Whispering gallery modes (WGMs) in circular or polygonal cavities have attracted a great deal of interest due to the attainable high-Q values originating from total internal reflection of light at the boundaries [1-5]. Various applications of WGMs have been presented, such as add-drop passive filters in dense wavelength-division multiplex (DWDM) communication and low-threshold microcavity lasers [6-10]. In many applications of WGMs, external waveguides are adapted as coupling devices. Because the evanescent field of waveguide modes or WGMs decreases exponentially from the boundary, a very small gap distance between the cavity and the waveguide is essential for optimal coupling strength, particularly in the lateral coupling scheme using circular cavities. In order to enhance the coupling strength with reasonable gap distances, square or rectangular cavities were studied because they have a longer interaction length than circular cavities . The entire flat boundary itself becomes the coupling region, which allows a relatively large gap distance for optimal coupling with external waveguides.
Figure 1 shows a schematic layout of the waveguidecoupled rectangular cavity add-drop filter [13,14]. The resonance modes of a rectangular cavity (refractive index m, size of
the rays form 4-bounce closed trajectories as shown in Fig. 1. The optical path length L of the closed modes is approximately given by
[FIG. 1.] Schematic layout of waveguide-coupled rectangular cavity add-drop filter. A closed trajectory corresponding to the 4-bounce WGMs is shown in the rectangular cavity.
In the previous add-drop filters using ring, square, or rectangular cavities, the input light on the add port should propagate opposite to that of the input port and the signal from the drop port also propagates in opposite direction to the input one. It is desirable to find a scheme using microcavities in which the drop and add port have same direction of propagation with the input port because it allows additional design choices in the arrangement of the waveguide array. In this work, we propose a grooved rectangular cavity satisfying the above requirement, and we investigate lasing properties in grooved rectangular semiconductor cavities. If this cavity is adapted in the add-drop filter, the add and drop port will have the same propagation direction to the input port as illustrated Fig. 2.
The proposed rectangular cavity is shown in Fig. 2. A groove is made on the center of a long side of the rectangular cavity (refractive index m, size of
The 6-bounce open orbit modes are also similarly possible to the case of a rectangular cavity. The resonance wavelength λ of bow-tie modes can be determined from the resonance condition as
[FIG. 2.] Proposed grooved rectangular cavity and schematic layout of corresponding filter. A closed orbit corresponding to the 6-bounce bow-tie modes is shown in the cavity.
The experimental setup for bow-tie mode lasing was similar to that used previously [15,16]. InGaAsP/InGaAs multiple quantum wells (8 MQWs, λg~1.3 μm) were surrounded by two confinement layers in the epistructure. The total thickness of the epistructure formed on an InP substrate was about 0.8 μm. Various cavities were lithographically patterned and etched vertically by the RIE (Reactive Ion Etching) process. The total etching depth was controlled to be about 4 μm. A pulsed Nd: YVO4 laser (wavelength of 1.06 μm, repetition rate of 10 kHz, pulse width of 150 ns) was loosely focused on a cavity using a lens and a beam splitter in order to optically pump MQWs. The illuminated cavity was monitored through the beam splitter using a CCD camera attached to a high-resolution microscope with a long working distance. A tapered fiber was approached to the cavity corner in order to collect the lasing signal. The lasing spectrum was measured using an optical spectrum analyzer (OSA).
Lasing spectra were measured from various rectangular cavities fabricated on the same wafer. Because the signal level of spontaneous emission was very low, no apparent spectrum was observed with the OSA below the threshold of lasing. When the pump intensity increased, a single lasing peak was observed at slightly above threshold. As the pump intensity increased further, the number of lasing peaks increased and their widths became broad. Figure 3 shows typical lasing spectra at high above threshold from a square, a rectangle, and grooved rectangles. The lasing spectrum from a square with
where M(λ) accounts for the dispersion in m of the semiconductor epiwafer and is a function of λ. From Eq. (1), the round-trip length
Figure 3(c) shows a lasing spectrum centered around 1275 nm~1280 nm, similarly to Fig. 3(b) from a grooved rectangle with
[FIG. 3.] Typical lasing spectra from various shaped rectangular semiconductor cavities: (a) a square (a=b=40 μm), (b) a rectangle (a=40 μm, b=80 μm), (c) a grooved rectangle (a=40 μm, b=80 μm), (d) a grooved rectangle (a=40 μm, b=100 μm).
100 μm). In this case, ΔλFSR was reduced to about 1.6 nm. From Eq. (2) and ΔλFSR~1.9 nm in Fig. 3(c), the expected ΔλFSR of bow-tie modes was calculated to be
which agreed well with the measured one. Therefore, the lasing modes in Fig. 3(d) should also be the bow-tie modes.
To confirm that the lasing modes from grooved rectangles are the proposed bow-tie modes, the lasing spectra were obtained from two adjacent corners (A and B) of the grooved cavity by changing the detection position of the fiber tip. The lasing spectra from a simple rectangle were also measured for comparison. Figure 4 shows two spectra of the 4-bounce WGMs from a rectangle with
Figure 5 shows two lasing spectra from a grooved rectangle with
[FIG. 4.] Lasing spectra measured from two adjacent corners of a rectangular cavity with a=30 μm and b=60 μm. The peak's positions and spectral envelopes appear different from each other.
[FIG. 5.] Lasing spectra measured from two adjacent corners of a grooved rectangular cavity with a=30 μm and b=60 μm. The lasing spectra show highly correlated patterns.
were similar to each other even though the relative peak strengths were slightly different. The high correlation must be due to the fact that the lasing light from A and B leaked from the same bow-tie orbit shown in the inset in Fig. 5. Because the two coupling geometries (distance or location of fiber tip with the corner) of the fiber tip are slightly different, the relative strengths of each peak could be detected slightly differently as observed. The highly correlated pattern in Fig. 5 is further strong evidence of the proposed 6- bounce bow-tie modes in a grooved rectangular cavity in addition to the reduced mode spacing. The result in Fig. 5 suggests a waveguide-coupled microcavity laser in which the two waveguide outputs have the same propagation direction with a highly correlated spectral property. If the grooved rectangle in Fig. 2 has gain for lasing, the lights coupled through the parallel waveguides will have the same propagation direction because the two outputs originate from a bow-tie mode having a particular direction of circulation.
In conclusion, bow-tie mode lasing was demonstrated in a grooved rectangular semiconductor cavity. The mode spacing of lasing peaks was reduced due to the increased round-trip length of the 6-bounce bow-tie modes compared to the 4-bounce WGMs observed from a simple rectangular cavity having the same outer size. Two spectra obtained from two adjacent corners of the grooved rectangle were highly correlated because they originated from the same bowtie modes, while those from a simple rectangle did not. The demonstrated grooved rectangular cavity could be applied to the waveguides-coupled microcavity laser having the same output direction and add-drop passive filter where add and drop ports have the same propagation direction to the input port.