Fig. 1. Schematic diagram of LPFG
Fig. 2. LPFG. (a) Three-layer structure model; (b) transverse refractive index
Fig. 3. Change of effective refractive index of core fundamental mode with wavelength
Fig. 4. Intensity distributions of the 8 lower order core modes
Fig. 5. Change of effective refractive index of cladding modes with wavelength for the first 19 times before the first diffraction order
Fig. 6. Intensity distributions of four low order cladding modes excited by circularly symmetric refractive index modulation of LPFG across the fiber cross-section
Fig. 7. Variation of coupling constants between fundamental core mode and cladding mode on the cladding mode order
Fig. 8. Transmission spectra and mode pattern of LPFG fabricated in B-Ge-codoped single-mode fiber
Fig. 9. Phase matching curves of the cladding modes of LPFG. (a) LP02 mode to LP0,20 mode; (b) LP0,11 mode to LP0,20 mode
Fig. 10. Schematic diagram of the LPFG inscription by the UV laser techniques. (a) Amplitude mask exposure technique; (b) point by point inscribing method
[19] Fig. 11. Typical transmission spectrum of a carbon dioxide laser written LPFG in a commercial B-Ge-codoped fiber (together with an image of the near-field pattern of the coupled LP cladding mode at the resonance wavelength of 1531 nm)
[7] Fig. 12. Schematic diagram of the experimental setup for the fabrication of helical LPFG with carbon dioxide laser
[30] Fig. 13. Schematic diagram of experimental setup for LPFG fabrication technique with femtosecond laser
[41] Fig. 14. Schematic diagram of arc-induced LPFG
[47] Fig. 15. Side view of a mechanically induced LPFG
[52] Fig. 16. Transmission spectra of mechanically induced LPFG with increasing applied pressure
[52] Fig. 17. Schematic diagram of HF etched LPFG
[58] Fig. 18. Evolution of transmission spectra when strain is applied to the etched LPFG
[58] Fig. 19. Schematic diagram of the experimental setup for fabrication of the micro-tapered LPFG
[66] Fig. 20. Schematic diagram of experiment. (a) Schematic of alignment of metal mask and fiber; (b) cross section of optical fiber after He ion implantation
[71] Fig. 21. Schematic diagram of the acoustic induced LPFG
[77] Fig. 22. Dependence of the grating contrast on the laser scanning cycle of carbon dioxide laser when the fiber is applied with external strain during the fabrication of the LPFG
[26] Fig. 23. Schematic diagram of the relation between glass volume and heating temperature for the fiber being heated and cooled at different conditions
[7] Fig. 24. Dual-dip resonance of LPFG at dispersion turning point
Fig. 25. Transmission spectra of LPFG. (a) Single LPFG; (b) cascaded LPFGs
[86] Fig. 26. Temperature characteristics of conventional LPFG with LP
06 cladding mode
[86] Fig. 27. Temperature characteristics of coated LPFG with LP
06 cladding mode. (a) Silicone rubber; (b) UV curing adhesive
[86] Fig. 28. LPFG inscribed in photonic crystal fiber by carbon dioxide laser
[24] Fig. 29. Strain characteristics of the carbon dioxide laser written LPFG with parallel inclined planes
[92] Fig. 30. Strain characteristics of the fast and slow axis modes of the helical LPFG written in polarization-maintaining fiber
[33] Fig. 31. Bending characteristics of cascaded tilted long-period fiber gratings
[97] Fig. 32. Structure of concave-lens-like long-period fiber grating
[99] Fig. 33. Bending characteristics of the LPFG written in the polarization-maintaining fiber. (a) Fast axis mode; (b) slow axis mode
Fig. 34. Twist characteristics of the LPFG inscribed in the double-cladding fiber by carbon dioxide laser
[101] Fig. 35. Twist characteristics of two-mode fiber LPFG. (a) Conventional LPFG; (b) tilted LPFGs
[9] Fig. 36. Twist characteristics of two-mode fiber LPFG. (a) Helical LPFG
[30]; (b) chiral LPFG
[32] Fig. 37. Twist characteristics of polarization-maintaining fiber LPFG
[33] Fig. 38. SRI characteristics of LPFG near dispersion turning point
[6] Fig. 39. Relationship between fiber cladding diameter and the period of LPFG
[114] Fig. 40. SRI characteristics of the LPFG written in the thin-cladding fiber
[114] Fig. 41. SRI characteristics of LPFG before and after the etching
[115] Fig. 42. The pH sensing characteristics of the PAH/PAA-coated LPFGs with and without clad etching
[115] Fig. 43. Schematic diagram of oxide film coated LPFG for environmental refractive index sensing
[118] Fig. 44. SEM picture of the cross section of the LPFG coated with Al
2O
3 nano-film
[27] Fig. 45. SRI characteristics of LPFG coating with Al
2O
3 nano film
[27] Fig. 46. SRI characteristics of LPFG coating with TiO
2 nano film
[122] Fig. 47. SEM images of the coated LPFG. (a) Fiber coated with pure PVA film; (b) fiber coated with PEG/PVA composite film; (c) cross-section of the coated LPFG; (d) film thickness of the coated film
[123] Fig. 48. Dependence of the resonance wavelength under the ascending and descending humidity process of PEG/PVA coated LPFG
[123] Fig. 49. Experimental setup of magnetic field sensor based on LPFG and magnetic fluid
[124] Fig. 50. Transverse profile schematic diagram of thin cladding polarization maintaining fiber immersion into magnetic fluid
[125] Fig. 51. Magnetic field characteristics of thin cladding polarization maintaining fiber immersion into magnetic fluid. (a) Fast axis mode; (b) slow axis mode
[125] Fig. 52. Diagram of the cascaded LPFG interferometer and spectrum of the interferometer
[126] Fig. 53. Schematic diagram of cascaded coated long period fiber grating interferometer
[83] Fig. 54. Transmission spectra of cascaded polarization-maintaining fiber LPFG
Fig. 55. Sensing characteristics of cascaded polarization-maintaining fiber LPFGs. (a) Temperature; (b) strain
Fig. 56. Schematic diagram of EDFA gain spectrum based on LPFG gain equalizer
[129] Fig. 57. LPFG. (a) Schematic of two and three phase-shifted LPFGs; (b) illustration of passband characteristics of filters based on LPFGs
[133] Fig. 58. Tunable all-fiber band rejection filters. (a) Schematic of the bandwidth-tunable all-fiber band rejection filters based on a carbon dioxide laser-induced helicoidal LPFG pair of opposite helicities; (b) spectral characteristic of the fabricated bandwidth-tunable all-fiber band rejection filters according to the rotation angle
[136] Fig. 59. Tunable bandwidth all-fiber rejection filters. Schematic diagrams of (a1) LPFG; (a2) R-LPFG; (b) spectral characteristics
[138] Fig. 60. Cascaded helical LPFGs written by carbon dioxide laser
[34] Fig. 61. Top view of the V groove holder that was used to keep part of the helical LPFG simmered in oil
[141] Fig. 62. Experimental diagram of fabrication of acousto-optic grating and generation of first order OAM
[143] Fig. 63. Far field patterns measured at the output of the acousto-optic mode converter. (a) LP
01 mode; (b) LP
11 mode; (c) LP
21 mode; (d) LP
02 mode
[145] Fig. 64. Experimental setup. (a) Experimental equipment diagram of fabrication of micro-bending grating and generation of OAM; (b) transmission spectrum of LP
01-LP
11 mode converter by the grating; (c) pattern and interference pattern of 1st order OAM
[146] Fig. 65. LPFG. (a) Spectrum of the LPFG with 15-period gratings; (b) mode field distribution at different wavelengths
[149] Fig. 66. Spot pattern and interference pattern at the output of (a) LPFG and (b) tilted LPFG
[9] Fig. 67. Mode converter based on LPFG. (a) Spectrum of a single mode converter based on a LPFG; (b) mode field distribution and interference pattern of a single mode converter; (c) spectrum of the cascaded mode converter; (d) intensity distribution and interference patterns of the cascaded mode converter
[150] Fig. 68. OAM mode converter based on PCF. (a) Interference patterns of the OAM
+6 mode generated by the helical PCF; (b) interference patterns of the OAM
+5 mode generated by the helical PCF
[36] Fig. 69. Transmission spectra and intensity distributions of the PM-PCF
[151] Fig. 70. (a) Schematic diagram of the cascaded few-mode fiber LPFGs; (b) transmission spectra of the cascaded few-mode fiber LPFGs with different grating periods in 1.55 μm and 2 μm waveband
[154] Fig. 71. LPFG-based polarizer. (a) PDL; (b) polarization extinction ratio
[160] Fig. 72. Transmission spectra of a 48 mm 45° TFG measured using a single wavelength at 1550 nm at two orthogonal polarization states (P1 and P2)
[163] Fig. 73. PDL and transmission spectra of helical LPFG with a polarization-preserving fiber LPFG with a period of 480 μm
[33] Fig. 74. Principle of operation of the wavelength-selective coupler based on LPFG
[165] Fig. 75. Evanescent-field coupling between a LPFG and an identical bare fiber and mode distributions
Fig. 76. Design of broadband coupler based on three parallel identical LPFGs
[169] Fig. 77. Schematics of a voltage-controllable coupler based on two LPFGs with divided coil heaters
[171] Fig. 78. Add-drop multiplexer using two mode couplers based on LPFGs
[165] Fig. 79. Wavelength-tunable add/drop multiplexer by using four identical LPGs and PZT fiber stretchers
[172] Fig. 80. Total conversion ratio of MADMs for LP
02 mode and LP
03 mode
[174] Fabrication method | Mechanism | Advantage and disadvantage | Reference |
---|
UV laser technique | Photosensitivity | High writing efficiency,good repeatability,need amplitude mask and photosensitive fiber,and low temperature stability | [2],[14-19] | Carbon dioxide laser technique | Residual stress relaxation,glass structure changes,physical deformation | High writing efficiency,good flexibility and repeatability,no need of photosensitive fiber,high temperature stability,and low cost | [20-28] | Femtosecond laser technique | Multiple photon absorption,glass structure changes | Good flexibility and repeatability,no need of photosensitive fiber,high temperature stability,and high cost | [41-45] | Arc-induced LPFG | Residual stress relaxation,glass structure changes,physical deformation | Good flexibility,no need of photosensitive fiber,high temperature stability,and low cost | [46-51] | Mechanically induced LPFG | Photoelastic effect | Good flexibility,grating degeneration,and low cost | [52-57] | Cladding etched LPFG | Physical deformation,residual stress relaxation | High coupling efficiency,high sensitivity,and fragile fiber | [58-62] | Micro-tapered LPFG | Physical deformation,residual stress relaxation | High sensitivity,fragile fiber,and low cost | [63-70] | Ion implanted LPFG | Ion implantation | High index modulation,and asymmetric index distribution | [71-73] | Acoustic induced LPFG | Photoelastic effect | Good flexibility,and low index modulation | [74-79] |
|
Table 1. Comparison of the methods for LPFG fabrication
Package material | Mode | Sensitivity /(pm·℃-1) | Temperature /℃ | Reference |
---|
Bare LPFG | LP06 mode | 82 | 20-140 | [86] | PDMS | LP05 mode | 255.4 | 20-80 | [91] | Silicone rubber | LP06 mode | 186 | 20-140 | [90] | UV Curable adhesive | LP06 mode | 5430 | 20-30 | [86] |
|
Table 2. Temperature characteristics of the LPFGs coated by different materials
Fiber type | Grating type | Mode | Sensitivity /(nm·rad-1·m-1) | Reference |
---|
Single mode fiber | Conventional LPFG | LP17 cladding mode | 0.0008 | [104] | Single mode fiber | Helical LPFG | LP14 cladding mode | -0.099 | [105] | Dispersion shift fiber | Helical LPFG | LP14 cladding mode | -0.038 | [105] | Single mode fiber | Chiral LPFG | LP14 cladding mode | -0.207 | [102] | Double cladding fiber | Conventional LPFG | LP15 cladding mode | 0.088 | [101] | Double cladding fiber | Helical LPFG | LP15 cladding mode | -0.384 | [106] | Two mode fiber | Conventional LPFG | LP11 core mode | 0.37 | [9] | Two mode fiber | Helical LPFG | LP11 core mode | 0.47 | [30] | Two mode fiber | Chiral LPFG | LP11 core mode | 0.7768 | [32] |
|
Table 3. Torsion characteristics of different kinds of LPFGs written by carbon dioxide laser
Cascaded LPFGs | Specification | Reference |
---|
Helical LPFG pair with opposite helicities and same grating period | Bandwidth tunable,15 dB bandwidth > 27 nm,grating length > 10 cm,and polarization insensitive | [136] | Cascaded LPFGs with different grating periods | Theoretical calculation | [137] | Cascaded gratings consists of conventional and helical LPFGs | Grating length < 5.13 cm,bandwidth tunable,15 dB bandwidth > 16.3 nm,and PDL < 0.9 dB | [138] | Helical LPFG pair with opposite helicities and same grating period | Grating length < 4.6 cm,and 1 dB bandwidth > 15 nm | [34] | Helical LPFG pair with opposite helicities and different grating periods | Grating length is 5.02 cm,1 dB bandwidth > 13 nm,and dependent on the incident polarization | [35] | Helical LPFG pair with opposite helicities,combined with a cladding-mode stripper | 1 dB bandwidth is 14 nm,and polarization insensitive | [141] |
|
Table 4. Comparison of cascaded long period fiber gratings