Photonic Crystal Microcavity Light Sources

Photonic Crystal Microcavity Light Sources

6.12 Photonic Crystal Microcavity Light Sources H Altug, Boston University, Boston, MA, USA D Englund and J Vuckovic, Stanford University, Stanford, C...

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6.12 Photonic Crystal Microcavity Light Sources H Altug, Boston University, Boston, MA, USA D Englund and J Vuckovic, Stanford University, Stanford, CA, USA ª 2011 Elsevier B.V. All rights reserved.

6.12.1 6.12.2 6.12.2.1 6.12.2.2 6.12.3 6.12.3.1 6.12.3.2 6.12.4 6.12.4.1 6.12.4.2 6.12.4.2.1 6.12.4.2.2 6.12.4.3 6.12.4.3.1 6.12.4.3.2 6.12.4.3.3 6.12.4.4 6.12.5 6.12.5.1 6.12.5.2 6.12.5.3 6.12.5.4 6.12.5.5 6.12.6 References

Introduction Photonic Crystals PhC Slabs PhC Nanocavities PhC Lasers Lasing Materials PhC Laser Fabrication Highly Efficient Photonic Crystal Lasers: Coupled Nanocavity Arrays 2D Coupled Nanocavity Arrays Dispersion Diagram of Coupled-Cavity Arrays Coupled dipole band Coupled quadrupole band Coupled-Cavity Array Laser Experimental setup Lasing spectrum and mode profile Light-in/light-out curve Comparison with Theory Ultrafast Photonic Crystal Lasers Experimentation Setup Lasing Spectrum Spontaneous Emission Rate Modification Ultrafast Dynamics of the Nanocavity Lasers Direct Modulation of Ultrafast Nanocavity Lasers On-Chip Integration of Photonic Crystal Waveguides and Lasers

6.12.1 Introduction During the last 30 years, we have witnessed the outcome of Moore’s law as the reduction in feature sizes of electronic devices continued to lead to denser and faster electronic circuits. While integration and density have improved by orders of magnitude, the basic physical implementations have remained largely the same. Increasingly, these implementations are running into limitations in electrical signaling, including loss, bandwidth, signal-to-noise, crosstalk, and latency. More importantly, metal interconnects pose fundamental problems in the next-generation electronic circuit due to high power consumption and electromagnetic interference (EMI). On-chip and chip-to-chip optical interconnects offer a solution to these problems by promising 486

486 487 487 488 489 490 490 491 492 492 494 494 494 496 496 497 499 499 501 502 502 503 505 505 506

higher bandwidths to keep pace with transistors, while lowering power consumption and being immune to EMI. On the other hand, realization of optical interconnects requires a new generation of optical devices, including compact, fast and efficient light sources, switches, detectors, and waveguides. Their high-density on-chip integration is also crucial. Realization of a fully integrated optical circuit will impact not only the development of optical interconnects of different length scales ranging from long haul to on chip, but also other fields such as biochemical sensing, spectroscopy, and optical data storage. In recent years, due to advances in nanofabrication and highly parallel computation, nanophotonics is emerging as the solution for many problems of the above-mentioned fields. Among several different

Photonic Crystal Microcavity Light Sources

nanophotonic approaches, photonic crystals (PhCs) are leading the field as they enable unprecedented control over photon manipulation and also offer the most suitable platform for compact on-chip integration. In this chapter, we describe PhC-based lasers and their unique advantages.

487

2r a z n

d

y x

Figure 1 Photonic crystal slab structure patterned with a triangular lattice, and the definition of its parameters.

6.12.2 Photonic Crystals PhCs (John, 1987; Yablonovitch, 1987) are structures with periodic dielectric modulation on the order of the wavelength of light. Because of this periodicity, their study is analogous to the study of semiconductors in solid-state physics. The periodicity of the electronic potential in semiconductor resulting from regular arrangement of atoms in a lattice gives rise to the electronic band gaps, the forbidden energy bands for electrons. Similarly, the periodicity of the refractive index (i.e., dielectric constant) gives rise to photonic band gaps, the forbidden energy bands for photons. Depending on the dimensionality of such periodicity, different classes of PhCs can be defined. One-dimensional (1D) PhC crystals, also known as the distributed Bragg reflectors (DBRs), have been known for a long time as mirrors. The periodicity of dielectric constant in more than one dimension has recently been suggested simultaneously by Yablonovitch (1987) and John (1987). Photonic crystal fibers are currently the most practical use of 2D PhCs (Knight et al., 1996). Although, 3D PhCs can have a complete photonic band gap and can control the light propagation in all directions, their fabrication is still significantly challenging (Fleming and Lin, 1999; Lodahl et al., 2004; Ogawa et al., 2004). 6.12.2.1

PhC Slabs

In recent years, the structure that has received significant attention is a thin semiconductor slab of thickness on the order of /(2n) (one-half of the optical wavelength) perforated with a 2D PhC lattice, as shown in Figure 1. These structures are known as PhC slabs (Villeneuve et al., 1998), and retain most of the important features of full 3D PhC. Their appreciated advantage comes from an easy fabrication procedure, which is compatible with standard planar technology used to make electronic circuits. In PhC slabs, the localization of light in the vertical direction is controlled by the total internal reflection (TIR) resulting from the high-index contrast between the high-index

slab and the low-index environment. On the other hand, the confinement in the lateral direction is controlled by the DBR resulting from the 2D PhC lattice. The optical properties of PhC slabs are described with their dispersion diagram, !(k). The dispersion diagram gives the frequencies of the Bloch modes of the periodic structure as a function of the in-plane wave vector. Figure 2 shows the dispersion diagram for the transverse-electric (TE)-like modes in a square lattice obtained by using 3D finite difference time domain (FDTD) method (Taflove and Hagness, 2000). TE-like modes, which are also referred as the even modes, have dominant Ex, Ey, and Bz components in the middle of the slab. In the PhC slab, since the structure is neither periodic nor infinite in the third dimension (z), photons incident to the interface between the semiconductor slab and air under angles smaller than the critical TIR angle can escape from the structure and couple to the continuum radiation modes. To take into account these radiation losses in the analysis of planar PhC slabs, we use the notion of the light line, indicated by the solid red line in Figure 2. The region above the light line corresponds to the leaky modes, which are not confined by TIR, and is generally shaded in the literature. The modes below the light line can be guided in the slab and are called guided modes. The photonic band gap exists between the bottom of the second band at the X point and the top of the first band at the M point, as shown in Figure 2. In this band gap, no guided modes exist for any propagation direction. As the electric field of the guided modes below the band gap is mostly concentrated in the dielectric region, these modes are called the dielectric band modes. Similarly, the guided modes above the band gap are called the air band modes as the electric field is mostly concentrated in the PhC holes. The dispersion and thus the width and the position of the photonic band gap strongly depend on the parameters of the slab such as the refractive index (n), the type of the PhC lattice (square, triangular, etc.),

488 Photonic Crystal Microcavity Light Sources

0.8

0.7

Normalized frequency (a /λ)

0.6

0.5

0.4

0.3

0.2

M Γ

0.1

0

Γ

X

X

Γ

M

Figure 2 Band diagram of eigenmodes of a silicon slab perforated with a 2D square photonic crystal lattice. The x-axis represents different directions in the reciprocal (k) space, and the y-axis represents normalized frequency in the units of a/ (where the wavelength is in free space). The solid red line represents the light line. The inset shows the directions of its first Brillion zone in the reciprocal space.

the lattice periodicity (a), and the hole radius (r). Therefore, one can control the band gap or tune the mirror properties of PhC slabs lithographically by simply changing the lattice type, (a) and (r). This significantly reduces both the fabrication complexity and cost compared to the fabrication of DBR stacks (1D PhCs), where the mirror properties are controlled by epitaxial growth.

6.12.2.2

PhC Nanocavities

PhCs can be used to make optical nanocavities that can trap the light in very small mode volumes (Vmode) and for a long period of time (proportional to the cavity quality factor Q). The strong light localization in photonic crystal nanocavities can dramatically increase the light–matter interaction and the photon–photon interaction, which are important for a wide range of applications. In addition, by designing PhC cavities in a linear configuration, one can construct compact waveguides that can also sharply bend while maintaining very low losses. These waveguides and cavities (either in passive form for wavelengthfiltering function or in active form for lasing action)

can be efficiently coupled on chip. These merits are important for compact and high-bandwidth opticalintegrated circuits. PhC nanocavities can be formed by modifying one or more holes (i.e., by changing the hole size or the refractive index) in an otherwise perfect periodic lattice. Such a break in the periodicity of the lattice introduces new energy levels within the photonic band gap. This is analogous to the creation of defect states within the semiconductor energy band gap by the addition of dopant atoms in crystals. An increase in the size of one (or more) holes in a dielectric PhC slab results in a defect state that is pulled up from the dielectric band into the band gap. The reduction of the hole sizes, on the other hand, decreases the energy of the mode and pulls down defect states from the air band into the band gap. Depending on the application, one can engineer the mode volume and the quality factor of nanocavities. The mode volume, Vmode, is defined as follows: Z Vmode ¼

d3 r"ðrÞjEmode ðrÞj2

V   max "ðrÞjEmode ðrÞj2

ð1Þ

Photonic Crystal Microcavity Light Sources

where "(r) is the refractive index variation in space, and Emode(r) is the electric field profile of the mode. As mentioned above, the vertical confinement in the slab is achieved by TIR. Therefore, the defect modes in the band gap will suffer from radiation losses due to their coupling to the continuum of radiation modes that exists within the light cone. This vertical (out-of-plane) loss can be described by Qver. In addition, the light can leak laterally due to the finite number of PhC layers surrounding the defect. This lateral (in-plane) loss can be described by Qlat. The total Q factor of the cavity can then be written as the superposition of these two factors as follows: 1 1 1 ¼ þ Qtotal Qver Qlat

ð2Þ

The lateral loss can be significantly suppressed (and Qlat can become very large) by increasing the number of PhC layers around the cavity operating at the frequency inside the band gap. Therefore, it is mostly the vertical loss (Qver) that determines the total Q of the cavity. In our lasing work that will be reviewed here, we have mainly worked with a single-defect cavity formed by a missing hole in a square lattice. Such a cavity supports three types of defect modes: quadrupole, dipole, and monopole. The quadrupole mode has the highest quality factor among them with a Qtotal  10 000 (with five PhC periods around the defect), while the dipole mode has a Qtotal  1500 limited by the vertical loss. Since the photon decay times are on the order of a picosecond, both modes are suitable for ultrafast laser applications (Altug et al., 2006). However, for certain applications such as the observation of strong coupling between a single photon and a single emitter (such as a quantum-dot (QD) or an atom), it is desirable to have cavities with ultrahigh Q. The optimization of cavity quality factor is currently an active research subject. Although in active devices (containing quantum-well or -dot) the Q’s are limited to a range of 104, in passive structures made of silicon PhCs, nanocavities with Q factors greater than 106 have been experimentally demonstrated (Song et al., 2005).

6.12.3 PhC Lasers The strong light–matter interaction in PhCs is under immense investigation for various applications ranging from communications to biosensing. In this chapter, the focus is on how enhanced light–matter

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interaction in 2D PhC slabs and cavities can be used to improve the performance of lasers. The use of PhCs in lasing is actually not new. 1D-PhC crystals (DBRs) and one-wavelength thick intentional defects in the middle of the structure have been successfully adopted in the operation of vertical cavity surface emitting lasers (VCSELs) as mirrors and cavities, respectively (Jewell et al., 1991). During the past 20 years, VCSELs have dominated the communication market due their relatively low thresholds, long lifetimes, and ease of integration compared to other semiconductor lasers such as edge emitters. Although the merits of individual VCSELs are relatively acceptable, they are not suitable for arraying on chip at large numbers. In array, their thresholds could introduce serious limitations by causing loss of power and unwanted heat. In addition, VCSELs are not the optimum choice for high-speed application as they suffer from problems with direct modulation above 20 GHz (Lear et al., 1997), multi-mode operation, and difficulty of growing their DBRs for long-haul telecommunications wavelengths. The ability of light confinement both in space (determined by the mode volume, Vmode) and in time (determined by the optical loss or quality factor, Q-factor) in multi-dimensional PhCs has recently attracted scientists to search for an ultimate laser. The reason behind this interest is that spontaneous emission rate of an emitter is not an inherent property but can be controlled by modifying the optical density of state (DOS) around it. This was first realized by Edward Purcell in 1946; hence, this change in the spontaneous emission rate ( cavity) with respect to free space ( free) is called the Purcell Factor (Fm). Emission rate (Fm) can be dramatically enhanced if we take care of the following three important terms: Fm ¼

cavity free

_

   E 2 Q 2c   2c þ 4ð – c Þ2 Emax  Vmode

ð3Þ

First, the emitter has to be spectrally on resonance with the cavity so that it can experience the highest DOS modification. In addition to the spectral overlap, there should also be a spatial overlap so that the emitter experiences high electromagnetic field. Finally, the enhancement increases if the cavity localizes the field in a very small area for a long period of time, given by the Q/Vmode ratio. In this respect, PhC nanocavities are an excellent choice,

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because they can achieve very high Q/Vmode ratios. Similarly, PhCs at their band edges and band gaps can also achieve dramatic DOS modification. If we increase DOS of the lasing mode and thus spontaneous emission rate through Purcell effect, we will have larger fractions of photons emitted into the lasing mode with respect to all other modes. This fraction is denoted as the spontaneous emissioncoupling factor, , and its enhancement reduces the lasing threshold (Painter et al., 1999; Loncar et al., 2002; Park et al., 2004): cavity

¼ cavity

þ

ð4Þ other

The -factor in VCSELs is typically less than 103, but it can be increased by two orders of magnitude in PhC nanocavities and dramatically reduce lasing threshold. Similarly, this spontaneous emission rate enhancement also means faster radiative recombination ( r !  r/Fm) and thus faster laser response.

6.12.3.1

Lasing Materials

For semiconductor-based PhCs, the two common gain media are quantum-wells (QWs) and quantumdots (QDs). A QW is a potential well that confines electrons and holes into a planar region. The confinement alters the energy of the carriers when the QW thickness becomes comparable to the de Broglie wavelength. This leads to the formation of energy subbands with discrete wave vectors in the direction of confinement. By controlling the QW thickness, the recombination energy of electron–hole pairs can then be tailored to fit the energy required in a device – for example, to match material gain to a cavity resonance and to the required emission wavelength. The confinement can also greatly improve the overlap between a photonic mode and the carrier recombination region. This improved overlap can be used to reduce threshold in a laser or to enhance absorption in a QW modulator, as well as many other applications that require a large light–matter interaction. QWs are formed by sandwiching one semiconductor layer inside a host semiconductor with a wider band gap. They provide large gain when embedded in the center of the PhC membrane, where the resonant TE-like mode has the maximum electric field energy density. A single QW in the PhC slab center would see the highest electric field and hence the highest gain overlap; however, to optimize

the laser current, it is often better to distribute carriers (or current) across several QWs (Coldren and Corzine, 1995). A QW-driven PhC nanocavity laser was first demonstrated with four InGaAsP QWs (Painter et al., 1999) and was soon followed by other demonstrations. For the work that will be presented in this chapter, we used InGaAs QWs inside GaAs and GaInAsP QWs inside InP for 950 nm and 1550 nm wavelength operation range. GaAs material system employs four 8-nm In0.2Ga0.8As QWs separated by 8-nm GaAs barriers. The top and bottom QWs are about 32 nm from the center of the PhC membrane and still experience 89% of the maximum field intensity. We use compressively strained QWs, which have higher differential gain, lower transparency carrier density (Ntr), and higher coupling to the TE-likepolarized cavity mode than unstrained QWs (Altug et al., 2006). The disadvantage of the GaAs material system is that it has large surface recombination rate, which results in large loss and higher lasing threshold. This is particularly a problem in PhC slab lasers where the etching goes all the way through the gain medium. This nonradiative (NR) loss can be suppressed by surface passivation in (NH4)S (Petrovykh et al., 2002). For 1550-nm emission, we used a 280-nm InP slab containing four compressively strained 9-nm thick InxGa1xAsyP1y QWs (x = 0.786, y = 0.445) separated by 20-nm InxGa1xAsyP1y (x = 0.78, y = 0.737) barrier InP materials. We have also employed QDs as gain medium in PhC-based emitters including lasers (Ellis et al., 2007) and single photon sources (Englund et al., 2005). A QD is a nanometer-sized structure that confines charge carriers in all directions to a small volume. The dot exhibits discrete energies, which can be tuned by controlling its size. Because of their lower carrier transparency and NR surface recombination (since they are not exposed by etching like QWs), they offer lower lasing threshold and better temperature stability. However, compared to QWs, they usually provide lower total gain and output powers. 6.12.3.2

PhC Laser Fabrication

Planar PhCs operating from visible to infrared wavelengths are most commonly fabricated by electron beam or optical lithography combined with wet and dry etching. They have also been fabricated by other techniques such as focused ion beam drilling (Chelnokov et al., 2000), gravity sedimentation of

Photonic Crystal Microcavity Light Sources

491

350nm PMMA 100nm PECVD Oxide

InGaAsP InP 1. Double layer mask deposition

3. Mask transfer, CHF3-O2 plasma dry etch

5. Cl2-based ECR-RIE

2. E-Beam Lithography and development

4. O2 Plasma descum

6. Undercutting, HCL wet etch

Figure 3 Fabrication procedure for PhC laser made in InGaAsP/InP material system: (1) double layer mask deposition by PECVD and spinning; (2) PhC pattern generation by e-beam lithography and development; (3) mask transfer from e-beam resist (PMMA) to the SiO2 hard mask; (4) O2 descum to remove left-over e-beam resist; (5) Cl2-based ECR-RIE etch to transfer pattern from SiO2 hard mask to InGaAsP and InP layer; and (6) undercutting of sacrificial InP layer to form a membrane.

colloidal particles (Holland et al., 1998; Lodahl et al., 2004), or nano-imprint techniques (Kim et al., 2007), but these methods are less common. The fabrication process flow for the InP-based PhC is shown in Figure 3. Other materials also share a similar process. In photonic crystal slab fabrication, the important step is to have low-index top and bottom cladding. Mostly, air is used as top cladding. For bottom cladding, one approach is to put a sacrificial layer during wafer growth, which can then be etched away chemically without perturbing the slab layer. This approach will result in free-standing membrane. Maximizing the index difference, this approach is preferred for achieving high Q values. The other approach is to use low-index material for support. For example, in silicon-based PhC slabs, a low-index SiO2 layer has been used. Similarly, for InP and GaAs materials, some research groups have bonded the active layer on low-index sapphire, which increases both thermal and mechanical stability. In e-beam lithography, the most commonly used resists are poly-methyl-methacrylate (PMMA) or ZEP-520. However, their etch resistivity is generally low and may not hold long enough during the etching of thick slab materials. In addition, these polymers may not also be suitable to use in certain dry etching conditions. We can use the masktransfer technique to overcome such limitations. For

example, the use of chlorine chemistry in the dry etching of InP results in a low-volatility by-product (InCl) at room temperature, and heating of the sample (above 160  C) during the dry etching is necessary to remove it. Since this temperature range is above the glass transition temperature of many e-beam resists, direct etching with an e-beam resist will cause the mask to overflow and consequently wash away the desired pattern. Therefore, to etch InP with Cl2 chemistry at high temperatures, we have transferred the pattern from PMMA to SiO2 or silicon nitride (Si3N4) layer and used it as a hard mask.

6.12.4 Highly Efficient Photonic Crystal Lasers: Coupled Nanocavity Arrays The parameters of the PhC such as lattice type and the arrangement of the defects in cavities dramatically alter Vmode and Q. Depending on the application, both parameters need to be finely adjusted. For example, for high-speed applications, the Q-value must be relatively large to achieve strong Purcell effects for fast turn-on but not too large to limit the laser’s response time during turn-off. On the other hand, for low-threshold applications, the Q-factor could be increased while Vmode is kept low.

492 Photonic Crystal Microcavity Light Sources

Because of this, double-heterostructure (Mock et al., 2008), single-hole (Ryu et al., 2002) and point-shift defect cavities (Nozaki and Baba, 2006), which have large Q-factor and small Vmode, are commonly used in low-threshold lasing. Unfortunately, small mode volume also means small gain and thus low output power levels – on the order of a few mW’s. In an attempt to increase output powers of PhC lasers, band-edge lasers, which operate in slow-group velocity (or high DOS) regions of the PhC dispersion, have been investigated (Meier et al., 1999; Noda et al., 2001). However, they lack lateral confinement and thus do not benefit from cavity effects, and they can also suffer from multi-mode lasing (Imada et al., 1999). A good alternative is to combine the strengths of the nanocavity and band-edge lasers by arranging defect cavities in a 2D array (Altug and Vuckovic, 2005a). If the cavities are sufficiently close, lasing from a common mode can be achieved. This coupled array laser has better directional emission and effectively larger active region than a single-defect laser, while providing a better lateral confinement than the band-edge laser. We note that the coupling of a small number of VCSELs has been previously investigated (Deppe et al., 1990; Orenstein et al., 1991; Warren et al., 1992; Raftery et al., 2005). However, it is very hard to control the uniformity of such arrays as well as the coupling between individual lasers necessary to achieve the phase-locked lasing from a large number of cavities. Moreover, a rather complicated fabrication procedure has been used to achieve phase-locked lasing even from a small number of coupled VCSELs in an array (Warren et al., 1992). With photonic crystal nanocavity arrays, we can control both the uniformity and the coupling very precisely. Since each cavity occupies an area of only 1.5 mm2 (much smaller than a typical VCSEL), we can generate high-density arrays and achieve larger output powers. Finally, our study shows that the full benefits resulting from the coupling of cavities are achievable only if strong cavity effects are present (i.e., for large  factor), implying that the coupling of PhC nanocavities is preferential over coupling of larger resonators (e.g., VCSELs). 6.12.4.1

2D Coupled Nanocavity Arrays

Before deriving the equations governing the properties of the array laser and showing the experimental laser results, we briefly introduce, in this section, the 2D coupled nanocavity array structure (Altug and Vuckovic, 2004, 2005b, 2005c). The structure is the

2D analog of the coupled resonator optical waveguides (CROW) introduced by Yariv et al. (1999). A CROW consists of a chain of resonators in which light propagates by tunneling from one resonator to its adjacent resonators. The unique property of CROW is that it enables reduction of group velocity along the axis of coupling. Structures enabling small group velocity are already important for construction of optical delay components. In addition, it has also been predicted theoretically that the reduction in the group velocity (so-called group velocity anomaly) is also important for lasing because it increases DOS, thereby decreasing lasing thresholds. This property has been in part employed to achieve lasing from 1D CROW structures (Happ et al., 2003). In 2D coupledcavity arrays, we achieve small group velocity (large optical DOSs) not only in one axis but along all crystal directions and over the entire range of wave vectors. This decreases the sensitivity of coupling and minimizes distortion of propagating optical pulses, which is important for delay line application. More importantly, the structure also finds an important application in lasing by increasing output powers while preserving low lasing thresholds as a result of a large group velocity anomaly in any PhC direction. 6.12.4.2 Dispersion Diagram of CoupledCavity Arrays 2D array structures studied in our laser demonstrations are constructed by periodically modifying holes of a square lattice PhC slab. For example, every third hole of a PhC lattice in both x- and y-directions can be removed, as shown in Figure 4(a). This results in the formation of coupled photonic crystal resonator arrays (CPCRAs) with unique dispersion relation. While our analysis focuses on nanocavities constructed in planar PhCs, it is straightforward to extend it to any type of optical cavities, and even to three-dimensional arrays of coupled cavities. Figure 4(b) shows the unit cell of the CPCRA from Figure 4(c) and the directions of high-symmetry points, , X, and M. This structure can be viewed as a 2D array of singledefect PhC cavities formed by removing a single air hole. An isolated cavity of this type supports three types of modes: doubly degenerate dipole, nondegenerate quadrupole, and nondegenerate monopole. As the lattice perturbation increases (i.e., the defect hole radius decreases), modes are pulled from the air band and are localized in the band gap. The first mode to be localized in

Photonic Crystal Microcavity Light Sources

Patterned, free-standing membrane (a) r a y x

M (b)

Γ

X

d Undercut air region (c)

Figure 4 (a) Schematic configuration of the studied coupled photonic crystal cavity array. (b) Unit cell and location of high symmetry points. (c) SEM picture of the twolayer coupled-cavity array fabricated in silicon.

this way is the dipole, and the last is the monopole. The cavity mode with the highest quality factor (Q-factor) is the quadrupole (Altug and Vuckovic, 2004). When the cavities are tiled together in a CPCRA, coupled-cavity bands form within the band gap. The band diagram of the structure from Figure 4(c) is shown in Figure 5. Since its unit cell (shown in Figure 4(b)) is 3 times bigger than the unit cell of

493

the original square lattice, we need to fold the square lattice band diagram 3 times in order to plot it together with the band diagram of the CPCRA. Moreover, we only kept the top branches (modes with the highest frequency) in each direction, and shaded all the states under them in gray. For the X direction, the modes outside the edge of the first Brillion zone of the square lattice (2/3a < kx < /a and ky = 2/3a) have been used as they have the highest frequency (therefore determine the top branch). In Figure 5, we assume that the positions and the shapes of the guided bands of the original square lattice PhC remain unchanged inside the CPCRA. This is only an approximation, as their frequencies may decrease due to the increased overlap with the high-index material, and new minigaps may open at the high symmetry points of the CPCRA. Dielectric and air bands are shaded in gray, as we are primarily interested in the coupled defect modes located in the band gap; these, in turn, are the portions of the band diagram that are easily accessible experimentally. Although we have shown here the coupled PhC cavity arrays in square lattice, the analyses and the conclusions can be extended to photonic crystal with triangular lattice. Since the size of the band gap of the triangular lattice PhC is larger, the total quality factors of the defect modes will be higher. In such a

0.36 0.34 0.32

(a/λ)

0.3 0.28

M

0.26

Quadrupole x-Dipole y-Dipole Diagonal dipole Monopole Band edge

0.24 0.22 0.2 Γ

Γ

X X

M

Γ

Figure 5 Band diagram for the TE-like modes in a 2D coupled nanocavity array structure with two PhC layers separating the cavities in both (x and y) directions. The parameters are r/a = 0.4, d/a = 0.55, and n = 3.5. In order to present the dispersion diagram of the square lattice (which is the underlying lattice of the analyzed structure) together with CPCRA, the dielectric and air bands of the square lattice are folded 3 times separately in the X, XM, and M directions. Only the top branches (modes with the highest frequency) in each direction are kept and all the states under them are shaded in gray. For the X direction, the modes outside the edge of the first Brillion zone of the square lattice (2/3a < kx < /a, and ky = 2/3a) have been used as they have the highest frequency (therefore, determine the top branch).

494 Photonic Crystal Microcavity Light Sources

lattice, the coupled defect bands will be different, with hexapole mode as the one with the flattest band diagram due to its sixfold rotational symmetry. 6.12.4.2.1

Coupled dipole band The dipole mode is doubly degenerate in an isolated PhC cavity (Altug and Vuckovic, 2004), but it splits into two bands corresponding to the x- and y-dipoles in the CPCRA structure, as shown in Figure 5. Although the coupled dipole bands are located below the top air band edge in the XM direction, they are included in the diagram to clarify the explanation of the coupled mode characteristics. The x(y) dipole has electric field polarized in the x(y) direction at the center of the defect and radiates mostly in the y(x) direction. Figure 6 shows the z-component, the only nonzero component of magnetic field in the middle of the slab, for the x-dipole band at the X point of the band diagram. Due to the previously described radiation pattern, the x-dipole is coupled more in the XM direction than in the X direction, and its band is thus flatter in the X than in the XM direction. The situation is opposite for the y-dipole. The preferential coupling of the dipole mode along a particular lattice direction implies that its coupled band properties are similar to a 1D CROW case. In the M direction, x- and y-dipoles combine to form a diagonal dipole, and its field pattern at the M-point is shown in Figure 6. We have also observed a coupled monopole band in this CPCRA structure. The magnetic field pattern of this band at the point is shown in Figure 6. Due to the poor mode confinement (low Q-factor), there is a significant slope in its band diagram. 6.12.4.2.2

Coupled quadrupole band Figure 6 shows magnetic field pattern of the coupled quadrupole mode at the -point. The quadrupole radiates equally in the four M directions and its radiation pattern thus has a fourfold symmetry. This also implies that the mode couples equally efficiently to all of its four neighbors in a

particular lattice direction (e.g., M or X). The lack of preferential coupling and good lateral confinement (high Q-factor) lead to a flat coupled-quadrupole band. In addition, this mode is nondegenerate and does not split into several subbands as does the coupled dipole band.

6.12.4.3

Coupled-Cavity Array Laser

This section discusses the benefits of arraying lasers when the cavity effects are strong (i.e., when  is large). Two important parameters of a laser are its threshold pump power (Lin,th) and differential quantum efficiency (DQE). The threshold pump power is the input power at which the photon number inside the optical mode volume is equal to 1 (a necessary condition to initiate the stimulated emission) (Imamoglu and Yamamoto, 1999). On the other hand, the DQE is the slope of the laser output– unput power curve (LL-curve) above threshold (Coldren and Corzine, 1995). These two parameters can be derived from the following rate equations, which describe the dynamics of the carrier density (N) and the photon density (P):   dN Lin N N – þ – G ðN ÞP ¼ h!p Va dt r nr

ð5Þ

dP N P ¼ G ðN ÞP þ  – dt r p

ð6Þ

The definitions of parameters used in the rate equations and their values for InGaAsP/InP multiple quantum-wells (MQWs) that we employed in our lasers are listed in Table 1. The other terms are: !p the pump laser frequency,  the fraction of the pump absorbed in the active region, Q the quality factor of the optical mode, !l the laser emission frequency, and  p = Q/!l the cavity photon lifetime. Equation (5) implies that the carrier density increases with the pump rate (first term), but decreases

Figure 6 Magnetic field patterns (z-components) at the center of the PhC slab for coupled quadrupole, x-dipole, y-dipole, diagonal dipole, and monopole mode. Coupled quadrupole and monopole are shown at the -point, diagonal dipole is shown at the M-point, while x- and y-dipoles are shown at the X-point of the band diagram.

Photonic Crystal Microcavity Light Sources Table 1 Typical parameters for InGaAsP–InP MQWs that are used in solving the rate equations Surface recombination velocity (vs) = 104cm s1 Bimolecular recombination coefficient (B) = 1.6  1010 cm3 s1 Auger nonradiative recombination rate (C) = 5  1029 cm6 s1 Transparency carrier density (Ntr) = 1.5  1018 cm3 Gain coefficient (G0) = 1500 cm1 Absorption ratio of pump in QW region () = 0.26 Confinement factor ( ) = 0.159 Pumped active volume (Va) = 2.2  1013 cm3 Optical mode volume for single cavity (Vmode) = 6  1014 cm3 Lasing wavelength (l) = 1.53  104 cm Pump laser wavelength (p) = 0.83  104 cm

by the radiative recombination (second term), the nonradiative recombination (third term), and the stimulated emission (fourth term). In this analysis, the radiative recombination rate is expressed as 1/ r = BN, where B is the bimolecular recombination coefficient given in Table 1. It should be noted that this expression is correct for bulk materials but is not exact for nanocavities since it does not include modification of radiative lifetime in the cavity. The only nonradiative processes included in our analysis are the surface recombination (1/ s = vs/da) and the Auger recombination (1/ A = CN2). Here, da is the thickness of the active region. The coefficients vs and C are given in Table 1. In Equation (5), the photon density increases with the stimulated emission (first term) and with the spontaneous emission that is coupled to the particular lasing mode (second term), but decreases with the cavity radiation loss 1/ p (third term). Following Baba (1997), we have assumed in our analysis that the gain is logarithmic, G(N) = G0c/neqlog(N/Ntr) with effective index neq = 2.65 for our structure (c is the speed of light). The carrier and photon densities are calculated in the steady state by using Equations (5) and (6). The carrier and photon numbers are then given by NVa and PVmode, respectively, where Va is the pumped active volume and Vmode the optical mode volume. The output power is calculated as Lout = h!lPVmode/  mirror, where 1/ mirror is the photon output rate toward the detection system. In the analysis, we also assume the ideal situation that  mirror =  p, that is, all emitted photons are collected. By solving the rate equations in a steady state, we obtain the following expressions for lasing threshold and differential quantum efficiency:

Lin;th ¼

  h!p Va 1 Nth Nth – þ p Vmode  r r

DQE ¼ 

!l Vmode 1 1 !p Va mirror G ðNth Þ

495

ð7Þ

ð8Þ

In these derivations, in contrast to the usual assumption that the  term can be neglected (Coldren and Corzine, 1995), we consider it because the term is significant in the nanocavities studied here. For Equation (7), the threshold is defined when the photon number in the cavity is 1, and the NR decay rate is assumed to be much slower than the radiative rate. In Equation (8), G(Nth) is the gain at the threshold. The other terms are defined above. From the rate equations, the gain at the threshold can be expressed as G ðNth Þ ¼

1 Nth Vmode – r p

ð9Þ

For the derivation of DQE, we assumed that the carrier density and the gain above threshold are clamped at their threshold values. Although this assumption is commonly used in conventional laser analysis, it is not strictly valid for the cavities with very large . Therefore, the expression in Equation (7) underestimates the value of DQE. When nc individual lasers are coupled in an array, both Vmode and Va increase by a factor roughly equal to nc (relative to a single laser). In addition, the photon storage time  p (and consequently  mirror) can increase (by nc times for ideal 3D coupled nanocavity arrays). Hence, for a non-negligible ,  mirror G(Nth) decreases in a coupled laser array, which leads to an increase in DQE. In an ideal case (  1), according to Equations (7)–(9), coupled-cavity lasers would have the same threshold as single-cavity lasers (since the second and third term in Equation (7) cancel each other and Lin,th becomes independent of nc), but with a much higher DQE. On the other hand, if  is negligible and Vmode is large (as it is in VCSELs), Lin,th of the laser array increases roughly nc times relative to an individual laser (as the third term in Equation (7) dominates), while DQE does not change (as the threshold gain is primarily determined by 1/ p in Equation (9)). As we have indicated above, PhC nanocavity arrays that are shown here are somewhere in between these two extreme cases as their  is nonnegligible. Moreover, their mode volume (Vmode) is also small, implying that different terms in the expression for Lin,th and G(Nth) become comparable. Therefore, DQE of the PhC cavity array lasers increases

496 Photonic Crystal Microcavity Light Sources

relative to that of a single PhC cavity laser, while the increase in the lasing threshold is slower than the increase in the number of cavities. It should also be pointed out that in PhC nanocavity array lasers, Va increases more slowly than Vmode with an increase in the number of cavities. Hence, the ratio Vmode/Va is larger for nanocavity array laser than for a single PhC cavity laser, leading to an additional increase in DQE, which we observe in our experiment below. This effect is a result of a more efficient pumping and a better overlap between the pumped area and the cavity mode. In a single PhC cavity laser, it is extremely difficult to pump only the central cavity region, and the pump also generates carriers inside the mirrors, which do not couple to the lasing mode. On the other hand, in a coupled array laser one can pack larger number of lasers more efficiently by reducing the space used as mirrors, and the overlap between the pumped region and the cavity mode is better. 6.12.4.3.1

Experimental setup The structures that we present here are arrays of nanocavities in a square PhC lattice, and we investigate the nondegenerate high Q-factor (2000) quadrupole mode. The electric field pattern of the array is shown in Figure 7(b). We fabricated such nanocavity arrays in the InP material system. The coupled cavities in a 9  9 array are separated by two layers of PhC. The important PhC parameters are the free-standing membrane thickness (d) of 280 nm, periodicity (a) of 500 nm, and the hole radius (r) tuned from 160 to 230 nm to change the resonance frequency of cavities. Single-cavity lasers are also fabricated on the same chip, with the same parameter range. With these parameters, the quadrupole mode frequency calculated by the FDTD method falls within the gain linewidth.

Figure 8 shows the micro-photoluminescence setup used for laser characterization. The coupled PhC nanocavity array lasers with sizes 15 mm are optically pulse-pumped normal to the structure at room temperature. A diode laser emitting at 808 nm is focused with an objective lens into a 15 mm spot on the sample. The pump pulses are 20 ns long with 1% duty cycle, chosen to reduce heating of the structure. Vertically emitted light is collected using the same optics and coupled to an optical spectrum analyzer. To compare the performance of the coupled-cavity array lasers to that of single nanocavity lasers (with size 4 mm), a similar setup with a smaller beam spot size of 5 mm is used. 6.12.4.3.2 profile

Lasing spectrum and mode

Single mode lasing is observed from coupled nanocavity array lasers (spectrum is shown in Figure 9) The lasing wavelength matches that of the phasecoupled quadrupole mode at the point calculated by FDTD. The collection angle of the objective lens is wide enough to collect the emission from any other possible modes. However, we observe only a single mode in the spectrum, even at low pump powers. A slight linewidth narrowing was observed above the threshold, while the spectrum below the threshold was hard to measure due to the poor sensitivity of our spectrum analyzer. The profiles of the lasing modes both from a single cavity and a coupled-cavity array laser taken with an infrared camera are shown in Figure 10. The setup used for probing a single cavity has a higher magnification and shows clearly the fourfold symmetry of the mode, which is expected for the quadrupole. At the center of the square, there is strong field localization, corresponding to the location of the single defect. (b)

(a)





Figure 7 (a) SEM pictures of a fabricated single PhC cavity laser and a coupled PhC cavity array laser. (b) Simulated electric field amplitude of the coupled-cavity array quadrupole mode at the point in the middle of the slab. Taken from Altug H and Vuckovic J (2005a) Photonic crystal nanocavity array laser. Optics Express 13: 8819–8828.

Photonic Crystal Microcavity Light Sources

OSA

single cavity, where both localized and leaking field components are well reproduced in the simulation.

Function generator

808 nm LD

MM fiber

497

10x OL 20x OL

6.12.4.3.3

Light-in/light-out curve Coupled nanocavity array lasers with different r/a ratios have been tested and Figure 11 shows the measured light-out/light-in (LL) curve of one of them (blue). We have observed single-mode lasing at 1534 nm with a threshold peak pump power of 2.4 mW. Several single cavity structures with different r/a have also been tested. The LL curve of one of them (with r/a  0.4) is shown in Figure 11 (red). The parameters of this cavity and therefore the emission wavelength at 1543 nm are quite similar to the coupled-cavity array laser, giving an additional indication that the quadrupole mode and the phasecoupled quadrupole band at the point are the lasing modes for a single-cavity laser and a couple nanocavity array laser, respectively. The threshold peak pump power for a single-cavity laser is around 320 mW. The  values are obtained from the experimental curves using laser rate equations and typical parameters of InGaAsP QWs. Within the acceptable range of material parameters, we obtained a range of  values given in Table 2; Figure 12 shows the fitted LL curves for a  value that is in this range. The  value of the coupled-cavity array laser is estimated to be slightly smaller than  of a single cavity, but it is still large enough to observe strong cavity effects mentioned above.

Polarizer IR-cam

BS BS

40x OL

Figure 8 Micro-photoluminescence setup for laser characterization. OL – objective lens, BS – beam splitter, LD – laser diode, MM fiber – multimode fiber, IR-cam – Infrared camera, OSA – optical spectrum analyzer.

A strong radiation leak outside the square is also visible, which is due to the fact that the cavity is surrounded by only four PhC layers. The setup used for probing coupled-cavity array laser has a lower magnification, and, therefore, individual cavities are hard to resolve, but emission from most of the array is visible. The radiation profiles for the quadrupole mode are simulated by the FDTD method, by calculating the time-averaged Poynting vector in the vertical direction. The radiation patterns corresponding to the plane positioned at 1 mm above the structure are very similar to the experimentally measured field patterns, as shown in Figure 10. The match is especially good for a

8

4

7

3

6

2.5 2

Intensity (a.u.)

3

Intensity (a.u.)

Intensity (a.u.)

3.5 2.5 2

0

3

1 0 1610 1350 1400 1450 1500 1550 1600 1650 λ (nm)

1

0.5

4

2

1.5

1.5 1

5

0.5 0

1533.5 1534 1534.5 1535

100 nm

λ (nm)

1470

1490

1510

1530

1550

1570

1590

1610

λ (nm) Figure 9 Spectrum of the coupled-cavity array laser with a peak at 1534 nm. The PhC hole radius in this structure is about 192 nm. The inset on the left shows the zoomed-in portion of the spectrum fitted with a Lorentzian (green dashed curve) of 0.23 nm linewidth. The inset on the right shows the QW photoluminescence from unprocessed wafer (QWs shown on the SEM image). Taken from Altug H and Vuckovic J (2005a) Photonic crystal nanocavity array laser. Optics Express 13: 8819–8828.

498 Photonic Crystal Microcavity Light Sources

(a)

(b)

Figure 10 (a) The IR-camera image (left) and the simulated time-averaged Poynting vector in the vertical direction (right) of the lasing mode for a single-cavity laser. The size of the structure is indicated by the dashed square. (b) The same for a coupled-cavity array laser. The white square box with dashed line is approximately 12  12 mm. As the structure is periodic, the simulation result on the right is only showing portion (5  5) of the full array. Taken from Altug H and Vuckovic J (2005a) Photonic crystal nanocavity array laser. Optics Express 13: 8819–8828.

4500 90

4000 Collected output power (a.u.)

Collected output power (a.u.)

80

3500 3000 2500 2000

70 60 50 40 30 20 10

1500

0 0.2 0.4 0.6 0.8

1000

1.2 1.4 1.6 1.8

Single cavity

500 0

1

Peak pump power (mW)

Coupled-cavity array 0

1

3 2 4 Peak pump power (mW)

5

6

Figure 11 LL curves of the single PhC cavity and the coupled PhC cavity array laser. The inset shows a magnified curve for the single PhC cavity.

Photonic Crystal Microcavity Light Sources Table 2 Averaged values of the measured thresholds and DQEs of several single-cavity and coupled-cavity lasers and their ratios

Single cavity Coupled-cavity array RATIO

Threshold (mW)

DQE

 factor

0.26 2.68

0.51 10.37

[0.09–0.15] [0.03–0.09]

10

20



Also shown are the  factor ranges obtained by fitting laser rate equations to the measured LL-curves

100

Output Power [a.u.]

101 102 103 104 105 106

0.2×10–3

10–3 Peak Power [W]

10–2

Figure 12 Measured LL curves of the single PhC cavity (red triangles) and the coupled PhC cavity array laser (blue circles) together with simulated LL curves (solid lines). For simulation, material parameters in Table 1 is used and  factor (given in Table 2) is taken a fitting parameter.

We have measured the peak pump power at the lasing threshold and DQE of the LL curve for several different coupled-cavity array and single nanocavity lasers; the averaged results are given in Table 2. The measured lasing threshold of coupled photonic crystal nanocavity arrays is about 10 times larger than for a single cavity. According to the parameters that we use in the  fit, the third term in Equation (6) dominates the threshold expression, so we expect that the threshold pump power scales with the pumped active volume Va. In the experiment, the pump beam size for coupled-cavity laser is almost 10 times larger than for a single-cavity laser, which explains the observed increase in threshold. On the other hand, the measured 20-fold increase in DQE of the cavity array is larger than the increase in threshold, implying that a

499

higher output power can be extracted per nanocavity in a coupled-cavity array laser in comparison to a single nanocavity laser, confirming the coherent coupling of individual nanocavities. In fact, the maximum power achieved from our coupled-cavity array laser with only 10 nanocavities (>12 mW) is about 100 times larger than a single-cavity laser (Figure 11). 6.12.4.4

Comparison with Theory

In our optically pumped lasers, the improvement of DQE can result from two effects: more effective pumping scheme (i.e., an increase in Vmode/Va), and cavity effects (i.e., reduction of  mirror G(Nth)), as explained in Section 6.12.4.3. In our experiment, we know that the pumped active region Va is approximately 9–10 times larger with respect to single-cavity laser, but we do not know the exact increase in Vmode, since some of the 81 cavities in the area may be uncoupled from the lasing mode. Figure 11 shows the output power from the coupled PhC array laser and a single-cavity laser, theoretically analyzed by solving rate equations with parameters corresponding to our experimental conditions (Table 2). Clearly, DQE increases with the number of coupled cavities (nc) that are lasing together (Vmode,array = ncVmode,single). On the other hand, the threshold does not change with nc, as it is primarily determined by the pumped active volume Va as explained above. By comparing theoretical analysis shown in Figure 13 with our experimental results shown in Figure 11, we conclude that the majority of the 81 cavities in the array are lasing together in our laser. With such a large number of coupled cavities, the coupled-cavity band forms, the lasing occurs from the high symmetry point ( ), and the individual cavity resonances are not visible as in the case of a small number of coupled resonators (Nakagawa et al., 2005; Happ et al., 2003).

6.12.5 Ultrafast Photonic Crystal Lasers As we have indicated in the beginning of Section 6.12.4, the spontaneous emission rate enhancement can not only reduce laser threshold but also increase laser modulation speeds (Yamamoto et al., 1991). There are two important laser modulation regimes employed in communication systems: small and large signal modulation (Coldren and Corzine, 1995; Chang et al., 2003). We analyze the laser dynamics by solving the laser rate

500 Photonic Crystal Microcavity Light Sources dðP0 þ PÞ ¼ G ðN0 þ N ÞðP0 þ PÞ dt N0 þ N P0 þ P – þ r p

7

Output power (a.u.)

6 5 4 3 2 1 0

0

1

2

3

4

5

6

Input power (mW) Figure 13 Output power as a function of the input pump power and the number of coupled-cavities in the array, analyzed using the rate equations under our experimental conditions (parameters given in Table 1). Single cavity results are shown in red and coupled-cavity array laser results in blue. Coupled-cavity laser has 10 times larger Va than single-cavity laser, while the mode volume Vmode increases relative to that of a single-cavity laser by a factor of 10 (diamond), 40 (circle), and 70 (square). By comparing theoretical analysis shown here with our experimental results shown in Figure 11, we conclude that majority of 81 PhC cavities in the array are lasing together in our laser. Taken from Altug H and Vuckovic J (2005a) Photonic crystal nanocavity array laser. Optics Express 13: 8819–8828.

equations (Coldren and Corzine, 1995) for photon and carrier densities. In the small signal regime, the laser is driven with an above-threshold direct current (DC) pump power Lin,0 and modulated with a small time-varying (alternating current, AC) signal Lin. The carrier and photon densities follow the pump with DC and AC components N0 + N and P0 + P, respectively. As discussed in Section 6.12.4, the parameters are defined as follows:  is the fraction of the pump absorbed in the active region, Va the pumped active volume, !p the pump laser frequency,  the total carrier lifetime,  r the carrier radiative lifetime, the confinement factor, G the gain, and  p = Q/!l is the photon lifetime (Q is the quality factor of the optical mode and !l the laser emission frequency). In order to derive modulation response, we start with the laser rate equations: dðN0 þ N Þ ðLin;0 þ LÞ N0 þ N – ¼ dt h!p Va  – G ðN0 þ N ÞðP0 þ PÞ

ð10Þ

ð11Þ

We assume that the DC input power Lin,0 is much greater than threshold power (Lth) so that carrier density N is clamped at its threshold value: N  No  Nth. In addition, we linearize the logarithmic gain. If we separate the DC and AC terms, neglect second-order terms coming from multiplication of P and N, assume a sinusoidal modulation for AC terms as P = Pmei!t, N = Nmei!t and L = Lmei!t, we can obtain a relation between the driving power and photon density modulation. The modulation response is given by Pm/Lm, and the bandwidth of the laser is limited by the following relaxation oscillation frequency: !R2

ag P0  N0 ¼ þ r0 þ r0 p Fm Fm P0 p

1  –  Fr0m

! ð12Þ

Here, we take into account that the radiative lifetime changes as  r =  r,0/Fm due to the spontaneous emission modification in the cavity compared to the intrinsic carrier radiative lifetime,  r,0 (as defined previously, Fm is the Purcell factor). In Equation (12),  is replaced with a g, where a represents the differential gain and  g is the group velocity of light. The value of differential gain (a) can be found in literature for a particular material system. In conventional semiconductor lasers, the fraction of spontaneously emitted photons that is coupled into a single cavity mode (denoted by the spontaneous emission-coupling factor ) is small due to the small F factor (Coldren and Corzine, 1995). Therefore, only the first term in Equation (12) is considered. The standard way of improving the modulation bandwidth is by increasing the photon density (Po) with stronger pumping, which increases the first term in Equation (12). However, this causes significant thermal problems and practically limits the modulation speeds to below 20 GHz (Lear et al., 1997). On the other hand, in nanocavity lasers with large Purcell effect,  can approach unity while the intrinsic radiative lifetime is reduced dramatically (i.e., Fm is large). This makes the additional terms in Equation (12) significant. These cavity-QED effects thus open a fundamentally new pathway for improving laser modulation bandwidth (Yamamoto et al., 1991).

Photonic Crystal Microcavity Light Sources

In large signal modulation (laser is turned on and off completely), there are two important time values. One of them is the time delay between the pump and laser peak responses, which is termed turn-on time. The turn-on delay arises as spontaneous emission builds the cavity field to the point when stimulated emission becomes dominant. The other is the decay time of the photons out of the cavity, which is termed delay time. The turn-on and delay times can be decreased by increasing spontaneous emission rate enhancement (Fm). Fm can be increased by using a cavity with large Q over Vmode ratio. To increase laser speed, one can consider increasing emission enhancement Fm by using high Q cavities alone, but this would also increase the delay time due to longer photon storage time in the cavity. Thus, ultrahigh Q cavities such as three hole defect PhCcavities (Song et al., 2005), microdisks (Fujita et al., 2000), or microtoroids (Armani et al., 2003) alone cannot achieve higher modulation speed. For example, for Q = 106 ( p  500 ps), the modulation speed is only 2 GHz. Thus, to increase emission enhancement we should decrease the cavity mode volume. In this respect, PhC cavities with very small mode volumes and moderate Q’s offer particularly striking advantages by dramatically reducing both turn-on and delay times. By contrast, photonic crystal nanocavities enable very large Purcell effects even with moderate Q values because of their ultrasmall cavity mode volumes, below (/n)3. In our lasers with large Purcell factor, the Q values can be as small as several thousands, allowing short cavity ring-down times ( p < 1 ps).

6.12.5.1

501

Experimentation Setup

To investigate time-domain characteristics using our streak camera (Hamamatsu N5716-03 streak tube) with detector response limited to wavelengths below 1 mm, we fabricated PhC lasers emitting between 900 and 980 nm by patterning single cavity and 9  9 cavity array on a free-standing 172 nm GaAs slab with four InGaAs QWs. QWs have a major drawback as gain media in photonic crystal devices. NR surface recombination rate is very large because the QW has a large surface area exposed to air at the hole walls. This poses a major problem particularly in GaAs-based photonic crystal lasers as it has nearly an order of larger surface recombination rates with respect to other semiconductor laser material systems (such as InP). In addition, the free-standing membrane geometry of the structures results in poor thermal conductivity. Because of these problems, without any treatment, single-defect cavity lasers are required to be cooled in a cryostat. To reduce losses arising from NR surface recombination, the sample was passivated in a (NH4)S solution, which resulted in a 3.7-fold reduction in the lasing threshold (Englund et al., 2007a). We found that surface passivation was critical in our samples for room-temperature and continuous-wave (CW) operation (Englund et al., 2007b). The structures are pumped optically with 3-ps short pulses at an 80 MHz repetition rate and at a wavelength centered at 750 nm using the confocal microscope as shown in Figure 14. High-resolution lasing spectra are measured with the spectrometer,

Femto-second Ti:sapphire CCD

Streak camera system

Cryostat Spectrometer Figure 14 Schematic of the experimental setup to analyze ultrafast time dynamics of PhC lasers.

502 Photonic Crystal Microcavity Light Sources

while time response is obtained using a streak camera with 3-ps resolution. 6.12.5.2

Lasing Spectrum

Single-mode lasing is observed from both singlecavity and coupled-cavity array structures. CCD images of the mode and structures are shown in Figure 15. Spectra of the single cavity below and above threshold are shown in Figure 16. The belowthreshold spectrum indicates a Q-value of 1200 from a Lorentzian fit (inset of Figure 16(a)). The lasing mode showed dipole symmetry (180 rotation). Its mode volume is calculated from FDTD simulation as 0.55(/n)3. The PhC array laser in Figure 15(c) (a)

(b)

supports a lasing mode at mode = 950 nm at low temperature (LT) of 10 K. Because of fabrication imperfections, PhC holes toward the edges of the structure were slightly smaller and cavities showed a higher resonance wavelength. As a result, we observed that coupled-cavity modes existed only on a subset of the full array. From images of the lasing mode, we estimate that it comprises only seven to nine cavities. 6.12.5.3 Spontaneous Emission Rate Modification We determine the Purcell factor Fm directly from lifetime measurements of the cavity array pumped below threshold, and comparing them to emission (c)

Figure 15 (a) The CCD image of the three single cavity structures. Both the cavities and trenches are observable. (b) The image of the PL and the mode. (c) CCD camera image of the mode for coupled-cavity array. The approximate location of the structure and trenches are indicated by dashed lines.

(a) 5

(b)

2.5

1.6

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1.4 1.2 1.0 0.8

2 0.6 0.4 935

1

935

937 λ (nm)

939

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940 950 λ (nm)

960

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0 920

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Intensity (a.u.)

4

3

970

0 850

900

950 λ (nm)

1000

1050

Figure 16 Spectra of the single-defect photonic crystal laser. (a) Spectrum below lasing threshold. The dashed box indicates the cavity mode and the inset, shows the Lorentzian fit (red) for its Q-factor estimation. (b) Spectrum above threshold. The inset shows the lasing curve, i.e., the output power vs. input pump power. Taken from Altug H, Englund D, and Vuckovic J (2006) Ultrafast photonic crystal nanocavity laser. Nature Physics 2: 484–488.

Photonic Crystal Microcavity Light Sources

(b) 1 0.8

Intensity

Intensity

(a)

503

Passivated, τ = 605 ps

1 0.8

Passivated, τ = 142 ps

0.6 0.6 Unpassivated, τ = 618 ps

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Unpassivated, τ = 34 ps

0.2 250

t (ps) 500 750 1000 1250 1500 1750 2000

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t (ps) 200

(c) Intensity

1 0.8 0.6

Passivated, τ = 19 ps

0.4 0.2

t (ps) 0

10

20

30

40

50

Figure 17 Micro-photoluminescence from (a) bulk quantum-well. (b) PhC (uncoupled to cavity array mode), and (c) nonlasing PhC cavity array at 1/2 threshold power (Pin = 12 mW before objective lens for original and 12 mW for passivated structures, pulse length 3.5 ps with 80 MHz repetition). Measurements are performed at 10 K. Solid fits are obtained using rate equations; dashed fits show exponential decay approximations. Taken from Englund D, Altug H, Ellis B, and Vuckovic J (2008) Ultrafast photonic crystal lasers. Laser and Photonics Reviews 2: 264–274.

lifetime in the unpatterned (bulk) sample (Altug et al., 2006; Englund et al., 2008). Decay times for the passivated cavity array structure are estimated from Figures 17(b) and 17(c), indicating that  uncoupled  142 ps and  coupled  19 ps. For the bulk and PhC regions at times long after the excitation pulse, the photoluminescence signal decays according to: 1 Fm þ FPC 1 ¼ þ r coupled PC;nr 1 uncoupled 1 bulk

¼

¼

FPC 1 þ r PC;nr

1 1 þ r bulk;nr

around 84. The high Purcell factor for single cavities is not surprising as they are expected to have a maximum F of 165 for the cavity with this set of Q and Vmode, indicating that spatial averaging over the mode reduced Fm by nearly 2 times. Baba et al. (2004) previously estimated SE lifetime enhancement exceeding 16 (detector response limited) for similar structures in GaInAsP PhC nanocavities.

ð13Þ ð14Þ ð15Þ

From bulk measurements (Figure 17(a)), we estimate the natural radiative lifetime  r is approximately 605 ps, assuming  bulk,nr >>  r. These three equations can be used to estimate Fm as 28. Repeating these measurements for an unpassivated single-defect cavity gives a spatially averaged Fm of

6.12.5.4 Ultrafast Dynamics of the Nanocavity Lasers Above lasing threshold, the decay time is reduced by another order of magnitude due to stimulated emission. Figures 18(a) and 18(b) show the time data for the single-defect cavity and coupled-cavity array lasers, respectively. The decays for both lasers are fitted by single exponentials with a decay constant of 2 ps. To understand the dynamics, we used the laser rate Equations (10) and (11) to simulate the photon and carrier densities as functions of time. Initially, the photon and carrier densities are taken as zero and

504 Photonic Crystal Microcavity Light Sources

(a)

(b)

τsingle∼2.13 ps

τcoupled array∼2.18 ps

1.2

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0 0

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12.5

15

τdelay∼1.5 ps PhC laser

2.5

(d)

2

1.4

Pump laser

Photon number (a.u.)

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1.2 1 8 6 4

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Figure 18 Time-resolved response of a photonic crystal laser above lasing threshold. (a, b) Time response (blue) of a single-defect cavity and coupled-cavity array laser at 7 K together with an exponential fit (red). (c) Delay-time measurement of a single-cavity laser (blue) with respect to pump laser (red). For this measurement, the cryostat temperature was raised from 7 K to 100 K to increase the relaxation rate of carriers from upper MQW levels to the lowest level by increasing phonon population. At 7 K, the delay time was 3–4 ps, while at 100 K, the delay time decreased to 1.5 ps. (d) Simulated photon number as a function of time for a single-defect cavity laser (red). The simulation result is convolved with a Gaussian of 4 ps width (blue) to take into account streak-camera response. Taken from Altug H, Englund D, and Vuckovic J (2006) Ultrafast photonic crystal nanocavity laser. Nature Physics 2: 484–488.

above the transparency condition, respectively. The simulated photon density is also convolved with a Gaussian of 4-ps width to take into account streak camera response. The simulation results are shown in Figure 18(d). The bare photon response (unconvolved data) shows that when the laser is pumped above threshold, the photon density decays with the cavity decay time ( p). For both the single and coupled-cavity array lasers, this is 0.5 ps (for Q of 1000), which is below the resolution limit of our streak

camera. The photon response convolved with the streak camera response shows a decay time of 2 ps, which agrees very well with our experimental results. As indicated above, one important parameter in this type of laser modulation scheme is the delay time, which decreases in high Purcell-factor cavities. We measured this delay time at 100 K (with 890 nm pump wavelength) to be 1.5 ps (shown in Figure 18(c)), which is close to the streak camera resolution limit. The delay time is nearly two orders

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reported to date. The figure also shows the laser response to a 15 ps repetition pump, where the streak camera resolution more clearly separates the pulses.

of magnitude lesser than in previous measurements on conventional semiconductor lasers.

6.12.5.5 Direct Modulation of Ultrafast Nanocavity Lasers

6.12.6 On-Chip Integration of Photonic Crystal Waveguides and Lasers

To further investigate ultrafast laser behavior, we directly modulate single-defect cavity lasers at very high speeds by pumping them with a series of femtosecond pulses generated using a Fabry–Perot etalon. The spacing of the pulse train is controlled by the etalon mirror separation. Only the first three pump pulses have sufficiently high power to turn on the nanocavity laser. Figure 19 shows the results for such a direct modulation of a nanocavity laser above 100 GHz. The response of the laser nicely follows the pump, whose peaks are separated by 9  0.5 ps (a slight nonperiodicity in the time separation between the consecutive pump pulses results from slight angular deviations of consecutive pulses from the etalon). This modulation speed is already an order of magnitude higher than the fastest semiconductor lasers

One of the particular strengths of PhCs is that they allow straightforward on-chip integration of photonic devices. As a step in that direction, we demonstrated a PhC nanocavity laser that is evanescently coupled to a section of a waveguide and then to a second cavity for out-coupling. Two nanocavities are coupled to a 25-mm-long section of a waveguide, with a cavity– waveguide separation of three holes (Figure 20(a)). The device was fabricated in a GaAs membrane containing four QWs, as described above. We pumped the source cavity on the left and observed emission from the target cavity on the right with a lasing threshold of 90 mW under pulsed excitation (measured before the objective lens) at room temperature. Figure 20(b)

Intensity of PhC laser

b

Intensity of pump laser

0

a

10

20

30 Tim 40 e (p s)

th

ng

50

60

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ele av W

0 5 10 15 20 25 30 35 40 Time (ps)

Figure 19 Direct modulation of a single-defect photonic crystal nanocavity laser. The direct modulation was performed with the pump repetition periods of (a) 9  0.5 ps and (b) 15 ps, corresponding to direct modulation rates of 100 and 66 GHz, respectively. The bottom figure shows a series of femto-second pump pulses separated by 9  0.5 ps, used as the excitation for (a), obtained by a Fabry–Perot etalon. The transmitted power of consecutive pulses from the etalon drops geometrically with the ratio R1R2 of the mirror reflectivities. Only the first three pump pulses had sufficient power to turn on laser. Both the femto-second pump pulses and the laser output pulses are broader, as a result of the slow response time (4 ps) of the streak camera, as described above. Taken from Altug H, Englund D, and Vuckovic J (2006) Ultrafast photonic crystal nanocavity laser. Nature Physics 2: 484–488.

506 Photonic Crystal Microcavity Light Sources

Pump

Observe

(a)

4 (b) 5 × 10

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910 920 λ (nm)

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Figure 20 PhC nanocavity laser integrated with an out-coupling waveguide. (a) SEM of structure. Two modified nanocavities are coupled to a 25-mm-long section of a waveguide, which terminates in second symmetrical nanocavity for scattering emission off the chip. (b) Transmitted intensity shows the laser mode (large peak) and side modes, which are standing waves inside the long cavity that makes up the terminated waveguide (small peaks).

shows the spectrum observed from the target cavity. It shows the source cavity’s mode (main peak) as well as some emission from standing waves inside the waveguides (small side peaks). Though the cavity/waveguide design will need to be optimized in future work, this demonstration already shows the feasibility to integrate sets of (possibly detuned) ultrasmall nanocavity lasers onto a waveguide channel. In this case, the QW gain material exists throughout the structure, which causes loss. A recent report by Nozaki et al. demonstrated a butt-joint regrowth technique to couple a passive waveguide to a PhC nanocavity (Nozaki et al., 2008).

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Further Reading Ahn S, Kim S, and Jeon H (2010) Single-defect photonic crystal cavity laser fabricated by a combination of laser holography and focused ion beam lithography. Applied Physics Letters 96: 131101. Atlasov KA, Calic M, Karlsson KF, et al. (2009) Photonic-crystal microcavity laser with site-controlled quantum-wire active medium. Optics Express 17(20): 18178–18183. Ellis B, Sarmiento T, Mayer M, et al. (2010) Electrically pumped photonic crystal nanocavity light sources using a laterally doped p-i-n junction. Applied Physics Letters 96: 181103. Giannopoulos AV, Li YJ, Long CM, Jin JM, and Choquette KD (2009) Optical properties of photonic crystal heterostructure cavity lasers. Optics Express 17(7): 5379–5390. Gong Y, Ellis B, Shambat G, Sarmiento T, Harris JS, and Vuckovic J (2010) Nanobeam photonic crystal cavity quantum dot laser. Optics Express 18(9): 8781–8789. Ho WD, Lu TW, Hsiao YH, and Lee PT (2009) Thermal properties of 12-fold quasi-photonic crystal microcavity laser with

508 Photonic Crystal Microcavity Light Sources size-controlled nano-post for electrical driving. Journal of Lightwave Technology 27(23): 5302–5307. Lu L, Mock A, Yang T, et al. (2009) 120 mW peak output power from edge-emitting photonic crystal double-heterostructure nanocavity lasers. Applied Physics Letters 94: 111101. Lu TC, Chen SW, Kao TT, and Liu TW (2008) Characteristics of GaN-based photonic crystal surface emitting lasers. Applied Physics Letters 93: 111111. Matsubara H, Yoshimoto S, Saito H, Jianglin Y, Tanaka Y, and Noda S (2008) GaN photonic-crystal surface-emitting laser at blue-violet wavelengths. Science 319(5862): 445–447.

No YS, Ee HS, Kwon SH, et al. (2009) Characteristics of dielectric-band modified single-cell photonic crystal lasers. Optics Express 17(3): 1679–1690. Noda S and Fujita M (2009) Photonic crystal efficiency boost. Nature Photonics 3: 129–130. Nomura M, Kumagai N, Iwamoto S, Ota Y, and Arakawa Y (2009) Photonic crystal nanocavity laser with a single quantum dot gain. Optics Express 17(18): 15975–15982. Raineri F, Yacomotti AM, Karle TJ, et al. (2009) Dynamics of band-edge photonic crystal lasers. Optics Express 17(5): 3165–3172.