearest-neighbour coupling, with the best results being 100 mW in beams (2-3) x DL [lo]. The breakthrough in diffraction-limited power was achieved by making resonantly coupled arrays via leaky waves [ll]. Thus, for the first time, one can have both parallel coupling and strong optical-mode confinement. The results speak for themselves: 1.5 W diffraction-limited power [12], and 5 W in a beam 3 x DL [13].

b

-

2

M o d e s of arrays of a n t i g u i d e s

The basic properties of a single real-index antiguide are schematically shown in Fig. 3. The antiguide core has an index, no lower than the index of the cladding n , . The to insure index depression, An is typically (2-5) x mode stability against gain spatial hole burning. The propagation constant of the fundamental mode Bo is below the index of the core. The quantum-mechanical equivalent is thus a quasibound state above a potential barrier. By contrast, the quantum-mechanical equivalent of the

Fig. 3

Schematic representation oJreal-index antiyuide

Index profile b Ray-optics picture ( O L is ~ edge radiation loss caefficient) c Near-field amplitude profile (i, is leaky wave periodicity in lateral direction) U

+

1, I/J[2n An (1/2412] and can be thought of as a radiation loss: ctR cc ( I

+ 1)’1’/d3J(An)

(14

(W

where d is the antiguide-core width, An is the lateral refractive-index step, 1is the vacuum wavelength, and I is the (lateral) mode number. For typical structures (d = 3 pm, An = 2-3 x at 1 = 0.85 pm typical 1, and aR values are 2 pm and 100 cm-’, respectively. Since aR cc ( I + l)’, the antiguide acts as a lateral-mode discriminator. For a proper mode to exist, aR has to be compensated for by gain in the antiguide core [lS]. Single antiguides have already been used for quite some time in CO, ‘waveguide’ lasers. We now examine a periodic variation of the real part of the refractive index (top of Fig. 4). Actually, it represents arrays of both positive-index guides and negativeindex guides (antiguides). The supported array modes are of the evanescent-wave type when the fields are peaked in the high-index regions and of propagation constants above no, and of the leaky-wave type when the fields are peaked in the low-index regions and of propagation constants below n o . Evanescent-wave modes can be solved

Table 1 : Comparison of various types of index-guided phase-locked arrays Coupling mechanism Evanescent-wave Y-junctions Diffraction Resonant leaky wave

Overall Optical-mode Operation interelement confinement coupling series parallel series series parallel

strong weak strong strong strong

multimode unstable** multimode multimode single-mode

Maximum power DL’

Narrow beam

0.04 W 0.05 W 0.05 W

0.2 W; 3 x DL 0.2 W; 3 x DL 0.4 W; 5 X DL 0.1 W; 3 x DL 5 W; 3 x DL

-

2.1 W

* Diffraction-limited. ** Strongly affected by thermal and/or carrier-induced index variations. IEE PROCEEDINGS-J, Vol. 139, N o . I , F E B R U A R Y 1992

15

either by exact theory or by coupled-mode theory [ 16, 171. Because coupled-mode theory is a simple method providing closed-form expressions for the fields it has been extensively used. However, coupled-mode theory a priori implies nearest-neighbour coupling, and thus it is not suited for any type of parallel-coupling scheme. The

become excited, for leaky-mode devices array modes composed of coupled fundamental (element) modes are favoured to lase even when the individual elements can support a large number of high-order modes (i.e. for An > 0.03). Thus, one can make in-phase mode operating antiguided arrays that are virtually immune to thermal gradient- or carrier-induced index variations. 3

b

Fig. 4

Antiguided-array structures

Ideally the high-index regions should be made transparent (i.e. no gain) as originally demonstrated by Ackley and Engelmann for buried-heterostructure arrays [25]. However, for practical devices the high-index regions have to be relatively narrow (1-3pm), which makes it impossible to fabricate high-index transparent regions by etch and regrowth. Instead, one can fabricate narrow, high-effective-index regions by periodically placed highindex guides in close proximity (0.1-0.2 pm) to the active region [26, 271 (see Fig. sa). In the newly created regions

e Modes of array of periodic real-index variations

Index profile b In-phase evdnescent-wave type c Out-of-phase evanescent-wave type d In-phase leaky-wave type e Out-of-phase leaky-wave type Respective propagation constants are 8,. 8,. 8. I and 8 - ,

D+-GOAS

(I

leaky array modes, by virtue of their oscillatory-like behaviour, cannot be solved for via conventional coupled-mode formalism. The alternatives are exact theory [18-211, a modified coupled-mode theory [22] and, more recently, the Bloch-function method [23,24]. Intuitively it is quite obvious that when gain is preferentially placed in the high-index array regions the evanescent-type modes will be preferred to lase over the leaky modes, whereas when gain is placed in the lowindex array regions the converse situation occurs. More specifically in antiguided arrays, gain is placed in the lowindex regions [25-281, with the high-index regions being transparent [25, 281 or deliberately made lossy [26, 271. By using the Bloch-function method, Eliseev et al. [23] were the first to solve for both the evanescent and leaky modes of arrays, and show which array modes are favoured to lase as a function of where the gain is placed. The discovery that leaky modes are favoured to lase when gain is enhanced in the low-index array regions was to be expected, and explains why some early proposals [29, 301 about how to make evanescent-wave arrays operate in phase were incorrect. Probably the most interesting result is that leaky modes composed of coupled fundamental element modes (Fig. 4d and e) are generally favoured to lase over all other modes, evanescent lowand high-order and leaky high-order, independent of the index step. Whereas for evanescent-wave arrays, the index step An always had to be limited to values below -0.005 so that higher-order element modes did not 16

I

I

optical mod:

optics' mode

/-

n-A10.6Ga0.4As

) - - n - A l o 6G00dAs

Schematic representation of way of making arrays a/ closely Fig. 5 spaced ontiguides, CSA array type and SAS array fype U

Practical way of making arrays of closely spaced antiguides

h Complimentary-self-aligned (CSA) array type [271 c Self-aligned-stripe (SAS) array type C31-331

the fundamental transverse mode is primarily confined to the passive guide layer. That is, between the antiguidedarray elements the modal gain is low. (The effect of the presence of a first-order transverse mode also is treated in Section 6). To further suppress oscillation of evanescentwave modes an optically absorbing material can be placed between elements (Fig. 5a). Two types of antiguided arrays have been fabricated to date: the complimentary-self aligned (CSA) stripe array [27] (Fig. ILL PROCEEDINGS-J, Vol. 139, No. I , F E B R U A R Y 1992

5b) and the self-aligned-stripe (SAS) array [28, 31-33] (Fig. 5c). In CSA-type arrays preferential chemical etch and metal-organic chemical vapour deposition (MOCVD) regrowth occurs in the interelement regions. For SAS-type arrays the interelement regions are built-in during the initial growth, and then etch and MOCVD regrowth occurs in the element regions. Note that for SAS-type devices the passive guides and loss regions between elements can be incorporated in just one layer

and X-Y junction arrays [38]. However, although conceptually sound, such schemes rely on the fabrication of 'perfect' Y-branches, a task known from integrated optics

n n

~311. R e s o n a n t l e a k y - w a v e coupling

4

As shown in Fig. 3c, owing to lateral radiation, a single antiguide can be thought of as a generator of laterally propagating travelling waves of wavelength 1,.Then, in an array of antiguides, elements will resonantly couple in-phase or out-of-phase when the interelement spacings correspond to an odd or even integral number of (lateral) half-wavelengths (J.J2), respectively (see Fig. 6). The resonance condition is s = m1,/2 m = odd resonant in-phase mode

m = even resonant out-of-phase mode (2) where s is the interelement spacing. Typical s values are 1 pm. Then, for in-phase mode resonance, 1, = 2 pm. nl

Fig. 6

no

"1

"0

"1

"0

"1

Near-field amplitude profiles in resonantly coupled arrays

a In-phase resonant made, m

=

1

h Out-of-phase resonant mode, m = 2 m is number of interelement near-field intensity peaks

When the resonance condition is met, the interelement spacings become Fabry-Perot resonators in the resonance condition. The situation is the opposite of that for antiresonant reflecting optical waveguide (ARROW) type waveguides [34, 351. In ARROW waveguide antiresonance is sought such that s = (2m + 1)1,/4. Arrays of ARROW passive waveguides [36] have, as a salient feature, lack of optical crosstalk between elements. By contrast, in resonant arrays of antiguides we have full communication between elements which, in effect, achieves parallel coupling. To emphasise complementarity to ARROW devices resonant arrays of antiguides have been named resonant optical waveguide (ROW) arrays. To illustrate parallel coupling we show in Fig. 7 light propagation in a ROW array. Light launched in a central antiguide is partially reflected at core-cladding interfaces and totally transmitted through the interelement (cladding) regions. Upon entering adjacent antiguides it couples in-phase or out-of-phase with rays there. A fan-out occurs, highlighted with heavier lines, reminescent of tree-array types made of Y-junctions [37]. It can easily be seen that after several bounces, rays originated in the central antiguide couple to rays in all antiguides (i.e. long-range coupling). Also, it is apparent that rays originated in other antiguides generate their respective 'tree-array' networks. That is, a ROW array can be thought of as interconnected 'tree-array' networks of rays, a fitting description for parallel coupling. Parallel coupling has been proposed in tree-array devices [37], IEE PROCEEDINGS-.I, Vol. 139, No. I , FEBRUARY I992

60pm . c )

R a y optics representation of leaky-wave fanout in resonant Fig. 7 array of antiguides

of being virtually impossible. ROW arrays are not that fabrication dependent because Y-branching is naturally done by light reflection and refraction at antiguide corecladding interfaces. By employing the Bloch-function method introduced by Eliseev et al. [23] it can be shown [24] that, simply based on array-mode overlap with the gain regions, the resonant mode is always the mode favoured to lase at and near its respective resonance. For finite-size arrays of > 10 elements, when edge and interelement losses are taken into account as well, the same conclusion emerges: the resonant mode is favoured to lase near its resonance [19]. The scenario is depicted by Fig. 8. As An varies, and s corresponds to different integer values of 1J2, 'in-phase' and 'out-of-phase' operational domains alternate. At and near resonace, owing to parallel coupling, the near-field intensity profile is uniform [19], which in turn provides for uniform gain usage and maximum intermodal discrimination. Away from resonance the near-field-intensity array mode: in-phase iresononce

z

Fig. 8

out-of-phase

in-phase

/

;

1

An=nl-no

Modal behaviour of antiguided array as An, index step varies

Arrows correspond to resonances fors = 3i,/2, i,and 4 1 2

envelope is cosine-shaped [19] due to nearest-neighbour coupling, and, in turn, at high drive levels adjacent modes can reach oscillation by using the excess gain available near the array edges. Only operating near resonance ensures sole in-phase mode operation to high drive levels. That is, ROW arrays act as excellent selectors of the inphase array mode. A good analogy can be made to dis17

tributed feedback (DFB) lasers. Whereas DFB lasers select a single longitudinal spatial mode, ROW arrays select a single lateral spatial mode. More specifically, the ROW array for the in-phase mode with one interelement standing-wave peak (Fig. 6a) corresponds to a secondorder DFB device [39], because the phase change across one period is 2 ~ .

high-gain regions: the antiguide cores. By contrast, the out-of-phase mode being nonresonant has a significant interelement field, and subsequently poor overlap with the high-gain regions. The behaviour of Ts for in-phase and out-of-phase modes is illustrated in Fig. 10 for a twoii

5

+

Mode discrimination mechanisms

There are three intrinsic modal discrimination mechanisms in arrays of antiguides: (a) modal overlap with the gain region [20, 401, so called r-effect [19] (b)edge radiation losses [19, 261 (c) interelement loss [19, 411. To understand them we plot in Fig. 9 the near-field intensity profiles of the in-phase mode (Fig. 9a), the

io"l

III 'J I

/

I

2

0.10,

,

Fig. 10 Two-dimensional mode confinement /actor interelemental width sfor two coupled antiguides

0.1 0

4

L

interelement spacing s. p m

r

as function of

= 3 pm, . ; = 0.86 pm 1401 m I S number of inlerelemenl near-field intensity peaks, arrows correspond lo mode resonances, i.e. when s = mi.,/Z ____ in-phase mode out-of-phase mode

d

x

.-

1

2 0.05

+

c

~

element array (d = 3 pm, s = 2 pm) [40]. At and near resonance the two-dimensional r of a given array mode is virtually the same as the transverse optical-mode confinement factor To in the element (i.e. 0.20). The antiresonant modes have significant field in interelement regions of a low transverse optical confinement factor r1= 0.04. Thus 2-D r values as low as 0.13 are reached. In turn, resonant modes are strongly preferred to lase over nonresonant modes. Hadley has predicted a similar preference in infinite-size arrays [20]. For 20-element arrays, typical ratios between r values of in-phase and out-ofphase array modes (near the in-phase mode resonance) are 1.3-1.5 [13]. In turn, the in-phase mode is heavily favoured to lase to high drive levels above threshold. The l- effect provides effective intermodal discrimination not only for linear antiguided arrays, but, as shown by Hadley [43], for two-dimensional phase-locked arrays of antiguided vertical-cavity surface emitters.

0

-20

-10

-20

-10

0

10

20

0

10

20

Y, p m h

5.2 Edge radiation losses The edge radiation loss for a single antiguide is given by eqn. 1. In an array, radiation that normally is lost laterally for a single antiguide is used to couple all elements. Only the edge elements leak outwardly giving a loss at resonance expressed by [19] C

Fig. 9

Near-field intensity profile5 for selected array modes element ROW array d

= 3 pm. I = 1 pm, .; = 0.86 pm. An a In-phase mode ( L = 18)

=

28 x

OJ

10-

[I91

b Out-of-phase mode ( L = 27) c Adlacent mode ( L = 19)

out-of-phase mode (Fig. 96) and the next highest mode to the in-phase mode, the so called adjacent mode (Fig. 9c) for a 10-element array designed to operate close to the resonance of the in-phase mode [19]. An 'extrinsic' modal discrimination mechanism: diffraction in Talbot type spatial filters [42] is treated in Section. 5.4.

5.1 r Effect Near its resonance the in-phase mode has negligible interelement field, and thus significant overlap r with the 18

E R R = %,IN (3) where N is the number of array elements. For a 20element array, uRR 1 5 cm-', a value that hardly affects the threshold. Eqn. 3 is only for resonant modes (e.g. the in-phase mode of Fig. 9a). Adjacent array modes (Fig. 9c) have a large field at the array edges and, in turn, larger edge losses. The difference A a is shown in Fig. 11. For a IO-element array [19], Aa = 10-15 cm-', which strongly suppresses oscillation of the adjacent mode and thus allows sole in-phase mode operation (i.e. diffractionlimited-beam operation) to high powers. Fig. 11 also shows the edge loss for an out-of-phase mode. Being nonresonant, mode 27 only has nearestneighbour-type coupling and subsequently a cosineshaped envelope of negligible field at the array edges. However, owing to the r-effect and interelement loss,

I E E P R O C E E D I N G S - J , Vol. 139, N o . I , F E B R U A R Y 1992

oscillation of the out-of-phase mode is suppressed in spite of its lower edge loss compared to the in-phase mode. 5.3 Interelement loss Interelement loss can be introduced by placing highly absorbing material in the interelement regions (see Fig.

’-i i

(4) where A is the array period, nefJ is the effective index, and I is the vacuum wavelength. At a distance of 2,/2 the in-phase mode image is displaced transversely by a half period, whereas the out-of-phase mode self-images [45, 461. Thus, a structure made of noncollinear arrays, spaced a distance Z T / 2 apart (Fig. 13), strongly favours

40

0

0.02

5.4 Diffraction in Talbot-type spatial filter Talbot-type spatial filters [42, 441 employ the imaging properties of freely diffracting radiation from periodically spaced sources [45, 461. The distance at which both inphase and out-of-phase sources self-image is called the Talbot distance:

0.04

0.06

0.08

lateral index differential An=n,-nO

Fig. 11 Modal radiation loss against lateral index step for modes IS, 19 and 27 of IO-element ROW array d = 3 pm, s = 1 pm, = 0.86 pm 1191 18 (in-phase) 21 (out-of-phase) . . 19 (adjacent) Insets are near-field intensity profiles ofmodes I8 and 19 near resonance ~

~

~~~

5a). Similarly to the r effect, nonresonant modes ‘see’ significantly more loss than resonant modes. The effect is illustrated in Fig. 12 for the same 10-element array

Fig. 13 Schematic representation of Talbot-type spatialfilter 1421 = A’N,,II

z,

in-phase mode operation over out-of-phase operation. In addition, because the adjacent array modes have high field at the array edges, they suffer more edge diffraction losses in the Talbot filter than the in-phase mode [19, 471. Van Eyck et al. [47]., in particular, have analysed how the Talbot filter affects adjacent array modes in 10/ 1 1-element arrays. In general, Talbot filters have two effects: (U) for resonant arrays they provide ‘cleaner’ far-field patterns at some price in efficiency [48] (b) for near-resonant arrays they ensure diffractionlimited-beam operation [13]. Table 2 summarises the effects of the various discrimination mechanisms in arrays of antiguides. At resonance Table 2: M o d e suppression mechanisms that ensure diffraction-limited-beam in-phase array-mode operation Suppression mechanism

Resonant array

Near-resonant array

Array modes suppressed

Low interelement To out-of-phase - 0

0

0.04 0.06 0.02 lateral index differential An

Fig. 12 Modal loss (radiation + interelement) against lateral index step for modes 18, 19 and 27 of IO-element ROW array with interelemental loss coefficient of5090 cm-’ d = 3 pm. .s = 1 pm. 1 = 0.86 pm [I91 ~.-~~18 (in-phase) ~~~~

21 (aut-of-phase) 19 (adjacent)

analysed in Fig. 11. An interelement loss coefficient of 50-80 cm- is considered [ 191. As can be seen, the resonant in-phase mode (mode 18) is hardly affected, whereas the out-of-phase mode (mode 27) has significantly increased losses. IEE PROCEEDINGS-J, Vol. 139, N o . I, FEBRUARY 1992

(r-effect) Edge radiation losses Interelement loss Talbot-type filter

adjacent

out-of-phase* -

out-of-phase out-of-phase* out-of-phase out-of-phase and adiacent and adiacent

* Primiarily on the high An-side of resoaance in the modal loss against An plots (Figs. 11 and 12) there is no need for Talbot-type spatial filters [21]. Off resonance, whereas the out-of-phase mode may be suppressed by intrinsic array discrimination mechanisms, adjacent modes are not, which in turn will give beamwidths (2-3) x diffraction limit. Then, to ensure diffraction-limited-beam operation, Talbot filters are necessary. 19

6

Rigorous modelling

All discussion so far refers to the use of the effective-index method (EIM) 1191. Hadley has analysed antiguided arrays using a finite-difference method [20]. However, the EIM is invalid when more than one transverse mode is supported in the interelement regions [49, 501, and, although the finite-difference approach gives a good qualitative picture, it cannot be readily used for device design. The basic structure to start with is a multiclad lateral waveguide (Fig. 14) which supports an even and an odd

of lateral half wavelengths. The reason is that interelement regions contain both travelling waves (the leaky components) as well as the tails of evanescent waves. Thus, the interelement region cannot be characterised by

15

I

effective-index calculation

:.

/?I,

modem calculation

VI 0

..'..

-\

./

\:

"

8 5 \

.'

0

001

0.02

0.03

004

0.05

0.06

An 1

i , outer region

1

34 32 30 A l % in guide layer core region

outer region

Fig. 14 Schematic representation of transverse modes in multiclad lateral waveguide evenmade ~~~- odd mode ~

transverse mode in the core regions. EIM is a good approximation only when the overlap integral of the fields of the transverse mode in the core region and one of the modes in the outer region(s) is close to unity. When substantial overlap occurs with the even mode (i.e. I CO,1' 1) [49] the lateral waveguide is close to a pure antiguide, a structure also known as LCSP 1511. When substantial overlap occurs with the odd mode (i.e. I CO,l2 Y 1) the lateral waveguide is a positive-index guide, the familiar CSP [52]. For intermediate cases the only rigorous solution is that pointed out by Amann [SO], i.e. match boundary conditions for fields and field derivatives of supported modes and 4-8 radiation modes. The number of modes in the core and outer regions must be the same; that is, if N radiation modes are considered in the core N - 1 radiation modes should be considered in the outer regions. We and Hadley et al. [21] have extended the model by Amann for multiclad waveguides to arrays of antiguides. Ten to twenty transverse modes are used for each element and interelement region. The novel 2-D code we developed is called MODEM [53] and has been applied to 20-element 3/1-geometry GRINSCH structures [48]. In Fig. 15 we show, for the first time, the main differences between EIM calculations and MODEM calculations. We plot the modal radiation losses of in-phase mode 38 and adjacent modes 37 and 39 as a function of An (which is the lateral index step in EIM) and the difference between the (interelement) even-mode propagation constant, and the (sole) transverse-mode propagation constant in the core in MODEM. The major difference is that resonance (i.e. the point of maximum radiation loss and uniform near-field intensity profile for the in-phase mode 38) occurs at significantly higher An values than for EIM. That means that to achieve resonance we have to incorporate -5% less AI in the passive guide layers of the interelement regions. We also note that the amount of discrimination between the in-phase mode and the adjacent modes decreases while remaining significant (45 cm- I). Although the practical impact is not serious, the conceptual impact is at the very least puzzling: the interelement region at resonance is no longer an odd number

1

28

Fig. 15 Modal radiation loss of modes 38, 37 and 39 of 20-element array 1481 as function of An, lateral index step in efective-index method ( E I M ) calculation, and digerence between propagation constants of even (interelement) transverse mode and fundamental (element)transverse mode in MODEM colculation N

=

20,d

__

20

I

=

3pm, s = I pm

38 (in-phase)

~~~

~

37 (adJaGSn1) 39 (adjacent)

an (effective) index of refraction. To find the condition for full optical transmission through such region(s) is nontrivial, and it is currently under study. All we can say at the present time is that, for multiclad antiguided array structures, the in-phase mode resonance has to be redefined as the place of maximum antiguided loss and of uniform near-field intensity profile. Note that the case presented in Fig. 15 is for poor overlap of the fields of the even mode and the element sole transverse mode: I C,,I' = 0.31. For structures with I C,,Iz 60% EIM is found to be a reasonably good approximation [19,21]. 7

Relevant results

Parallel coupling in strong index-guided structures has allowed ROW arrays to reach diffraction-limited powers 20-30 times higher than for other array types (see Table 1). This finally fulfills the phase-locked array promise of vastly improved coherent power by comparison with single-element devices. In pulsed operation 20-element devices have demonstrated diffraction-limited beams to 1.5 W and 10.7 x threshold (Fig. 16) [12]. Only 60% of the power is in the main lobe, but with further improvement we should be able to approach the theoretical limit of 81% 1541. In any event, as long as the emission is coherent we can use aperture-filling optical techniques [55] to gather close to 100% of the energy in the main lobe. More recently, by using the first resonant SAS-type structure. Mawst et al. [33] have demonstrated diffraction-limited-beam operation to 2.1 W. In CW operation we are limited by thermal effects (Fig. 17). The best result is 0.5 W CW D L (Fig. 17). The result has been achieved by optimising the device overall efficiency. For 1000 ,um long devices with HR and AR facet coatings (98 and 4% reflectivity) slope efficiencies of 48% were observed, and the power conversion efficiency reaches 20% at 0.5 W output. Preliminary lifetests show roomtemperature extrapolated lifetimes in excess of 10 000 h*. ~

* JANSEN, M.,

ROTH, T.J., BOTEZ, D., and MAWST, L.J.: unpub-

lished work IEE PROCEEDINGS-.I, Vol. 139, N o . I , FEBRUARY 1992

These

results

are

for

AlGaAs/GaAs

structures

(A = 0.84-0.86 pm). Antiguided arrays have also been made

from

strained-layer

quantum-well

material

(2. = 0.92-0.98 pm) in the SAS-type array configuration

[28, 311 (Fig. 5c). In pulsed operation, narrow-beam

( ztwice the diffraction limit) is obtained because the

devices are nonresonant [28, 311. Early CW results [56] showed thermal-induced focusing due to relatively small built-in index steps (0.005-0.01). By using significantly larger index steps (-0.12) Major et al. [28] have demonstrated stable and efficient CW operation to 0.5 W in a beam 1.5 x diffraction limit. For near-resonant devices, Talbot filters proved crucial in obtaining diffraction-limited beams [131. As shown in Fig. 18, diffraction-limited operation is

I

I

I

-20" -10"

1

-100

I

1

0"

10"

I

l

,

I

0" 10" angle, degrees

I

I

20"

Fig. 18 Lateral far-field patterns at various peak power levels for near-resonant 20-element arrays of antiguides with Talbot-type spatial filters [I31

angle, degrees

Fig. 16 Lateral far-field patterns at various peak pulsed powers for 20-element ROW array 1121

Threshold current I,, = 270 mA. qr = 31% (I 0.75 W, I = 7.31,, b 2 W,I = 191,, c 0.3 W,I = 3.61,, d 1.25 W, I = 10.71,,

I = 10.7 I,, at 1.5 W

0.5

04

rId='0

o\l

I

-10 0 10 angle. degrees

I

% i

$0: a 0 c

3

a I

0 7

2 0 2

I

I 01

0

obtained to 1 W, and then, owing to the oscillation onset of an adjacent mode, at 2 W the beamwidth is 1.5 x DL. Two Talbot filters are used because they provide more discrimination than one ZT/2-long filter, while having less edge-diffraction loss than one filter of 32,/2 length [13]. Uniform devices had beams (2-3) x DL which were maintained up to 5 W pulsed power and 45 x threshold (Fig. 19). It appears that the excitation of one or two adjacent modes creates a virtually uniform near-field intensity profile which, in turn, does not allow for the excitation of other higher-order modes. Forty-element antiguided arrays have also been fabricated and tested*. To maintain the same intermodal discrimination [13] as for 20-element devices the element size is reduced from 3 pm to 2 pm. Preliminary results are 0.95O-wide beams (2 x DL) at 2 W pulsed, and a 1.1"wide beam (2.5 x DL) up to 0.6 W CW power. Further work continues toward achieving 1 W CW in a diffraction-limited beam. There has been concern that, owing to their large size, arrays will have relatively slow pulse response. In fact, as shown in Fig. 20, 3 dB modulation bandwidths of 1.8 GHz can be achieved at only 1.5 x threshold [57]. Theoretically these meet expectations when considering that single-element devices are theoretically capable of 30-35 GHz bandwidths. Preliminary tests show pulse response times of < 200 ps.

Fig. 17 C W operation of optimised 20-element ROW arrays: lightcurrent characteristic and lateral farjield patterns at various power levels

*

Beam pattern is diffraction-limited up to 0.5 W

on IlO-element antiguided arrays

IEE PROCEEDINGS-J, Vol. 139, No. I , FEBRUARY 1992

MAWST, L.J., BOTEZ, D., and PETERSON, G . :unpublished work 21

Spectrally, CW devices start in a single-longitudinal mode [48] which holds up to -100 mW. Then, probably due to band tilling, another single longitudinal mode appears on the low-wavelength side at -40-50 A away

wavelength the emitted beams are stable, unlike the beam steering experienced in injection-locked broad-area oscillators. 8

Conclusions

Owing to parallel coupling, ROW arrays have many desirable features, namely maximum intermodal discrimination, full coherence and a uniform intensity profile. In turn, pure in-phase mode operation to Watt-range power has become feasible. The future for ROW arrays appears quite promising. We estimate that up to 5 W coherent CW power can ultimately be obtained from edge emitters, and, by extending resonant leaky-wave coupling in two dimensions, surface emitters delivering over 10 W coherent power may become a reality in the near future. 9

1

I

I

-100 0” 100 anqie, degrees

Fig. 19 Lateral Jar:freld putterns ut uarious peak power levels for near-resonant Zf)-element arrays of antiquides oJ ungorm longitudinal geometry 1/31 Threshold current I,,

=

260 mA.

vd = 35”1,)

5 W. I = 451.. h 4 W, I = 341,, 2.8 w,I = 231,, U



0.1

2.1

modulation frequency. GHz Fig. 20

Small-aiqnal frequency response Jor 20-element ROW urruy

At I 5 x threshold. 3 dB modulation bandwidth

5

I X5 C H I

from the original mode 128, 481. Above e 2 0 0 m W all spectra are multimode. However, if the device is resonant [48] the far-tield pattern remains diffraction limited. ROW arrays can be made single-frequency by injection locking 1581. Only a narrow (5 pm wide) injection spot on the device back facet, is needed for full array injection, a consequence of parallel coupling in the device. The master-oscillator wavelength can be changed over a >30 A interval, before locking is no longer possible. The most interesting result is that while tuning the ‘L

References

1 SCIFRES, D.R., BURNHAM, R.D., and STREIFER, W.: ’Phase locked semiconductor laser array’, Appl. Phys. Lett., December 1978, 33, pp. 1015-1017 2 FADER, W.J., and PALMA, G.E.: ‘Normal modes of N coupled lasers’, Opt. Lett., 1985, 10, pp. 381-383 3 MUKAI, S., LINDSEY, C., KATZ, J., KAPON, E., RAV-NOY, Z., MARGALIT, S., and YARIV, A.: ’Fundamental mode oscillation of a buried ridge waveguide laser array’, Appl. Phys. Lett., 1984,45, (8). pp. 834-835 4 BOTEZ, D., and CONNOLLY, J.C.: ‘High power phase locked arrays of index guided diode lasers’, Appl. Phys. Lett., December 1983.43, pp. 1096-1098 5 CHEN, K.L., and WANG, S.: ‘Single-lobe symmetric coupled laser arrays’, Electron. Lett., 1985, 21, (8), pp. 347-349 6 WELCH, D.F., CROSS, P., SCIFRES, D.R., STREIFER, W., and BURNHAM, R.D.: ‘In-phase emission from index guided laser array up to 400 mW’, Electron. Lett.. 1986,22, (6), pp. 293-295 7 WELCH, D.F., STREIFER, W., and SCIFRES, D.: ‘High power coherent laser diodes’, Optics News, March 1989, pp. 7-10 8 KATZ, J., MARGALIT, S., and YARIV, A.: ‘Diffraction-coupled phase-locked semiconductor laser array’, Appl. Phys. Left , 1983, 42, pp. 554-556 9 WANG, S., WILCOX, J., JANSEN, M., and YANG, J.J.: ‘In-phase locking in diffraction-cloupled phased-array diode lasers’, Appl. Phys. Lett., 1986.48, pp. 1770-1772 10 MEHUYS, D., MITSUNAGA, K., ENG, L., MARSHALL, W., and YARIV, A.: ‘Supermode control in diffraction-coupled laser arrays’, Appl. Phys. Lett., 1988, 53, pp. 1165-1 167 I I BOTEZ, D., MAWST, L.J.,PETERSON, G., and ROTH, T.J.: ’Resonant optical transmission and coupling in phase-locked diode laser arrays of antiguides: the resonant optical waveguide array’, Appl. Phys. Lett., 1989,54, pp. 2183-2185 12 MAWST. L.J., BOTEZ, D. JANSEN, M., ROTH, T.J., and ROZENBERGS, J.: ‘1.5 W diffraction-limited-beam operation from resonant-optical-waveguide (ROW) array’, Electron. Lett , 1991, 27, (4) pp. 369-371 13 BOTEZ, D., JANSEN, M., MAWST, L.J., PETERSON, G., and ROTH, T.J.: ‘Watt-range, coherent, uniphase powers from phaselocked arrays of antiguided diode lasers’, Appl. Phys. Lett., 1991, 58, (19), pp. 2070-2072 14 BOTEZ, D., MAWST, L.J., and PETERSON, G.: ‘Resonant leakywave coupling in linear arrays of antiguides’, Electron. Lett., 1988. 24, pp. 1328-1330 15 ENGELMANN, R.W.H., and KERPS. D.: ‘Leaky modes in active three-layer slab waveguides’, IEE Proc. I, Solid State & Electron Devices, 1980, 127, (6), pp. 330-336 16 BUTLER, J.K., ACKLEY, D.E.. and BOTEZ, D.: ‘Coupled-mode analysis of phase-locked injection laser arrays’, Appl. Phys. Lett., 1984,44, pp. 292-293; erratum p. 935 17 KAPON. E., KATZ, J., and YARIV, A.: ‘Supermodes analysis of phase-locked arrays of semiconductor lasers’, Opt. Left., 1984, 9, pp. 125-127; erratum p. 318 18 MARSHALL, W.K., and KATZ, J.: ‘Direct analysis of gain-guided phase-locked semiconductor laser arrays’, IEEE J . Quantum Electron, 1986, QE-22, pp. 827-832 19 BOTEZ, D., MAWST, L J., PETERSON, G.L., and ROTH, T.J.: ’Phase-locked arrays of antiguides: Modal content and discrimination’, IEEE J Quantum Electron., 1990,26, pp. 482-495 20 HADLEY, G.R.: ‘Two-dimensional waveguide modelling of leakymode arrays’, Opt. Lett., 1989, 14, (16), pp. 859-861 IEE PROCEEDINGS-J, Vol. 139, N o . I , FEBRUARY 1992

21 HADLEY, G.R., BOTEZ, D., and MAWST, L.J.: ‘Modal discrimination in leaky-mode (Antiguided) arrays’, IEEE J . Quantum Electron., 1991, 27, pp. 921-930 22 HADLEY, G.R.: ‘Two-dimensional coupled-mode theory for modeling leaky-mode arrays’, Opt. Lett., 1990,15, pp. 27-29 23 ELISEEV, P.G., NABIEV, R.F., and POPOV, YU.M.: ‘Analysis of laser-structure anisotropic semiconductors by the Bloch-function method, J . Sou. Laser Res., 1989, 10, (6), pp. 449-458 24 BOTEZ, D., and HOLCOMB, T.: ‘Bloch-function analysis of resonant arrays of antiguided diode lasers’, Appl. Phys. Lett., 1992,60, pp. 539-51 1 25 ACKLEY, D.E., and ENGELMANN, R.W.H: ‘High-power leakymode multiple-stripe laser’, Appl. Phys. Lett., 1981,39, pp. 27-29 26 BOTEZ, D., MAWST, L.J., HAYASHIDA, P., PETERSON, G., and ROTH, T.J: ‘High-power, diffraction-limited-beam operation from phase-locked diode-laser arrays of closely spaced “leaky” waveguides (antiguides)’, Appl. Phys. Lett., 1988,53, pp. 464-466 27 MAWST, L.J., BOTEZ, D., ROTH, T.J., and PETERSON, G.: ‘High power, in-phase-mode operation from resonant phase-locked arrays of antiguided diode lasers’, Appl. Phys. Lett., 1989, 55, pp. 10-12 28 MAJOR, J.S., MEHUYS, D., WELCH, D.F., and SCIFRES, D.R.: ‘High power high elliciency antiguide laser arrays’, Appl. Phys. Lett., 1991,59, pp. 2210-2212 29 STREIFER, W., HARDY, A., BURNHAM, R.D., and SCIFRES, D.R.: ‘Single-lobe phased-array diode lasers’. Electron. Lett.. 1985. 21, (3), pp.-118-120 30 STREIFER, W., HARDY, A., BURNHAM, R.D., THORNTON, R.L.. and SCIFRES. D.R.: ‘Criteria for desien of sinde-lobe ohasedarray diode lasers’, Electron. Lett., 1985,21,?1 I), pp.jO5-50, 31 SHIAU, T.H., SUN, S., SCHAUS, C.F., ZHENG, K., and HADLEY, G.R.: ‘Highly stable strained layer leaky-mode diode laser arrays’, IEEE Photonics Technol. Lett., 1990, 2, pp. 534-536 32 MAWST, L.J., BOTEZ, D., OU, S.S., SERGANT, M., and ROTH, T.J.: ‘Self-aligned stripe antiguided diode-laser array’. Tech. Dig., OSA Annual Mtg., 1990, Paper MK2, p. 14 33 MAWST, L.J., BOTEZ, D., ZMUDZINSKI, C.A., JANSEN, M., TU, C., ROTH, T.J., and YUN, F.: ‘Resonant self-aligned-stripe antiguided diode laser arrays’, Appl. Phys. Lett., February 1992,60 34 DUGUAY, M.A., KOKUBUN, Y., KOCH, T. L., and PFEIFFER, L.: ‘Antiresonant reflecting optical waveguides in SiO,-Si multilayer structures’, Appl. Phys. Lett., July 1986, 49, pp. 13-15 35 KOCH, T.L., BURKHARDT, E.G., STORZ, F.G., BRIDGES, T.L., and SIZER, T.: ‘Vertical grating-coupled ARROW structures for 111-V integrated optics’, IEEE J . Quantum. Electron., June 1987, QE23, pp. 889-897 36 BABA, T., KOKUBUN, Y., SASAKI, T., and IGA, K.: ‘Loss reduction of an ARROW waveguide in shorter wavelength and its stack configuration’, J . Lightwave Techno[., 1988.6, (9). p. 1440 37 WHITEAWAY, J.E.A., MOULE, D.J., and CLEMENTS, S.J.: ‘Tree array lasers’, Electron. Lett., 1989, 25, (12). pp. 779-781 38 STREIFER, W., HARDY, A., WELCH, D.F., SCIFRES, D.R., and CROSS, P.S.: ‘Improved Y-X junction laser array’, Electron. Lett., 1990,26, pp. 1730-1731 39 ZMUDZINSKY, C.A., BOTEZ, D., and MAWST, L.J.: ‘Simple description of laterally resonant, distributed feedback-like modes of arrays of antiguides’, kppl. Phys. Lett., 1992, 60 40 BOTEZ, D., PETERSON, G., MAWST, L.J., and ROTH, T.J.: ‘Inphase operating resonant arrays of antiguides without Talbot type

IEE PROCEEDINGS-J, Vol. 139, NO. I, FEBRUARY 1992

spatial filters’. Conf. Lasers and Electro-Optics 1990, Technical Digest Series, Optical Society of America, Washington, DC, 1990,7, pp. 432-433 41 HADLEY, G.R.: ‘Index-guided arrays with a large index step’, Opt. Left., 1989, 14, pp. 308-310 42 MAWST, L.J., BOTEZ, D., ROTH, T.J., SIMMONS, W.W., PETERSON, G., JANSEN, M., WILCOX, J.Z., and YANG, J.J.: ‘Phase-locked array of antiguided lasers with monolithic spatial filter’, Electron. Lett., 1989.25. pp. 365-366 43 HADLEY, G.R.: ‘Modes of a two-dimensional phase-locked array of vertical-cavity surface-emitting lasers’, Opt. Lett., 1990, 15, pp. 1215-1217 44 WILCOX, J.Z., SIMMONS, W.W., BOTEZ, D., JANSEN, M., MAWST, L.J., PETERSON, G., and YANG, J.J.: ‘Design of diffraction coupled arrays with monolithically integrated self-imaging cavities’, Appl. Phys. Lett., 1989,54, pp. 1848-1850 45 GOLUBENTSEV, A.A., LIKHANSKII, V.V., and NAPARTOVICH, A.P.: ‘Theory of phase locking of an array of lasers’, Sou. Phys. JETP, 1987,66, pp. 676-682 46 LEGER, J.R., SCOTT, M.L., and VELDKAMP, W.B.: ‘Coherent addition of AlGaAs lasers using microlenses and diffractive coupling’, Appl. Phys. Lett., 1988,52, pp. 1771-1773 47 VAN EIJK, P.D., REGLAT, M., VASILIEFF, G., KRIJNEN, G.J.M., DRIESSEN, A., and MOUTHAAN, A.J.: ‘Analysis of modal behaviour of an antiguide diode laser array with Talbot filter’, J. Lightwave Technol., 1991,9, pp. 629-634 48 MAWST, L.J., BOTEZ, D. ROTH, T.J., PETERSON, G., and ROZENBERGS, J. : ‘CW high-power diffraction-limited-beam operation from resonant-optical-waveguide arrays of diode lasers’, Appl. Phys. Lett., 1991,58, (l), pp. 22-24 49 CHINN, R., and SPIERS, R.J.: ‘Calculation of separated multicladlayer stripe geometry laser modes’, IEEE J. Quantum Electron., June 1982, QE-18, pp. 984-991 50 AMANN, M.-C.: ‘Rigorous waveguiding analysis of the separated multiclad-layer stripe-geometry laser’, IEEE J . Quantum Electron., October 1986, QE22, pp. 1992-1998 51 LEE, S.J., FIGUEROA, L., and RAMASWAMY, R.V.: ‘Leakyguided channeled substrate planar (LCSP) laser with reduced substrate radiation and heating’, IEEE J. Quantum Electron., July 1989, QE-25, pp. 1632-1645 52 AIKI, K., NAKAMURA, M., KURODA, T., UMEDA, J., ITO, R., CHINONE, N., and MAEDA, M.: ‘Transverse mode stabilized AI,Ga, _,As injection lasers with channel-subtrate-planar structures’, IEEE J . Quantum Electron., 1989, QEl4, pp. 89-97 53 PETERSON, G. and BOTEZ, D.: to be published 54 BOTEZ, D., and FRANTZ, L.: to be published 55 LEGER, J.R., SWANSON, G.J., and HOLZ, M.: ‘Ellicient side lobe suppression of laser diode arrays’, Appl. Phys. Lett., 1987, 50, pp. 1044-1046 56 HOHIMER, J.P., HADLEY, G.R., CRAFT, D.C., SHIAU, T.H., SUN, S., and SCHAUS, C.F.: ‘Stable-mode operation of leakymode diode laser arrays at high pulsed and CW currents’, Appl. Phys. Lett., 1991,58, (3,pp. 452-454 57 ANDERSON, E., JANSEN, M., BOTEZ, D.. MAWST, L.J., and ROTH, T.J.: ‘Modulation characteristics of high-power phaselocked arrays of antiguides’, submitted to Photonics Technol. Lett. 58 JANSEN, M., BOTEZ, D., MAWST, L.J., and ROTH, T.J.: ‘Injection locking of antiguided resonant optical waveguided (ROW) arrays’, Appl. Phys. Lett., January 1992,60, pp. 2 6 2 8

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