• 沒有找到結果。

Organizational commitment, supervisory commitment, and employee outcomes in the Chinese context: Proximal hypothesis or global hypothesis?

N/A
N/A
Protected

Academic year: 2021

Share "Organizational commitment, supervisory commitment, and employee outcomes in the Chinese context: Proximal hypothesis or global hypothesis?"

Copied!
4
0
0

加載中.... (立即查看全文)

全文

(1)

Anticompetition of laser modes

Ching-Fuh Lin,a)Chi-Chia Huang, Fei-Hung Chu, and Yi-Shin Su

Graduate Institute of Electro-Optical Engineering, National Taiwan University, Taipei 106, Taiwan, Republic of China

共Received 13 January 2003; accepted 4 April 2003兲

Anticompetition of laser modes is observed. In this behavior, the increase of intensity in one lasing mode could enhance the intensity of another mode, which is opposite to the usual competition behavior and so-called anticompetition. In our experiments using the semiconductor laser with very broadband gain medium, anticompetition exists when the laser modes have their wavelengths widely separated. Anticompetition can be observed for spectral separation of 138 nm and is even more prominent for spectral separation up to 167 nm. Theoretical analysis shows that anticompetition is due to the physics similar to optical pumping. © 2003 American Institute of Physics. 关DOI: 10.1063/1.1578708兴

Mode competition is a common phenomenon in lasers. Soon after the invention of lasers,1,2 competition of laser modes was noticed and analyzed.3Because the total gain of a laser medium is constant under a fixed pumping level, the modes under oscillation compete for the total gain. As a re-sult, when one mode increases its intensity, it suppresses the other modes. The competition could lead to phenomena such as bistability,4,5 tristability,6,7 and even chaotic behaviors,8,9 which were found useful for optical logic, optical switching, data encryption, etc.10,11 Competition dynamics is also in-volved in injection locking,12 mode locking,13–15and cross-gain modulation in optical amplifiers.16For decades, compe-tition has been thought to be inevitable among laser modes. However, we discover that laser modes could behave in a way opposite to the competition. In our discovery, the in-crease of intensity in one lasing mode was found to enhance the intensity of another mode. We call such behavior as an-ticompetition of laser modes.

The anticompetition of laser modes is explored using the laser system schematically shown in Fig. 1. The system has a reflected-type grating telescope configuration of external cavity. The gain medium used in the cavity is a bent-stripe ridge waveguide semiconductor optical amplifier 共SOA兲.17 The waveguide has its right-hand side normal to the cleaved facet of the SOA, while its left-hand side is bent and oriented at an angle of 7° to the normal of another cleaved facet. Nonidentical multiple quantum wells 共MQWs兲 are used in the SOA to provide a very broad gain bandwidth.18 Past ex-periments showed that such broadband gain could be used to support two modes with spectral separation tunable from a few to 170 nm.19 Two collimators are used to collect light emitted from the SOA. The laser cavity is formed between the right-hand facet of the SOA and the mirrors A and B. The grating in the cavity is Au-coated and has 600 lines/mm. It is used to disperse the light of different wavelengths. A lens with a focal length of 10 cm was placed at the distance of 10 cm from both the grating and mirrors A and B. According to the grating principle, the beams of different wavelengths are

horizontally dispersed at the mirrors with a spatial separation W⬃L(1/⌳)1/cosR⌬␭, where ⌬␭ is the spectral separation,

⌳ is the grating period,␪R is the first-order diffraction angle,

and L is the distance between the lens and the grating. Two modes are selected using double slits in front of mirrors A and B for the competition experiment. The separation of the two slits is adjustable so that the spectral separation of the two modes can be varied. The output light is divided into two beams by a beam splitter. One beam is delivered into a monochromator for spectrum analysis. The other beam is dispersed by another grating for the measurement of the in-tensities at two wavelengths.

A neutral-density 共ND兲 filter with variable loss is in-serted in either path of the two modes so that the intensity of one mode can be controlled. If competition exists between the two modes, increasing the intensity of one mode leads to the decreased intensity of another mode and vice versa for anticompetition. The phenomenon of anticompetition is ob-served when the two modes are widely separated.

Figure 2 shows the lasing spectra of the two modes with anticompetition. The wavelengths of the two modes are

a兲Also with: the Department of Electrical Engineering and Graduate Institute

of Electronics Engineering; electronic mail: cflin@cc.ee.ntu.edu.tw

FIG. 1. A schematic of the laser system for the experiment of anticompeti-tion between laser modes. The system has the reflected-type grating tele-scope configuration of external cavity.

APPLIED PHYSICS LETTERS VOLUME 82, NUMBER 21 26 MAY 2003

3611

(2)

around 1363.5 and 1530.5 nm, respectively. The current in-jected into the SOA is 146 mA and the temperature is con-trolled at 22.7 °C. In these measurements, the ND filter is inserted in the optical path of the short-wavelength mode. Therefore, the intensity of the 1363.5-nm mode is controlled, while the intensity of the 1530.5-nm mode varies accord-ingly. The solid and dashed lines show the spectra for the 1363.5-nm mode controlled at small and large intensities, respectively. As the intensity of the 1363.5-nm mode is con-trolled to be small, the intensity of the 1530.5-nm mode is also small. On the other hand, if the intensity of the 1363.5-nm mode is large, the intensity of the 1530.5-nm mode increases, too. This phenomenon is opposite to the usual behavior of mode competition. To clearly demonstrate the conditions of anticompetition, the variation of the inten-sity of 1530.5-nm mode (I2) with the intensity of 1363.5-nm mode (I1) is measured, and is shown in Fig. 3共a兲. It is obvi-ous that I2 increases with I1 as the intensity of I1 increases from zero to 0.35 mW.

The two modes with reduced spectral separation are also studied. Under the same injection current and the same tem-perature, as the spacing of the double slits is reduced, the laser shown in Fig. 1 could oscillate at two other wave-lengths: 1388 nm (I1) and 1526 nm (I2). Again, the variable ND filter is placed in the optical path of the short-wavelength mode to control the I1 intensity. The anticompetition still exists, but only for a small regime of I1 values. When I1 is larger than 0.25 mW, the two modes have usual competition. The corresponding I2 versus I1 curve is shown in Fig. 3共b兲. If the spectral separation is further reduced, only competition exists. Figure 3共c兲 shows I2 versus I1 curve for this situation with wavelengths selected at 1378 and 1413 nm.

Previous models of competition usually use the follow-ing rate equations to describe the gain saturation:7,20

dI1 dt

g10 1⫹S1I1⫹C12I2 ⫺l1

I1, 共1a兲 dI2 dt

g20 1⫹S2I2⫹C21I1 ⫺l2

I2, 共1b兲

where the first term in parentheses关Eq. 共1a兲兴 represents the gain with self- and cross-saturation; g10and g20 are the un-saturated gains of the modes I1 and I2, respectively; l1 and l2 are losses of the modes I1 and I2, respectively. In reality, the denominators in Eqs. 共1a兲 and 共1b兲 are not linear func-tions of I1and I2.20The rate equations can be put into more general forms:

FIG. 2. The lasing spectra of the two modes with anticompetition. The solid line shows the spectrum for the short-wavelength path with large loss, con-trolled by the ND filter. The short-wavelength and the long-wavelength modes both have low intensities. The dashed line shows the spectrum for the short-wavelength path with small loss, controlled by the ND filter. The short-wavelength and the long-wavelength modes both have increased in-tensities.

FIG. 3. Variation of I2with I1. The intensity of I1is controlled by the loss

of the ND filter inserted in this optical path, while the intensity of I2changes

accordingly. 共a兲 wavelength of I1⫽1363.5 nm, wavelength of I2

⫽1530.5 nm; 共b兲 wavelength of I1⫽1388 nm, wavelength of I2

⫽1526 nm, and 共c兲 wavelength of I1⫽1413 nm, wavelength of I2

⫽1378 nm. Square dots: experimental data; solid line: fitted curve.

(3)

dI1

dt ⫽关G1共I1,I2兲⫺l1兴I1, 共2a兲

dI2

dt ⫽关G2共I1,I2兲⫺l2兴I2, 共2b兲

with G1(I1,I2) and G2(I1,I2) representing general relations of the gains and the intensities I1and I2. In the steady state, dI1/dt⫽dI2/dt⫽0. Equations 共2a兲 and 共2b兲 can then be written as

关G1共I1,I2兲⫺l1兴I1⫽0, 共3a兲

关G2共I1,I2兲⫺l2兴I2⫽0, 共3b兲

where G1(I1,I2)⫺l1⫽0 and G2(I1,I2)⫺l2⫽0 represent two curves on the I1– I2 phase plane.

Equations 共3a兲 and 共3b兲 have three nontrivial steady-state solutions: 共i兲 I1⫽0 and G2(I1,I2)⫺l2⫽0, 共ii兲 G1(I1,I2)⫺l1⫽0 and I2⫽0, and 共iii兲 G1(I1,I2)⫺l1⫽0 and G2(I1,I2)⫺l2⫽0. The solutions of the first two cases are on the axes of the I1– I2phase plane, so either I1 or I2 is zero. For the third case, the intersection of the two curves gives the intensities of the two modes, I1 and I2, which both are not zero. Although the exact mathematical forms of G1(I1,I2) and G2(I1,I2) are generally not known, they can be determined by experiment. With the loss l1 varied, the equation G1(I1,I2)⫺l1⫽0 gives a family of curves. The intersection of this family of curves with the curve G2(I1,I2)⫺l2⫽0 共with l2 fixed兲 then traces out part of the curve G2(I1,I2)⫺l2⫽0. Similarly, with the loss l2 varied, the curve G1(I1,I2)⫺l1⫽0 共with l1 fixed兲 can be partially traced out. Therefore, Figs. 3共a兲–3共c兲 represent the gain function G2(I1,I2)⫺l2⫽0 for three spectral separations.

The saturation effect causes the gain to decrease with the intensity, so the self-saturation leads to ⳵G2/⳵I2⬍0. The competition is due to cross-saturation,4,5,20 so ⳵G2/⳵I1⬍0. Thus, for competition situation, the gain curve G2(I1,I2) ⫺l2⫽0 should have the slope dI1/dI2⬍0, which is the case for Fig. 3共c兲 and for previous experiments.5,8For the case of anticompetition shown in Figs. 3共a兲 and 3共b兲, dI1/dI2⬎0. Because self-saturation still gives ⳵G2/⳵I2⬍0, it must be that ⳵G2/⳵I1⬎0. As a result, the power-series expansion of G2(I1,I2) consists of a term (⳵G2/⳵I1)I1(⫽␥I1⬎0), which means the condition like optical pumping. That is, the short-wavelength mode gives away its optical power to the long-wavelength mode. However, the two-mode operation is not exactly the same as optical pumping. As shown in Figs. 3共a兲 and 3共b兲, some regime of competition still exists, indicating that the cross-saturation plays an important role again for certain intensity of I1.

The experiments have also been done with the ND filter placed in the path of the long-wavelength mode. No anti-competition is observed for this situation, whether the spec-tral separation is large or small. It shows that the long-wavelength mode, having a lower energy than the short-wavelength mode, cannot provide a function like optical pumping.

In conclusion, anticompetition of laser modes is discov-ered. The phenomenon of anticompetition exists when the laser modes have their wavelengths widely separated. In our experiments using the semiconductor laser with nonidentical MQWs anticompetition can be observed for spectral separa-tion of 138 nm. The anticompetisepara-tion is even more prominent for spectral separation up to 167 nm. Theoretical analysis shows that anticompetition is due to the physics similar to optical pumping.

This work is supported in part by National Science Council, Taipei, Taiwan, R.O.C. under the contract No. NSC91-2215-E-002-025.

1

T. H. Maiman, Nature共London兲 6, 106 共1960兲.

2A. Javan, W. R. Bennett, Jr., and D. R. Herriot, Phys. Rev. Lett. 6, 106

共1961兲.

3W. E. Lamb, Phys. Rev. A 134, 1429共1964兲. 4

K. Shimoda, Introduction to Laser Physics共Springer, Berlin, 1984兲, p. 187.

5

A. E. Siegman, Lasers共University Science Books, 1986兲.

6M. Watanabe, H. Itoh, S. Mukai, and H. Yajima, Appl. Phys. Lett. 50, 427

共1987兲.

7C.-F. Lin and P.-C. Ku, IEEE J. Quantum Electron. 32, 1377共1996兲. 8

H. Kawaguchi, Bistability and Nonlinearities in Laser Diodes 共Artech House, Norwood, MA, 1994兲, p. 199.

9S. Sivaprakasam, P. S. Spencer, P. Rees, and K. A. Shore, IEEE J.

Quan-tum Electron. 38, 1155共2002兲.

10H. Kawaguchi and I. S. Hidayat, Electron. Lett. 31, 1150共1995兲. 11G. D. VanWiggeren and R. Roy, Science共Washington, DC, U.S.兲 279,

1198共1998兲.

12X. Jin and S. L. Chuang, Appl. Phys. Lett. 77, 1250共2000兲. 13

H. Statz and C. L. Tang, J. Appl. Phys. 36, 3923共1965兲.

14L. E. Hargrove, R. L. Fork, and M. A. Pollack, Appl. Phys. Lett. 5, 4

共1964兲.

15

P. W. Smith, Proc. IEEE 58, 1342共1970兲.

16I. White, R. Penty, M. Webster, Y. J. Chai, A. Wonfor, and Sadegh

Shah-kooh, IEEE Communications Magazine 40, 74共2002兲.

17C.-F. Lin and C.-S. Juang, IEEE Photonics Technol. Lett. 8, 206共1996兲. 18C.-F. Lin, B.-R. Wu, L.-W. Laih, and T.-T. Shih, Opt. Lett. 26, 1099

共2001兲.

19C.-H. Chen, C.-F. Lin, Y.-S. Su, C.-C. Huang, and B.-R. Wu, CLEO2002,

Long Beach, CA, 2002, Paper CWK.

20

M. Sargent, III, M. O. Scully, and W. E. Lamb, Jr., Laser Physics 共Addison-Wesley, Reading, MA 1974兲, p. 115.

3613 Appl. Phys. Lett., Vol. 82, No. 21, 26 May 2003 Linet al.

(4)

數據

Figure 2 shows the lasing spectra of the two modes with anticompetition. The wavelengths of the two modes are
FIG. 2. The lasing spectra of the two modes with anticompetition. The solid line shows the spectrum for the short-wavelength path with large loss,  con-trolled by the ND filter

參考文獻

相關文件

After students have had ample practice with developing characters, describing a setting and writing realistic dialogue, they will need to go back to the Short Story Writing Task

Robinson Crusoe is an Englishman from the 1) t_______ of York in the seventeenth century, the youngest son of a merchant of German origin. This trip is financially successful,

fostering independent application of reading strategies Strategy 7: Provide opportunities for students to track, reflect on, and share their learning progress (destination). •

Strategy 3: Offer descriptive feedback during the learning process (enabling strategy). Where the

This paper will present a Bayes factor for the comparison of an inequality constrained hypothesis with its complement or an unconstrained hypothesis. Equivalent sets of hypotheses

Like the proximal point algorithm using D-function [5, 8], we under some mild assumptions es- tablish the global convergence of the algorithm expressed in terms of function values,

There are existing learning resources that cater for different learning abilities, styles and interests. Teachers can easily create differentiated learning resources/tasks for CLD and

• If we use the authentic biography to show grammar in context, which language features / patterns might we guide students to notice and help them infer rules or hypothesis.. •