1. Introduction

Various types of surface or interface electromagnetic waves propagating along a boundary between two media and decaying in both directions away from the boundary attract a strong interest, both fundamental and practical. In most cases very special criteria are required to enable such waves. Thus an interface wave on a boundary between two homogeneous media is possible only if the dielectric permittivity ε of one media is negative [1], which can be provided by the plasma contribution to ε [2], e. g. in metals. Photonic crystal [3] may allow propagation of resonant surface waves on its boundary [4]. Structuring of a surface using gratings or ridges can also support surface waves [5]. Other examples include interface waves in chiral materials [6], on a boundary of a gyrotropic material and a negative phase velocity medium [7] or at a non–linear interface [8]. An optically anisotropic medium with optical axes tilted with respect to the interface may support interface waves in a narrow interval of in–plane angles [9].

Arising new applications of semiconductor diode lasers require devices with substantially advanced performance over presently available ones. Thus recently proposed design concepts [10–35] have led to devices with novel functionality. In this regard, there arises a question of existence of surface waves beyond complex systems of [1–9], i. e., waves bounded to a surface of conventional semiconductor materials, and of a possibility to employ such waves in practical devices.

A surface of a DBR is likely to be the simplest structure of this type. In our earlier work [36] we studied DBR–containing devices, namely those based on VCSEL epiwafers, capable to high performance operation once fabricated as oxide–confined VCSELs. The structures in [36] were grown in line with the antiwaveguiding VCSEL (A–VCSEL) design [37, 38] where the in–plane waveguide mode is prohibited due to the reduced overlap with the active medium. Electroluminescence (EL) studies revealed three different types of modes. The longest wavelength mode (mode A) is a VCSEL–like mode at ~854 nm emitting normal to the surface with a full width at half maximum (FWHM) of the far field ~10°. Accordingly the lasing wavelength demonstrates a thermal shift at a rate 0.07 nm/K. Mode B was at a shorter wavelength of ~840 nm at room temperature, emitting light in two symmetric lobes tilted with respect to the normal to the surface in the directions parallel to the stripe. The emission wavelength of this mode shifts at a rate 0.22 nm/K according to the GaAs bandgap shift. The tilt angle of mode B with respect to the normal reduces as the wavelength approaches the vertical cavity etalon wavelength and this mode finally merges with the VCSEL mode. Mode B hops between different lateral modes of the VCSEL forming a dense spectrum due to significant longitudinal cavity length. Mode C was at ~820 nm, shifting upon temperature at the rate 0.06 nm/K. The wavelength of mode C matches the wavelength of the tilted mode propagating in the semiconductor structure at the critical angle for total internal reflection for light impinging from the semiconductor chip on the semiconductor/air interface. This suggests that mode C could be related to a specific surface mode. Indeed, modeling performed in Ref [36] suggested that the lasing mode C represents a coupled state between the TM–polarized surface–trapped optical mode and the VCSEL cavity mode. However, polarization of the light emission was not measured.

In the present paper we extend the studies of Ref [36]. We address theoretically a fundamental phenomenon of the surface electromagnetic waves in a generic structure of a DBR terminated by a free surface, without mixing with a resonant cavity. Further, we investigate experimentally the electroluminescence and lasing properties of a device formed of a similar epitaxial structure as in Ref [36] but with a smaller detuning between the gain spectrum and the cavity resonance. The second structure reveals a similar behavior emitting in the same three types of the modes. We measure the polarization of all the modes and confirm the theoretical predictions.

2. Electromagnetic waves on a surface of a DBR

Let a DBR be formed of 25 pairs of layers alternating in the z direction, namely layers of a high (n₁) and a low (n₂) refractive indices with thickness of one quarter of the material wavelength, i. e. with d₁ = λ₀/(4n₁) and d₂ = λ₀/(4n₂), where λ₀ is the wavelength of the peak reflectivity. The structure is formed on a substrate with the refractive index n₁ and is terminated by air from the top at the surface z = z₀. The topmost layer is the high index layer, which is typically used in VCSELs to provide in–phase reflection at the semiconductor/air interface and maximize the photon lifetime. To specify, we choose n₁ = 3.5 and n₂ = 3.0 which mimics typical refractive indices of Ga_1–xAl_xAs alloy with low and high Al composition, respectively.

Consider a TM wave propagating along the x–direction and having only one component of the magnetic field in the y–direction,

The second criterion for the existence of the surface mode reads that the mode should decay within the DBR, i. e. the mode wavelength should be within the reflectivity stopband of the DBR corresponding to the effective mode index n_eff. The effective mode angle defined for the DBR material with a high refractive index n₁ = 3.5 equals ${\vartheta }_{eff}={\sin }^{-1}\left(n_{eff}/n_1\right)$. Since we seek surface modes with n_eff close to 1, it is of particular interest to consider the DBR properties for the light impinging from material #1 at the tilt angle ${\vartheta }_{eff}={\sin }^{-1}\left(1/3.5\right)\approx {16.6}^0$, which corresponds to the onset of the total internal reflectance at the surface of material #1. Figure 1(a) shows the optical power reflectance (OR) spectrum at normal incidence, equal for both TE and TM light. Figures 1(b) and 1(c) display OR spectra for the oblique incidence at the angle 16.6° for TE and TM light, respectfully. Both spectra reveal stopband shifted to shorter wavelengths with respect to λ₀, the spectrum for TE mode having a broader stopband, and the spectrum for TM mode having a more narrow stopband that the one for the normal incidence, as noticed also in [39]. A drastic difference between TE– and TM–polarized light appears once the OR spectra for gliding light impinging from the air at the angle 89.9° are considered. Once the OR spectrum for TE light (Fig. 1(d)) shows no extra features within the stopband, the TM light reveals a clear reflectivity dip (Fig. 1(e)) indicating presence of an effective virtual cavity at the surface capable to localize an optical mode.

 

Fig. 1 Optical power reflectance (OR) spectra of the model DBR. (a)–(c) Modeled spectra for light impinging from material #1 onto the DBR. (d), (e) Modeled spectra for light impinging from the air at ϑ = 89.9°.

Download Full Size | PDF

Figures 2(a) and 2(b) display modeled OR spectra for light impinging from the air at different glancing angles of incidence. One can see that the dip position pointing at the transparency wavelength, in the interval of glancing angles from 86° to 90°, where the dip is pronounced, is not a function of the angle allowing angle–insensitive filters. The dip narrows once the glancing angle approaches 90 degrees, which is in line with the general trend of increasing the DBR reflectivity at glancing angles pointed out in [39].

 

Fig. 2 (a, b) Modeled optical power reflectance spectra for light impinging from the air at different glancing angles of incidence. One can see that the within the interval of angles from 86° to 90° the spectral position of the dip, or the transparency wavelength is not a function of the glancing angle allowing angle–insensitive filters.

Download Full Size | PDF

Results of the solution of Eq. (2) for TM polarized modes are presented in Fig. 3, wherein the generic case valid for an arbitrary wavelength λ₀ is presented for the particular value of λ₀ = 850 nm. At the wavelength 0.96λ₀ the solution yields multiple modes, in which the mode decaying in the DBR is coupled to some of the modes of the air (not shown). At λ = 0.95λ₀ the mode becomes localized but decays very slowly in the air and is extended over a few tens of micrometers. As this wavelength is close to the center of the DBR reflectivity stopband in Figs. 1(c) and 1(e), the mode decays rapidly in the DBR. Upon decrease of the mode wavelength, the extension length of the surface mode in the air decreases. Further, as the mode wavelength shits away from the center of the stopband to its short wavelength boundary (in Figs. 1(c) and 1(e)), it decays weaker in the DBR. The mode corresponding to λ = 0.91λ₀ is close to the stopband edge and the exponential decay of the field oscillation amplitude in the DBR nearly vanishes. The wavelength λ = 0.90λ₀ is beyond the DBR stopband, and the mode is no longer a surface mode.

 

Fig. 3 Refractive index profile of the model DBR and magnetic field strength profile in surface TM modes at different wavelengths.

Download Full Size | PDF

A large extension of the TM mode in the air implies that the effective refractive index of the mode is close to 1, and the effective angle of the mode propagation in the material layer is close to the onset of the total internal reflection at the semiconductor/air interface. Upon wavelength decrease as in Fig. 3, the extension of the mode in the air also decreases, and both n_eff and ${\vartheta }_{eff}={\sin }^{-1}\left(n_{eff}/n_1\right)$ increase. As the localized mode does not propagate in the air, it does not manifest itself in the optical reflectance spectra of the structure for the light impinging from the air (as in Figs. 1(e), 2(a) and 2(b)). Some features of these modes in part of the mode decay within the DBR can be addressed, once the transmittance or reflectance of the DBR for the light impinging from semiconductor material (e. g., material #1, like in Fig. 1(c)) is considered. As ${\vartheta }_{eff}$ increases, the DBR reflectivity stopband shifts towards shorter wavelengths, but slower than the mode wavelength, and at 0.91λ₀ the mode wavelength comes out of the stopband. Thus, the spectral region of the existing TM surface modes is bound from the long wavelength side, once the mode no longer decays in the air and is a radiative mode, and is bound from the short wavelength side once the wavelength comes out of the DBR reflectivity stopband.

Once a near–field device, i. e., a device with a certain mode extension in the air is targeted, the important features of the mode are the mode extension length in the air l_ext, the mode intensity in the active region, and the mode leakage losses to the substrate. Figure 3 suggests that, depending on a particularly sought application, an optimum mode wavelength can be found within the spectral range, in which the surface mode exists.

The spectral range, in which the surface TM mode exists, can be tuned, e. g., by varying the thickness of the topmost layer of the DBR. Such a change can be implemented by epitaxial growth of a thicker top layer or by partial etching of the grown wafer, which is also known for VCSELs and can be applied to tune the photon lifetime [40]. The dispersion curves in Fig. 4 display the mode confinement coefficient of the surface mode which is inverse proportional to l_ext, $\beta =\lambda /\left(4\pi l_{ext}\right)$. Plots are presented for the nominal thickness of the topmost layer λ₀/(4n₁) as well as for a smaller and a larger thickness (5/6 and 7/6 of the nominal thickness, respectively). The surface mode exists in a broader spectral range for a thicker topmost layer.

 

Fig. 4 Mode confinement coefficient of the surface TM mode which is inverse proportional to the mode extension length in the air, $\beta =\lambda /\left(4\pi l_{ext}\right)$, versus mode wavelength for different thickness of the topmost layer.

Download Full Size | PDF

It should be noted that a TE surface mode does not exist for the structures considered. A near–field TE mode could be allowed only if an artificial cavity is formed on top of the DBR. The detailed analysis of the properties of near–field modes on the boundary of a DBR will be presented and possible applications will be discussed elsewhere [41].

3. Structure

A VCSEL–type GaAlAs–based structure was grown in a multiwafer industrial reactor by metalorganic vapor phase epitaxy. The structure contained a resonant λ/2 cavity with five compressively strained GaInAs quantum wells as active region, the cavity being sandwiched between a 34–periods GaAlAs–based n–doped bottom DBR and a 21.5–periods p–doped top DBR. The structure was cleaved in rectangular–shaped ~350 × 400 µm pieces with perpendicular facets. The contact grid region has a total width of w~70 µm. d = 7 µm–wide metal stripes serving as non–alloyed metal contact form periodic rectangular openings of a size b × a = 10 × 40 µm. The chosen dimensions of the contact grid allow a good electric contact and efficient in–plane current spreading from the contact region to ensure laterally–uniform current injection into the active region, on the one hand, and a sufficient open area, from which light can be emitted, on the other hand. Copper wire was bonded directly on top of the contact grid. Surface emission through the windows on top of the chip was measured at temperatures from 90 to 380 K. The schematics of the chip is presented in Fig. 5(a) and the image is shown in Fig. 5(b). Unlike typical VCSELs, where the current path is contracted by oxide–confined aperture or by proton bombardment area, no such electric confinement occurs in the structures studied. Current flowing from the top contact grid through the ~2.5 µm–thick top DBR is spread across the entire active region, and the resistance of the device is defined by the chip area and not by the grid area. In this connection it is worth noting that the emission occurs only in the region of the contact grid presumably due to in–plane localization of the optical modes by the grid.

 

Fig. 5 (a) Perspective view of a chip with a metal grid contact on top surface. The chip is a rectangular–shaped ~350 × 400 µm piece with perpendicular facets. The contact grid region has a total width of w~70 µm. d = 7 µm–wide metal stripes serving as non–alloyed metal contact forms periodic rectangular openings having a size of b × a = 10 × 40 µm. Numbers 1, 2, 3 indicate various positions of the photodetector measuring electroluminescence. (b) Infrared image of the lasing device. Gray structure in the center is the copper wire bonded on top of the grid.

Download Full Size | PDF

4. Electroluminescence studies

Figure 5(a) displays several positions of the photodetector used to measure electroluminescence (EL) spectra from the device from different observation points to address various optical modes. In Ref [36]. EL spectra of the chip recorded from the chip facet (by detector #1 in Fig. 5(a)) in a broad range of temperatures are displayed. The spectra were measured by using a lens collecting light from an angle of ~20°. Typically the spectra contain three different peaks (see, e. g., Fig. 6).

 

Fig. 6 Electroluminescence spectrum measured from the edge of the device in the stripe direction.

Download Full Size | PDF

To elucidate the physical features of each of the modes we consider the temperature behavior of each of the three peaks (Fig. 7(a)) as well as the far field profile of the emission (Figs. 8(a) and 8(b)). The longest wavelength mode (mode A) is a VCSEL–like mode at ~854 nm emitting predominantly normal to the surface (Figs. 8(a) and 8(b)). This mode exhibits a thermal shift of the wavelength of ~0.07 nm/K.

 

Fig. 7 (a) Shift of three electroluminescence (EL) peaks versus temperature. (b) Evolution of the EL spectrum versus temperatures while passing the resonance between mode B and mode C.

Download Full Size | PDF

 

Fig. 8 (a) Far field profile of the electroluminescence (EL). (b) Spectrally–resolved far field profile of EL.

Download Full Size | PDF

Mode B is at shorter wavelengths of ~840 nm at room temperature, emitting light at two symmetric lobes tilted with respect to the normal to the surface in the directions parallel to the stripe (Fig. 8(a)). The mode lies within the continuum spectrum of tilted modes, having the vertical profile of the optical field same as the VCSEL mode and propagating forth and back in the rectangular chip acting as an in–plane Fabry–Pérot resonator. Such modes are also known to represent slow light in VCSEL amplifiers (see, e. g., [42] are references therein). The emission wavelength of mode B shifts at a rate 0.22 nm/K according to GaAs bandgap shift. Upon temperature increase the angle of the mode with respect to the normal reduces (Fig. 8(a)) as the wavelength approaches the vertical cavity etalon wavelength and mode B finally merges with the VCSEL mode A.

It is important to note a strong resonance effect once the wavelengths of mode B and mode C match (Fig. 7(b)). At this temperature the intensity of the related feature increases more than by an order of magnitude with respect to that at non–resonant wavelengths. It was necessary to reduce the drive current 6–fold to reduce the intensity of the emitted light to avoid saturation of the detector. The resonant enhancement of the light emission occurs once the gain spectrum matches the wavelength of mode C and indicates a possibility to channel all the power to the surface–trapped mode, achieve light amplification and lasing in the surface–trapped TM– polarized near–field mode.

Far–field emission profiles were measured with the spectral resolution by scanning an angle ϑ_x at which the optical fiber is directed towards the sample in the (xz)–plane as noted in Fig. 5(a). The light from the exit of the fiber was directed to a monochromator. The spectrally–resolved far–field profiles (Fig. 8(b)) show that the angle for each particular mode is fixed, the far field of each mode is narrow, and the broadening of the far field in Fig. 8(a) is related to the spectral broadening of the tilted emission. The far field measured at 852 nm reveals the full width at half maximum of the VCSEL mode ~10°.

As the theoretical modeling demonstrates that the mode C combining the VCSEL cavity mode and the surface–trapped mode [36], exists only in TM polarization, it is important to measure polarization–resolved EL spectra. Figure 9 displays polarization–resolved spectra measured from position 1 in Fig. 5(a). In the long–wavelength part of the spectrum, close to 854 nm related to mode A and close to 840 nm related to mode B, TE–polarized emission dominates, as should be expected for a device based on III–V semiconductor materials. Indeed, as pointed out in [43], because of microscopic selection rules associated with the unit cell wavefunctions in III–Vs, for the TM polarization, the conduction–to–heavy–hole transitions are forbidden, and only conduction–to–light–hole transitions contribute to the emission of light. Since there are more heavy holes than light holes in thermal equilibrium due to a higher density of states, the gain associated with heavy holes is larger, and hence the gain is larger for the TE polarization. The feature persists in compressively strained quantum wells, where the splitting of the degenerated valence band pushes the light hole band towards higher energies of holes keeping the valence band more populated with heavy holes. For this reason, the stimulated emission in modes A and B is predominantly TE–polarized. On the contrary, since mode C exists in TM polarization only, the emission at ~821 nm is completely TM–polarized, in full agreement with the modeling.

 

Fig. 9 Polarization–resolved electroluminescence (EL) spectra of the device.

Download Full Size | PDF

For a further comparison with the modeling we note that the topmost layer of the structure has an extended thickness of $\left(7/6\right){\lambda }_0/\left(4n_1\right)$. According to the corresponding dispersion curve of Fig. 4, the spectral range of existing surface modes is extended up to 0.97λ₀ and includes the value 0.96λ₀ equal to the ratio of the wavelengths of modes C and A.

It should be noted that the observed EL spectrum of the device is governed by the competition of these three types of the modes. It is possible to influence this competition by intentionally scratching the rear facet of the chip and destroying its mirror properties. Figures 10(a) and 10(b) compare EL spectra of a chip with as–cleaved mirror–like facets (Fig. 10(a)) and of a chip with the rear facet scratched (Fig. 10(b)), the rear facet being marked in Fig. 8(a). The EL spectrum in a conventional in–plane Fabry-Pérot resonator at a moderate current reveals all three modes (Fig. 10(a)), whereas an increase in current results in mode B strongly dominating the spectrum. Once the rear facet is scratched, the EL spectrum reveals two strong features related to mode A and mode C, mode C dominating the spectrum, mode B being suppressed. Thus, the scratched facet affects the tilted mode B stronger than mode C, in which a significant portion of the electromagnetic field propagates in the air in the near–field zone close to the surface. Further, Fig. 10(b) demonstrates a superlinear increase of the EL intensity upon injection current, indicating a possibility to reach lasing.

 

Fig. 10 Effect of the facet scratching on the mode competition in electroluminescence (EL) spectra. (a) Device with cleaved facets emits light in all three modes. Increase in drive current leads to lasing in the tilted mode B. (b) In a device with the rear facet scratched, the tilted mode B is suppressed, and mode C coupled with the surface mode dominates the EL spectrum.

Download Full Size | PDF

Apart from scratching chip facets as addressed in Fig. 10(b), it is possible to support mode C by designing the device such that the gain spectrum will match the wavelength of the surface mode, allowing lasing in the mode significantly extended to the air. Further suppression of the vertical mode A can be achieved by reducing the number of the top DBR pairs thus increasing the mode losses. The combined mode C will be formed at a stronger coupling and, hence, at a broader resonance between the cavity mode and the surface mode, will be less wavelength–stabilized, but will have a larger intensity of the near field in the air. Continuing this trend will bring the active region to the top of the structure removing both the top DBR and the resonant VCSEL cavity, returning to the structure considered above in Section 2. The operation of such device will be considered in detail in [41].

Thus, by optimizing the thickness of the top DBR it is possible to suppress undesired VCSEL mode and to fabricate a device operating exclusively in the wavelength–stabilized near–field mode, including a near field laser. Such a device will then be advantageous for direct coupling into an optical fiber or a waveguide [19] for generation of a high–brightness beam. Further, a temperature stable distributed feedback (DFB) laser can be fabricated if the top layer of the DBR is formed of a dielectric material with nearly temperature–independent refractive index.

5. Summary

To conclude, we have presented modeling results demonstrating the existence of a near–field TM–polarized electromagnetic mode on a surface of a DBR, wherein the mode propagates along the surface, decays evanescently in the air and decays in an oscillating manner in the DBR. The mode allows near–field optoelectronic devices like diode lasers, superluminescent light–emitting diodes, novel types of wavelength–stabilized filters or couplers. A VCSEL structure containing a resonant cavity enables resonant coupling between the cavity mode and the surface mode rendering the resulting near–field mode wavelength–stabilized. A VCSEL structure fabricated in the form of an in–plane Fabry–Pérot resonator shows EL spectra containing three types of modes, namely a vertical VCSEL–like mode, a tilted mode, and a combined near–field mode with the cavity mode. The dominating lasing mechanism at room temperature is the tilted wave lasing. The tilt angle of the VCSEL mode is governed by the wavelength of the maximum gain. At small detuning of the VCSEL etalon wavelength from the gain towards the longer wavelengths the mode in the air is tilted with respect to the normal to the surface. At large detuning the mode angle in the crystal reaches the critical angle of the total internal reflection at semiconductor/air interface and becomes coupled to a surface–trapped in–plane mode with significant extension of the optical field to the air at the edge through in–plane emission lobe. By relative positioning the gain spectrum, by changing the number of the top DBR pairs (or DBR reflectivity), or by destroying the facet mirrors one can select the desirable lasing mechanism. Modeling shows that the near–field surface mode is necessarily TM–polarized. Polarization studies indeed reveal the reversal of polarization across the spectrum from TE–polarized tilted modes to purely TM–polarized near–field surface–trapped mode.