Research PaperNo Access

Brainware University, Barasat, Kolkata 700125, West Bengal, India

Corresponding author.

Search for more papers by this author

Rahul Ghosh

https://orcid.org/0000-0002-0291-504X

The Dynamics Lab, Department of Chemistry, Indian Institute of Technology Delhi, New Delhi 110016, India

Department of Physics, Shiv Nadar Institution of Eminence, Gautam Buddha Nagar, Uttar Pradesh 203207, India

E-mail Address: rg928@snu.edu.in

Search for more papers by this author

, and

Sauvik Sen

https://orcid.org/0000-0003-3392-0383

Department of Physics, Shiv Nadar Institution of Eminence, Gautam Buddha Nagar, Uttar Pradesh 203207, India

E-mail Address: sauviksen.physics@gmail.com

Search for more papers by this author

https://doi.org/10.1142/S0217732324500822Cited by:0 (Source: Crossref)

Abstract

By mapping the scalar Helmholtz equation (SHE) to the Schrödinger form we investigate the behavior of $𝒫 𝒯$ optical structure when the refractive index distribution n admits variation in the longitudinal direction only. Interpreting the Schrödinger equation in terms of a superpotential we determine the supersymmetric partners for n. We also obtain new analytical solutions for the refractive index profiles and provide graphical illustrations for them.

Keywords:

PACS: 03.65.−w, 03.50.De, 12.60.Jv, 78.20.Ci

References

1. V. S. Vladimirov , Equations of Mathematical Physics ( Mir, 1984). Google Scholar
2. S. Das and E. C. Vagenas , Phys. Rev. Lett. 101, 221301 (2008). Crossref, Web of Science, ADS, Google Scholar
3. I. Pikovski, M. R. Vanner, M. Aspelmeyer, M. S. Kim and Č. Brukner , Nat. Phys. 8, 393 (2012). Crossref, Web of Science, ADS, Google Scholar
4. S. Sen, S. Bhattacharyya and S. Gangopadhyay , Class. Quantum Grav. 39, 075020 (2022). Crossref, Web of Science, Google Scholar
5. P. Bosso, S. Das and R. B. Mann , Phys. Lett. B 785, 498 (2018). Crossref, Web of Science, ADS, Google Scholar
6. C. Conti , Phys. Rev. A 89, 061801(R) (2014). Crossref, Web of Science, ADS, Google Scholar
7. M. C. Braidotti, Z. H. Musslimani and C. Conti , Physica D 338, 34 (2017). Crossref, Web of Science, ADS, Google Scholar
8. A. Kempf, G. Mangano and R. B. Mann , Phys. Rev. D 52, 1108 (1995). Crossref, Web of Science, ADS, Google Scholar
9. M. Gomes and V. G. Kupriyanov , Phys. Rev. D 79, 125011 (2009). Crossref, Web of Science, ADS, Google Scholar
10. B. Bagchi and A. Fring , Phys. Lett. A 373, 4307 (2009). Crossref, Web of Science, ADS, Google Scholar
11. C. Quesne and V. M. Tkachuk , Phys. Rev. A 81, 012106 (2010). Crossref, Web of Science, ADS, Google Scholar
12. S. Dey, Solvable models on noncommutative spaces with minimal length uncertainty relations, Ph.D. thesis, arXiv:1410.3193. Google Scholar
13. M. Faizal and B. P. Mandal , Gravit. Cosmol. 21, 270 (2015). Crossref, Web of Science, ADS, Google Scholar
14. S. Dey, A. Fring and V. Hussin , Springer Proc. Phys. 205, 209 (2018). Crossref, Google Scholar
15. S. Hossenfelder , Living Rev. Relativ. 16, 2 (2013). Crossref, Web of Science, ADS, Google Scholar
16. M. J. Lake et al., Class. Quantum Grav. 36, 155012 (2019). Crossref, Web of Science, ADS, Google Scholar
17. B. Carr, J. Mureika and P. Nicolini , JHEP 7, 052 (2015). Crossref, ADS, Google Scholar
18. A. A. Zyablovsky, A. P. Vinogradov, A. A. Pukhov, A. V. Dorofeenko and A. A. Lisyansky , Phys.-Usp. 57, 1063 (2014). Crossref, Web of Science, ADS, Google Scholar
19. O. Steuernagel , Am. J. Phys. 73, 625 (2005). Crossref, Web of Science, ADS, Google Scholar
20. Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao and D. N. Christodoulides , Phys. Rev. Lett. 106, 213901 (2011). Crossref, Web of Science, ADS, Google Scholar
21. H. F. Jones , J. Phys. A: Math. Theor. 45, 135306 (2012). Crossref, Web of Science, ADS, Google Scholar
22. H. F. Jones and M. Kulishov , J. Opt. 18, 055101 (2016). Crossref, Google Scholar
23. K. G. Makris, R. El-Ganainy and D. N. Christodoulides , Phys. Rev. Lett. 100, 103904 (2008). Crossref, Web of Science, ADS, Google Scholar
24. A. Mostafazadeh , Phys. Rev. A 92, 023831 (2015). Crossref, Web of Science, ADS, Google Scholar
25. S. Longhi , J. Phys. A: Math. Theor. 44, 485302 (2011). Crossref, Web of Science, Google Scholar
26. M.-A. Miri, M. Heinrich, R. El-Ganainy and D. N. Chritodoulides , Phys. Rev. Lett. 110, 233902 (2013). Crossref, Web of Science, ADS, Google Scholar
27. A. Pal, S. Modak, A. Shukla and P. K. Panigrahi , Proc. Roy. Soc. A 477, 20210494 (2021). Crossref, ADS, Google Scholar
28. C. H. Liang, D. D. Scott and Y. N. Joglekar , Phys. Rev. A 89, 030102 (2014). Crossref, Web of Science, ADS, Google Scholar
29. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr and D. R. Smith , Science 314, 977 (2006). Crossref, Web of Science, ADS, Google Scholar
30. A. Alù and N. Engheta, Phys. Rev. E 72, 016623 (2005) [Erratum-ibid 73, 019906 (2006)]. Google Scholar
31. W. Cai, U. K. Chettiar, A. V. Kildishev and V. M. Shalaev , Nat. Photon. 1, 224 (2007). Crossref, Web of Science, ADS, Google Scholar
32. I. I. Smolyaninov, V. N. Smolyaninova, A. V. Kildishev and V. M. Shalaev , Phys. Rev. Lett. 102, 213901 (2009). Crossref, Web of Science, ADS, Google Scholar
33. T. Ergin, N. Stenger, P. Brenner, J. B. Pendry and M. Wegener , Science 328, 337 (2010). Crossref, Web of Science, ADS, Google Scholar
34. M.-A. Miri, Parity-time and supersymmetry in optics, Ph.D. thesis, University of Central Florida, USA (2014). Google Scholar
35. B. Mielnik and O. Rosas-Ortiz , J. Phys. A: Math. Gen. 37, 10007 (2004). Crossref, ADS, Google Scholar
36. S.-H. Dong , Factorization Method in Quantum Mechanics ( Springer, 2007). Crossref, Google Scholar
37. A. A. Andrianov and M. V. Ioffe , J. Phys. A: Math. Theor. 45, 503001 (2012). Crossref, Web of Science, Google Scholar
38. D. Bermudez and D. J. Fernandez C. , AIP Conf. Proc. 1575, 50 (2014). Crossref, ADS, Google Scholar
39. G. Junker , Supersymmetric Methods in Quantum and Statistical Physics ( Springer, 1996). Crossref, Google Scholar
40. B. Bagchi , Supersymmetry in Quantum and Classical Mechanics ( Chapman and Hall/CRC, 2000). Crossref, Google Scholar
41. F. Cooper, A. Khare and U. Sukhatme , Supersymmetry in Quantum Mechanics ( World Scientific, 2001). Link, Google Scholar
42. D. J. Fernandez C. , AIP Conf. Proc. 1287, 3 (2010). ADS, Google Scholar
43. M.-L. Cai, Y.-K. Wu, Q.-X. Mei, W.-D. Zhao, Y. Jiang, L. Yao, L. He, Z.-C. Zhou and L.-M. Duan , Nat. Comm. 13, 3412 (2022). Crossref, Web of Science, ADS, Google Scholar
44. S. M. Chumakov and K. B. Wolf , Phys. Let. A 193, 51 (1994). Crossref, Web of Science, ADS, Google Scholar
45. A. A. Andrianov, M. V. Ioffe, F. Cannata and J.-P. Dedonder , Int. J. Mod. Phys. A 14, 2675 (1999). Link, Web of Science, ADS, Google Scholar
46. B. Bagchi, S. Mallik and C. Quesne , Int. J. Mod. Phys. A 16, 2859 (2001). Link, Web of Science, ADS, Google Scholar
47. M. Znojil, F. Cannata, B. Bagchi and R. Roychoudhury , Phys. Lett. B 483, 284 (2000). Crossref, Web of Science, ADS, Google Scholar
48. E.-M. Graefe and H. F. Jones , Phys. Rev. A 84, 013818 (2011). Crossref, Web of Science, ADS, Google Scholar
49. B. Midya, B. Roy and R. Roychoudhury , Phys. Lett. A 374, 2605 (2010). Crossref, Web of Science, ADS, Google Scholar