Watt-class high-power, high-beam-quality photonic- crystal lasers · 2014-04-25 · 1 Supplementary information Watt-class high-power, high-beam-quality photonic-crystal lasers Kazuyoshi

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Supplementary information

Watt-class high-power, high-beam-quality photonic-

crystal lasers

Kazuyoshi Hirose1,2*†, Yong Liang2†, Yoshitaka Kurosaka1,2, Akiyoshi Watanabe1,

Takahiro Sugiyama1 and Susumu Noda2,3*

1Material Research Group, Central Research Laboratory, Hamamatsu Photonics K.K.,

Shizuoka 434-8601, Japan. 2Department of Electronic Science and Engineering, Kyoto

University, Kyoto 615-8510, Japan. 3JST ACCEL, Kyoto University, Kyoto 615-8510.

*e-mail: [email protected], [email protected]

† These authors contributed equally to this work.

Supplementary methods

1. Lasing principle and theoretical model of photonic-crystal surface-

emitting lasers (PCSELs)

Here, we first present the lasing principle of PCSELs and then describe the

theoretical model used for calculating the lasing characteristics of the resonant modes.

The PCSEL structure depicted in Fig. 1a is designed such that it supports only a single

fundamental guided mode. In this case, the light is guided and amplified in the active

layer. The two-dimensionally (2D) patterned square-lattice photonic crystal (PC) layer

is placed close to the active layer. Although the light is confined to the region close to

the active layer, the evanescent wave penetrates into the PC layer. Here, the pitch of the

square-lattice PC is designed to match to the wavelength of the light propagating in the

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active layer. In this case, the propagating light inside the PC layer will undergo multiple

Bragg diffraction. Fig. S1a shows a schematic of diffraction of lightwaves in a square-

lattice PC structure. The lattice constant (a) in both the x and y directions equals one

wavelength. When the lightwave propagates in the +y direction (0°), it is reflected

backwards because the second-order Bragg diffraction condition is satisfied. In addition,

the lightwave is also diffracted to the perpendicular directions (+90° and -90°) because

the first-order Bragg diffraction conditions are satisfied for these directions, and these

diffracted lightwaves are again reflected backwards. Consequently, lightwaves

propagating in four directions are coupled with each other, and a 2D standing wave state

(or 2D large-area cavity mode) is formed in the PC plane. Furthermore, the in-plane

lightwaves in resonance is also diffracted toward the vertical (z) direction due to the

first-order Bragg diffraction condition, as shown in Fig. S1b. This vertically diffracted

lightwave constitutes the surface-emission output of PCSELs.

The diffraction described in Fig. S1 is simply an intuitive description of

lightwave interactions in real space, in which only four dominant wave-vector

components with propagation constant of 2π / a are considered. However, in reality,

the (Bloch) lightwaves propagating inside a periodic 2D PC include a large number of

wave-vector components and they interact with each other in a more complex manner.

To accurately describe the wave interactions, we must consider a full set of wave-vector

components in the reciprocal space of PC, as shown in Fig. S2. The 2D standing wave

state described in Fig. S1 is primarily made up of fields of four wavevectors which we

refer to as basic waves xR , xS , yR and yS , as shown in Fig. S2a (the short, lightly shaded

arrows in the center of the figure). In the case of transverse-electric (TE) polarization,

counter-propagating basic waves couple directly due to conventional one-dimensional

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(1D) feedback (green arrows)S1, and basic waves propagating in orthogonal directions

couple indirectly (dashed purple arrows) via higher-order wave vectors (black arrows)S2.

The latter 2D coupling effect is unique to the PC structure and is also crucial for

modeling our PCSELs. This 2D coupling provides a multidirectionally distributed

feedback mechanism to form a 2D standing wave state in PC plane. Fig. S2b illustrates

the out-of-plane coupling between the basic waves and radiative waves (red arrow) that

is induced by first-order Bragg diffraction (dashed red arrow). All coupling effects

described in Fig. S2 can be analytically treated using a three-dimensional (3D) coupled-

wave theory (CWT)S2-S4, in which both the surface emission (i.e. the device output) in

the vertical direction and the 2D resonance in the PC plane are taken into account. The

derived coupled-wave equation is as follows:

(δ + i α2

)

Rx

Sx

Ry

Sy

= C[ ] ⋅

Rx

Sx

Ry

Sy

+ i

∂Rx / ∂x−∂Sx / ∂x∂Ry / ∂y

−∂Sy / ∂y

(1)

Here, C is a 4×4 matrix, the individual elements of which are dependent on the PC

geometry and the laser waveguide structure and are determined analytically as described

in refs. S2-4. δ and α represent the frequency deviation from the Bragg condition and

the threshold gain, respectively. Note that here α accounts for the total optical (modal

power) losses (α = α⊥ +α // : α⊥ represents the vertical radiation loss and α // represents

the in-plane radiation loss) of the laser cavity. Solutions of Eq. (1) provide the lasing

characteristics (e.g., mode frequency, cavity losses, field distribution, etc.) of the

resonant modes in PCSELs. These modes correspond to the band-edge modes A-D

schematically shown in Fig. S3a, for which the group velocity of light is equal to zero.




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The field distributions of these four band-edge modes are shown in Fig. S3b. Note that

the field distribution profiles are closely related to radiation loss (i.e., output power)S2.

The threshold condition corresponds to the situation when the modal (threshold)

gain balances the total optical cavity losses. In our model, we have applied a uniform

gain distribution. This is because the carrier density within the MQWs active layer can

be assumed to be uniform at or near the threshold condition, and the PC layer is located

far away enough (65 nm) from the MQWs active layer such that the spatial gain is not

modulated by the periodic PC air holes. In addition, for our material system, the modal

gain provided by the MQWs active layer is in the order of several hundreds of cm-1,

which is sufficient to compensate the optical cavity loss (typically in the order of

several tens of cm-1 for the lasing modes of our PCSELsS2-4). Since the lasing action is

onset at the resonant mode with the lowest threshold gain, the mode with the smallest α

will be the first mode to reach the threshold. The cavity-loss difference between the

first-lowest threshold mode and the second-lowest threshold mode determines the side

mode suppression ratio and, hence, mode selection.

To solve Eq. (1) within a finite-size laser cavity, we introduce a boundary

condition defined as

Rx (0, y) = Sx (L, y) = Ry(x, 0) = Sy (x, L) = 0 (2)

which indicates that the amplitudes of the basic waves always start from zero at the

boundaries. This generalizes a similar concept for the distributed feedback laser

structure originally proposed by Kogelnik and ShankS1. By solving Eq. (1) as a

generalized eigenvalue problem using a finite-difference method, we can obtain the

normalized eigenvalues (δ + iα / 2)L and the spatially-dependent eigenvectors Rx, Sx, Ry




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and Sy . It is noteworthy that since the 3D-CWT algorithm is a semi-analytical

algorithm, our calculation takes a very short calculation time (less than 1 minute). In

contrast, the widely used finite-difference time-domain (FDTD) simulation requires

substantial computational time and resourcesS5. This is because the laser structure

presented in this work has an extremely large dimension in the x-y plane, 700a×700a

(200 μm×200 μm), and the PC air holes formed by metal organic chemical vapor

deposition (MOCVD) have a complicated geometry extended in the x, y, and z

directions (see Fig. 1).

2. Effect of vertical asymmetry on output property

The asymmetry introduced in the x-y plane has been theoretically studied in

previous worksS2, S6 and is found to be beneficial for improving the output power and

slope efficiency. However, the effect of asymmetry in the z direction has not been fully

investigated for realistic PCSEL structures. Here, we study the effect of this vertical

asymmetry on the laser output property (beam profile and output power). For simplicity

and clarity, we assume that both the upper and lower surfaces of the device are anti-

reflection coated. Reflection induced by the p-side gold electrode may rescale the

magnitude of the vertical radiation power but would not change the output beam profile.

This reflection effect will be discussed in detail in the next section.

The epitaxial structure that was modeled is shown in Fig. S4a, where both the

thickness and refractive index of each layer were estimated from the fabricated sample.

The PC layer is embedded inside the multilayer structure that was designed to support

only a single fundamental guided mode. Fig. S4b shows a schematic picture of the PC

laser cavity, covering an area of 200 μm×200 μm. In the fabricated sample, SEM




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images showed that the air holes exhibit a right-angled isosceles triangular (RIT) shape

in the x-y plane but are tapered along the -z direction due to the regrowth process (Figs.

1b and c). We modeled this geometry as shown in Fig. S4c. The upper part of the air

hole was approximated by a triangular prism and the lower part by a triangular pyramid

that was truncated before the apex. The heights of the prism and pyramid are 116 nm

and 119 nm, respectively. The in-plane cross sections of the two parts are also shown in

Fig. S4c, both of which adopt RIT shapes. The triangular faces of the upper prism have

a side length of 175 nm and a curvature of 30 nm at each vertex. The triangular cross-

section of the pyramid has the same shape as the faces of the prism but its side length

gradually decreases along the –z direction. The pyramid is truncated before its apex by a

smaller triangle with a side length of 58 nm (corresponding to a filling fraction of 2%).

Here, the parameter dx (red arrow) represents the shift of the right-angled corner of the

triangle on the lower face of the pyramid with respect to the corresponding corner of the

prism. Based on our observation of the air-hole SEM images, the shift distance of dx is

estimated within in the range of 0~20 nm.

Fig. S5a shows the calculated peak intensity of the far-field pattern (FFP) for

different polarization angles θ (definition shown in lower-left inset). The calculations

were performed for the lowest-threshold mode B at dx=0, 5, 10 15, and 20 nm (upper-

right inset). The shift dx critically affects the polarization profile of the FFP and when

dx<20 nm, the polarization has maximum intensity in the θ = 45 direction. It is

important to note here that when dx=0 nm (i.e., when the right-angled corner of the

lower surface of the pyramid coincides with that of the prism), the FFP shows identical

polarized intensity in the x and y directions. This is because of the symmetric nature of

the air holes with respect to the y=x direction. However, this polarization profile is not




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in agreement with our experimental results (see Fig. 4c), where the intensity in the x

direction is higher than in the y direction. For this reason, we need to take the effect of

dx into consideration. It is apparent from Fig. S5a that increasing dx leads to larger

polarization intensity in the x direction and accordingly to decreased intensity in the y

direction. In particular, at dx=10 nm the calculated FFP profile and polarization profile

are presented in Figs. 4d and e, in excellent agreement with our experimental

observations. Therefore, we infer that the fabricated PC air-hole structure has a shift of

dx=10 nm in the -x direction.

Fig. S5b shows the calculated radiation constant (i.e., the modal power loss due

to surface emission) of the lowest-threshold mode B for air-hole structures with and

without vertical asymmetry. The calculated radiation constant of the fabricated air-hole

structure (with dx=10 nm) is ~36 cm-1. In comparison, the radiation constant of a

structure with a prismatic, vertically symmetric air holes (whose sidewalls in the z

direction are perfectly vertical) and the same height of 235 nm, is ~3 cm-1. This is more

than one order of magnitude smaller than the radiation constant of the air-hole structure

with vertical asymmetry. Such a small radiation constant might be a consequence of the

height of the prism, which causes destructive interference in the z directionS7.

Nevertheless, our results illustrate the benefit of air holes with vertical asymmetry. We

also confirmed that a larger radiation constant of ~47 cm-1 can be obtained at dx=0 nm,

indicating a further possibility of power enhancement (a factor of 1.3) by modifying the

asymmetry of the air holes. Therefore, we conclude that vertical asymmetry is a key

factor in the significant improvement of surface-emission output power demonstrated

by our device.




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3. Effect of p-electrode reflection on slope efficiency

A relation between the light output power and the injection current in the

PCSEL can be derived as followsS8:

Pout = hνe

ηiα⊥

α⊥ +α // + ai

ηup(I − Ith ), (3)

where ν is the mode frequency, the unit charge is e = 1.6 ×10−19 C, ηi is the internal

quantum efficiency, α⊥ represents the total vertical radiation loss, α // represents the in-

plane radiation loss, and αi is the intrinsic loss due mainly to free carrier absorption of

the waveguide material and to scattering loss caused by the roughness of the waveguide

wall. The term ηup = α⊥up /α⊥ accounts for the ratio of upward-radiated loss (output)

through the n-side electrode window with respect to the total vertical radiation loss, and

Ith represents the threshold current. When the resonant wavelength λ (in units of μm)

is known, the slope efficiency η can be expressed as follows:

η = 1.24λ

ηiα⊥

α⊥ +α // + ai

ηup. (4)

For our fabricated device, λ = 0.94 μm, ηi ≈ 0.9, and αi ≈ 5 cm-1. From Eq. (4), it is

clear that a large vertical radiation constant α⊥ is a key factor for obtaining a high slope

efficiency. This can be realized by the vertical asymmetry of the PC air holes, as

described in the previous section. We also note that reducing the in-plane loss α // is

important in improving the slope efficiency. This can be realized by using a device with

a large area. Our calculations (assuming that both the upper and lower device surfaces

are anti-reflection-coated) show that for a side length of L=200 μm, α // ≈ 1 cm-1, which

is negligibly small compared to α⊥ ≈ 38 cm-1. As a result, a high differential quantum




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efficiency [i.e., α⊥ / (α⊥ +α // + ai )] of ~86% can be obtained. Our final concern is the

term ηup = α⊥up /α⊥ , which takes into account the fact that the vertical radiation consists

of both upward and downward radiated components, and that only the upward-radiated

component (Pu) contributes to the laser output, as depicted in Fig. S6a. Therefore, to

maximize the upward vertical radiation, the p-side gold electrode was used as a partial

reflector to redirect the downward-radiated component (Pd) in the upward direction. The

upper device surface (i.e., the n-side surface) is anti-reflection-coated to maximize

upward-radiated light.

In order to efficiently utilize the downward-radiated optical power, it is critical

to precisely match the phase of the back-reflected lightwaves with that of the upward-

radiated waves such that constructive interference occurs when they are coupled into

free space. Otherwise, the slope efficiency might be reduced significantlyS9.

Accordingly, the thickness of the p-GaAs contact layer (just above the p-side electrode)

dp can be adjusted to tune the phase difference between the upward-radiated and back-

reflected lightwaves. After performing calculations of slope efficiency at various

thicknesses, we found that the phase-matching condition is satisfied at an optimal

thickness of ~210 nm, leading to a maximum slope efficiency of 1.07 W/A. In our

calculations, the mirror reflectivities of the top and bottom layers were set to 0.0 and

0.8exp(i*2π/3), respectively. For the latter, the gold-electrode reflector is characterized

by a complex refractive index at λ = 0.94 μm by taking the electrode surface roughness

into account. These reflectivities were incorporated into the generalized Green’s

function derived in ref. S3 in order to modify the boundary condition of the vertically

radiated waves. Fig. S6b shows the calculated slope efficiency of the lowest-threshold




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mode B (red curve) as a function of the deviation from the optimal p-contact layer

thickness (~210 nm). For reference, the dashed black line (slope efficiency=0.43 W/A)

corresponds to the case where both the upper and lower device surfaces are anti-

reflection-coated. We note that this value is not consistent with the high slope efficiency

(0.66 W/A under c.w. operation) obtained in our experiments. Therefore, the

contribution of the p-electrode reflection must also be taken into account. Our fabricated

device had a p-GaAs contact layer thickness of ~190 nm. This thickness corresponds to

slope efficiency = 0.77 W/A, which is slightly larger than the experimental value of

0.66 W/A but within the error range involved in measuring the thickness/roughness of

the epitaxial structure. From the curve presented in Fig. S6b, we believe that the slope

efficiency can be further enhanced by a factor of ~1.6 by optimizing the p-GaAs contact

layer thickness.

References

S1. Kogelnik, L. & Shank, C., V. Coupled-wave theory of distributed feedback lasers. J.

Appl. Phys. 43, 2327-2335 (1972).

S2. Liang, Y., Peng, C., Sakai, K., Iwahashi, S. & Noda, S. Three-dimensional coupled-

wave model for square-lattice photonic crystal lasers with transverse electric

polarization: A general approach. Phys. Rev. B 84, 195119 (2011).

S3. Peng, C., Liang, Y., Sakai, K., Iwahashi, S. & Noda, S. Coupled-wave analysis for

photonic-crystal surface-emitting lasers on air holes with arbitrary sidewalls. Opt.

Express 19, 24672-24686 (2011).

S4. Liang, Y., Peng, C., Sakai, K., Iwahashi, S. & Noda, S. Three-dimensional coupled-

wave analysis for square-lattice photonic-crystal lasers with transverse electric




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polarization: Finite-size effects. Opt. Express 20, 15945-15961 (2012).

S5. Yokoyama, M. & Noda, S. Finite-difference time-domain simulation of two-

dimensional photonic crystal surface-emitting laser. Opt. Express 13, 2869-2880 (2005).

S6. Kurosaka, Y., Sakai, K., Miyai, E. & Noda, S. Controlling vertical optical

confinement in two-dimensional surface-emitting photonic-crystal lasers by shape of air

holes. Opt. Express 16, 18485-18494 (2008).

S7. Iwahashi, S., Sakai, K., Kurosaka, Y. & Noda, S. Air-hole design in a vertical

direction for high-power two-dimensional photonic-crystal surface-emitting lasers. J.

Opt. Soc. Am. B 27, 1204-1207 (2010).

S8. Chuang, S. L. Physics of photonic devices, 2nd ed. (Wiley, 2009).

S9. Sakaguchi, T. et al. Surface-emitting photonic-crystal lasers with 35W peak power.

Technical Digest of Conference of Lasers and Electro-Optics (CLEO) CTuH1 2009.




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Supplementary Figures and Legends

a

a

-90º +90º

0º 180º

x

y

yx

z

a

b

Supplementary Figure S1 Diffraction of lightwaves in a square-lattice photonic crystal laser cavity. a, In-plane diffraction. The yellow arrows indicate in-plane (x-y) propagating lightwaves. The lattice constant a is equal to one wavelength. b, Vertical diffraction. The red arrows indicate lightwaves diffracted into the vertical (z) direction.




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Γ-Y

Γ-X

Γ-M

Surface emission

2π/a

2π/a

Γ-Y

Γ-X

Sx Rx

Sy

Ry

a

b

Supplementary Figure S2 Coupling diagram shown in the reciprocal space of a square-lattice PC. a, In-plane coupling diagram. The lightly shaded and black arrows indicate basic and higher-order waves, respectively. The dashed green and purple arrows represent one-dimensional and two-dimensional couplings, respectively. b, Out-of-plane coupling due to first-order Bragg diffraction (dashed arrow).




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0.290

0.295

0.300

Γ X M

A B

D C

+

-

0

A B

DC

a

b

0

0.1

0.2

0.3

0.4Fr

eque

ncy

(c/a

)

Γ X M Γ

Γ2

x

y

Supplementary Figure S3 Two-dimensional band-edge resonant modes. a, Photonic band structure of a square-lattice PC with circular air holes calculated for transverse-electric (TE)-like mode. Right Inset shows the detailed band structure at the second-order Γ point (Γ2: red square), in which band-edge modes A-D are indicated. b, Field distributions around the air hole at the individual band-edge modes A-D. Amplitudes of magnetic fields in the direction perpendicular to the PC plane are indicated by colors. Arrows indicate the electric-field vectors in PC plane, and thick circles indicate the border of air holes.




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a

z=-2035-dp nm Electrode (0.196-i6.021)p-GaAs contact (3.553)

p-clad (3.273)

n-clad (3.122)

PC (GaAs: 3.553/Air: 1.0)

i-GaAs (3.553)Active (3.435)

Antireflection-coated layer

z=0 nm

z=-235 nm

z=-2035 nm

z=65 nm z=245 nm

z=2245 nm

z

x

b

L

L=200 μm p-Clad

c

x

y z

x

y

175 nm

175 nm

116 nm

119 nm

In-plane deviation of right-angle corners, dx

58 nm

58 nm

x

yz

Supplementary Figure S4 Description of the calculated structures. a, Illustration of epitaxial structure comprising PCSEL. The upper device surface is anti-reflection coated, whereas the p-side gold electrode acts as a partial reflector. The thickness of the p-GaAs contact layer dp can be varied. b, Schematic view of photonic crystal laser cavity (area 200 μm×200 μm). c, Top (left) and side (right) views of single air hole. The experimental air-hole structure is approximated by the combination of a triangular prism (upper part) and a triangular pyramid (lower part). The right-angled corner of the bottom surface of the pyramid is shifted by a distance of dx in the –x direction with respect to that of the prism faces.




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0

10

20

30

40

50

Conventional structure

θ

x

y

dx

Present structure

Rad

iatio

n co

nsta

nt (c

m-1

)

Polarization angle θ (degree)

Inte

nsity

(a.u

.)

a

b

Supplementary Figure S5 Calculated polarization profiles and radiation constants. In the calculations, we assumed that both the upper and lower surfaces of the device are anti-reflection coated. a, Intensity of polarized components at four typical polarization angles (lower-left inset: definition of polarization angle θ) calculated for various values of right-angled corner shift dx (upper-right inset). The polarized intensities at θ=45º are normalized to 1.0 in order to compare with the experiments. b, Comparison of the radiation constant (for the lowest-threshold mode B) of air-hole structure without (blue bar) and with (red bar) vertical asymmetry (dx=10 nm). The calculations were performed for PC air holes with identical overall air-hole depth of 235 nm.




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Deviation from the optimal thickness (nm)

Slo

pe e

ffici

ency

(W/A

)

b

a

dp z=-2035-dp nm

Antireflection-coated layer

z=0 nm

z=-235 nm

z=-2035 nm

z=65 nmz=245 nm

z=2245 nm

Gold electrode

Pd

Pin

x=0 x=L

y x

z

Pu

(Partical reflector)

1.2

1.0

0.8

0.6

0.4

0.2

0.0 -60 -40 -20 0 20 40 60 80

Supplementary Figure S6 Calculation of slope efficiency and effect of the p-electrode reflection. a, Schematic illustration of the upward-radiated (Pu), downward-radiated (Pd), and the in-plane radiated power (Pin). The gold electrode acts as a partial reflector to reflect the down-radiated waves into the upward direction. b, Calculated slope efficiency as a function of the deviation from the optimal p-contact layer thickness (210 nm). In the calculations, the cavity side length L=200 μm, and mirror reflectivities of the top and bottom layers are set to be 0.0 and 0.8exp(i*2π/3), respectively. The dashed black line in b indicates the case when mirror reflectivities of both the top and bottom layers are set to be 0.0 (anti-reflection coated).




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Watt-class high-power, high-beam-quality photonic- crystal lasers · 2014-04-25 · 1 Supplementary information Watt-class high-power, high-beam-quality photonic-crystal lasers Kazuyoshi